A spatially distributed, deterministic approach to modeling Typha domingensis (cattail) in an Everglades wetland

MISSING IMAGE

Material Information

Title:
A spatially distributed, deterministic approach to modeling Typha domingensis (cattail) in an Everglades wetland
Physical Description:
Mixed Material
Language:
English
Creator:
Lagerwall, Gareth
Kiker, Gregory
Munoz-Carpena, Rafael
Convertion, Matteo
James, Andrew
Wang, Naiming
Publisher:
BioMed Central (Ecological Processes)
Publication Date:

Notes

Abstract:
Introduction: The emergent wetland species Typha domingensis (cattail) is a native Florida Everglades monocotyledonous macrophyte. It has become invasive due to anthropogenic disturbances and is out-competing other vegetation in the region, especially in areas historically dominated by Cladium jamaicense (sawgrass). There is a need for a quantitative, deterministic model in order to accurately simulate the regional-scale cattail dynamics in the Everglades. Methods: The Regional Simulation Model (RSM), combined with the Transport and Reaction Simulation Engine (TARSE), was adapted to simulate ecology. This provides a framework for user-defineable equations and relationships and enables multiple theories with different levels of complexity to be tested simultaneously. Five models, or levels, of increasing complexity were used to simulate cattail dynamics across Water Conservation Area 2A (WCA2A), which is located just south of Lake Okeechobee, in Florida, USA. These levels of complexity were formulated to correspond with five hypotheses regarding the growth and spread of cattail. The first level of complexity assumed a logistic growth pattern to test whether cattail growth is density dependent. The second level of complexity built on the first and included a Habitat Suitability Index (HSI) factor influenced by water depth to test whether this might be an important factor for cattail expansion. The third level of complexity built on the second and included an HSI factor influenced by soil phosphorus concentration to test whether this is a contributing factor for cattail expansion. The fourth level of complexity built on the third and included an HSI factor influenced by (a level 1–simulated) sawgrass density to determine whether sawgrass density impacted the rate of cattail expansion. The fifth level of complexity built on the fourth and included a feedback mechanism whereby the cattail densities influenced the sawgrass densities to determine the impact of inter-species interactions on the cattail dynamics. Results: All the simulation results from the different levels of complexity were compared to observed data for the years 1995 and 2003. Their performance was analyzed using a number of different statistics that each represent a different perspective on the ecological dynamics of the system. These statistics include box-plots, abundance-area curves, Moran’s I, and classified difference. The statistics were summarized using the Nash-Sutcliffe coefficient. The results from all of these comparisons indicate that the more complex level 4 and level 5 models were able to simulate the observed data with a reasonable degree of accuracy. Conclusions: A user-defineable, quantitative, deterministic modeling framework was introduced and tested against various hypotheses. It was determined that the more complex models (levels 4 and 5) were able to adequately simulate the observed patterns of cattail densities within the WCA2A region. These models require testing for uncertainty and sensitivity of their various parameters in order to better understand them but could eventually be used to provide insight for management decisions concerning the WCA2A region and the Everglades in general. Keywords: Typha, Modeling, Ecology, Dynamics, Model complexity, Water conservation area 2A, Transport and reaction simulation engine, Regional simulation model.
General Note:
Lagerwall et al. Ecological Processes 2012, 1:10 http://www.ecologicalprocesses.com/content/1/1/10; Pages 1-21
General Note:
doi:10.1186/2192-1709-1-10 Cite this article as: Lagerwall et al.: A spatially distributed, deterministic approach to modeling Typha domingensis (cattail) in an Everglades wetland. Ecological Processes 2012 1:10.
General Note:
Publication of this article was funded in part by the University of Florida Open-Access publishing Fund. In addition, requestors receiving funding through the UFOAP project are expected to submit a post-review, final draft of the article to UF's institutional repository, IR @ UF, (www.uflib.ufl.edu/UFir) at the time of funding. The institutional Repository at the University of Florida community, with research, news, outreach, and educational materials.

Record Information

Source Institution:
University of Florida
Holding Location:
University of Florida
Rights Management:
All rights reserved by the source institution.
System ID:
AA00013656:00001


This item is only available as the following downloads:


Full Text


Lagerwall et al. Ecological Processes 2012, 1:10
http://www.ecologicalprocesses.com/content/1/1/10


0 Ecological Processes
a SpringerOpen Journal


A spatially distributed, deterministic approach

to modeling Typha domingensis (cattail) in an

Everglades wetland

Gareth Lagerwall Gregory Kiker", Rafael Munoz-Carpenal, Matteo Convertinol, Andrew James2
and Naiming Wang3


Abstract
Introduction: The emergent wetland species Typha domingensis (cattail) is a native Florida Everglades
monocotyledonous macrophyte. It has become invasive due to anthropogenic disturbances and is out-competing
other vegetation in the region, especially in areas historically dominated by Cladium jamaicense (sawgrass). There is
a need for a quantitative, deterministic model in order to accurately simulate the regional-scale cattail dynamics in
the Everglades.
Methods: The Regional Simulation Model (RSM), combined with the Transport and Reaction Simulation Engine
(TARSE), was adapted to simulate ecology. This provides a framework for user-defineable equations and
relationships and enables multiple theories with different levels of complexity to be tested simultaneously. Five
models, or levels, of increasing complexity were used to simulate cattail dynamics across Water Conservation Area
2A (WCA2A), which is located just south of Lake Okeechobee, in Florida, USA. These levels of complexity were
formulated to correspond with five hypotheses regarding the growth and spread of cattail. The first level of
complexity assumed a logistic growth pattern to test whether cattail growth is density dependent. The second
level of complexity built on the first and included a Habitat Suitability Index (HSI) factor influenced by water depth
to test whether this might be an important factor for cattail expansion. The third level of complexity built on the
second and included an HSI factor influenced by soil phosphorus concentration to test whether this is a
contributing factor for cattail expansion. The fourth level of complexity built on the third and included an HSI factor
influenced by (a level 1-simulated) sawgrass density to determine whether sawgrass density impacted the rate of
cattail expansion. The fifth level of complexity built on the fourth and included a feedback mechanism whereby the
cattail densities influenced the sawgrass densities to determine the impact of inter-species interactions on the
cattail dynamics.
Results: All the simulation results from the different levels of complexity were compared to observed data for the
years 1995 and 2003. Their performance was analyzed using a number of different statistics that each represent a
different perspective on the ecological dynamics of the system. These statistics include box-plots, abundance-area
curves, Moran's /, and classified difference. The statistics were summarized using the Nash-Sutcliffe coefficient. The
results from all of these comparisons indicate that the more complex level 4 and level 5 models were able to
simulate the observed data with a reasonable degree of accuracy.
(Continued on next page)


* Correspondence gkiker@ufl edu
Frazier Rogers Hall, University of Florida, PO Box 110570, Gainesville,
32611-0570, USA
Full list of author information is available at the end of the article


IL Springer


2012 Lagerwall et al., licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons
Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction
in any medium, provided the original work is properly cited.






Lagerwall et al. Ecological Processes 2012, 1:10
http://www.ecologicalprocesses.com/content/1/1/10


Introduction
The Everglades, commonly known as the "River Of
Grass" Douglas (1947), in southern Florida, USA, once
covered some 28,500 km2. This wetland ecosystem was
sustained by the Kissimmee River, flowing through Lake
Okeechobee and southwards as a shallow, slow-moving
sheet of water flowing freely to the estuaries of Biscayne
Bay, Ten Thousand Islands, and Florida Bay. The chan-
nelization of the Everglades around 1948 caused the re-
duction of the original wetland areas by up to 50%, with
related declines in dependent wildlife. In addition to the
changes in hydrology, continuous mining, agriculture,
and urbanization activities have resulted in invasive and
exotic plants becoming established in place of the ori-
ginal vegetation, altering habitats and often forming
mono-crop stands (single species environments) (Odum
et al. 2000).
The Comprehensive Everglades Restoration Plan (CERP)
was implemented in 2000 (USACE, S.F.R.O 2010a) with
the explicit goal of restoring some of the Everglades' former
extent and ecosystem functioning. The main focus of
CERP has been on improved management of water quan-
tity and water quality with the assumption that if the water
quantity and quality are adequate, the ecology will follow
suit. There is, however, an increasing focus on the eco-
logical impacts of various management decisions, and
these efforts center on improving species diversity and pro-
tecting existing habitats (USACE, S.F.R.O 2010b). In an
effort to achieve these goals, stormwater treatment areas
(STA) were constructed just south of the Everglades agri-
cultural area (EAA) to filter out phosphorus from the
water before releasing it into the water conservation areas
(WCA). The WCAs act as impoundments for water
storage and flood control as well as serving as wildlife habi-
tat. Water flows from these WCAs into the Everglades
National Park (Guardo et al. 1995).


Typha domingensis as an invasive species
The emergent wetland species Typha domingensis (cattail)
is a native Everglades monocotyledonous macrophyte,
typically occurring as a sparse complement alongside
Cladium jamaicense (sawgrass) stands. These two species
have significantly different morphology, growth, and life


history characteristics (Miao and Sklar 1998), and this has
enabled the cattail to expand prolifically under the altered
conditions in the Everglades. In the 1980s, the area
covered by cattail stands in WCA2A doubled, expanding
southward into the sawgrass marshes (Willard 2010).
Cattail has hence been labeled as an indicator species, or
species of concern, and its distribution is used to deter-
mine the effectiveness of various water management deci-
sions. Cattail expansion has been studied extensively
(Miao 2004; Wu et al. 1997; Newman et al. 1998), and it
has been determined that there are four main external fac-
tors that affect its growth and aid in cattail's dominance
over sawgrass. These factors include water depth, hydro-
period, soil phosphorus concentration, and disturbance
(Newman et al. 1998). It was determined that the
optimum water depth at which cattail grows is between
24 and 95 cm (Grace 1989), with a hydroperiod of 180-
280 days (Wetzel 2001). In terms of soil phosphorus
concentration, cattail has been found to be invading the
natural sawgrass habitats of WCA2A along a soil phos-
phorus gradient running from the northwest (high con-
centrations) to the southeast (low concentrations). Urban
et al. (1993) mention that, given an adequate water depth,
soil phosphorus concentration is the next most important
factor in determining cattail expansion/invasion. In creat-
ing their water quality model for simulating soil phos-
phorus concentrations downstream of the Everglades
STAs, Walker and Kadlec (1996) determined that the
lower bound soil phosphorus concentration for the
optimum growth of cattail was 540 mg/kg. Fires and other
disturbances such as hurricanes were also found to affect
the colonization of areas by cattail by altering local topog-
raphy and nutrient concentrations (Newman et al. 1998).


Ecological model designs to address everglades systems
In order to assess these various influences on cattail and
other ecological components, a variety of computation
models were designed and implemented. These models
aid our understanding of complex systems and allow
scientists and managers to evaluate different ecological
outcomes of decisions before the more costly task of their
implementation (Fitz et al. 2011). To ensure numerical
efficiency, most spatially distributed models have their


Page 2 of 21


(Continued from previous page)
Conclusions: A user-defineable, quantitative, deterministic modeling framework was introduced and tested against
various hypotheses. It was determined that the more complex models (levels 4 and 5) were able to adequately
simulate the observed patterns of cattail densities within the WCA2A region. These models require testing for
uncertainty and sensitivity of their various parameters in order to better understand them but could eventually be
used to provide insight for management decisions concerning the WCA2A region and the Everglades in general.
Keywords: Typha, Modeling, Ecology, Dynamics, Model complexity, Water conservation area 2A, Transport and
reaction simulation engine, Regional simulation model






Lagerwall et al. Ecological Processes 2012, 1:10
http://www.ecologicalprocesses.com/content/1/1/10


equations, laws, and assumptions "hard-coded" into their
programming code. This creates a "fixed-form" model,
with changes in the functioning coming through extensive
code re-writes and careful redesign around logical struc-
tures. Dynamic "free-form" simulation models, such as
STELLA (Costanza and Voinov 2001), QnD (Kiker and
Linkov 2006; Kiker et al. 2006), and the Kepler system
(Ludascher et al. 2006) are generally written using an
object-oriented programming (OOP) language such as
C++ (Stroustrup 2000) or Java (Arnold and Gosling 1998),
as opposed to a linear language such as FORTRAN (Cary
et al. 1998). When interacting with free-form models and
their algorithms, designers do not interact directly with the
program code. Rather, they influence objects through
placing data, storage, and logical structures into either a
graphical user interface (STELLA, Kepler) or within a
meta-code structure such as the eXtensible Markup
Language (XML) (Harold 1998).
There are a number of fixed-form ecological models
currently in use across the Everglades region. Of these,
the Across Trophic Level System Simulation (ATLSS)
(Gross 1996) and the Everglades Landscape Model
(ELM) (Fitz and Trimble 2006b) are probably the most
well-known. These and most other models available for
modeling cattail in the Everglades are entirely qualita-
tive, that is, they involve switching between one species
and another. The majority of these current ecological
models are also stochastic, that is, based on probabilities
and a degree of randomness and uncertainty. They gen-
erally run as post-process models, using hydrological
data output by other models such as the South Florida
Water Management Model (SFWMM) (Fitz et al. 2011).
The ATLSS vegetation succession model is used to deter-
mine the succession of one habitat type to another
(e.g., sawgrass to cattail). The ATLSS model simulates with
an annual time step on square 500 m cells and uses a sto-
chastic cellular automata model to switch between vegeta-
tion types. Currently there is no way to determine vegetation
densities within vegetation types (Duke-Sylvester 2005).
The ELM model uses a counter to switch between spe-
cies by accumulating days of water level and soil phos-
phorus concentration above certain limits. The model then
switches between species based on their preferred hydro-
period and historical soil phosphorus concentrations (Fitz
and Trimble 2006a). The ELM model is the only currently
available simulation tool for evaluating water quality across
the Everglades landscape and does not simulate detailed
ecological features (Fitz et al. 2011).
Another modeling effort by Wu et al. (1997) used
Markov chain probabilities to switch between Cladium and
Typha species. This model was in fact used to inform the
ATLSS nutrient and fire disturbance model (Wetzel 2003).
Again, this is a stochastic, species-specific, presence/ab-
sence-type model.


A modeling effort by Tarboton et al. (2004) developed
a set of habitat suitability indices (HSI) for evaluating
water management alternatives. These HSIs provided a
range of probabilities for a particular species occurring
across the landscape and were based predominantly on
local hydrological conditions such as depth (maximum,
minimum, and mean), hydroperiod, velocity, and flow
direction.
Given that water quantity (depth) and quality (soil
phosphorus concentration) affect cattail (and other
plants) growth and distribution, there is a need to inte-
grate these components to determine the more detailed
biological outcomes of an Everglades ecological model.
There is also a need for a quantitative model to provide
continuous density values for specific vegetation rather
than simply presence/absence information. Given that
the Everglades restoration includes a large and ongoing
research effort, there is a need to efficiently test and
explore potentially useful algorithms in an adaptable,
ecological modeling engine.

The RSM/TARSE ecological model
A combined effort of the University of Florida, the South
Florida Water Management District (SFWMD), and the
US Geological Survey created the Transport and Reac-
tion Simulation Engine (TARSE) (Jawitz et al. 2008),
which was originally designed to run in line with the
SFWMD-developed Regional Simulation Model (RSM)
(SFWMD 2005c) to simulate soil phosphorus dynamics
in the Everglades system. The OOP structure of this
coupled hydrologic/water quality model, along with the
user-definable inputs and interactions, allowed for the
extension of this model beyond its original purpose into
ecological processes and features. The coupled RSM/
TARSE (henceforth referred to as RTE) model, imple-
mented with the goal of modeling ecological features
within the southern Florida landscape and presented in
this paper, is a spatially distributed, free-form model simu-
lating cattail biomass distribution and dynamics across
WCA2A. Using the RTE model to couple vegetation
dynamics with phosphorus dynamics has been alluded to
by Jawitz et al. (2008), Muller (2010), and Perez-Ovilla
(2010) during their respective TARSE-influenced, WQ
simulations. Zajac (2010) used vegetation types to
influence Manning's n and evapotranspiration coefficients.
These parameters were informed by initial vegetation
types and not by changing vegetation distribution and
density over time.
There is therefore a definite need for the RTE model,
which allows one to model a vegetation species quantita-
tively and ultimately determine the ecological impact of
various management scenarios falling under the CERP ini-
tiative. This new engine would accommodate different
algorithms or new species as available data or new


Page 3 of 21






Lagerwall et al. Ecological Processes 2012, 1:10
http://www.ecologicalprocesses.com/content/1/1/10


knowledge becomes available. It would allow for interac-
tions and feedback effects within species as well as among
different species and with other environmental factors.

Objectives and hypotheses
The primary objective of this paper is to test and apply a new
spatially distributed, deterministic, free-form (user-definable),
quantitative ecological model of cattail dynamics. A signifi-
cant advantage of this free-form modeling approach is that
multiple ecological algorithms of differing complexity can
be quickly implemented and tested simultaneously, instead
of through time-consuming code additions. As a first step
of our objective, we tested the influence of increasing cattail
model complexity on reducing uncertainty in simulated
output (Lindenschmidt 2006). Five levels of increasing
complexity were selected to model the cattail densities.
These five levels of complexity were chosen to correspond
with various hypotheses regarding the growth and spread
of cattail in the Everglades, namely:

1. Whether cattail growth is density dependent.
2. Whether water depth is an important factor for
cattail expansion.
3. Whether soil phosphorous is a contributing factor
for cattail expansion.
4. Whether sawgrass density impacts the rate of cattail
expansion.
5. Whether inter-species interactions between cattail and
sawgrass contribute to the observed cattail dynamics.

Following the methodology used by Jawitz et al.
(2008), a simple logistic function (Keen and Spain 1992)
formed the base of the complexities with water depth and
soil phosphorus concentration [the two most important
factors influencing cattail growth according to Newman
et al. (1998)] and sawgrass interaction influencing the
higher levels of complexity. A second step in our objective
was to use an existing ecosystem and its monitoring data
to analyze performance of our five candidate models. The
entire WCA2A vegetation dataset (1991, 1995, and 2003),
obtained from Rutchey et al. (2008), was chronologically
divided into model training and testing sections. Training
of the model was conducted for the years 1991-1995,
where the growth factor (found in Equation 3) was fitted
to the level 1 complexity. As a third step in our objective,
model testing was conducted on the two time periods of
1991-2003 (testing 1) and 1995-2003 (testing 2), respect-
ively, with the testing 2 time period being equivalent to a
blind test (due to different initial conditions). The 1991
and 1995 vegetation maps were used to initialize the
training, testing 1, and testing 2 simulations, respectively.
Model output from the training, testing 1, and testing
2 simulations was compared with the 1995 and 2003
vegetation maps. Model output was compared to


observed patterns, and the most accurate level of
complexity thus determined.

Methods
In order to reproduce the observed cattail patterns, both
hydrological and water quality data were used as inputs
for the ecological model. To this end, it was decided to
use the Regional Simulation Model (RSM), which was
developed by the South Florida Water Management Dis-
trict (SFWMD) to replace the popular SFWMM, coupled
with the Transport and Reaction Simulation Engine
(TARSE) to provide the base structure for modeling
cattail dynamics across the test site.

The Regional Simulation Model (RSM)
Developed by SFWMD, the RSM simulates hydrology
over the South Florida region. It is often thought of as the
successor to the successful SFWMM, referred to as the
"2-by-2" model for its 2 mile resolution (SFWMD 2005a).
The RSM operates over a variable triangular mesh grid, in
contrast to the 3.22 km (2 mile) square grid of the
SFWMM; this enables higher resolution in areas of con-
cern as well as the ability to delineate canals (SFWMD
2005c). The RSM uses a weighted, implicit, finite volume
method to simulate two-dimensional diffusional flow and
hence implicitly simulates groundwater flow and surface
water flow (SFWMD 2005c). The OOP design structure of
RSM allows for the abstraction and modularity of various
components (SFWMD 2005b). A result of this is that
there are two engines that comprise the RSM, namely the
Hydrologic Simulation Engine (HSE) and the Manage-
ment Simulation Engine (MSE). The HSE simulates all the
hydrological processes, while the MSE simulates various
management or control regimes. These two engines
interact at runtime to provide an accurate representation
of the hydrodynamics of the region (SFWMD 2005c).

Simulating transport and reactions using TARSE
The TARSE was recently developed to simulate water
quality (WQ) components within the RSM model for areas
in the Everglades system (Jawitz et al. 2008). The TARSE
model was designed to be as generic as possible, to allow
multiple water quality components to be simulated with a
simple change in the input file. It was first implemented as
another engine to be incorporated within the RSM frame-
work, along with the HSE and MSE, called the Water
Quality Engine (WQE). Due to its structure, the WQE
does not simulate hydrology and requires a hydrologic
driver to feed it values of flow and depth at every time step
(SFWMD 2008b). TARSE has since been decoupled from
RSM and implemented with other hydrologic drivers such
as Flow and Transport in a Linked Overland-Aquifer
Density Dependent System (FTLOADDS) (Wang et al.
2007; Muller 2010) and VFSMOD (Mufioz-Carpena et al.


Page 4 of 21






Lagerwall et al. Ecological Processes 2012, 1:10
http://www.ecologicalprocesses.com/content/1/1/10


1999; Perez-Ovilla 2010). TARSE solves the advection-
dispersion-reaction equations (ADRE) over an unstruc-
tured triangular mesh (James and Jawitz 2007). The ADRE
is represented by Equation 1, and every term is a function
of a two-dimensional spatial coordinate x, with compo-
nents (xl, x2), and time, t.

d(Ohc) + V(chu hD* .Vc) + hf2c = hfic (1)
dt
Where t is time [T], c(x,t) is the concentration [M/L 3],
and O(x,t) is the porosity of the medium (which may be
1 for surface water) [L 3/L3]. h(x,t) is the water depth [L]
or thickness of the saturated zone in groundwater flow,
u(x,t) is the specific discharge [L/T] of water (either sur-
face or groundwater), and D =D (u(x,t)) is the dispersion
tensor (a function of u). fl(x,t) is a source rate [M/L3 T]
with associated concentration cl, and f2(x,t) is a first-
order decay rate [M/L T]. The density [M/L3] of the
water is assumed to be constant.
The basis of TARSE involves transfers (e.g., settling,
diffusion, growth) between various stores, such as soil
water column solutes, pore water solutes, macrophytes,
and suspended solids. The specifics of these stores, and
the transfers among them are user-definable in the XML
input file (Jawitz et al. 2008). TARSE equations are com-
posed of pre-equations, equations, and post-equations.
Pre- and post-equations are used for implementing con-
ditional ("if-then-else") statements as part of pre- and
post-processing after the main processing in the equa-
tions. For example, pre-processing could be used to de-
termine if the current water depth [m] is above the
threshold for cattail optimum growth and thus reduce
the depth influence factor accordingly. If the depth is
less than the optimum growing depth, then the influence
factor decreases accordingly. The logic just described is
represented by Equation 2, as described by Grace (1989),
where cattail optimum depth is 70 cm.

If (depth > cattailoptimum-depth)
Then


depthHSI


1 (depth cattail-optimum-depth
109


(cattail optimum-depth depth)
depthHSI = 1 -_ (caal 112

(2)
The main equations are structured as ordinary differ-
ential equations (ODE) (SFWMD 2008a).
The RSM/TARSE coupling represents possibly the first
time that a free-form dynamic system model has been
integrated with a fixed-form, spatially distributed, hydro-
logic model (Muller 2010). This unique coupling,
with user-defined interactions operating across a
spatially distributed domain, lends itself to simulating


ecological behaviors (growth, death, movement, and
feeding) as well as the original WQ interactions. The
model can currently only solve ADRE movement and
as such is insufficient for ecological/animal move-
ment. Attempts to include some form of Lagrangian-
type movement in this model are discussed by
Lagerwall (2011).

Model application
In order to test the influence of increasing complexity on
reducing uncertainty in model output (Lindenschmidt
2006), five levels of increasing complexity were selected to
model the cattail densities. Following the methodology
used by Jawitz et al. (2008), a logistic function (Keen and
Spain 1992) was used for the most basic, level 1
complexity, due to its density dependent growth and rapid
(exponential) early stages of growth. The logistic function
is represented in Equation 3.

dt GFxPx 1-- (3)
dt K)

Where P is the population density [M/L2], t is time
[T], GF is the constant growth rate [T-], and K is the
carrying capacity or maximum population density [M/L2].
Level 2 is a water-depth-influenced level 1 complexity.
A water depth factor (habitat suitability index) ranging
from 0 to 1 is multiplied by the carrying capacity in the
logistic function. The depth factor decreases linearly
from 1 as the current depth either rises above or drops
below the optimum (70 cm) growing depth. This depth
factor can be seen in Equation 4.

dP =GFxPx 1- (4)
dt GFK x DepthF) (4)

Where P is the population density [M/L2], t is time
[T], GF is a constant growth rate [T-1], DepthF is the
water depth factor [L/L], K is the carrying capacity or
maximum population density [M/L2].
Level 3 is a soil-phosphorus-influenced level 2 com-
plexity, with the soil phosphorus factor being incorpo-
rated in a similar fashion to the depth factor and can be
seen in Equation 5.

dt GFxPx 1- 2 (5)
dt = G K x (DepthF +phosphorusF)/2)

Where P is the population density [M/L2], t is
time [T], GF is a constant growth rate [T- ], DepthF
is the water depth factor [L/L], phosphorusF is the
soil phosphorus factor [M/L 3/M/L 3], and K is the
carrying capacity or maximum population density
[M/L2]. The soil phosphorus factor behaves like a lo-
gistic function, increasing from 0 to 1 as soil phos-
phorus concentration increases to 1,800 from 200


Page 5 of 21






Lagerwall et al. Ecological Processes 2012, 1:10
http://www.ecologicalprocesses.com/content/1/1/10


mg/kg, as described by Walker and Kadlec (1996),
and can be seen in Equation 6.


phosphorusF


( +e


phosphorus-1034 1
144


Where phosphorusF is the soil phosphorus HSI, ran-
ging from 0 to 1, and phosphorus is the current soil
phosphorus concentration (mg/kg).
Level 4 builds on a level 3 complexity with an added
sawgrass interaction factor, much like the soil phos-
phorus and depth factors. It decreases linearly from 1 to
0.16 as sawgrass densities increase to 1,958 from 0 g/m2
(Doren et al. 1999), which is their reported maximum
density (Miao and Sklar 1998). The sawgrass is set to
grow according to a level 1 complexity as in Equation 4,
thus the level 4 complexity is represented by Equation 7.

dP GF P
dt \ K(DepthF + phosphorusF + sawgrassF)/3
(7)
Where P is the population density [M/L2], t is time
[T], GF is a constant growth rate [T- ], DepthF is the
water depth factor [L/L], phosphorusF is the soil phos-
phorus factor [M/L 3/M/L 3], sawgrassF is the sawgrass
influence factor [M/L2/M/L2], and K is the carrying cap-
acity or maximum population density [M/L2]. The saw-
grass factor varies according to Equation 8.

sawgrassF = 1 + (-0.84 x (sawgrass/KsAw)) (8)


Where sawgrassF is the sawgrass HSI ranging from 0
to 1, sawgrass is the current sawgrass density, and KSAW
is the sawgrass carrying capacity.
The level 5 complexity is the same as level 4, but with
a density-dependent influence on the level 1 sawgrass
model, which is represented by Equations 9 and 10, re-
spectively.


GF xPx 1 x attal
K x cattailF


Where P is the population density [M/L2], t is time
[T], GF is a constant growth rate [T- ], cattailF is the
cattail factor ranging from 0 to 1, and K is the carrying
capacity or maximum population density [M/L2].
cattailF = 1 + (-0.84 x (cattail/KcAT)) (10)

Where cattailF is the cattail HSI ranging from 0 to 1,
cattail is the current cattail density, and KCAT is the cat-
tail carrying capacity.


The depth, soil phosphorus, and sawgrass interaction
factors are all calculated using the pre-equations, similar
to that presented in Equation 2. These factors are then
incorporated into the main growth equations, presented
in Equations 4, 5, 7 and 9 representing levels of com-
plexity 2 through 5, respectively.
In TARSE, components are listed as either mobile or
stabile. Mobile components are moved in the water
using the ADRE equations, while the stabile components
do not move and only undergo the reaction part of the
ADRE. Given the complexities associated with simulat-
ing wind-borne or water-borne transportation of seeds
and rhizome expansion-which is another mode of ex-
pansion noted by Miao (2004)-all mesh elements were
initialized (seeded) with cattail, with areas originally not
containing cattail being seeded with the minimum value
of 10 g(dry weight)/m2. This assumption represents the
presence of a seed bank, providing cattail the opportun-
ity to colonize an area as soon as conditions become fa-
vorable. Vegetation then is modeled as a stabile
component, with no means for dispersal, or in another
way we assume "infinite dispersal." The latter assump-
tion is supported by very high values of dispersal for
seeds in the Everglades, enhanced by the diffused pres-
ence of biotic (animals) and abiotic (water, wind) disper-
sal vectors (Miao and Sklar 1998). Also, as a result of
this current inability for modeled dispersal, the max-
imum influence that the aforementioned factors such as
phosphorusF, sawgrassF, and cattailF can have has been
limited so that they reduce the cattail population to 1%
of its maximum density.

Test site
The test site used for ecological model development and
testing was the WCA2A (Figure 1). WCA2A is a 547
km2 managed wetland just south of Lake Okeechobee,
FL, and accounts for about 6.5% of the total area of the
Everglades. It came into existence in 1961 with the con-
struction of the L35-B canal and receives inflow from
the Stormwater Treatment Areas (STAs), before dischar-
ging into downstream water conservation areas, and
eventually into the Everglades National Park (Urban
et al. 1993). According to Rivero et al. (2007b), the re-
gion has an average annual temperature of 20oC, and
precipitation between 1,175 and 1,550 mm. The eleva-
tion range in WCA2A is between 2.0 and 3.6 m above
sea level, which generates a slow sheet flow from the
northwest to the southwest of the region. The hydrology
is controlled by the SFWMD at a number of inlet and
outlet structures (green squares in Figure 1) along the
surrounding canals (blue lines in Figure 1). The land-
scape is composed of dominant sawgrass marshes, shrub
and tree island communities, and invasive cattail com-
munities (van der Valk and Rosburg 1997). WCA2A has


Page 6 of 21







Lagerwall et al. Ecological Processes 2012, 1:10
http://www.ecologicalprocesses.com/content/1/1/10


Page 7 of 21


.~ -flr~

S


:1? *


a I


Figure 1 Test site, Water Conservation Area 2A (WCA2A), in the northern Everglades. Green squares represent inlet and outlet control
structures; blue lines represent canal structures. Triangles represent the mesh used for simulation, with green triangles representing the border
cells used in the central difference method. The red squares fall on zonal elements 209, 244, and 380, representing regions of typically high,
medium, and low cattail densities, respectively.


been used extensively as a research site by the
SFWMD, with extensive trial and monitoring pro-
grams for a number of biogeochemical components,
especially soil phosphorus and vegetative structure
(Rivero et al. 2007a). The triangular mesh grid used
for simulation is also displayed in Figure 1, with the
green border cells used for numerical stability of the
hydrological RSM component. An overview of the
HSE setup for WCA2A, which provides the


hydrological operating conditions, can be found in
SFWMD (2008c).

Initial conditions, boundary conditions, and time
series data
Cattail vegetation maps (Figure 2) are used for the initial
conditions as well as for comparing model output with
measured data. Hydrological time series are used for initial
and boundary conditions along the surrounding canals.







Lagerwall et al. Ecological Processes 2012, 1:10
http://www.ecologicalprocesses.com/content/1/1/10


Raw Data


a) 1991


b) 1995


c) 2003


1 High = 2 Medium 3 Low = 4 Minimum


Figure 2 Formatting of cattail input maps. (a) 1991, (b) 1995, (c) 2003 from Rutchey et al. (2008). Rasterized raw data on the left, overlaid witl
the WCA2A triangular mesh in the middle, and the final triangular mesh cattail input map on the right.


Page 8 of 21


Mesh Overlay

'A


Input Mesh






Lagerwall et al. Ecological Processes 2012, 1:10
http://www.ecologicalprocesses.com/content/1/1/10


Using RSM, the hydrological boundary conditions are con-
verted into depth values across the domain, which are then
used as inputs in the level 2 complexity algorithm. Soil
phosphorus concentration maps provide initial conditions
and an influence factor for the level 3 complexity algo-
rithm. Sawgrass vegetation maps are used as initial condi-
tions for the level 1 complexity sawgrass model, which
serves as an influence factor for the level 4 and level 5
complexity cattail algorithms. The following sections pro-
vide additional detail on these model inputs.

Hydrological time series
The hydrology of WCA2A is controlled primarily by the
operation of control points along the S10 and L35-B
canals. The hydrology data were obtained from the
SFWMD, which uses the WCA2A site as a test site for the
RSM. The average depth for the region ranges from 60 to
90 cm (SFWMD, 2008c). The input dataset consisted of a
daily time series of hydraulic head values (m) at the inlet
and outlet control structures of WCA2A (represented by
the green squares in Figure 1) for the years 1979-2000
(Wang 2009). The time series have since been updated to
2008 for all control structures using data collected from
the DBHYDRO website (SFWMD 2009).

Soil phosphorus
A gradient of soil phosphorus exists along WCA2A, with
a high concentration near the inlets at the north, and a
low concentration at the outlets in the south. This soil
phosphorus gradient has been widely documented and
studied (DeBusk et al. 1994; Grunwald et al. 2004, 2008;
Rivero et al. 2007a,b; Grunwald 2010). Given the unavail-
ability of spatial soil phosphorus data beyond map classifi-
cations (Grunwald 2010), soil phosphorus input maps
were created by overlaying the WCA2A mesh on the
existing maps obtained from Grunwald et al. (2004, 2008).
The soil phosphorus map of 1990 was used for the model
training period of 1991-1995, while the soil phosphorus
map of 2003 was used for both the testing 1 (1991-2003)
and testing 2 (1995-2003) simulation periods. Due to the
poor quality of these soil phosphorus input maps and the
inability of TARSE to adequately simulate phosphorus dy-
namics in the WCA2A region (as it is still in develop-
ment), the soil phosphorus concentration itself was not
simulated, i.e., the static soil phosphorus concentration
provided by the input maps was used to inform the model
throughout the simulation period.

Cattail and sawgrass
Vegetation maps for WCA2A were obtained for the years
1991, 1995 (Rutchey 2011), and 2003 (Wang 2009), which
were all used in Rutchey et al. (2008). These maps pro-
vided density (g/m 2) distributions across the test site for
cattail. The negative correlation between sawgrass and


cattail has been reported by Doren et al. (1999) and
Richardson et al. (2008), and various other vegetation
maps of the area, namely 1991 (Jensen et al. 1995), 1995
(SFWMD 1995), 1999 (SFWMD 1999), and 2003 (Wang
2009), confirm this negative correlation. Although saw-
grass density is related to more environmental factors
than only cattail density (Miao and Sklar 1998), a simple
negative correlation with the cattail maps was used in
order to assign densities to the sawgrass maps. For ex-
ample, high sawgrass density values (1,600 g/m2) were
assigned to regions with typically low cattail density
values, and low sawgrass density values (600 g/m2) were
assigned to regions with high cattail density values.
The program ArcMap (ESRI Environmental Systems
Resource Institute 2010) was used to create a uniform
raster map from the original images which had a mini-
mum mapping unit of 50 m2 (Rutchey et al. 2008). The
vegetation class values were converted to density values
according to Table 1, with vegetation class 4 (other) re-
lating to the absolute minimum (residual) cattail density,
representing the seed bank. The input file was created
by overlaying the mesh grid of 385 triangles (510 trian-
gles total-which includes a row of triangles along the
border) on the rasterized vegetation map and calculating
the mean value of all raster cell density values within
each triangular element. This new aggregated map was
used to create the input file. A graphical overview of this
process for the data maps can be seen in Figure 2.
The final sawgrass maps are viewable in Figure 3. The
maximum densities of 1,240 g/m2 for cattail and 1,958 g/m2
for sawgrass were reported by Miao and Sklar (1998). An
overview of the parameter descriptions for the increasing
levels of complexity can be found in Table 2.

Statistical analysis of simulated and monitored biomass
Besides a side-by-side visual comparison of the model
output, there were three sets of statistical analysis tech-
niques that were used to compare the model results and
the raw data. These metrics, commonly used in litera-
ture for comparing both single- and multi-species pat-
terns (Fortin and Dale 2005; Muneepeerakul et al. 2008;
Convertino et al. 2009), analyzed the local, global, and
autocorrelation structure of observed and modeled vege-
tation patterns. All metrics were accompanied by a

Table 1 Cattail class and density values for formatting
data maps


Vegetation class

1 High density cattail
2 Medium density cattai
3 Low density cattail
4 Other


Cattail density Sawgrass density
value (g/m2) value (g/m2)


Page 9 of 21







Lagerwall et al. Ecological Processes 2012, 1:10
http://www.ecologicalprocesses.com/content/1/1/10


a) 1991 A b) 1995















1 High = 2 Medium 3 Low



Figure 3 Sawgrass input maps for the years 1991, 1995, and 2003, respectively.


Nash-Sutcliffe coefficient (McCuen et al. 2006), repre-
sented by Equation 11, which provides a singular num-
ber for the comparison of the model statistics and how
they compare to the observed data. The coefficient is a
comparison of model results vwith the mean of the data.


Ef = 1 Y- i-2 (11)
Ell '(yi -y)2
Where Ef is the Nash-Sutcliffe coefficient, y is the pre-
dicted variable, yi is the observed variable, y is the mean
of the observed variable, and n is the sample size. A
Nash-Sutcliffe value of 1 means that the model com-
pletely matches the data, while a value of 0 means
that the model performs no better than the mean of
the data. Any value less than 0 is interpreted as a
poor representation of the data.
A direct comparison between model output and the
data was performed with the use of a classified difference
technique (Kiker 1998). Since the data maps were initia-
lized with a minimum density of 10 g/m2 to account for
movement between triangular elements that is not simu-
lated in this model application, a difference between
model output and the data value falling within 20 g/m2


c) 2003


S4 Minimum


was considered a "perfect" match. This is loosely based on
the fact that Miao and Sklar (1998) reported a roughly
10% error in measurement of the maximum density of
1,240 g/m So, for example, if the data value was 10 g/m2
(representing a typical non-cattail region), and the model
output was 12 g/m with a difference of 2 g/m (falling
within the 20 g/m2 range), then this would be considered
a "perfect" match. The next class of differences lies within
the 200 g/m2 range, which is the value assigned to the low
cattail density class during the formatting and creation of
the input data maps. This 200 g/m2 range is also half the
range between the successively higher cattail density
classes. The third class of differences lies within 400 g/m ,
which can be thought of as a data class difference (e.g., be-
tween low and medium densities) or also as being within
40% of the maximum possible difference (the maximum
data density is set as 1,000 g/m2). Finally, any difference
above the 400 g/m2 threshold is placed in the fourth class
of differences and represents a significant misrepresenta-
tion of the data by the model.
A box and whiskers plot (Ott and Longnecker 2004)
was created with all model element values compared
with their corresponding data element values. The
desired figure is a plot with the means and ranges


Table 2 Parameter description for the increasing levels of complexity studied
Parameter Parameter description Levels Affected variables
influenced


Cattail density
Cattail growth rate


CATGF


1,2,3,4,5 Cattai
1,2,3,4,5 Cattai


Parameter
equation/logic
Population density
Rate of increase of populate


DepthF Water depth influence
phosphorusF Soil phosphorus concentrating
Sawgrass Sawgrass density
SAWGF Sawarass Growth rate


2,3,4,5
luence 3,4,5
4,5


Cattail carrying capacity, Cattail Equation 2
Cattail carrying capacity, cattail Equation 6
Sawgrass, cattail carrying capacity, cattail Population density


Page 10 of 21


4,5 Sawgrass


Rate of increase of populate






Lagerwall et al. Ecological Processes 2012, 1:10
http://www.ecologicalprocesses.com/content/1/1/10


corresponding to the associated data ranges. The box
and whiskers plots cover the entire range of possible
values from 0 to 1,240 g/m2.
Moran's I statistic (Cliff and Ord 1970; Paradis 2010)
was used to determine the spatial autocorrelation be-
tween cells separated by an increasing distance. Moran's
I is represented by Equation 12.


S1 (Xi x)(xj x)
I= E ( )2 (12)
WE ="Ixi- X)2

Where xi is the current cell value, xj is the value of the
cell separated by a given distance, x(bar) is the mean,
and W is the number of cells surrounding the current
one and found within the given distance. These values
are plotted against an increasing cell-pairwise distance,


as in Marani et al. (2006), to determine the trend in
spatial autocorrelation across the entire region.
A landscape-scale abundance-area plot (Martin 1980;
Michalski and Peres 2007) was used to measure the
average change in density across the test site. One hun-
dred randomly distributed cells are used as base cells.
From these, the densities of all cells falling within a
given radius are summed. This total is then divided by
the number of base cells and plotted against the area of
circles with an increasing radius as in Martin (1980).
A trend in the regional mean density was plotted with
a daily timestep for a visual comparison of the trends be-
tween the different levels of complexity. This was
repeated for the individual levels of complexity and
selected zones (elements) within the region, for a more
detailed view of the effect of external parameters on dif-
ferent areas of the region. Elements 209, 244, and 380,


Page 11 of 21


100-200 200-400 400-600 I 500-800 800-1000 -1000-1240 (g/m2)


Figure 4 Results for (a) training (1991-1995), (b) testing 1 (1991-2003), and (c) testing 2 (1995-2003) simulations for the level 1, 2, 3,
4, and 5 complexities. The historical patterns these results are compared to are in the first column. Densities have been aggregated into eight
classes for visual comparison only.








Lagerwall et al. Ecological Processes 2012, 1:10
http://www.ecologicalprocesses.com/content/1/1/10


a) Training
1991 to 1995


Level
140
120

E 100
80


40
2C

Level 2
140
120
100
80

+i 60
40
20

Level 3
140
120
100
01
80

"7 60
C 40

20

Level 4
140
120
100

80

-A 60
40
20

Level 5
140
120
100

S80

60
S 40

20


10

10

o0

o0


0
0
10 ..........---------- -






0 -
0
0
0

0

0
0












o
0 ---


















o









0
0
0

0
0
0 ------------- .- .------------------

















i0


i0
i0
i0








0 '"' ------- -- -- --- ------


) 500 1500 2500 3 7


Time (days) Time (days)

Model: Element 209 Model: Element 244 Model: Element 380
Data: Element 209 Data: Element 244 0 Data: Element 380


Figure 5 Regional and zonal trends for (a) training, (b) testing 1, and (c) testing 2 simulation periods, for all five levels of complexity.
The points at the beginning and end of t rends represent the observed data densities.


Page 12 of 21


b) Testing
1991 to 2003



































3
---- -






- -- .- -- -- -






- - -- -
+- ---- ----------------


0 200


400 600 800 1000 12001400
Time (days)

- Model: Regional -
* Data: Regional 4


C)Testing
1995 to 2003











.- --------- -----t













*,..-.- ----* I----* --------- ---










-.-- ---- --


*-------.------------------ *--- -








--------- -


















0 500 1500 2500







Lagerwall et al. Ecological Processes 2012, 1:10
http://www.ecologicalprocesses.com/content/1/1/10


located in the northeast, central, and southwest, were
selected as representative elements for typically high,
medium, and low cattail densities, respectively. These
elements are marked by red squares in Figure 1 and are
useful for evaluating local vegetation indicators.

Model training and testing
There were three time periods over which the model
was simulated using the available data maps of 1991,
1995, and 2003. Training was performed for the time
period 1991-1995 using the level 1 complexity to es-
tablish the growth rate (6.7 x 10-9 g/g s), and results
from the other levels will be due solely to the effect
of their included external parameters. It is therefore
expected that the results of the other levels of com-
plexity will not be as accurate as the level 1 com-
plexity for this time period. Testing of the model
was performed for the time period 1991-2003. This
provides an extended forecast based on the original
calibration time period and initial data. Finally the
1995-2003 time period was used as a blind test of
the model, using different initial conditions and de-
termining its ability to accurately predict the density
distribution of the 2003 cattail map.


a) Regional Mean Trend


c


1400
E 1200
1000


c 600
E 400
200
0


0o Level 1
o- Level 2
Level 3
10 Level 4
o0 Level 5
o0 Data




0 200 400 600 800 1000 1200 1400 1600
Time (days)

Box-Plot


Data LI L2 L3 L4 L5


Results and discussion
From the cattail maps of Figure 2 and those in Rutchey
et al. (2008), a trend in cattail distribution over the years
is observable. It appears that cattail density and distribu-
tion increased from 1991 to 1995. From 1995 to 2003
the general distribution continued to increase but with
more dispersed patches of high-density cattail. This may
be related to a reduction in the overall dispersal or to an
increased local speciation. Through the use of best
management practices, the total phosphorus load
entering WCA2A for the period 1995-2004 was reduced
by roughly 36% (Richardson et al. 2008), which may have
also had a role in the dispersal noted above.
The results of the simulations and analyses are dis-
played in Figures 4, 5, 6, 7, and 8. Figure 4 shows the
model output maps for the different simulation periods,
and all five levels of complexity, compared to the final
data maps. These density maps have had their values
aggregated into eight classes for visual comparison only.
A better depiction of these trends is found in the classi-
fied difference maps of Figure 9 below. Figure 5 shows a
time series plot for the five levels of complexity across
all three simulation periods. It provides added insight
into the trends of the model, without relying purely on


b) Abundance-Area


1-

800
4'
* 600
C
3400









2

2



-1


Suu

00

00

00

00

0


0 6080 12160 1824024320 30400364
Lag/Distance (m)

d) Moran's I


0 Level
'.5 Level 2
Level 3
o0 Level 4
Level 5
-Data

-0
0 5 .

0 6080 12160 1824024320 304003641
Lag/Distance (m)


Figure 6 Regional statistics for training period (1991-1995) and all five levels of complexity. (a) Rec
initial and final data values), (b) abundance-area (the black line represents the data), (c) box plot (data plot
black line represents the data).


na mean trend (red dots represent
the left), and (d) Moran's / (the


Page 13 of 21


- Level 1
- Level 2
- Level 3
Level 4
- Level 5
-Data


t i t <
4 +, t1


ljCE







Lagerwall et al. Ecological Processes 2012, 1:10
http://www.ecologicalprocesses.com/content/1/1/10


a) Regional Mean Trend
1400 Le
Le
1200 Le
Le
1000 Le
800 Le
D
600


vel 1
vel 2
vel 3
vel 4
vel 5
ata


500 10001500 2000 2500 3000 35004000 45
Time (days)


C) Box-Plot
1400
1200
1000
800
600
400


20If


Data L1 L2 L3 L4 L5


b) Abundance-Area


"E
80000

60000

S40000

c 20000

0


- Level 1
- Level 2
Level 3
Level 4
- Level 5
-Data





6080 12160 1824024320 30400364
Lag/Distance (m)


d) Moran's I


3.0


Lag/Distance (m)


Figure 7 Regional statistics for testing 1 period (1991-2003) and all five levels of complexity. (a) Regional mean trend (red dots represent
initial and final data values), (b) abundance-area (the black line represents the data), (c) box plot (data plot on the left), and (d) Moran's / (the
black line represents the data).


the end points. The plots are for the regional mean
density (R), in red, and elements 209 (blue), 244 (green),
and 380 cyann). The three statistics and comparison time
series for the calibration period 1991-1995 can be found
in Figure 6. The regional mean time series plot for all
five levels of complexity can be found in Figure 6a, the
abundance-area plot in Figure 6b, the boxplot in
Figure 6c enables a comparison of the spread of model
densities with that of the observed data, and the Moran's
I plot is found in Figure 6d. Figures 7 and 8 display the
same three statistics and regional mean density trends as
in Figure 6 for the other two simulation periods, namely
1991-2003 and 1995-2003.
When considering the first hypothesis, or level of
complexity, that cattail growth is density dependent, we
note the following points. For the training (1991-1995)
time period, the level 1 complexity's spatial density dis-
tribution (Figures 4 and 9) is the most similar to the
observed 1995 data. The density trend (Figure 5) is
smooth and slowly increasing for all observed points
(red dots). The regional trend ends directly on the data
density. The southwest (element 380) and central
(element 244) trends over-predict the data points. The


abundance-area statistic (Figure 6b) follows the data
trend (black line) the closest. The mean and distribution
of densities (Figure 6c) are relatively close to the data.
The Moran's I statistic follows the data (black line) trend
relatively closely (Figure 6d). All of these results from
the training period are expected because this level of
complexity was used for calibration over this time
period. For the two testing simulation periods, the level
1 complexity clearly overestimates the historical data
(Figures 4 and 9). The density trend (Figure 5b,c)
remains smooth but overestimates the observed data, ex-
cept for element 380 in Figure 5c which remains low,
possibly due to the low initial starting density and rela-
tively short time period. The abundance-area statistic
(Figures 7b and 8b) shows significant over-prediction of
the data trend (black line). The mean density is still low,
but the distribution is significantly skewed toward the
higher densities (Figures 7c and 8c). This is evidence
that a spatial distribution of densities is more inform-
ative than simply using the mean for the area or a pres-
ence/absence type model. Moran's I statistic follows the
data (black line) trend relatively closely (Figures 7d and
8d). The results of these analyses confirm that although


Page 14 of 21


!



i i i


Level 1
Level 2
Level 3
Level 4
--- Level 5
-Data




) 6080 12160 1824024320 304003641


80







Lagerwall et al. Ecological Processes 2012, 1:10
http://www.ecologicalprocesses.com/content/1/1/10


a) Regional Mean Trend
1400 Level 1
1200 Level 2
Level 3
1000 Level 4
800 Level 5
Data
600
400
200
--- .-.- --- -- --- .-- -----
0 500 1000 1500 2000 2500 3000
Time (days)

C) Box-Plot


1400
r 1200
1000
S800
600
400
200
0


b) Abundance-Area


8000C

S6000C

S 4000C
E
C 2000C
4,


- Level 1
- Level 2
Level 3
Level 4
Level 5
-Data





6080 12160 18240 24320 3040036480
Lag/Distance (m)


d) Moran's I


3


0 6080 12160 18240 24320 3040036480
Lag/Distance (m)


Figure 8 Regional statistics for testing 2 period (1995-2003) and all
initial and final data values), (b) abundance-area (the black line represents
black line represents the data).




cattail may indeed have a density-dependent/logistic
growth pattern as we are able to simulate observed data
during the training period, our inability to simulate
observed data for the two training periods indicates that
there are certainly other parameters affecting the growth
and distribution of this species.
When considering the second hypothesis, or level of
complexity, that cattail growth/expansion is dependent
on water depth, we note the following points. For all
time periods (training, testing 1, and testing 2), the level
2 complexity's spatial density distribution (Figures 4 and 9)
is consistently lower than the observed values. This is
confirmed in the trend analysis (Figure 5a,b,c), where all
the observed elements (209, 244, and 380) and the re-
gional trend are consistently below the observed values.
The only exception is element 380 in Figure 5a, where
there is hardly any change in the element's density, and
this is possibly due to the low initial density value of that
element. The abundance-area statistic for all time periods
(Figures 6b, 7b, 8b) is significantly lower than the
observed trend. Similarly, the distribution of densities for
all time periods (Figures 6c, 7c, 8c) is much reduced. For
the Moran's I statistic, the model is relatively close to the


five levels of complexity. (a) Regional mean trend (red dots represent
the data), (c) box plot (data plot on the left), and (d) Moran's / (the


data trend but consistently has a longer (the longest) tail.
This implies that cells further away have an observable
impact on the density of any other cell. This would be
due to the fact that the water depth in every cell has an
effect/influence on every other cell in the region. We
know that water depth is an influential factor in cattail
growth (Newman et al. 1998; Miao and Sklar 1998), how-
ever the results of these analyses indicate that the current
model (level 2 complexity) is overly influenced by this
parameter. It is expected that the influence of this param-
eter will be reduced as it is "diluted" with other para-
meters in the higher complexity models.
When considering the third hypothesis, or level of
complexity, that cattail growth/expansion is dependent
on soil phosphorus concentration, we note the following
points. The spatial density distribution (Figures 4 and 9)
for level 3 lies somewhat in-between that for level 1 and
level 2. Except for the training period, which slightly
under-predicts the observed values, the two testing peri-
ods appear to more accurately predict the observed
density distribution. This is confirmed with the trend
analysis (Figure 5a,b,c), where at least the regional trend
is at or relatively close to the observed values. As with


Page 15 of 21


Data L1 L2 L3 L4 L5


0 Level 1

.5 Level 2
Level 3
.0 Level 4
Level 5
5Data




0 ---C' ---------






Page 16 of 21


Lagerwall et al. Ecological Processes 2012, 1:10
http://www.ecologicalprocesses.com/content/1/1/10


Data
a) Training 1991 to 1995
a


Level 1 Level 2 Level 3 Level 4 Level 5


S


b)Testing 1991 to 2003 A





-^k~~~~, 17 n <- ^ ^ y <1

r TV '9 A


A 195to20 A A A


V 1 0 A


44
tI"t,


1 (<200 g/m2)


- 0 (<20 g/m2)


Figure 9 Classified difference maps for (a) training (1991-1995), (b) testing 1 (1991-2003), and (c) testing 2 (1995-2003) simulations
for the level 1, 2, 3, 4, and 5 complexities. The classified differences of the data maps these results are compared to are in the first column
(historical patterns).


the level 2 complexity, element 380 tends to under-
predict the observed value. However, element 209 tends
to predict the observed value better than either of the
previous two levels of complexity. The abundance-area
statistic (Figures 6b, 7b, 8b) shows consistent under-
prediction of the observed trend, but also shows consist-
ently higher values than the level 2 trend and is closer to
the data than the level 1 trend. The distribution of dens-
ities for all time periods (Figures 6c, 7c, 8c), although
greater than the level 2 complexity, is still significantly
lower than the observed distribution. The Moran's I
trend is followed closely for all time periods (Figures 6d,
7d, 8d). The results of these analyses confirm that soil
phosphorus is a significant influencing factor in the dis-
tribution of cattail, although the water depth parameter
remains highly influential. The level 3 complexity is


2(<400g/m2) 3 4O Og/im2|


better able to predict cattail in areas of typically high
phosphorus or of high cattail density than the previous
two levels of complexity.
When considering the fourth hypothesis, or level of
complexity, that sawgrass density may impact the rate
of cattail expansion, we note the following points.
The spatial density distribution (Figures 4 and 9) is
closer to the observed values than the previous levels
of complexity. This is confirmed in the trend analysis
(Figure 5 a,b,c), where most notably all of the ele-
ments tend to better predict the observed values,
except for element 244 in Figure 5c, which over-
predicts the observed density and in turn raises the
regional trend above the observed value as well. The
abundance-area statistic only slightly under-predicts
the observed trend during the training time period


Level 1


Level 2


Level 3


Level 4


Level 5






Lagerwall et al. Ecological Processes 2012, 1:10
http://www.ecologicalprocesses.com/content/1/1/10


(Figure 6b). During the two testing time periods, the
statistic indicates a slight over-prediction of the
observed trend, but results show better predictions
than any of the previous levels of complexity. The
density distribution (Figures 6c, 7c, 8c) is significantly
higher than the level 2 and level 3 complexities, and
equal to (Figure 6c; training) or less than (Figures 7c,
8c; testing) the level 1 complexity. This means that
the level 4 complexity consistently approximates the
observed densities for the region better than the other
levels of complexity for all time periods, albeit with
slightly elevated minimum densities. The Moran's I
statistic (Figures 6d, 7d, 8d) follows the observed
trend relatively well for all time periods. Although the


level 4 complexity tends to have slightly elevated
minimum densities, like the level 1 complexity, the
general result from these analyses is that the level 4
complexity is able to simulate the cattail densities
through the region consistently better than any of the
previous levels of complexity. We can thus conclude
that including a simulated sawgrass density does in-
deed impact the rate of cattail expansion and improve
simulation results.
When considering the fifth hypothesis, or level of
complexity, that inter-species interactions between
cattail and sawgrass contribute to the observed cattail
dynamics, we find the following: The spatial density
distribution (Figures 4 and 9) does not predict the


I ii''


III''


a) Classified Difference 1991 to 1995


100%
80%
60%
40%
20%
0%


b) Classified Difference 1991 to 2003


100%
80%
60%
40%
20%
0%


c) Classified Difference 1995 to 2003
100% -. -
80%





011 111
20%
Li L2 L3 L4 L5


Levels of Complexity
1(Within 200 g/m2) 2 (Within 400 g/m2) 3 (400 g/m2)


a 0 (Within 20 g/m2)


Figure 10 Classified difference summary. Percentage of cells occurring within each class, for all levels of complexity and time periods (a)
training (1991-1995), (b) testing 1 (1991-2003), and (c) testing 2 (1995-2003).


Page 17 of 21







Lagerwall et al. Ecological Processes 2012, 1:10
http://www.ecologicalprocesses.com/content/1/1/10


observed values significantly better than the level 4
complexity. The trend analysis (Figure 5a,b,c) is al-
most identical to that of the level 4 complexity in
every respect. All of the statistical analyses and distri-
butions for all time periods (Figures 6b,c,d; 7b,c,d; 8b,
c,d) are almost identical to those of the level 4 com-
plexity. The result of these analyses is that the level 5
complexity does not predict the observed values with
greater success than the level 4 complexity. While
inter-species interactions might well have an effect
with a different model structure, the current modeling
arrangement has shown the beginning of diminishing
returns with respect to model complexity and
predictive capability.
With regard to the Moran's I statistic, all the complexity
levels followed the same basic trend as the data (repre-
sented by the black line) and were all 0 by around the
18,240 m mark. This distance corresponds approximately
to the width of the region, while the total distance of
36,480 m in the plot corresponds to the longest north-
south distance of the region. It is believed that the statistic
drops to 0 by the 18,240 m mark due to overlapping and
boundary effects and that this elevates the Nash-Sutcliffe
coefficient for all levels of complexity in this statistic.
A summary of the Figure 9 classified difference maps
can be found in the bar chart of Figure 10, which shows
the percentage of triangular elements falling within each
class for all five levels of complexity and simulation peri-
ods. Upon further inspection of these plots, the level
4 and level 5 complexities consistently outperform the
other levels of complexity, with either the highest
percentage of combined classes 0 (< 20 g/m2) and 1
(< 200 g/m ), or the lowest percentage of combined
classes 2 (< 400 g/m2) and 3 (> 400 g/m2).
A summary of the three statistics found in Figures 6b,c,d;
7b,c,d; and 8b,c,d is provided by the Nash-Sutcliffe coeffi-
cients in Table 3 and can be visually compared in Figure 11,
with the box plots (or 1-to-1 comparisons) located in
Figure 11a, abundance-area in Figure 11b, and Moran's I in
Figure 1c. From Figure 11 it can be noted that the level 4
and 5 complexities, which include depth, soil phosphorus,
and sawgrass interactions, consistently perform better than
the other levels of complexity. A point to note regarding
the level 5 complexity is that despite the fact that it does
not offer a significant improvement in predictive capability
over the level 4 complexity, it does not predict the observed
values any worse than the level 4 complexity either.

Conclusions
The methods of modeling cattail for ecological models cur-
rently in use were compared, their similarities and differ-
ences were noted, and a knowledge gap identified: there
doesn't yet exist a method of quantitatively and determinis-
tically determining the spatial distribution of cattail in the


Table 3 Summary of Nash-Sutcliffe values comparing
model and observed data for box plot, Moran's I, and
abundance-area statistics (represented by Figures 6, 7,
and 8, respectively) for level 1, level 2, level 3, level 4,
level 5, training (199-1995), testing 1 (1991-2003), and
testing 2 (1995-2003) simulations


Year
1991-199,


level 1-to-1 Box plot
1 0.74
2 0.13


Moran's I Abundance
0.98 0.98


991-2003


049


995-2003


0.14


0.39


Everglades. A coupled free-form/fixed-form model was
introduced to solve this problem. An added benefit of the
free-form nature of the RSM/TARSE coupled model is the
user-definable equations of interaction, which can be
modified as data and/or new theories become available.
This new ecological implementation of the model (RTE)
was successfully applied towards modeling cattail dynamics
across the WCA2A test site for training (1991-1995),
testing (1991-2003), and blind test (1995-2003) simu-
lation periods. Five algorithms, with increasing com-
plexity, were used to match the historical data. Upon
analysis of the performance of these different levels, it
can be concluded that the level 4 and 5 complexities,
which include depth, soil phosphorus, and sawgrass
interaction parameters, are the most suitable models for
matching the historical data. The Nash-Sutcliffe coefficient
was used to distinguish the success of different models.
Both local and landscape-scale indicators were used to
perform the comparison between historical and modeled
cattail patterns. The average local cattail density was
estimated with a box-plot analysis; the pairwise-cell
comparison of local cattail densities was analyzed with
Moran's I; and, the regional increase with area of the
local cattail density was estimated through the
abundance-area relationship. The box-plot and the
abundance-area were the most meaningful patterns to
discriminate models in terms of their ability to represent
the observed patterns.


Page 18 of 21







Lagerwall et al. Ecological Processes 2012, 1:10
http://www.ecologicalprocesses.com/content/1/1/10


1


6






0

z


b)







UJ

-0


z


C




-0



iU
z


L2 L3
.5


-1


Abundance-Area
.5










Levels of Complexity



Moran's I






0
L1 L2 L3
.5Levels of Complexity

-1
Levels of Cmnplexity


* 1991 to 1995 U 1991 to 2003 1995 to 2003


Figure 11 Nash-Sutcliffe summary of statistics. A graphical representati
consistently well in comparison with all the other models.


The autocorrelation structure of the cattail patterns were
well represented by all the models at each complexity level.
This is possibly due to the fact that through overlapping
and boundary effects, cattail densities leveled off after
roughly half the distance (top to bottom) that was used to
calculate the statistic. It may be more representative if fu-
ture calculations considered only half this maximum dis-
tance, where the variations would carry a greater weighting.


Table 3. The level 4 and


complexity models perform


Our simulation results would be in agreement with the
studies of Newman et al. (1998) and Miao and Sklar
(1998), in which water depth and soil phosphorus concen-
tration were the most important factors aiding in cattail ex-
pansion. Our results also include an interaction parameter
with sawgrass, which is of interest in the region. Thus, we
confirm the importance of considering species dependen-
cies or interactions in reproducing the cattail patterns even


Page 19 of 21


Box-Plot


Levels of Complexity


L4







Lagerwall et al. Ecological Processes 2012, 1:10
http://www.ecologicalprocesses.com/content/1/1/10


in water-controlled areas in which the anthropic-driven
variables would be expected to dominate the species
processes and the resulting patterns.
Limitations of our current modeling approach may in-
clude the element/triangle size, with a range of 0.5-1.7
km2 (Wang 2009). This constraint was dictated by the
choice of the RSM that simulates hydrological processes.
Although the imposed grid-unit has a relatively coarse
size in which there is still considerable heterogeneity of
the environmental features (Zajac 2010), RTE has
proven to be capable of reproducing the dynamics of
cattail and sawgrass at the landscape scale using the level
4 and level 5 complexities. This makes it a valuable tool
for exploring potential management scenarios in water
conservation areas in the Everglades and possibly in
other water-controlled wetlands.
Further investigations would consider the quantifica-
tion of the importance of water-controlled drivers and
species traits (dispersal) for vegetation patterns, the sta-
bility/instability states of species under varying stressors,
the prediction of future management scenarios, and the
comparison with neutral-based models.
In terms of further model development and added com-
plexity, efforts have been made towards more accurate rep-
resentation of fauna movement through the use of
Eulerian-Lagrangian (grid-independent) particle move-
ment (Lagerwall 2011), as well as using vegetation types/
densities to influence the hydrology with a dynamically
linked Manning's n parameter (Zajac 2010). While creating
more dynamically linked parameters is an ongoing task,
these linkages remain a challenge to implement due to the
difficulties associated with parameterizing (training) a
model with feedback effects. This feedback relationship be-
tween ecological and hydrological model components may
be quite important to the function and resilience of these
ecosystems and is certainly a subject of further research.

Competing interests
The authors declare that they have no competing interests

Authors' contributions
GL conducted the majority of the research, model adaptation for ecology,
and writing of the paper GK provided ecological modeling expertise,
general guidance, help in developing the five levels of complexity, paper
writing, and review contributions RMC provided statistical insights, provided
critical review on model design, and ensured that the general logic of the
paper was maintained MC provided expertise in the ecological statistics and
contributed to paper writing, formatting, and review AJ provided RSM/
TARSE model expertise NW provided RSM and WCA2A expertise, supplied
raw vegetation maps, and provided critical review on model design All
authors read and approved the final manuscript

Acknowledgements
Financial support for this research was provided by the South Florida Water
Management District and the U S Geological Survey Water Resources
Research Center at the University of Florida

Author details
Frazier Rogers Hall, University of Florida, PO Box 110570, Gainesville, FL
32611-0570, USA 2Soil and Water Engineering Technology, Inc, 3960


Magnolia Leaf L, SuwaneeGA 30024, USA Hydrologic and Environmental
Systems Modeling, South Florida Water Management District, 3301 Gun Club
Rd, West Palm Beach, FL 33406, USA

Received: 2 July 2012 Accepted: 7 October 2012
Published: 1 November 2012


References
Arnold K, Gosling J (1998) The Java programming language, 2nd edn Prentice
Hall, Upper Saddle River, NJ
Cary JR, Shasharina SG, Cummings JC, Reynders JVW, Hinker PJ (1998)
Comparison of C++ and Fortran 90 for object-oriented scientific
programming Comp Phys Comm 105'20-36
Cliff AD, Ord K (1970) Spatial autocorrelation a review of existing and new
measures with applications Econ Geography 46'269-292
Convertino M, Muneepeerakul R, Azaele S, Bertuzzo E, Rinaldo A, Rodriguez- Iturbe
I (2009) On neutral metacommunity patterns of river basins at different
scales of aggregation Water Resour Res 45W08424
Costanza R, Voinov A (2001) Modeling ecological and economic systems with
STELLA part III Ecol Model 143'1-7
DeBusk WF, Reddy KR, Koch MS, Wang Y (1994) Spatial distribution of soil
nutrients in a northern-Everglades marsh Water Conservation Area 2A Soil
Soc Am 58'543-552
Doren RF, Armentano Thomas V, Whiteaker Louis D, Jones Ronald D (1999)
Marsh vegetation patterns and soil phosphorus gradients in the Everglades
ecosystem Aqua Bot 56'145-163
Douglas MS (1947) The Everglades river of grass Rinehart, New York
Duke-Sylvester S (2005) Initial performance measures and information related to
the ATLSS vegetation succession model i i i i Accessed 31
July 2010
ESRI (Environmental Systems Resource Institute) (2010) ArcMap 10 0 ESRI,
Redlands, CA
Fitz CH, Trimble B (2006a) Documentation of the Everglades Landscape Model
ELM v25 South Florida Water Management District, West Palm Beach, FL
Fitz CH, Trimble B (2006b) Everglades Landscape Model i1- i, i. i i I
portal/page/portal/xweb%20-%20release%202/elm Accessed 31 July 2010
Fitz HC, Kiker GA, Kim JB (2011) Integrated ecological modeling and decision
analysis within the Everglades landscape Crit Rev Environ Sci Technol 41
(S1)517-547
Fortin MJ, Dale MRT (2005) Spatial analysis, a guide for ecologists Cambridge
University Press, Cambridge
Grace JBL (1989) Effects of water depth on Typha latifolia and Typha domingensis
Am J Bot 76 762-768
Gross LJ (1996) ATLSS home page http'//atlss org/ Accessed 31 July 2010
Grunwald S (2010) Phosphorus data for WCA2A Personal Communication
University of Florida, Gainesville
Grunwald S, Reddy KR, Newman S, DeBusk WF (2004) Spatial variability,
distribution and uncertainty assessment of soil phosphorus in a South Florida
wetland Environmetrics 15811-825
Grunwald S, Ozborne TZ, Reddy KR (2008) Temporal trajectories of phosphorus
and pedo-patterns mapped in Water Conservation Area 2, Everglades,
Florida, USA Geoderma 146'1-13
Guardo M, Fink L, Fontaine Thomas D, Newman S, Chimney M, Bearzotti R,
Goforth G (1995) Large-scale constructed wetlands for nutrient removal from
stormwater runoff an Everglades restoration project Environ Manage 19
(6)879-889
Harold ER (1998) XML' Extensible Markup Language, 1st edn IDG, Foster City
James AI, Jawitz JW (2007) Modeling two-dimensional reactive transport using a
Godunov-mixed finite element method J Hydrol 33828-41
Jawitz JW, Munoz-Carpena R, Muller S, Grace KA, James AI (2008) Development,
testing, and sensitivity and uncertainty analyses of a Transport and Reaction
Simulation Engine (TaRSE) for spatially distributed modeling of phosphorus
in South Florida peat marsh wetlands Scientific Investigations Report 2008-
5029 United States Geological Survey, Reston, VA
Jensen JR, Rutchey K, Koch MS, Narumalani S (1995) Inland wetland change
detection in the Everglades Water Conservation Area 2A using a time series
of remotely sensed data Photogramm Eng Rem Sens 61 (2)199-209
Keen RE, Spain JD (1992) Computer simulation in biology Wiley-Liss, New York
Kiker GA (1998) Development and comparison of savanna ecosystem models to
explore the concept of carrying capacity PhD Dissertation Cornell
University, Ithaca


Page 20 of 21








Lagerwall et al. Ecological Processes 2012, 1:10
http://www.ecologicalprocesses.com/content/1/1/10


Kiker, G A & Linkov, I 2006 The QnD Model/Game System Integrating
Questions and Decisions for Multiple Stressors pp 203-225 in Arapis, G,
Goncharova, N & Baveye, P Ecotoxicology, Ecological Risk Assessment and
Multiple Stressors Netherlands Springer (1-4020 4475-5)
Kiker, G A, Rivers-Moore, N A, Kiker, M K & Linkov, I 2006 QnD A modeling
game system for integrating environmental processes and practical
management decisions pp 151-185 in Morel, B & Linkov, I Environmental
Security and Environmental Management The Role of Risk Assessment
Netherlands Springer (1-4020-3892-5)
Lagerwall GL (2011) Modeling Typha domingensis in an Everglades wetland
Dissertation University of Florida, Gainesville
Lindenschmidt KE (2006) The effect of complexity on parameter sensitivity and
model uncertainty in river water quality modeling Ecol Model 19072-86
Ludascher B, Altintas I, Berkley C, Higgins D, Jaeger E, Jones M, Lee Edward A,
Tao J, Zhao Y (2006) Scientific workflow management and the Kepler system
Concurr Comp Pract Exper 18 1039-1065
Marani M, Tommaso Z, Belluco E, Silvestri S, Maritan A (2006) Non-neutral
vegetation dynamics PLoS One 1(1)'e78
Martin TE (1980) Diversity and abundance of spring migratory birds using habitat
islands on the Great Plains Cooper Ornithol Soc 82430-439
McCuen RH, Knight Z, Cutter AG (2006) Evaluation of the Nash-Sutcliffe Efficiency
Index Hydrol Eng 11597-602
Miao S (2004) Rhizome growth and nutrient resorption mechanisms underlying
the replacement of two clonal species in Florida Everglades Aquat Bot
7855-66
Miao SL, Sklar FH (1998) Biomass and nutrient allocation of sawgrass and cattail
along a nutrient gradient in the Florida Everglades Wetlands Ecol Manage
5245-264
Michalski F, Peres CA (2007) Disturbance-mediated mammal persistence and
abundance-area relationships in Amazonian forest fragments Conserv Biol
21 1626-1640
Muller S (2010) Adaptive spatially-distributed water-quality modeling an
application to mechanistically simulate phosphorus conditions in the
variable-density surface-waters of coastal Everglades wetlands PhD
Dissertation University of Florida, Gainesville
Muneepeerakul R, Bertuzzo E, Lynch HJ, Fagan WF, Rinaldo A, Rodriguez-Iturbe I
(2008) Neutral metacommunity models predict fish diversity patterns in
Mississippi -Missouri basin Nature 453'220-222
Muhoz-Carpena R, Parsons JE, Gilliam JW (1999) Modeling hydrology and
sediment transport in vegetative filter strips J Hydrol 214'111-129
Newman S, Schutte J, Grace J, Rutchey K, Fontaine T, Reddy K, Pietrucha M
(1998) Factors influencing cattail abundance in the northern Everglades
Aquat Bot 60265-280
Odum HT, Odum EC, Brown MT (2000) Wetlands management In Environment
and society in Florida CRC Press, Boca Raton
Ott RL, Longnecker MT (2004) A first course in statistical methods Curt Hinrichs,
Belmont, CA
Paradise E (2010) Moran's autocorrelation coefficient in comparative methods
I I I.,I I I I I 11 1 yII II Accessed 7
August 2010
Perez-Ovilla 0 (2010) Modeling runoff pollutant dynamics through vegetative
filter strips a flexible numerical approach PhD Dissertation University of
Florida, Gainesville
Richardson CJ, King Ryan S, Vymazal J, Romanowicz Edwin A, Pahl James W
(2008) Macrophyte community responses in the Everglades with an
emphasis on cattail (Typha domingensis) and sawgrass (Cladium jmoaicense)
interactions along a gradient of long-term nutrient additions, altered
hydroperiod, and fire Ecol Stud 201 215-260
Rivero RG, Grunwald S, Bruland GL (2007a) Incorporation of spectral data into
multivariate geostatistical models to map soil phosphorus variability in a
Florida wetland Geoderma 140428-443
Rivero RG, Grunwald S, Osborne TZ, Reddy KR, Newman S (2007b)
Characterization of the spatial distribution of soil properties in Water
Conservation Area 2A, Everglades, Florida Soil Sci 172'149-166
Rutchey K (2011) Typha domingensis maps of WCA2A for the years 1991 and
1995 Personal communication South Florida Water Management District,
West Palm Beach
Rutchey K, Schall T, Sklar F (2008) Development of vegetation maps for assessing
Everglades restoration progress Wetlands 172(2)806-816
SFWMD (1995) Land cover land use i. i i ii, 1 i
sfwmdxwebdc/dataview aspquery=unq_id=297 Accessed 11 November 2009


SFWMD (1999) Land cover land use 1999 i I i i i i
sfwmdxwebdc/dataviewaspquery=unq_id=1593 Accessed 11 November 2009
SFWMD (2005a) Documentation of the South Florida Water Management Model
version 55 South Florida Water Management District, West Palm Beach, FL
SFWMD (2005b) Regional Simulation Model (RSM) Hydrologic Simulation Engine
(HSE) user's manual South Florida Water Management District, West Palm
Beach, FL
SFWMD (2005c) Regional Simulation Model (RSM) theory manual South Florida
Water Management District, West Palm Beach, FL
SFWMD (2008a) RSM water quality user manual (draft) South Florida Water
Management District, West Palm Beach, FL
SFWMD (2008b) RSMWQE theory manual (draft) South Florida Water
Management District, West Palm Beach, FL
SFWMD (2008c) WCA2A HSE setup South Florida Water Management District,
West Palm Beach, FL
SFWMD (2009) DBHYDRO i i i i I i. i. Ii i. _dbkey_info
main_menu Accessed 04 August 2010
Stroustrup B (2000) The C++ programming language, specialty edn Addison-
Wesley, Westford, MA
Tarboton KC, Irizarry-Ortiz MM, Loucks DP, Davis SM, Obeysekera JT (2004)
Habitat suitability indices for evaluating water management alternatives
South Florida Water Management District, West Palm Beach, FL
Urban NH, Davis SM, Aumen NG (1993) Fluctuations in sawgrass and cattail
densities in Everglades Water Conservation Area 2A under varying nutrient,
hydrologic, and fire regimes Aquat Bot 46'203-223
USACE, S F RO (2010a) CERP The plan in depth- part 1 http//www
evergladesplanorg/about/rest_plan_pt_01 aspx Accessed 3 August 2010
USACE, S F RO (201b) CERP The plan in depth part 2 http//www
evergladesplanorg/about/rest_plan_pt_02 aspx Accessed 3 August 2010
van der Valk AG, Rosburg TR (1997) Seed bank composition along a phosphorus
gradient in the northern Florida Everglades Wetlands 17(2)'228-236
Walker WW, Kadlec RH (1996) A model for simulating phosphorus concentrations
in waters and soils downstream of Everglades stormwater treatment areas
Draft US Department of the Interior Everglades National Park, Homestead,
FL, http//publicfiles dep state fl us/DEAR/GoldAdministrativeRecord/Item%
2027/018752 PDF
Wang N (2009) 2003 Vegetation map; i i, ih i i 1 ,I 1.1 Personal
communication South Florida Water Management District, West Palm Beach, FL
Wang JD, Swain ED, Wolfert MA, Langevin CD, James DE, Telis PA (2007)
Application of FTLOADDS to simulate flow, salinity, and surface-water stage
in the southern Everglades, Florida Scientific Investigations Report 2007-
2010 United States Geological Survey, Florida
Wetzel PR (2001) Plant community parameter estimates and documentation for
the Across Trophic Level System Simulation (ATLSS) East Tennessee State
University, Johnson City
Wetzel PR (2003) Nutrient and fire disturbance and model evaluation
documentation for the Actoss Trophic level System Simulation (ATLSS) East
Tennessee State University, Johnson City
WillardDA(2010) SOFIA FS- 14696 i i i ll .. i /14696/
Accessed 3 August 2010
Wu Y, Sklar FH, Rutchey K (1997) Analysis and simulation of fragmentation
patterns in the Everglades Ecol Appl 7(1)'268-276
Zajac ZB (2010) Global sensitivity and uncertainty analysis of spatially distributed
watershed models PhD Dissertation University of Florida, Gainesville

doi:10.1186/2192-1709-1-10
Cite this article as: Lagerwall et al A spatially distributed, deterministic
approach to modeling Typha domingensis (cattail) in an Everglades
wetland. Ecological Processes 2012 1 10


Page 21 of 21




Full Text
!DOCTYPE art SYSTEM 'http:www.biomedcentral.comxmlarticle.dtd'
ui 2192-1709-1-10
ji 2192-1709
fm
dochead Research
bibl
title
p A spatially distributed, deterministic approach to modeling it Typha domingensis (cattail) in an Everglades wetland
aug
au id A1 snm Lagerwallfnm Garethinsr iid I1 email gareth83@ufl.edu
A2 ca yes KikerGregorygkiker@ufl.edu
A3 Muñoz-CarpenaRafaelcarpena@ufl.edu
A4 ConvertinoMatteomconvertino@ufl.edu
A5 JamesAndrewI2 ajames@swet.com
A6 WangNaimingI3 nwang@sfwmd.gov
insg
ins Frazier Rogers Hall, University of Florida, PO Box 110570, Gainesville, FL, 32611-0570, USA
Soil and Water Engineering Technology, Inc., 3960 Magnolia Leaf L, Suwanee, GA, 30024, USA
Hydrologic and Environmental Systems Modeling, South Florida Water Management District, 3301 Gun Club Rd, West Palm Beach, FL, 33406, USA
source Ecological Processes
issn 2192-1709
pubdate 2012
volume 1
issue 1
fpage 10
url http://www.ecologicalprocesses.com/content/1/1/10
xrefbib pubid idtype doi 10.1186/2192-1709-1-10
history rec date day 2month 7year 2012acc 7102012pub 1112012
cpyrt 2012collab Lagerwall et al.; licensee Springer.note This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
kwdg
kwd Typha
Modeling
Ecology
Dynamics
Model complexity
Water conservation area 2A
Transport and reaction simulation engine
Regional simulation model
abs
sec
st
Abstract
Introduction
The emergent wetland species Typha domingensis (cattail) is a native Florida Everglades monocotyledonous macrophyte. It has become invasive due to anthropogenic disturbances and is out-competing other vegetation in the region, especially in areas historically dominated by Cladium jamaicense (sawgrass). There is a need for a quantitative, deterministic model in order to accurately simulate the regional-scale cattail dynamics in the Everglades.
Methods
The Regional Simulation Model (RSM), combined with the Transport and Reaction Simulation Engine (TARSE), was adapted to simulate ecology. This provides a framework for user-defineable equations and relationships and enables multiple theories with different levels of complexity to be tested simultaneously. Five models, or levels, of increasing complexity were used to simulate cattail dynamics across Water Conservation Area 2A (WCA2A), which is located just south of Lake Okeechobee, in Florida, USA. These levels of complexity were formulated to correspond with five hypotheses regarding the growth and spread of cattail. The first level of complexity assumed a logistic growth pattern to test whether cattail growth is density dependent. The second level of complexity built on the first and included a Habitat Suitability Index (HSI) factor influenced by water depth to test whether this might be an important factor for cattail expansion. The third level of complexity built on the second and included an HSI factor influenced by soil phosphorus concentration to test whether this is a contributing factor for cattail expansion. The fourth level of complexity built on the third and included an HSI factor influenced by (a level 1–simulated) sawgrass density to determine whether sawgrass density impacted the rate of cattail expansion. The fifth level of complexity built on the fourth and included a feedback mechanism whereby the cattail densities influenced the sawgrass densities to determine the impact of inter-species interactions on the cattail dynamics.
Results
All the simulation results from the different levels of complexity were compared to observed data for the years 1995 and 2003. Their performance was analyzed using a number of different statistics that each represent a different perspective on the ecological dynamics of the system. These statistics include box-plots, abundance-area curves, Moran’s I, and classified difference. The statistics were summarized using the Nash-Sutcliffe coefficient. The results from all of these comparisons indicate that the more complex level 4 and level 5 models were able to simulate the observed data with a reasonable degree of accuracy.
Conclusions
A user-defineable, quantitative, deterministic modeling framework was introduced and tested against various hypotheses. It was determined that the more complex models (levels 4 and 5) were able to adequately simulate the observed patterns of cattail densities within the WCA2A region. These models require testing for uncertainty and sensitivity of their various parameters in order to better understand them but could eventually be used to provide insight for management decisions concerning the WCA2A region and the Everglades in general.
meta classifications classification WCW subtype theme_series_title type BMC Wetlands in a complex worldtheme_series_editor Matteo Convertinobdy
Introduction
The Everglades, commonly known as the “River Of Grass” Douglas (abbr bid B8 1947), in southern Florida, USA, once covered some 28,500 kmsup 2. This wetland ecosystem was sustained by the Kissimmee River, flowing through Lake Okeechobee and southwards as a shallow, slow-moving sheet of water flowing freely to the estuaries of Biscayne Bay, Ten Thousand Islands, and Florida Bay. The channelization of the Everglades around 1948 caused the reduction of the original wetland areas by up to 50%, with related declines in dependent wildlife. In addition to the changes in hydrology, continuous mining, agriculture, and urbanization activities have resulted in invasive and exotic plants becoming established in place of the original vegetation, altering habitats and often forming mono-crop stands (single species environments) (Odum et al. B42 2000).The Comprehensive Everglades Restoration Plan (CERP) was implemented in 2000 (USACE, S.F.R.O B63 2010a) with the explicit goal of restoring some of the Everglades’ former extent and ecosystem functioning. The main focus of CERP has been on improved management of water quantity and water quality with the assumption that if the water quantity and quality are adequate, the ecology will follow suit. There is, however, an increasing focus on the ecological impacts of various management decisions, and these efforts center on improving species diversity and protecting existing habitats (USACE, S.F.R.O B64 2010b). In an effort to achieve these goals, stormwater treatment areas (STA) were constructed just south of the Everglades agricultural area (EAA) to filter out phosphorus from the water before releasing it into the water conservation areas (WCA). The WCAs act as impoundments for water storage and flood control as well as serving as wildlife habitat. Water flows from these WCAs into the Everglades National Park (Guardo et al. B20 1995).
Typha domingensis as an invasive species
The emergent wetland species Typha domingensis (cattail) is a native Everglades monocotyledonous macrophyte, typically occurring as a sparse complement alongside Cladium jamaicense (sawgrass) stands. These two species have significantly different morphology, growth, and life history characteristics (Miao and Sklar B36 1998), and this has enabled the cattail to expand prolifically under the altered conditions in the Everglades. In the 1980s, the area covered by cattail stands in WCA2A doubled, expanding southward into the sawgrass marshes (Willard B71 2010). Cattail has hence been labeled as an indicator species, or species of concern, and its distribution is used to determine the effectiveness of various water management decisions. Cattail expansion has been studied extensively (Miao B35 2004; Wu et al. B72 1997; Newman et al. B41 1998), and it has been determined that there are four main external factors that affect its growth and aid in cattail’s dominance over sawgrass. These factors include water depth, hydroperiod, soil phosphorus concentration, and disturbance (Newman et al. 1998). It was determined that the optimum water depth at which cattail grows is between 24 and 95 cm (Grace B15 1989), with a hydroperiod of 180–280 days (Wetzel B69 2001). In terms of soil phosphorus concentration, cattail has been found to be invading the natural sawgrass habitats of WCA2A along a soil phosphorus gradient running from the northwest (high concentrations) to the southeast (low concentrations). Urban et al. (B62 1993) mention that, given an adequate water depth, soil phosphorus concentration is the next most important factor in determining cattail expansion/invasion. In creating their water quality model for simulating soil phosphorus concentrations downstream of the Everglades STAs, Walker and Kadlec (B66 1996) determined that the lower bound soil phosphorus concentration for the optimum growth of cattail was 540 mg/kg. Fires and other disturbances such as hurricanes were also found to affect the colonization of areas by cattail by altering local topography and nutrient concentrations (Newman et al. 1998).
Ecological model designs to address everglades systems
In order to assess these various influences on cattail and other ecological components, a variety of computation models were designed and implemented. These models aid our understanding of complex systems and allow scientists and managers to evaluate different ecological outcomes of decisions before the more costly task of their implementation (Fitz et al. B13 2011). To ensure numerical efficiency, most spatially distributed models have their equations, laws, and assumptions “hard-coded” into their programming code. This creates a “fixed-form” model, with changes in the functioning coming through extensive code re-writes and careful redesign around logical structures. Dynamic “free-form” simulation models, such as STELLA (Costanza and Voinov B5 2001), QnD (Kiker and Linkov B27 2006; Kiker et al. B28 2006), and the Kepler system (Ludascher et al. B31 2006) are generally written using an object-oriented programming (OOP) language such as C++ (Stroustrup B60 2000) or Java (Arnold and Gosling B1 1998), as opposed to a linear language such as FORTRAN (Cary et al. B2 1998). When interacting with free-form models and their algorithms, designers do not interact directly with the program code. Rather, they influence objects through placing data, storage, and logical structures into either a graphical user interface (STELLA, Kepler) or within a meta-code structure such as the eXtensible Markup Language (XML) (Harold B21 1998).There are a number of fixed-form ecological models currently in use across the Everglades region. Of these, the Across Trophic Level System Simulation (ATLSS) (Gross B16 1996) and the Everglades Landscape Model (ELM) (Fitz and Trimble B12 2006b) are probably the most well-known. These and most other models available for modeling cattail in the Everglades are entirely qualitative, that is, they involve switching between one species and another. The majority of these current ecological models are also stochastic, that is, based on probabilities and a degree of randomness and uncertainty. They generally run as post-process models, using hydrological data output by other models such as the South Florida Water Management Model (SFWMM) (Fitz et al. 2011).The ATLSS vegetation succession model is used to determine the succession of one habitat type to another (e.g., sawgrass to cattail). The ATLSS model simulates with an annual time step on square 500 m cells and uses a stochastic cellular automata model to switch between vegetation types. Currently there is no way to determine vegetation densities within vegetation types (Duke-Sylvester B9 2005).The ELM model uses a counter to switch between species by accumulating days of water level and soil phosphorus concentration above certain limits. The model then switches between species based on their preferred hydroperiod and historical soil phosphorus concentrations (Fitz and Trimble B11 2006a). The ELM model is the only currently available simulation tool for evaluating water quality across the Everglades landscape and does not simulate detailed ecological features (Fitz et al. 2011).Another modeling effort by Wu et al. (1997) used Markov chain probabilities to switch between Cladium and Typha species. This model was in fact used to inform the ATLSS nutrient and fire disturbance model (Wetzel B70 2003). Again, this is a stochastic, species-specific, presence/absence-type model.A modeling effort by Tarboton et al. (B61 2004) developed a set of habitat suitability indices (HSI) for evaluating water management alternatives. These HSIs provided a range of probabilities for a particular species occurring across the landscape and were based predominantly on local hydrological conditions such as depth (maximum, minimum, and mean), hydroperiod, velocity, and flow direction.Given that water quantity (depth) and quality (soil phosphorus concentration) affect cattail (and other plants) growth and distribution, there is a need to integrate these components to determine the more detailed biological outcomes of an Everglades ecological model. There is also a need for a quantitative model to provide continuous density values for specific vegetation rather than simply presence/absence information. Given that the Everglades restoration includes a large and ongoing research effort, there is a need to efficiently test and explore potentially useful algorithms in an adaptable, ecological modeling engine.
The RSM/TARSE ecological model
A combined effort of the University of Florida, the South Florida Water Management District (SFWMD), and the US Geological Survey created the Transport and Reaction Simulation Engine (TARSE) (Jawitz et al. B23 2008), which was originally designed to run in line with the SFWMD-developed Regional Simulation Model (RSM) (SFWMD B55 2005c) to simulate soil phosphorus dynamics in the Everglades system. The OOP structure of this coupled hydrologic/water quality model, along with the user-definable inputs and interactions, allowed for the extension of this model beyond its original purpose into ecological processes and features. The coupled RSM/TARSE (henceforth referred to as RTE) model, implemented with the goal of modeling ecological features within the southern Florida landscape and presented in this paper, is a spatially distributed, free-form model simulating cattail biomass distribution and dynamics across WCA2A. Using the RTE model to couple vegetation dynamics with phosphorus dynamics has been alluded to by Jawitz et al. (2008), Muller (B38 2010), and Perez-Ovilla (B45 2010) during their respective TARSE-influenced, WQ simulations. Zajac (B73 2010) used vegetation types to influence Manning’s n and evapotranspiration coefficients. These parameters were informed by initial vegetation types and not by changing vegetation distribution and density over time.There is therefore a definite need for the RTE model, which allows one to model a vegetation species quantitatively and ultimately determine the ecological impact of various management scenarios falling under the CERP initiative. This new engine would accommodate different algorithms or new species as available data or new knowledge becomes available. It would allow for interactions and feedback effects within species as well as among different species and with other environmental factors.
Objectives and hypotheses
The primary objective of this paper is to test and apply a new spatially distributed, deterministic, free-form (user-definable), quantitative ecological model of cattail dynamics. A significant advantage of this free-form modeling approach is that multiple ecological algorithms of differing complexity can be quickly implemented and tested simultaneously, instead of through time-consuming code additions. As a first step of our objective, we tested the influence of increasing cattail model complexity on reducing uncertainty in simulated output ( Lindenschmidt B30 2006). Five levels of increasing complexity were selected to model the cattail densities. These five levels of complexity were chosen to correspond with various hypotheses regarding the growth and spread of cattail in the Everglades, namely:indent 1 1. Whether cattail growth is density dependent.2. Whether water depth is an important factor for cattail expansion.3. Whether soil phosphorous is a contributing factor for cattail expansion.4. Whether sawgrass density impacts the rate of cattail expansion.5. Whether inter-species interactions between cattail and sawgrass contribute to the observed cattail dynamics.
Following the methodology used by Jawitz et al. (2008), a simple logistic function (Keen and Spain B25 1992) formed the base of the complexities with water depth and soil phosphorus concentration [the two most important factors influencing cattail growth according to Newman et al. (1998)] and sawgrass interaction influencing the higher levels of complexity. A second step in our objective was to use an existing ecosystem and its monitoring data to analyze performance of our five candidate models. The entire WCA2A vegetation dataset (1991, 1995, and 2003), obtained from Rutchey et al. (B50 2008), was chronologically divided into model training and testing sections. Training of the model was conducted for the years 1991–1995, where the growth factor (found in Equation 3) was fitted to the level 1 complexity. As a third step in our objective, model testing was conducted on the two time periods of 1991–2003 (testing 1) and 1995–2003 (testing 2), respectively, with the testing 2 time period being equivalent to a blind test (due to different initial conditions). The 1991 and 1995 vegetation maps were used to initialize the training, testing 1, and testing 2 simulations, respectively. Model output from the training, testing 1, and testing 2 simulations was compared with the 1995 and 2003 vegetation maps. Model output was compared to observed patterns, and the most accurate level of complexity thus determined.
Methods
In order to reproduce the observed cattail patterns, both hydrological and water quality data were used as inputs for the ecological model. To this end, it was decided to use the Regional Simulation Model (RSM), which was developed by the South Florida Water Management District (SFWMD) to replace the popular SFWMM, coupled with the Transport and Reaction Simulation Engine (TARSE) to provide the base structure for modeling cattail dynamics across the test site.
The Regional Simulation Model (RSM)
Developed by SFWMD, the RSM simulates hydrology over the South Florida region. It is often thought of as the successor to the successful SFWMM, referred to as the “2-by-2” model for its 2 mile resolution (SFWMD B53 2005a). The RSM operates over a variable triangular mesh grid, in contrast to the 3.22 km (2 mile) square grid of the SFWMM; this enables higher resolution in areas of concern as well as the ability to delineate canals (SFWMD 2005c). The RSM uses a weighted, implicit, finite volume method to simulate two-dimensional diffusional flow and hence implicitly simulates groundwater flow and surface water flow (SFWMD 2005c). The OOP design structure of RSM allows for the abstraction and modularity of various components (SFWMD B54 2005b). A result of this is that there are two engines that comprise the RSM, namely the Hydrologic Simulation Engine (HSE) and the Management Simulation Engine (MSE). The HSE simulates all the hydrological processes, while the MSE simulates various management or control regimes. These two engines interact at runtime to provide an accurate representation of the hydrodynamics of the region (SFWMD 2005c).
Simulating transport and reactions using TARSE
The TARSE was recently developed to simulate water quality (WQ) components within the RSM model for areas in the Everglades system (Jawitz et al. 2008). The TARSE model was designed to be as generic as possible, to allow multiple water quality components to be simulated with a simple change in the input file. It was first implemented as another engine to be incorporated within the RSM framework, along with the HSE and MSE, called the Water Quality Engine (WQE). Due to its structure, the WQE does not simulate hydrology and requires a hydrologic driver to feed it values of flow and depth at every time step (SFWMD B57 2008b). TARSE has since been decoupled from RSM and implemented with other hydrologic drivers such as Flow and Transport in a Linked Overland-Aquifer Density Dependent System (FTLOADDS) (Wang et al. B68 2007; Muller 2010) and VFSMOD (Muñoz-Carpena et al. B40 1999; Perez-Ovilla 2010). TARSE solves the advection-dispersion-reaction equations (ADRE) over an unstructured triangular mesh (James and Jawitz B22 2007). The ADRE is represented by Equation 1, and every term is a function of a two-dimensional spatial coordinate x, with components (x
sub
1
, x
2
), and time, t.
display-formula M1
m:math name 2192-1709-1-10-i1 xmlns:m http:www.w3.org1998MathMathML m:mrow
m:mfrac
m:mi d
m:mfenced open ( close )
Φ
h
c
d
t
m:mo +

c
h
u

h
m:msup
D
*


c
+
h
m:msub
f
m:mn 2
c
=
h
f
1
c
1
Where t is time [T], c(x,t) is the concentration [M/L3], and Φ(x,t) is the porosity of the medium (which may be 1 for surface water) [L3/L3]. h(x,t) is the water depth [L] or thickness of the saturated zone in groundwater flow, u(x,t) is the specific discharge [L/T] of water (either surface or groundwater), and D
*
=D
*
(u(x,t)) is the dispersion tensor (a function of u). f
1
(x,t) is a source rate [M/L3.T] with associated concentration c
1
, and f
2
(x,t) is a first-order decay rate [M/L3.T]. The density [M/L3] of the water is assumed to be constant.The basis of TARSE involves transfers (e.g., settling, diffusion, growth) between various stores, such as soil water column solutes, pore water solutes, macrophytes, and suspended solids. The specifics of these stores, and the transfers among them are user-definable in the XML input file (Jawitz et al. 2008). TARSE equations are composed of pre-equations, equations, and post-equations. Pre- and post-equations are used for implementing conditional (“if-then-else”) statements as part of pre- and post-processing after the main processing in the equations. For example, pre-processing could be used to determine if the current water depth [m] is above the threshold for cattail optimum growth and thus reduce the depth influence factor accordingly. If the depth is less than the optimum growing depth, then the influence factor decreases accordingly. The logic just described is represented by Equation 2, as described by Grace (1989), where cattail optimum depth is 70 cm.
M2
2192-1709-1-10-i2 m:mtable columnalign left
m:mtr
m:mtd
I
f
stretchy true (
d
e
p
t
h
/m:mo
m:mic/m:mi
m:mia/m:mi
m:mit/m:mi
m:mit/m:mi
m:mia/m:mi
m:mii/m:mi
m:mil/m:mi
m:mo_/m:mo
m:mio/m:mi
m:mip/m:mi
m:mit/m:mi
m:mii/m:mi
m:mim/m:mi
m:miu/m:mi
m:mim/m:mi
m:mo_/m:mo
m:mid/m:mi
m:mie/m:mi
m:mip/m:mi
m:mit/m:mi
m:mih/m:mi
m:mo stretchy="true")/m:mo
/m:mtd
/m:mtr
m:mtr
m:mtd
m:miT/m:mi
m:mih/m:mi
m:mie/m:mi
m:min/m:mi
/m:mtd
/m:mtr
m:mtr
m:mtd
m:mid/m:mi
m:mie/m:mi
m:mip/m:mi
m:mit/m:mi
m:mih/m:mi
m:mo_/m:mo
m:miH/m:mi
m:miS/m:mi
m:miI/m:mi
m:mo=/m:mo
m:mn1/m:mn
m:mo−/m:mo
m:mfenced open="(" close=")"
m:mfrac
m:mrow
m:mid/m:mi
m:mie/m:mi
m:mip/m:mi
m:mit/m:mi
m:mih/m:mi
m:mo−/m:mo
m:mic/m:mi
m:mia/m:mi
m:mit/m:mi
m:mit/m:mi
m:mia/m:mi
m:mii/m:mi
m:mil/m:mi
m:mo_/m:mo
m:mio/m:mi
m:mip/m:mi
m:mit/m:mi
m:mii/m:mi
m:mim/m:mi
m:miu/m:mi
m:mim/m:mi
m:mo_/m:mo
m:mid/m:mi
m:mie/m:mi
m:mip/m:mi
m:mit/m:mi
m:mih/m:mi
/m:mrow
m:mn109/m:mn
/m:mfrac
/m:mfenced
/m:mtd
/m:mtr
m:mtr
m:mtd
m:miE/m:mi
m:mil/m:mi
m:mis/m:mi
m:mie/m:mi
/m:mtd
/m:mtr
m:mtr
m:mtd
m:mid/m:mi
m:mie/m:mi
m:mip/m:mi
m:mit/m:mi
m:mih/m:mi
m:mo_/m:mo
m:miH/m:mi
m:miS/m:mi
m:miI/m:mi
m:mo=/m:mo
m:mn1/m:mn
m:mo−/m:mo
m:mfenced open="(" close=")"
m:mfrac
m:mrow
m:mic/m:mi
m:mia/m:mi
m:mit/m:mi
m:mit/m:mi
m:mia/m:mi
m:mii/m:mi
m:mil/m:mi
m:mo_/m:mo
m:mio/m:mi
m:mip/m:mi
m:mit/m:mi
m:mii/m:mi
m:mim/m:mi
m:miu/m:mi
m:mim/m:mi
m:mo_/m:mo
m:mid/m:mi
m:mie/m:mi
m:mip/m:mi
m:mit/m:mi
m:mih/m:mi
m:mo−/m:mo
m:mid/m:mi
m:mie/m:mi
m:mip/m:mi
m:mit/m:mi
m:mih/m:mi
/m:mrow
m:mn112/m:mn
/m:mfrac
/m:mfenced
/m:mtd
/m:mtr
/m:mtable
/m:math
/display-formula
/pp/
pThe main equations are structured as ordinary differential equations (ODE) (SFWMD abbr bid="B56"2008/abbra)./ppThe RSMTARSE coupling represents possibly the first time that a free-form dynamic system model has been integrated with a fixed-form, spatially distributed, hydrologic model (Muller abbr bid="B38"2010/abbr). This unique coupling, with user-defined interactions operating across a spatially distributed domain, lends itself to simulating ecological behaviors (growth, death, movement, and feeding) as well as the original WQ interactions. The model can currently only solve ADRE movement and as such is insufficient for ecologicalanimal movement. Attempts to include some form of Lagrangian-type movement in this model are discussed by Lagerwall (abbr bid="B29"2011/abbr)./p
/sec
sec
st
pModel application/p
/stpIn order to test the influence of increasing complexity on reducing uncertainty in model output (Lindenschmidt abbr bid="B30"2006/abbr), five levels of increasing complexity were selected to model the cattail densities. Following the methodology used by Jawitz et al. (abbr bid="B23"2008/abbr), a logistic function (Keen and Spain abbr bid="B25"1992/abbr) was used for the most basic, level 1 complexity, due to its density dependent growth and rapid (exponential) early stages of growth. The logistic function is represented in Equation 3./pp
display-formula id="M3"
m:math name="2192-1709-1-10-i3" xmlns:m="http://www.w3.org/1998/Math/MathML"m:mrow
m:mfrac
m:mrow
m:mid/m:mi
m:miP/m:mi
/m:mrow
m:mrow
m:mid/m:mi
m:mit/m:mi
/m:mrow
/m:mfrac
m:mo=/m:mo
m:miG/m:mi
m:miF/m:mi
m:mo×/m:mo
m:miP/m:mi
m:mo×/m:mo
m:mfenced open="(" close=")"
m:mrow
m:mn1/m:mn
m:mo−/m:mo
m:mfrac
m:miP/m:mi
m:miK/m:mi
/m:mfrac
/m:mrow
/m:mfenced
/m:mrow
/m:math
/display-formula
/pp/
pWhere itP/it is the population density [MLsup2/sup], itt/it is time [T], itGF/it is the constant growth rate [Tsup-1/sup], and itK/it is the carrying capacity or maximum population density [MLsup2/sup]./ppLevel 2 is a water-depth-influenced level 1 complexity. A water depth factor (habitat suitability index) ranging from 0 to 1 is multiplied by the carrying capacity in the logistic function. The depth factor decreases linearly from 1 as the current depth either rises above or drops below the optimum (70 cm) growing depth. This depth factor can be seen in Equation 4./pp
display-formula id="M4"
m:math name="2192-1709-1-10-i4" xmlns:m="http://www.w3.org/1998/Math/MathML"m:mrow
m:mfrac
m:mrow
m:mid/m:mi
m:miP/m:mi
/m:mrow
m:mrow
m:mid/m:mi
m:mit/m:mi
/m:mrow
/m:mfrac
m:mo=/m:mo
m:miG/m:mi
m:miF/m:mi
m:mo×/m:mo
m:miP/m:mi
m:mo×/m:mo
m:mfenced open="(" close=")"
m:mrow
m:mn1/m:mn
m:mo−/m:mo
m:mfrac
m:miP/m:mi
m:mrow
m:miK/m:mi
m:mo×/m:mo
m:miD/m:mi
m:mie/m:mi
m:mip/m:mi
m:mit/m:mi
m:mih/m:mi
m:miF/m:mi
/m:mrow
/m:mfrac
/m:mrow
/m:mfenced
/m:mrow
/m:math
/display-formula
/pp/
pWhere itP/it is the population density [MLsup2/sup], itt/it is time [T], itGF/it is a constant growth rate [Tsup-1/sup], itDepthF/it is the water depth factor [LL], itK/it is the carrying capacity or maximum population density [MLsup2/sup]./ppLevel 3 is a soil-phosphorus-influenced level 2 complexity, with the soil phosphorus factor being incorporated in a similar fashion to the depth factor and can be seen in Equation 5./pp
display-formula id="M5"
m:math name="2192-1709-1-10-i5" xmlns:m="http://www.w3.org/1998/Math/MathML"m:mrow
m:mfrac
m:mrow
m:mid/m:mi
m:miP/m:mi
/m:mrow
m:mrow
m:mid/m:mi
m:mit/m:mi
/m:mrow
/m:mfrac
m:mo=/m:mo
m:miG/m:mi
m:miF/m:mi
m:mo×/m:mo
m:miP/m:mi
m:mo×/m:mo
m:mfenced open="(" close=")"
m:mrow
m:mn1/m:mn
m:mo−/m:mo
m:mfrac
m:miP/m:mi
m:mrow
m:miK/m:mi
m:mo×/m:mo
m:mfenced open="(" close=")"
m:mrow
m:miD/m:mi
m:mie/m:mi
m:mip/m:mi
m:mit/m:mi
m:mih/m:mi
m:miF/m:mi
m:mo+/m:mo
m:mip/m:mi
m:mih/m:mi
m:mio/m:mi
m:mis/m:mi
m:mip/m:mi
m:mih/m:mi
m:mio/m:mi
m:mir/m:mi
m:miu/m:mi
m:mis/m:mi
m:miF/m:mi
/m:mrow
/m:mfenced
m:mo/m:mo
m:mn2/m:mn
/m:mrow
/m:mfrac
/m:mrow
/m:mfenced
/m:mrow
/m:math
/display-formula
/pp/
pWhere itP/it is the population density [MLsup2/sup, itt/it is time [T], itGF/it is a constant growth rate [Tsup-1/sup, itDepthF/it is the water depth factor [LL], itphosphorusF/it is the soil phosphorus factor [MLsup3/supMLsup3/sup, and itK/it is the carrying capacity or maximum population density [MLsup2/sup. The soil phosphorus factor behaves like a logistic function, increasing from 0 to 1 as soil phosphorus concentration increases to 1,800 from 200 mgkg, as described by Walker and Kadlec (abbr bid="B66"1996/abbr), and can be seen in Equation 6./pp
display-formula id="M6"
m:math name="2192-1709-1-10-i6" xmlns:m="http://www.w3.org/1998/Math/MathML"m:mrow
m:mtextphosphorusF/m:mtext
m:mo=/m:mo
m:msup
m:mfenced open="(" close=")"
m:mrow
m:mn1/m:mn
m:mo+/m:mo
m:msup
m:mtexte/m:mtext
m:mrow
m:mo−/m:mo
m:mfrac
m:mrow
m:mtextphosphorus/m:mtext
m:mo−/m:mo
m:mn1034/m:mn
/m:mrow
m:mn144/m:mn
/m:mfrac
/m:mrow
/m:msup
/m:mrow
/m:mfenced
m:mrow
m:mo−/m:mo
m:mn1/m:mn
/m:mrow
/m:msup
/m:mrow
/m:math
/display-formula
/pp/
pWhere itphosphorusF/it is the soil phosphorus HSI, ranging from 0 to 1, and itphosphorus/it is the current soil phosphorus concentration (mgkg)./ppLevel 4 builds on a level 3 complexity with an added sawgrass interaction factor, much like the soil phosphorus and depth factors. It decreases linearly from 1 to 0.16 as sawgrass densities increase to 1,958 from 0 gmsup2/sup (Doren et al. abbr bid="B7"1999/abbr), which is their reported maximum density ( Miao and Sklar abbr bid="B36"1998/abbr). The sawgrass is set to grow according to a level 1 complexity as in Equation 4, thus the level 4 complexity is represented by Equation 7./pp
display-formula id="M7"
m:math name="2192-1709-1-10-i7" xmlns:m="http://www.w3.org/1998/Math/MathML"m:mrow
m:mfrac
m:mrow
m:mid/m:mi
m:miP/m:mi
/m:mrow
m:mrow
m:mid/m:mi
m:mit/m:mi
/m:mrow
/m:mfrac
m:mo=/m:mo
m:miG/m:mi
m:miF/m:mi
m:mo×/m:mo
m:miP/m:mi
m:mo×/m:mo
m:mfenced open="(" close=")"
m:mrow
m:mn1/m:mn
m:mo−/m:mo
m:mfrac
m:miP/m:mi
m:mrow
m:miK/m:mi
m:mfenced open="(" close=")"
m:mrow
m:miD/m:mi
m:mie/m:mi
m:mip/m:mi
m:mit/m:mi
m:mih/m:mi
m:miF/m:mi
m:mo+/m:mo
m:mip/m:mi
m:mih/m:mi
m:mio/m:mi
m:mis/m:mi
m:mip/m:mi
m:mih/m:mi
m:mio/m:mi
m:mir/m:mi
m:miu/m:mi
m:mis/m:mi
m:miF/m:mi
m:mo+/m:mo
m:mis/m:mi
m:mia/m:mi
m:miw/m:mi
m:mig/m:mi
m:mir/m:mi
m:mia/m:mi
m:mis/m:mi
m:mis/m:mi
m:miF/m:mi
/m:mrow
/m:mfenced
m:mo/m:mo
m:mn3/m:mn
/m:mrow
/m:mfrac
/m:mrow
/m:mfenced
/m:mrow
/m:math
/display-formula
/pp/
pWhere itP/it is the population density [MLsup2/sup], itt/it is time [T], itGF/it is a constant growth rate [Tsup-1/sup], itDepthF/it is the water depth factor [LL], itphosphorusF/it is the soil phosphorus factor [MLsup3/supMLsup3/sup], itsawgrassF/it is the sawgrass influence factor [MLsup2/supMLsup2/sup], and itK/it is the carrying capacity or maximum population density [MLsup2/sup]. The sawgrass factor varies according to Equation 8./pp
display-formula id="M8"
m:math name="2192-1709-1-10-i8" xmlns:m="http://www.w3.org/1998/Math/MathML"m:mrow
m:mtextsawgrassF/m:mtext
m:mo=/m:mo
m:mn1/m:mn
m:mo+/m:mo
m:mfenced open="(" close=")"
m:mrow
m:mo−/m:mo
m:mn0.84/m:mn
m:mo×/m:mo
m:mfenced open="(" close=")"
m:mrow
m:mtextsawgrass/m:mtext
m:mo/m:mo
m:msub
m:mtextK/m:mtext
m:mtextSAW/m:mtext
/m:msub
/m:mrow
/m:mfenced
/m:mrow
/m:mfenced
/m:mrow
/m:math
/display-formula
/pp/
pWhere itsawgrassF/it is the sawgrass HSI ranging from 0 to 1, itsawgrass/it is the current sawgrass density, and itK/it
sub
itSAW/it
/sub is the sawgrass carrying capacity./ppThe level 5 complexity is the same as level 4, but with a density-dependent influence on the level 1 sawgrass model, which is represented by Equations 9 and 10, respectively./pp
display-formula id="M9"
m:math name="2192-1709-1-10-i9" xmlns:m="http://www.w3.org/1998/Math/MathML"m:mrow
m:mfrac
m:mrow
m:mid/m:mi
m:miP/m:mi
/m:mrow
m:mrow
m:mid/m:mi
m:mit/m:mi
/m:mrow
/m:mfrac
m:mo=/m:mo
m:miG/m:mi
m:miF/m:mi
m:mo×/m:mo
m:miP/m:mi
m:mo×/m:mo
m:mfenced open="(" close=")"
m:mrow
m:mn1/m:mn
m:mo−/m:mo
m:mfrac
m:miP/m:mi
m:mrow
m:miK/m:mi
m:mo×/m:mo
m:mic/m:mi
m:mia/m:mi
m:mit/m:mi
m:mit/m:mi
m:mia/m:mi
m:mii/m:mi
m:mil/m:mi
m:miF/m:mi
/m:mrow
/m:mfrac
/m:mrow
/m:mfenced
/m:mrow
/m:math
/display-formula
/pp/
pWhere itP/it is the population density [MLsup2/sup], itt/it is time [T], itGF/it is a constant growth rate [Tsup-1/sup], itcattailF/it is the cattail factor ranging from 0 to 1, and itK/it is the carrying capacity or maximum population density [MLsup2/sup]./pp
display-formula id="M10"
m:math name="2192-1709-1-10-i10" xmlns:m="http://www.w3.org/1998/Math/MathML"m:mrow
m:mtextcattailF/m:mtext
m:mo=/m:mo
m:mn1/m:mn
m:mo+/m:mo
m:mfenced open="(" close=")"
m:mrow
m:mo−/m:mo
m:mn0.84/m:mn
m:mo×/m:mo
m:mfenced open="(" close=")"
m:mrow
m:mtextcattail/m:mtext
m:mo/m:mo
m:msub
m:mtextK/m:mtext
m:mtextCAT/m:mtext
/m:msub
/m:mrow
/m:mfenced
/m:mrow
/m:mfenced
/m:mrow
/m:math
/display-formula
/pp/
pWhere itcattailF/it is the cattail HSI ranging from 0 to 1, itcattail/it is the current cattail density, and itK/it
sub
itCAT/it
/sub is the cattail carrying capacity./ppThe depth, soil phosphorus, and sawgrass interaction factors are all calculated using the pre-equations, similar to that presented in Equation 2. These factors are then incorporated into the main growth equations, presented in Equations 4, 5, 7 and 9 representing levels of complexity 2 through 5, respectively./ppIn TARSE, components are listed as either mobile or stabile. Mobile components are moved in the water using the ADRE equations, while the stabile components do not move and only undergo the reaction part of the ADRE. Given the complexities associated with simulating wind-borne or water-borne transportation of seeds and rhizome expansion—which is another mode of expansion noted by Miao (abbr bid="B35"2004/abbr)—all mesh elements were initialized (seeded) with cattail, with areas originally not containing cattail being seeded with the minimum value of 10 g(dry weight)msup2/sup. This assumption represents the presence of a seed bank, providing cattail the opportunity to colonize an area as soon as conditions become favorable. Vegetation then is modeled as a stabile component, with no means for dispersal, or in another way we assume “infinite dispersal.” The latter assumption is supported by very high values of dispersal for seeds in the Everglades, enhanced by the diffused presence of biotic (animals) and abiotic (water, wind) dispersal vectors (Miao and Sklar abbr bid="B36"1998/abbr). Also, as a result of this current inability for modeled dispersal, the maximum influence that the aforementioned factors such as phosphorusF, sawgrassF, and cattailF can have has been limited so that they reduce the cattail population to 1% of its maximum density./p
/sec
sec
st
pTest site/p
/stpThe test site used for ecological model development and testing was the WCA2A (Figure figr fid="F1"1/figr). WCA2A is a 547 kmsup2/sup managed wetland just south of Lake Okeechobee, FL, and accounts for about 6.5% of the total area of the Everglades. It came into existence in 1961 with the construction of the L35-B canal and receives inflow from the Stormwater Treatment Areas (STAs), before discharging into downstream water conservation areas, and eventually into the Everglades National Park (Urban et al. abbr bid="B62"1993/abbr). According to Rivero et al. (abbr bid="B48"2007b/abbr), the region has an average annual temperature of 20°C, and precipitation between 1,175 and 1,550 mm. The elevation range in WCA2A is between 2.0 and 3.6 m above sea level, which generates a slow sheet flow from the northwest to the southwest of the region. The hydrology is controlled by the SFWMD at a number of inlet and outlet structures (green squares in Figure figr fid="F1"1/figr) along the surrounding canals (blue lines in Figure figr fid="F1"1/figr). The landscape is composed of dominant sawgrass marshes, shrub and tree island communities, and invasive cattail communities (van der Valk and Rosburg abbr bid="B65"1997/abbr). WCA2A has been used extensively as a research site by the SFWMD, with extensive trial and monitoring programs for a number of biogeochemical components, especially soil phosphorus and vegetative structure (Rivero et al. abbr bid="B47"2007/abbra). The triangular mesh grid used for simulation is also displayed in Figure figr fid="F1"1/figr, with the green border cells used for numerical stability of the hydrological RSM component. An overview of the HSE setup for WCA2A, which provides the hydrological operating conditions, can be found in SFWMD (abbr bid="B58"2008/abbrc). /p
fig id="F1"titlepFigure 1/p/titlecaptionpTest site, Water Conservation Area 2A (WCA2A), in the northern Everglades/p/captiontext
pbTest site, Water Conservation Area 2A (WCA2A), in the northern Everglades./b Green squares represent inlet and outlet control structures; blue lines represent canal structures. Triangles represent the mesh used for simulation, with green triangles representing the border cells used in the central difference method. The red squares fall on zonal elements 209, 244, and 380, representing regions of typically high, medium, and low cattail densities, respectively./p
/textgraphic file="2192-1709-1-10-1"//fig
/sec
sec
st
pInitial conditions, boundary conditions, and time series data/p
/stpCattail vegetation maps (Figure figr fid="F2"2/figr) are used for the initial conditions as well as for comparing model output with measured data. Hydrological time series are used for initial and boundary conditions along the surrounding canals. Using RSM, the hydrological boundary conditions are converted into depth values across the domain, which are then used as inputs in the level 2 complexity algorithm. Soil phosphorus concentration maps provide initial conditions and an influence factor for the level 3 complexity algorithm. Sawgrass vegetation maps are used as initial conditions for the level 1 complexity sawgrass model, which serves as an influence factor for the level 4 and level 5 complexity cattail algorithms. The following sections provide additional detail on these model inputs./p
fig id="F2"titlepFigure 2/p/titlecaptionpFormatting of cattail input maps/p/captiontext
pbFormatting of cattail input maps./b (ba/b) 1991, (bb/b) 1995, (bc/b) 2003 from Rutchey et al. (abbr bid="B50"2008/abbr). Rasterized raw data on the left, overlaid with the WCA2A triangular mesh in the middle, and the final triangular mesh cattail input map on the right./p
/textgraphic file="2192-1709-1-10-2"//fig
/sec
sec
st
pHydrological time series/p
/stpThe hydrology of WCA2A is controlled primarily by the operation of control points along the S10 and L35-B canals. The hydrology data were obtained from the SFWMD, which uses the WCA2A site as a test site for the RSM. The average depth for the region ranges from 60 to 90 cm (SFWMD, abbr bid="B58"2008c/abbr). The input dataset consisted of a daily time series of hydraulic head values (m) at the inlet and outlet control structures of WCA2A (represented by the green squares in Figure figr fid="F1"1/figr) for the years 1979–2000 (Wang abbr bid="B67"2009/abbr). The time series have since been updated to 2008 for all control structures using data collected from the DBHYDRO website (SFWMD abbr bid="B59"2009/abbr)./p
/sec
sec
st
pSoil phosphorus/p
/stpA gradient of soil phosphorus exists along WCA2A, with a high concentration near the inlets at the north, and a low concentration at the outlets in the south. This soil phosphorus gradient has been widely documented and studied (DeBusk et al. abbr bid="B6"1994/abbr; Grunwald et al. abbr bid="B18"2004/abbr
abbr bid="B19"2008/abbr; Rivero et al. abbr bid="B47"2007/abbra,b; Grunwald abbr bid="B17"2010/abbr). Given the unavailability of spatial soil phosphorus data beyond map classifications (Grunwald abbr bid="B17"2010/abbr), soil phosphorus input maps were created by overlaying the WCA2A mesh on the existing maps obtained from Grunwald et al. (abbr bid="B18"2004/abbr
abbr bid="B19"2008/abbr). The soil phosphorus map of 1990 was used for the model training period of 1991–1995, while the soil phosphorus map of 2003 was used for both the testing 1 (1991–2003) and testing 2 (1995–2003) simulation periods. Due to the poor quality of these soil phosphorus input maps and the inability of TARSE to adequately simulate phosphorus dynamics in the WCA2A region (as it is still in development), the soil phosphorus concentration itself was not simulated, i.e., the static soil phosphorus concentration provided by the input maps was used to inform the model throughout the simulation period./p
/sec
sec
st
pCattail and sawgrass/p
/stpVegetation maps for WCA2A were obtained for the years 1991, 1995 (Rutchey abbr bid="B49"2011/abbr), and 2003 (Wang abbr bid="B67"2009/abbr), which were all used in Rutchey et al. (abbr bid="B50"2008/abbr). These maps provided density (gmsup2/sup) distributions across the test site for cattail. The negative correlation between sawgrass and cattail has been reported by Doren et al. (abbr bid="B7"1999/abbr) and Richardson et al. (abbr bid="B46"2008/abbr), and various other vegetation maps of the area, namely 1991 (Jensen et al. abbr bid="B24"1995/abbr), 1995 (SFWMD abbr bid="B51"1995/abbr), 1999 (SFWMD abbr bid="B52"1999/abbr), and 2003 (Wang abbr bid="B67"2009/abbr), confirm this negative correlation. Although sawgrass density is related to more environmental factors than only cattail density (Miao and Sklar abbr bid="B36"1998/abbr), a simple negative correlation with the cattail maps was used in order to assign densities to the sawgrass maps. For example, high sawgrass density values (1,600 gmsup2/sup) were assigned to regions with typically low cattail density values, and low sawgrass density values (600 gmsup2/sup) were assigned to regions with high cattail density values./ppThe program ArcMap (ESRI Environmental Systems Resource Institute abbr bid="B10"2010/abbr) was used to create a uniform raster map from the original images which had a minimum mapping unit of 50 msup2/sup (Rutchey et al. abbr bid="B50"2008/abbr). The vegetation class values were converted to density values according to Table tblr tid="T1"1/tblr, with vegetation class 4 (other) relating to the absolute minimum (residual) cattail density, representing the seed bank. The input file was created by overlaying the mesh grid of 385 triangles (510 triangles total—which includes a row of triangles along the border) on the rasterized vegetation map and calculating the mean value of all raster cell density values within each triangular element. This new aggregated map was used to create the input file. A graphical overview of this process for the data maps can be seen in Figure figr fid="F2"2/figr. /p
table id="T1"
title
pTable 1/p
/title
caption
p
bCattail class and density values for formatting data maps/b
/p
/caption
tgroup align="left" cols="3"
colspec align="left" colname="c1" colnum="1" colwidth="1*"/
colspec align="left" colname="c2" colnum="2" colwidth="1*"/
colspec align="left" colname="c3" colnum="3" colwidth="1*"/
thead valign="top"
row rowsep="1"
entry colname="c1"
p
bVegetation class/b
/p
/entry
entry colname="c2"
p
bCattail density value (gm/b
sup
b2/b
/supb)/b
/p
/entry
entry colname="c3"
p
bSawgrass density value (gm/b
sup
b2/b
/supb)/b
/p
/entry
/row
/thead
tbody valign="top"
row
entry colname="c1"
p1 High density cattail/p
/entry
entry colname="c2"
p1,000/p
/entry
entry colname="c3"
p10/p
/entry
/row
row
entry colname="c1"
p2 Medium density cattail/p
/entry
entry colname="c2"
p600/p
/entry
entry colname="c3"
p600/p
/entry
/row
row
entry colname="c1"
p3 Low density cattail/p
/entry
entry colname="c2"
p200/p
/entry
entry colname="c3"
p1,000/p
/entry
/row
row rowsep="1"
entry colname="c1"
p4 Other/p
/entry
entry colname="c2"
p10/p
/entry
entry colname="c3"
p1,600/p
/entry
/row
/tbody
/tgroup
/tablepThe final sawgrass maps are viewable in Figure figr fid="F3"3/figr. The maximum densities of 1,240 gmsup2/sup for cattail and 1,958 gmsup2/sup for sawgrass were reported by Miao and Sklar (abbr bid="B36"1998/abbr). An overview of the parameter descriptions for the increasing levels of complexity can be found in Table tblr tid="T2"2/tblr. /p
fig id="F3"titlepFigure 3/p/titlecaptionpSawgrass input maps for the years 1991, 1995, and 2003, respectively/p/captiontext
p
bSawgrass input maps for the years 1991, 1995, and 2003, respectively./b
/p
/textgraphic file="2192-1709-1-10-3"//fig
table id="T2"
title
pTable 2/p
/title
caption
p
bParameter description for the increasing levels of complexity studied/b
/p
/caption
tgroup align="left" cols="5"
colspec align="left" colname="c1" colnum="1" colwidth="1*"/
colspec align="left" colname="c2" colnum="2" colwidth="1*"/
colspec align="left" colname="c3" colnum="3" colwidth="1*"/
colspec align="left" colname="c4" colnum="4" colwidth="1*"/
colspec align="left" colname="c5" colnum="5" colwidth="1*"/
thead valign="top"
row rowsep="1"
entry colname="c1"
p
bParameter/b
/p
/entry
entry colname="c2"
p
bParameter description/b
/p
/entry
entry colname="c3"
p
bLevels influenced/b
/p
/entry
entry colname="c4"
p
bAffected variables/b
/p
/entry
entry colname="c5"
p
bParameter equationlogic/b
/p
/entry
/row
/thead
tbody valign="top"
row
entry colname="c1"
pCattail/p
/entry
entry colname="c2"
pCattail density/p
/entry
entry colname="c3"
p1,2,3,4,5/p
/entry
entry colname="c4"
pCattail/p
/entry
entry colname="c5"
pPopulation density/p
/entry
/row
row
entry colname="c1"
pCATGF/p
/entry
entry colname="c2"
pCattail growth rate/p
/entry
entry colname="c3"
p1,2,3,4,5/p
/entry
entry colname="c4"
pCattail/p
/entry
entry colname="c5"
pRate of increase of population/p
/entry
/row
row
entry colname="c1"
pDepthF/p
/entry
entry colname="c2"
pWater depth influence/p
/entry
entry colname="c3"
p2,3,4,5/p
/entry
entry colname="c4"
pCattail carrying capacity, Cattail/p
/entry
entry colname="c5"
pEquation 2/p
/entry
/row
row
entry colname="c1"
pphosphorusF/p
/entry
entry colname="c2"
pSoil phosphorus concentration influence/p
/entry
entry colname="c3"
p3,4,5/p
/entry
entry colname="c4"
pCattail carrying capacity, cattail/p
/entry
entry colname="c5"
pEquation 6/p
/entry
/row
row
entry colname="c1"
pSawgrass/p
/entry
entry colname="c2"
pSawgrass density/p
/entry
entry colname="c3"
p4,5/p
/entry
entry colname="c4"
pSawgrass, cattail carrying capacity, cattail/p
/entry
entry colname="c5"
pPopulation density/p
/entry
/row
row rowsep="1"
entry colname="c1"
pSAWGF/p
/entry
entry colname="c2"
pSawgrass growth rate/p
/entry
entry colname="c3"
p4,5/p
/entry
entry colname="c4"
pSawgrass/p
/entry
entry colname="c5"
pRate of increase of population/p
/entry
/row
/tbody
/tgroup
/table
/sec
sec
st
pStatistical analysis of simulated and monitored biomass/p
/stpBesides a side-by-side visual comparison of the model output, there were three sets of statistical analysis techniques that were used to compare the model results and the raw data. These metrics, commonly used in literature for comparing both single- and multi-species patterns ( Fortin and Dale abbr bid="B14"2005/abbr; Muneepeerakul et al. abbr bid="B39"2008/abbr; Convertino et al. abbr bid="B4"2009/abbr), analyzed the local, global, and autocorrelation structure of observed and modeled vegetation patterns. All metrics were accompanied by a Nash-Sutcliffe coefficient (McCuen et al. abbr bid="B34"2006/abbr), represented by Equation 11, which provides a singular number for the comparison of the model statistics and how they compare to the observed data. The coefficient is a comparison of model results vwith the mean of the data./pp
display-formula id="M11"
m:math name="2192-1709-1-10-i11" xmlns:m="http://www.w3.org/1998/Math/MathML"m:mrow
m:msub
m:miE/m:mi
m:mif/m:mi
/m:msub
m:mo=/m:mo
m:mn1/m:mn
m:mo−/m:mo
m:mfrac
m:mrow
m:msubsup
m:mstyle displaystyle="true"
m:mo∑/m:mo
/m:mstyle
m:mrow
m:mii/m:mi
m:mo=/m:mo
m:mn0/m:mn
/m:mrow
m:min/m:mi
/m:msubsup
m:msup
m:mfenced open="(" close=")"
m:mrow
m:msub
m:miy/m:mi
m:mii/m:mi
/m:msub
m:mo−/m:mo
m:mover
m:miy/m:mi
m:moˆ/m:mo
/m:mover
/m:mrow
/m:mfenced
m:mn2/m:mn
/m:msup
/m:mrow
m:mrow
m:msubsup
m:mstyle displaystyle="true"
m:mo∑/m:mo
/m:mstyle
m:mrow
m:mii/m:mi
m:mo=/m:mo
m:mn0/m:mn
/m:mrow
m:min/m:mi
/m:msubsup
m:msup
m:mfenced open="(" close=")"
m:mrow
m:msub
m:miy/m:mi
m:mii/m:mi
/m:msub
m:mo−/m:mo
m:mover
m:miy/m:mi
m:mo¯/m:mo
/m:mover
/m:mrow
/m:mfenced
m:mn2/m:mn
/m:msup
/m:mrow
/m:mfrac
/m:mrow
/m:math
/display-formula
/pp/
pWhere itE/it
sub
itf/it
/sub is the Nash-Sutcliffe coefficient, inline-formula
m:math name="2192-1709-1-10-i12" xmlns:m="http://www.w3.org/1998/Math/MathML"m:mover accent="true"
m:miy/m:mi
m:mo^/m:mo
/m:mover
/m:math
/inline-formula is the predicted variable, ity/it
sub
iti/it
/sub is the observed variable, inline-formula
m:math name="2192-1709-1-10-i13" xmlns:m="http://www.w3.org/1998/Math/MathML"m:mover accent="true"
m:miy/m:mi
m:mo¯/m:mo
/m:mover
/m:math
/inline-formula is the mean of the observed variable, and itn/it is the sample size. A Nash-Sutcliffe value of 1 means that the model completely matches the data, while a value of 0 means that the model performs no better than the mean of the data. Any value less than 0 is interpreted as a poor representation of the data./ppA direct comparison between model output and the data was performed with the use of a classified difference technique (Kiker abbr bid="B26"1998/abbr). Since the data maps were initialized with a minimum density of 10 gmsup2/sup to account for movement between triangular elements that is not simulated in this model application, a difference between model output and the data value falling within 20 gmsup2/sup was considered a “perfect” match. This is loosely based on the fact that Miao and Sklar (abbr bid="B36"1998/abbr) reported a roughly 10% error in measurement of the maximum density of 1,240 gmsup2/sup. So, for example, if the data value was 10 gmsup2/sup (representing a typical non-cattail region), and the model output was 12 gmsup2/sup, with a difference of 2 gmsup2/sup (falling within the 20 gmsup2/sup range), then this would be considered a “perfect” match. The next class of differences lies within the 200 gmsup2/sup range, which is the value assigned to the low cattail density class during the formatting and creation of the input data maps. This 200 gmsup2/sup range is also half the range between the successively higher cattail density classes. The third class of differences lies within 400 gmsup2/sup, which can be thought of as a data class difference (e.g., between low and medium densities) or also as being within 40% of the maximum possible difference (the maximum data density is set as 1,000 gmsup2/sup). Finally, any difference above the 400 gmsup2/sup threshold is placed in the fourth class of differences and represents a significant misrepresentation of the data by the model./ppA box and whiskers plot ( Ott and Longnecker abbr bid="B43"2004/abbr) was created with all model element values compared with their corresponding data element values. The desired figure is a plot with the means and ranges corresponding to the associated data ranges. The box and whiskers plots cover the entire range of possible values from 0 to 1,240 gmsup2/sup./ppMoran’s itI/it statistic ( Cliff and Ord abbr bid="B3"1970/abbr; Paradis abbr bid="B44"2010/abbr) was used to determine the spatial autocorrelation between cells separated by an increasing distance. Moran’s itI/it is represented by Equation 12./pp
display-formula id="M12"
m:math name="2192-1709-1-10-i14" xmlns:m="http://www.w3.org/1998/Math/MathML"m:mrow
m:miI/m:mi
m:mo=/m:mo
m:mfrac
m:mrow
m:msubsup
m:mstyle displaystyle="true"
m:mo∑/m:mo
/m:mstyle
m:mrow
m:mii/m:mi
m:mo=/m:mo
m:mn1/m:mn
/m:mrow
m:min/m:mi
/m:msubsup
m:msubsup
m:mstyle displaystyle="true"
m:mo∑/m:mo
/m:mstyle
m:mrow
m:mij/m:mi
m:mo=/m:mo
m:mn1/m:mn
/m:mrow
m:min/m:mi
/m:msubsup
m:mfenced open="(" close=")"
m:mrow
m:msub
m:mix/m:mi
m:mii/m:mi
/m:msub
m:mo−/m:mo
m:mix/m:mi
/m:mrow
/m:mfenced
m:mfenced open="(" close=")"
m:mrow
m:msub
m:mix/m:mi
m:mij/m:mi
/m:msub
m:mo−/m:mo
m:mix/m:mi
/m:mrow
/m:mfenced
/m:mrow
m:mrow
m:miW/m:mi
m:msubsup
m:mstyle displaystyle="true"
m:mo∑/m:mo
/m:mstyle
m:mrow
m:mii/m:mi
m:mo=/m:mo
m:mn1/m:mn
/m:mrow
m:min/m:mi
/m:msubsup
m:msup
m:mfenced open="(" close=")"
m:mrow
m:msub
m:mix/m:mi
m:mii/m:mi
/m:msub
m:mo−/m:mo
m:mover
m:mix/m:mi
m:mo¯/m:mo
/m:mover
/m:mrow
/m:mfenced
m:mn2/m:mn
/m:msup
/m:mrow
/m:mfrac
/m:mrow
/m:math
/display-formula
/pp/
pWhere itx/it
sub
iti/it
/sub is the current cell value, itx/it
sub
itj/it
/sub is the value of the cell separated by a given distance, itx/it(bar) is the mean, and itW/it is the number of cells surrounding the current one and found within the given distance. These values are plotted against an increasing cell-pairwise distance, as in Marani et al. (abbr bid="B32"2006/abbr), to determine the trend in spatial autocorrelation across the entire region./ppA landscape-scale abundance-area plot (Martin abbr bid="B33"1980/abbr; Michalski and Peres abbr bid="B37"2007/abbr) was used to measure the average change in density across the test site. One hundred randomly distributed cells are used as base cells. From these, the densities of all cells falling within a given radius are summed. This total is then divided by the number of base cells and plotted against the area of circles with an increasing radius as in Martin (abbr bid="B33"1980/abbr)./ppA trend in the regional mean density was plotted with a daily timestep for a visual comparison of the trends between the different levels of complexity. This was repeated for the individual levels of complexity and selected zones (elements) within the region, for a more detailed view of the effect of external parameters on different areas of the region. Elements 209, 244, and 380, located in the northeast, central, and southwest, were selected as representative elements for typically high, medium, and low cattail densities, respectively. These elements are marked by red squares in Figure figr fid="F1"1/figr and are useful for evaluating local vegetation indicators./p
/sec
sec
st
pModel training and testing/p
/stpThere were three time periods over which the model was simulated using the available data maps of 1991, 1995, and 2003. Training was performed for the time period 1991–1995 using the level 1 complexity to establish the growth rate (6.7 × 10sup-9/sup ggsup./sups), and results from the other levels will be due solely to the effect of their included external parameters. It is therefore expected that the results of the other levels of complexity will not be as accurate as the level 1 complexity for this time period. Testing of the model was performed for the time period 1991–2003. This provides an extended forecast based on the original calibration time period and initial data. Finally the 1995–2003 time period was used as a blind test of the model, using different initial conditions and determining its ability to accurately predict the density distribution of the 2003 cattail map./p
/sec
/sec
sec
st
pResults and discussion/p
/stpFrom the cattail maps of Figure figr fid="F2"2/figr and those in Rutchey et al. (abbr bid="B50"2008/abbr), a trend in cattail distribution over the years is observable. It appears that cattail density and distribution increased from 1991 to 1995. From 1995 to 2003 the general distribution continued to increase but with more dispersed patches of high-density cattail. This may be related to a reduction in the overall dispersal or to an increased local speciation. Through the use of best management practices, the total phosphorus load entering WCA2A for the period 1995–2004 was reduced by roughly 36% (Richardson et al. abbr bid="B46"2008/abbr), which may have also had a role in the dispersal noted above./ppThe results of the simulations and analyses are displayed in Figures figr fid="F4"4/figr, figr fid="F5"5/figr, figr fid="F6"6/figr, figr fid="F7"7/figr, and figr fid="F8"8/figr. Figure figr fid="F4"4/figr shows the model output maps for the different simulation periods, and all five levels of complexity, compared to the final data maps. These density maps have had their values aggregated into eight classes for visual comparison only. A better depiction of these trends is found in the classified difference maps of Figure figr fid="F9"9/figr below. Figure figr fid="F5"5/figr shows a time series plot for the five levels of complexity across all three simulation periods. It provides added insight into the trends of the model, without relying purely on the end points. The plots are for the regional mean density (R), in red, and elements 209 (blue), 244 (green), and 380 (cyan). The three statistics and comparison time series for the calibration period 1991–1995 can be found in Figure figr fid="F6"6/figr. The regional mean time series plot for all five levels of complexity can be found in Figure figr fid="F6"6a/figr, the abundance-area plot in Figure figr fid="F6"6b/figr, the boxplot in Figure figr fid="F6"6c/figr enables a comparison of the spread of model densities with that of the observed data, and the Moran’s itI/it plot is found in Figure figr fid="F6"6d/figr. Figures figr fid="F7"7/figr and figr fid="F8"8/figr display the same three statistics and regional mean density trends as in Figure figr fid="F6"6/figr for the other two simulation periods, namely 1991–2003 and 1995–2003./p
fig id="F4"titlepFigure 4/p/titlecaptionpResults for (a) training (1991–1995), (b) testing 1 (1991–2003), and (c) testing 2 (1995–2003) simulations for the level 1, 2, 3, 4, and 5 complexities/p/captiontext
pbResults for (a) training (1991–1995), (b) testing 1 (1991–2003), and (c) testing 2 (1995–2003) simulations for the level 1, 2, 3, 4, and 5 complexities./b The historical patterns these results are compared to are in the first column. Densities have been aggregated into eight classes for visual comparison only./p
/textgraphic file="2192-1709-1-10-4"//fig
fig id="F5"titlepFigure 5/p/titlecaptionpRegional and zonal trends for (a) training, (b) testing 1, and (c) testing 2 simulation periods, for all five levels of complexity/p/captiontext
pbRegional and zonal trends for (a) training, (b) testing 1, and (c) testing 2 simulation periods, for all five levels of complexity./b The points at the beginning and end of the trends represent the observed data densities./p
/textgraphic file="2192-1709-1-10-5"//fig
fig id="F6"titlepFigure 6/p/titlecaptionpRegional statistics for training period (1991–1995) and all five levels of complexity/p/captiontext
pbRegional statistics for training period (1991–1995) and all five levels of complexity./b (ba/b) Regional mean trend (red dots represent initial and final data values), (bb/b) abundance-area (the black line represents the data), (bc/b) box plot (data plot on the left), and (bd/b) Moran’s itI/it (the black line represents the data)./p
/textgraphic file="2192-1709-1-10-6"//fig
fig id="F7"titlepFigure 7/p/titlecaptionpRegional statistics for testing 1 period (1991–2003) and all five levels of complexity/p/captiontext
pbRegional statistics for testing 1 period (1991–2003) and all five levels of complexity./b (ba/b) Regional mean trend (red dots represent initial and final data values), (bb/b) abundance-area (the black line represents the data), (bc/b) box plot (data plot on the left), and (bd/b) Moran’s itI/it (the black line represents the data)./p
/textgraphic file="2192-1709-1-10-7"//fig
fig id="F8"titlepFigure 8/p/titlecaptionpRegional statistics for testing 2 period (1995–2003) and all five levels of complexity/p/captiontext
pbRegional statistics for testing 2 period (1995–2003) and all five levels of complexity./b (ba/b) Regional mean trend (red dots represent initial and final data values), (bb/b) abundance-area (the black line represents the data), (bc/b) box plot (data plot on the left), and (bd/b) Moran’s itI/it (the black line represents the data)./p
/textgraphic file="2192-1709-1-10-8"//fig
fig id="F9"titlepFigure 9/p/titlecaptionpClassified difference maps for (a) training (1991–1995), (b) testing 1 (1991–2003), and (c) testing 2 (1995–2003) simulations for the level 1, 2, 3, 4, and 5 complexities/p/captiontext
pbClassified difference maps for (a) training (1991–1995), (b) testing 1 (1991–2003), and (c) testing 2 (1995–2003) simulations for the level 1, 2, 3, 4, and 5 complexities./b The classified differences of the data maps these results are compared to are in the first column (historical patterns)./p
/textgraphic file="2192-1709-1-10-9"//figpWhen considering the first hypothesis, or level of complexity, that cattail growth is density dependent, we note the following points. For the training (1991–1995) time period, the level 1 complexity’s spatial density distribution (Figures figr fid="F4"4/figr and figr fid="F9"9/figr) is the most similar to the observed 1995 data. The density trend (Figure figr fid="F5"5/figr) is smooth and slowly increasing for all observed points (red dots). The regional trend ends directly on the data density. The southwest (element 380) and central (element 244) trends over-predict the data points. The abundance-area statistic (Figure figr fid="F6"6b/figr) follows the data trend (black line) the closest. The mean and distribution of densities (Figure figr fid="F6"6c/figr) are relatively close to the data. The Moran’s itI/it statistic follows the data (black line) trend relatively closely (Figure figr fid="F6"6d/figr). All of these results from the training period are expected because this level of complexity was used for calibration over this time period. For the two testing simulation periods, the level 1 complexity clearly overestimates the historical data (Figures figr fid="F4"4/figr and figr fid="F9"9/figr). The density trend (Figure figr fid="F5"5b/figr,c) remains smooth but overestimates the observed data, except for element 380 in Figure figr fid="F5"5/figrc which remains low, possibly due to the low initial starting density and relatively short time period. The abundance-area statistic (Figures figr fid="F7"7b/figr and figr fid="F8"8b/figr) shows significant over-prediction of the data trend (black line). The mean density is still low, but the distribution is significantly skewed toward the higher densities (Figures figr fid="F7"7c/figr and figr fid="F8"8c/figr). This is evidence that a spatial distribution of densities is more informative than simply using the mean for the area or a presenceabsence type model. Moran’s itI/it statistic follows the data (black line) trend relatively closely (Figures figr fid="F7"7d/figr and figr fid="F8"8d/figr). The results of these analyses confirm that although cattail may indeed have a density-dependentlogistic growth pattern as we are able to simulate observed data during the training period, our inability to simulate observed data for the two training periods indicates that there are certainly other parameters affecting the growth and distribution of this species./ppWhen considering the second hypothesis, or level of complexity, that cattail growthexpansion is dependent on water depth, we note the following points. For all time periods (training, testing 1, and testing 2), the level 2 complexity’s spatial density distribution (Figures figr fid="F4"4/figr and figr fid="F9"9/figr) is consistently lower than the observed values. This is confirmed in the trend analysis (Figure figr fid="F5"5a/figr,b,c), where all the observed elements (209, 244, and 380) and the regional trend are consistently below the observed values. The only exception is element 380 in Figure figr fid="F5"5a/figr, where there is hardly any change in the element’s density, and this is possibly due to the low initial density value of that element. The abundance-area statistic for all time periods (Figures figr fid="F6"6/figrb, figr fid="F7"7/figrb, figr fid="F8"8/figrb) is significantly lower than the observed trend. Similarly, the distribution of densities for all time periods (Figures figr fid="F6"6/figrc, figr fid="F7"7/figrc, figr fid="F8"8/figrc) is much reduced. For the Moran’s itI/it statistic, the model is relatively close to the data trend but consistently has a longer (the longest) tail. This implies that cells further away have an observable impact on the density of any other cell. This would be due to the fact that the water depth in every cell has an effectinfluence on every other cell in the region. We know that water depth is an influential factor in cattail growth (Newman et al. abbr bid="B41"1998/abbr; Miao and Sklar abbr bid="B36"1998/abbr), however the results of these analyses indicate that the current model (level 2 complexity) is overly influenced by this parameter. It is expected that the influence of this parameter will be reduced as it is “diluted” with other parameters in the higher complexity models./ppWhen considering the third hypothesis, or level of complexity, that cattail growthexpansion is dependent on soil phosphorus concentration, we note the following points. The spatial density distribution (Figures figr fid="F4"4/figr and figr fid="F9"9/figr) for level 3 lies somewhat in-between that for level 1 and level 2. Except for the training period, which slightly under-predicts the observed values, the two testing periods appear to more accurately predict the observed density distribution. This is confirmed with the trend analysis (Figure figr fid="F5"5a/figr,b,c), where at least the regional trend is at or relatively close to the observed values. As with the level 2 complexity, element 380 tends to under-predict the observed value. However, element 209 tends to predict the observed value better than either of the previous two levels of complexity. The abundance-area statistic (Figures figr fid="F6"6b/figr, figr fid="F7"7/figrb, figr fid="F8"8/figrb) shows consistent under-prediction of the observed trend, but also shows consistently higher values than the level 2 trend and is closer to the data than the level 1 trend. The distribution of densities for all time periods (Figures figr fid="F6"6c/figr, figr fid="F7"7c/figr, figr fid="F8"8c/figr), although greater than the level 2 complexity, is still significantly lower than the observed distribution. The Moran’s itI/it trend is followed closely for all time periods (Figures figr fid="F6"6d/figr, figr fid="F7"7d/figr, figr fid="F8"8d/figr). The results of these analyses confirm that soil phosphorus is a significant influencing factor in the distribution of cattail, although the water depth parameter remains highly influential. The level 3 complexity is better able to predict cattail in areas of typically high phosphorus or of high cattail density than the previous two levels of complexity./ppWhen considering the fourth hypothesis, or level of complexity, that sawgrass density may impact the rate of cattail expansion, we note the following points. The spatial density distribution (Figures figr fid="F4"4/figr and figr fid="F9"9/figr) is closer to the observed values than the previous levels of complexity. This is confirmed in the trend analysis (Figure figr fid="F5"5a/figr,b,c), where most notably all of the elements tend to better predict the observed values, except for element 244 in Figure figr fid="F5"5c/figr, which over-predicts the observed density and in turn raises the regional trend above the observed value as well. The abundance-area statistic only slightly under-predicts the observed trend during the training time period (Figure figr fid="F6"6b/figr). During the two testing time periods, the statistic indicates a slight over-prediction of the observed trend, but results show better predictions than any of the previous levels of complexity. The density distribution (Figures figr fid="F6"6c/figr, figr fid="F7"7c/figr, figr fid="F8"8c/figr) is significantly higher than the level 2 and level 3 complexities, and equal to (Figure figr fid="F6"6c/figr; training) or less than (Figures figr fid="F7"7c/figr, figr fid="F8"8c/figr; testing) the level 1 complexity. This means that the level 4 complexity consistently approximates the observed densities for the region better than the other levels of complexity for all time periods, albeit with slightly elevated minimum densities. The Moran’s itI/it statistic (Figures figr fid="F6"6d/figr, figr fid="F7"7d/figr, figr fid="F8"8d/figr) follows the observed trend relatively well for all time periods. Although the level 4 complexity tends to have slightly elevated minimum densities, like the level 1 complexity, the general result from these analyses is that the level 4 complexity is able to simulate the cattail densities through the region consistently better than any of the previous levels of complexity. We can thus conclude that including a simulated sawgrass density does indeed impact the rate of cattail expansion and improve simulation results./ppWhen considering the fifth hypothesis, or level of complexity, that inter-species interactions between cattail and sawgrass contribute to the observed cattail dynamics, we find the following: The spatial density distribution (Figures figr fid="F4"4/figr and figr fid="F9"9/figr) does not predict the observed values significantly better than the level 4 complexity. The trend analysis (Figure figr fid="F5"5a/figr,b,c) is almost identical to that of the level 4 complexity in every respect. All of the statistical analyses and distributions for all time periods (Figures figr fid="F6"6b/figr,c,d; figr fid="F7"7b/figr,c,d; figr fid="F8"8b/figr,c,d) are almost identical to those of the level 4 complexity. The result of these analyses is that the level 5 complexity does not predict the observed values with greater success than the level 4 complexity. While inter-species interactions might well have an effect with a different model structure, the current modeling arrangement has shown the beginning of diminishing returns with respect to model complexity and predictive capability./ppWith regard to the Moran’s itI/it statistic, all the complexity levels followed the same basic trend as the data (represented by the black line) and were all 0 by around the 18,240 m mark. This distance corresponds approximately to the width of the region, while the total distance of 36,480 m in the plot corresponds to the longest north–south distance of the region. It is believed that the statistic drops to 0 by the 18,240 m mark due to overlapping and boundary effects and that this elevates the Nash-Sutcliffe coefficient for all levels of complexity in this statistic./ppA summary of the Figure figr fid="F9"9/figr classified difference maps can be found in the bar chart of Figure figr fid="F10"10/figr, which shows the percentage of triangular elements falling within each class for all five levels of complexity and simulation periods. Upon further inspection of these plots, the level 4 and level 5 complexities consistently outperform the other levels of complexity, with either the highest percentage of combined classes 0 (< 20 gmsup2/sup) and 1 (< 200 gmsup2/sup), or the lowest percentage of combined classes 2 (< 400 gmsup2/sup) and 3 (> 400 gmsup2/sup)./p
fig id="F10"titlepFigure 10/p/titlecaptionpClassified difference summary/p/captiontext
pbClassified difference summary./b Percentage of cells occurring within each class, for all levels of complexity and time periods (ba/b) training (1991–1995), (bb/b) testing 1 (1991–2003), and (bc/b) testing 2 (1995–2003)./p
/textgraphic file="2192-1709-1-10-10"//figpA summary of the three statistics found in Figures figr fid="F6"6b/figr,c,d; figr fid="F7"7/figrb,c,d; and figr fid="F8"8b/figr,c,d is provided by the Nash-Sutcliffe coefficients in Table tblr tid="T3"3/tblr and can be visually compared in Figure figr fid="F11"11/figr, with the box plots (or 1-to-1 comparisons) located in Figure figr fid="F11"11a/figr, abundance-area in Figure figr fid="F11"11b/figr, and Moran’s itI/it in Figure figr fid="F11"11c/figr. From Figure figr fid="F11"11/figr it can be noted that the level 4 and 5 complexities, which include depth, soil phosphorus, and sawgrass interactions, consistently perform better than the other levels of complexity. A point to note regarding the level 5 complexity is that despite the fact that it does not offer a significant improvement in predictive capability over the level 4 complexity, it does not predict the observed values any worse than the level 4 complexity either./p
table id="T3"
title
pTable 3/p
/title
caption
p
bSummary of Nash-Sutcliffe values comparing model and observed data for box plot, Moran’s/bb
it I/it
/bb, and abundance-area statistics (represented by Figures/b
figr fid="F6" 6/figrb,/b
figr fid="F7" 7/figrb, and/b
figr fid="F8" 8/figrb, respectively) for level 1, level 2, level 3, level 4, level 5, training (199–1995), testing 1 (1991–2003), and testing 2 (1995–2003) simulations/b
/p
/caption
tgroup align="left" cols="5"
colspec align="left" colname="c1" colnum="1" colwidth="1*"/
colspec align="left" colname="c2" colnum="2" colwidth="1*"/
colspec align="char" colname="c3" colnum="3" colwidth="1*"/
colspec align="char" colname="c4" colnum="4" colwidth="1*"/
colspec align="char" colname="c5" colnum="5" colwidth="1*"/
thead valign="top"
row rowsep="1"
entry colname="c1"
p
bYear/b
/p
/entry
entry colname="c2"
p
blevel/b
/p
/entry
entry align="char" colname="c3"
p
b1-to-1 Box plot/b
/p
/entry
entry align="char" colname="c4"
p
bMoran’s/bb
it I/it
/b
/p
/entry
entry align="char" colname="c5"
p
bAbundance/b
/p
/entry
/row
/thead
tbody valign="top"
row
entry colname="c1"
p1991-1995/p
/entry
entry colname="c2"
p1/p
/entry
entry align="char" char="." colname="c3"
p0.74/p
/entry
entry align="char" char="." colname="c4"
p0.98/p
/entry
entry align="char" char="." colname="c5"
p0.98/p
/entry
/row
row
entry colname="c1"/
entry colname="c2"
p2/p
/entry
entry align="char" char="." colname="c3"
p0.13/p
/entry
entry align="char" char="." colname="c4"
p0.99/p
/entry
entry align="char" char="." colname="c5"
p−0.94/p
/entry
/row
row
entry colname="c1"/
entry colname="c2"
p3/p
/entry
entry align="char" char="." colname="c3"
p0.49/p
/entry
entry align="char" char="." colname="c4"
p0.95/p
/entry
entry align="char" char="." colname="c5"
p0.23/p
/entry
/row
row
entry colname="c1"/
entry colname="c2"
p4/p
/entry
entry align="char" char="." colname="c3"
p0.74/p
/entry
entry align="char" char="." colname="c4"
p0.98/p
/entry
entry align="char" char="." colname="c5"
p0.96/p
/entry
/row
row
entry colname="c1"/
entry colname="c2"
p5/p
/entry
entry align="char" char="." colname="c3"
p0.74/p
/entry
entry align="char" char="." colname="c4"
p0.98/p
/entry
entry align="char" char="." colname="c5"
p0.96/p
/entry
/row
row
entry colname="c1"
p1991-2003/p
/entry
entry colname="c2"
p1/p
/entry
entry align="char" char="." colname="c3"
p−0.75/p
/entry
entry align="char" char="." colname="c4"
p0.97/p
/entry
entry align="char" char="." colname="c5"
p−1.89/p
/entry
/row
row
entry colname="c1"/
entry colname="c2"
p2/p
/entry
entry align="char" char="." colname="c3"
p0.02/p
/entry
entry align="char" char="." colname="c4"
p0.86/p
/entry
entry align="char" char="." colname="c5"
p−0.35/p
/entry
/row
row
entry colname="c1"/
entry colname="c2"
p3/p
/entry
entry align="char" char="." colname="c3"
p0.23/p
/entry
entry align="char" char="." colname="c4"
p0.98/p
/entry
entry align="char" char="." colname="c5"
p0.44/p
/entry
/row
row
entry colname="c1"/
entry colname="c2"
p4/p
/entry
entry align="char" char="." colname="c3"
p0.49/p
/entry
entry align="char" char="." colname="c4"
p0.98/p
/entry
entry align="char" char="." colname="c5"
p0.77/p
/entry
/row
row
entry colname="c1"/
entry colname="c2"
p5/p
/entry
entry align="char" char="." colname="c3"
p0.49/p
/entry
entry align="char" char="." colname="c4"
p0.98/p
/entry
entry align="char" char="." colname="c5"
p0.76/p
/entry
/row
row
entry colname="c1"
p1995-2003/p
/entry
entry colname="c2"
p1/p
/entry
entry align="char" char="." colname="c3"
p−0.95/p
/entry
entry align="char" char="." colname="c4"
p0.99/p
/entry
entry align="char" char="." colname="c5"
p−0.80/p
/entry
/row
row
entry colname="c1"/
entry colname="c2"
p2/p
/entry
entry align="char" char="." colname="c3"
p0.14/p
/entry
entry align="char" char="." colname="c4"
p0.94/p
/entry
entry align="char" char="." colname="c5"
p−0.29/p
/entry
/row
row
entry colname="c1"/
entry colname="c2"
p3/p
/entry
entry align="char" char="." colname="c3"
p0.36/p
/entry
entry align="char" char="." colname="c4"
p0.97/p
/entry
entry align="char" char="." colname="c5"
p0.51/p
/entry
/row
row
entry colname="c1"/
entry colname="c2"
p4/p
/entry
entry align="char" char="." colname="c3"
p0.39/p
/entry
entry align="char" char="." colname="c4"
p0.99/p
/entry
entry align="char" char="." colname="c5"
p0.77/p
/entry
/row
row rowsep="1"
entry colname="c1"/
entry colname="c2"
p5/p
/entry
entry align="char" char="." colname="c3"
p0.39/p
/entry
entry align="char" char="." colname="c4"
p0.99/p
/entry
entry align="char" char="." colname="c5"
p0.77/p
/entry
/row
/tbody
/tgroup
/table
fig id="F11"titlepFigure 11/p/titlecaptionpNash-Sutcliffe summary of statistics/p/captiontext
pbNash-Sutcliffe summary of statistics./b A graphical representation of Table tblr tid="T3"3/tblr. The level 4 and 5 complexity models perform consistently well in comparison with all the other models./p
/textgraphic file="2192-1709-1-10-11"//fig
/sec
sec
st
pConclusions/p
/stpThe methods of modeling cattail for ecological models currently in use were compared, their similarities and differences were noted, and a knowledge gap identified: there doesn’t yet exist a method of quantitatively and deterministically determining the spatial distribution of cattail in the Everglades. A coupled free-formfixed-form model was introduced to solve this problem. An added benefit of the free-form nature of the RSMTARSE coupled model is the user-definable equations of interaction, which can be modified as data andor new theories become available. This new ecological implementation of the model (RTE) was successfully applied towards modeling cattail dynamics across the WCA2A test site for training (1991–1995), testing (1991–2003), and blind test (1995–2003) simulation periods. Five algorithms, with increasing complexity, were used to match the historical data. Upon analysis of the performance of these different levels, it can be concluded that the level 4 and 5 complexities, which include depth, soil phosphorus, and sawgrass interaction parameters, are the most suitable models for matching the historical data. The Nash-Sutcliffe coefficient was used to distinguish the success of different models./ppBoth local and landscape-scale indicators were used to perform the comparison between historical and modeled cattail patterns. The average local cattail density was estimated with a box-plot analysis; the pairwise-cell comparison of local cattail densities was analyzed with Moran’s itI/it; and, the regional increase with area of the local cattail density was estimated through the abundance-area relationship. The box-plot and the abundance-area were the most meaningful patterns to discriminate models in terms of their ability to represent the observed patterns./ppThe autocorrelation structure of the cattail patterns were well represented by all the models at each complexity level. This is possibly due to the fact that through overlapping and boundary effects, cattail densities leveled off after roughly half the distance (top to bottom) that was used to calculate the statistic. It may be more representative if future calculations considered only half this maximum distance, where the variations would carry a greater weighting./ppOur simulation results would be in agreement with the studies of Newman et al. (abbr bid="B41"1998/abbr) and Miao and Sklar (abbr bid="B36"1998/abbr), in which water depth and soil phosphorus concentration were the most important factors aiding in cattail expansion. Our results also include an interaction parameter with sawgrass, which is of interest in the region. Thus, we confirm the importance of considering species dependencies or interactions in reproducing the cattail patterns even in water-controlled areas in which the anthropic-driven variables would be expected to dominate the species processes and the resulting patterns./ppLimitations of our current modeling approach may include the elementtriangle size, with a range of 0.5–1.7 kmsup2/sup (Wang abbr bid="B67"2009/abbr). This constraint was dictated by the choice of the RSM that simulates hydrological processes. Although the imposed grid-unit has a relatively coarse size in which there is still considerable heterogeneity of the environmental features (Zajac abbr bid="B73"2010/abbr), RTE has proven to be capable of reproducing the dynamics of cattail and sawgrass at the landscape scale using the level 4 and level 5 complexities. This makes it a valuable tool for exploring potential management scenarios in water conservation areas in the Everglades and possibly in other water-controlled wetlands./ppFurther investigations would consider the quantification of the importance of water-controlled drivers and species traits (dispersal) for vegetation patterns, the stabilityinstability states of species under varying stressors, the prediction of future management scenarios, and the comparison with neutral-based models./ppIn terms of further model development and added complexity, efforts have been made towards more accurate representation of fauna movement through the use of Eulerian–Lagrangian (grid-independent) particle movement (Lagerwall abbr bid="B29"2011/abbr), as well as using vegetation typesdensities to influence the hydrology with a dynamically linked Manning’s itn/it parameter (Zajac abbr bid="B73"2010/abbr). While creating more dynamically linked parameters is an ongoing task, these linkages remain a challenge to implement due to the difficulties associated with parameterizing (training) a model with feedback effects. This feedback relationship between ecological and hydrological model components may be quite important to the function and resilience of these ecosystems and is certainly a subject of further research./p
/sec
sec
st
pCompeting interests/p
/stpThe authors declare that they have no competing interests./p
/sec
sec
st
pAuthors’ contributions/p
/stpGL conducted the majority of the research, model adaptation for ecology, and writing of the paper. GK provided ecological modeling expertise, general guidance, help in developing the five levels of complexity, paper writing, and review contributions. RMC provided statistical insights, provided critical review on model design, and ensured that the general logic of the paper was maintained. MC provided expertise in the ecological statistics and contributed to paper writing, formatting, and review. AJ provided RSMTARSE model expertise. NW provided RSM and WCA2A expertise, supplied raw vegetation maps, and provided critical review on model design. All authors read and approved the final manuscript./p
/sec
/bdy
bm
ack
sec
st
pAcknowledgements/p
/stpFinancial support for this research was provided by the South Florida Water Management District and the U.S. Geological Survey Water Resources Research Center at the University of Florida./p
/sec
/ack
refgrpbibl id="B1"augausnmArnold/snmfnmK/fnm/auausnmGosling/snmfnmJ/fnm/au/augsourceThe Java programming language/sourcepublisherPrentice Hall, Upper Saddle River, NJ/publisheredition2/editionpubdate1998/pubdate/biblbibl id="B2"titlepComparison of C++ and Fortran 90 for object-oriented scientific programming/p/titleaugausnmCary/snmfnmJR/fnm/auausnmShasharina/snmfnmSG/fnm/auausnmCummings/snmfnmJC/fnm/auausnmReynders/snmfnmJVW/fnm/auausnmHinker/snmfnmPJ/fnm/au/augsourceComp Phys Comm/sourcepubdate1998/pubdatevolume105/volumefpage20/fpagelpage36/lpage/biblbibl id="B3"titlepSpatial autocorrelation: a review of existing and new measures with applications/p/titleaugausnmCliff/snmfnmAD/fnm/auausnmOrd/snmfnmK/fnm/au/augsourceEcon Geography/sourcepubdate1970/pubdatevolume46/volumefpage269/fpagelpage292/lpage/biblbibl id="B4"titlepOn neutral metacommunity patterns of river basins at different scales of aggregation/p/titleaugausnmConvertino/snmfnmM/fnm/auausnmMuneepeerakul/snmfnmR/fnm/auausnmAzaele/snmfnmS/fnm/auausnmBertuzzo/snmfnmE/fnm/auausnmRinaldo/snmfnmA/fnm/auausnmRodriguez-Iturbe/snmfnmI/fnm/au/augsourceWater Resour Res/sourcepubdate2009/pubdatevolume45/volumefpageW08424/fpage/biblbibl id="B5"titlepModeling ecological and economic systems with STELLA: part III/p/titleaugausnmCostanza/snmfnmR/fnm/auausnmVoinov/snmfnmA/fnm/au/augsourceEcol Model/sourcepubdate2001/pubdatevolume143/volumefpage1/fpagelpage7/lpagexrefbibpubid idtype="doi"10.1016S0304-3800(01)00358-1/pubid/xrefbib/biblbibl id="B6"titlepSpatial distribution of soil nutrients in a northern-Everglades marsh: Water Conservation Area 2A/p/titleaugausnmDeBusk/snmfnmWF/fnm/auausnmReddy/snmfnmKR/fnm/auausnmKoch/snmfnmMS/fnm/auausnmWang/snmfnmY/fnm/au/augsourceSoil Soc Am/sourcepubdate1994/pubdatevolume58/volumefpage543/fpagelpage552/lpagexrefbibpubid idtype="doi"10.2136sssaj1994.03615995005800020042x/pubid/xrefbib/biblbibl id="B7"titlepMarsh vegetation patterns and soil phosphorus gradients in the Everglades ecosystem/p/titleaugausnmDoren/snmfnmRF/fnm/auausnmArmentano Thomas/snmfnmV/fnm/auausnmWhiteaker Louis/snmfnmD/fnm/auausnmJones Ronald/snmfnmD/fnm/au/augsourceAqua Bot/sourcepubdate1999/pubdatevolume56/volumefpage145/fpagelpage163/lpage/biblbibl id="B8"augausnmDouglas/snmfnmMS/fnm/au/augsourceThe Everglades: river of grass/sourcepublisherRinehart, New York/publisherpubdate1947/pubdate/biblbibl id="B9"augausnmDuke-Sylvester/snmfnmS/fnm/au/augsourceInitial performance measures and information related to the ATLSS vegetation succession model/sourcepubdate2005/pubdatenoteurlhttp:atlss.orgVSMod/url. Accessed 31 July 2010/note/biblbibl id="B10"augaucnmESRI (Environmental Systems Resource Institute)/cnm/au/augsourceArcMap 10.0/sourcepublisherESRI, Redlands, CA/publisherpubdate2010/pubdate/biblbibl id="B11"augausnmFitz/snmfnmCH/fnm/auausnmTrimble/snmfnmB/fnm/au/augsourceDocumentation of the Everglades Landscape Model: ELM v2.5/sourcepublisherSouth Florida Water Management District, West Palm Beach, FL/publisherpubdate2006a/pubdate/biblbibl id="B12"augausnmFitz/snmfnmCH/fnm/auausnmTrimble/snmfnmB/fnm/au/augsourceEverglades Landscape Model (ELM)/sourcepubdate2006b/pubdatenoteurlhttp:my.sfwmd.govportalpageportalxweb%20-%20release%202elm/url. Accessed 31 July 2010/note/biblbibl id="B13"titlepIntegrated ecological modeling and decision analysis within the Everglades landscape/p/titleaugausnmFitz/snmfnmHC/fnm/auausnmKiker/snmfnmGA/fnm/auausnmKim/snmfnmJB/fnm/au/augsourceCrit Rev Environ Sci Technol/sourcepubdate2011/pubdatevolume41/volumeissueS1/issuefpage517/fpagelpage547/lpage/biblbibl id="B14"augausnmFortin/snmfnmMJ/fnm/auausnmDale/snmfnmMRT/fnm/au/augsourceSpatial analysis, a guide for ecologists/sourcepublisherCambridge University Press, Cambridge/publisherpubdate2005/pubdate/biblbibl id="B15"titlepEffects of water depth on Typha latifolia and Typha domingensis/p/titleaugausnmGrace/snmfnmJBL/fnm/au/augsourceAm J Bot/sourcepubdate1989/pubdatevolume76/volumefpage762/fpagelpage768/lpagexrefbibpubid idtype="doi"10.23072444423/pubid/xrefbib/biblbibl id="B16"augausnmGross/snmfnmLJ/fnm/au/augsourceATLSS home page/sourcepubdate1996/pubdatenoteurlhttp:atlss.org/url. Accessed 31 July 2010/note/biblbibl id="B17"augausnmGrunwald/snmfnmS/fnm/au/augsourcePhosphorus data for WCA2A. Personal Communication/sourcepublisherUniversity of Florida, Gainesville/publisherpubdate2010/pubdate/biblbibl id="B18"titlepSpatial variability, distribution and uncertainty assessment of soil phosphorus in a South Florida wetland/p/titleaugausnmGrunwald/snmfnmS/fnm/auausnmReddy/snmfnmKR/fnm/auausnmNewman/snmfnmS/fnm/auausnmDeBusk/snmfnmWF/fnm/au/augsourceEnvironmetrics/sourcepubdate2004/pubdatevolume15/volumefpage811/fpagelpage825/lpagexrefbibpubid idtype="doi"10.1002env.668/pubid/xrefbib/biblbibl id="B19"titlepTemporal trajectories of phosphorus and pedo-patterns mapped in Water Conservation Area 2, Everglades, Florida, USA/p/titleaugausnmGrunwald/snmfnmS/fnm/auausnmOzborne/snmfnmTZ/fnm/auausnmReddy/snmfnmKR/fnm/au/augsourceGeoderma/sourcepubdate2008/pubdatevolume146/volumefpage1/fpagelpage13/lpagexrefbibpubid idtype="doi"10.1016j.geoderma.2008.03.023/pubid/xrefbib/biblbibl id="B20"titlepLarge-scale constructed wetlands for nutrient removal from stormwater runoff: an Everglades restoration project/p/titleaugausnmGuardo/snmfnmM/fnm/auausnmFink/snmfnmL/fnm/auausnmFontaine Thomas/snmfnmD/fnm/auausnmNewman/snmfnmS/fnm/auausnmChimney/snmfnmM/fnm/auausnmBearzotti/snmfnmR/fnm/auausnmGoforth/snmfnmG/fnm/au/augsourceEnviron Manage/sourcepubdate1995/pubdatevolume19/volumeissue6/issuefpage879/fpagelpage889/lpagexrefbibpubid idtype="doi"10.1007BF02471939/pubid/xrefbib/biblbibl id="B21"augausnmHarold/snmfnmER/fnm/au/augsourceXML: Extensible Markup Language/sourcepublisherIDG, Foster City/publisheredition1/editionpubdate1998/pubdate/biblbibl id="B22"titlepModeling two-dimensional reactive transport using a Godunov-mixed finite element method/p/titleaugausnmJames/snmfnmAI/fnm/auausnmJawitz/snmfnmJW/fnm/au/augsourceJ Hydrol/sourcepubdate2007/pubdatevolume338/volumefpage28/fpagelpage41/lpagexrefbibpubid idtype="doi"10.1016j.jhydrol.2007.02.007/pubid/xrefbib/biblbibl id="B23"augausnmJawitz/snmfnmJW/fnm/auausnmMuñoz-Carpena/snmfnmR/fnm/auausnmMuller/snmfnmS/fnm/auausnmGrace/snmfnmKA/fnm/auausnmJames/snmfnmAI/fnm/au/augsourceDevelopment, testing, and sensitivity and uncertainty analyses of a Transport and Reaction Simulation Engine (TaRSE) for spatially distributed modeling of phosphorus in South Florida peat marsh wetlands. Scientific Investigations Report 2008–5029/sourcepublisherUnited States Geological Survey, Reston, VA/publisherpubdate2008/pubdate/biblbibl id="B24"titlepInland wetland change detection in the Everglades Water Conservation Area 2A using a time series of remotely sensed data/p/titleaugausnmJensen/snmfnmJR/fnm/auausnmRutchey/snmfnmK/fnm/auausnmKoch/snmfnmMS/fnm/auausnmNarumalani/snmfnmS/fnm/au/augsourcePhotogramm Eng Rem Sens/sourcepubdate1995/pubdatevolume61/volumeissue2/issuefpage199/fpagelpage209/lpage/biblbibl id="B25"augausnmKeen/snmfnmRE/fnm/auausnmSpain/snmfnmJD/fnm/au/augsourceComputer simulation in biology/sourcepublisherWiley-Liss, New York/publisherpubdate1992/pubdate/biblbibl id="B26"augausnmKiker/snmfnmGA/fnm/au/augsourceDevelopment and comparison of savanna ecosystem models to explore the concept of carrying capacity. PhD Dissertation/sourcepublisherCornell University, Ithaca/publisherpubdate1998/pubdate/biblbibl id="B27"augausnmKiker/snmfnmGA/fnm/auausnmLinkov/snmfnmI/fnm/au/augsourceThe QnD ModelGame System: Integrating Questions and Decisions for Multiple Stressors/sourcepublisherSpringer, Netherlands/publisherpubdate2006/pubdate/biblbibl id="B28"titlepQnD: A modeling game system for integrating environmental processes and practical management decisions/p/titleaugausnmKiker/snmfnmGA/fnm/auausnmRivers-Moore/snmfnmN A/fnm/auausnmKiker/snmfnmM K/fnm/auausnmLinkov/snmfnmI/fnm/au/augsourceEnvironmental Security and Environmental Management: The Role of Risk Assessment. Netherlands/sourcepubdate2006/pubdate/biblbibl id="B29"augausnmLagerwall/snmfnmGL/fnm/au/augsourceModeling Typha domingensis in an Everglades wetland. Dissertation/sourcepublisherUniversity of Florida, Gainesville/publisherpubdate2011/pubdate/biblbibl id="B30"titlepThe effect of complexity on parameter sensitivity and model uncertainty in river water quality modeling/p/titleaugausnmLindenschmidt/snmfnmKE/fnm/au/augsourceEcol Model/sourcepubdate2006/pubdatevolume190/volumefpage72/fpagelpage86/lpagexrefbibpubid idtype="doi"10.1016j.ecolmodel.2005.04.016/pubid/xrefbib/biblbibl id="B31"titlepScientific workflow management and the Kepler system/p/titleaugausnmLudascher/snmfnmB/fnm/auausnmAltintas/snmfnmI/fnm/auausnmBerkley/snmfnmC/fnm/auausnmHiggins/snmfnmD/fnm/auausnmJaeger/snmfnmE/fnm/auausnmJones/snmfnmM/fnm/auausnmLee Edward/snmfnmA/fnm/auausnmTao/snmfnmJ/fnm/auausnmZhao/snmfnmY/fnm/au/augsourceConcurr Comp Pract Exper/sourcepubdate2006/pubdatevolume18/volumefpage1039/fpagelpage1065/lpagexrefbibpubid idtype="doi"10.1002cpe.994/pubid/xrefbib/biblbibl id="B32"titlepNon-neutral vegetation dynamics/p/titleaugausnmMarani/snmfnmM/fnm/auausnmTommaso/snmfnmZ/fnm/auausnmBelluco/snmfnmE/fnm/auausnmSilvestri/snmfnmS/fnm/auausnmMaritan/snmfnmA/fnm/au/augsourcePLoS One/sourcepubdate2006/pubdatevolume1/volumeissue1/issuefpagee78/fpagexrefbibpubidlistpubid idtype="doi"10.1371journal.pone.0000078/pubidpubid idtype="pmcid"1762364/pubidpubid idtype="pmpid" link="fulltext"17183710/pubid/pubidlist/xrefbib/biblbibl id="B33"titlepDiversity and abundance of spring migratory birds using habitat islands on the Great Plains/p/titleaugausnmMartin/snmfnmTE/fnm/au/augsourceCooper Ornithol Soc/sourcepubdate1980/pubdatevolume82/volumefpage430/fpagelpage439/lpage/biblbibl id="B34"titlepEvaluation of the Nash-Sutcliffe Efficiency Index/p/titleaugausnmMcCuen/snmfnmRH/fnm/auausnmKnight/snmfnmZ/fnm/auausnmCutter/snmfnmAG/fnm/au/augsourceHydrol Eng/sourcepubdate2006/pubdatevolume11/volumefpage597/fpagelpage602/lpagexrefbibpubid idtype="doi"10.1061(ASCE)1084-0699(2006)11:6(597)/pubid/xrefbib/biblbibl id="B35"titlepRhizome growth and nutrient resorption: mechanisms underlying the replacement of two clonal species in Florida Everglades/p/titleaugausnmMiao/snmfnmS/fnm/au/augsourceAquat Bot/sourcepubdate2004/pubdatevolume78/volumefpage55/fpagelpage66/lpagexrefbibpubid idtype="doi"10.1016j.aquabot.2003.09.001/pubid/xrefbib/biblbibl id="B36"titlepBiomass and nutrient allocation of sawgrass and cattail along a nutrient gradient in the Florida Everglades/p/titleaugausnmMiao/snmfnmSL/fnm/auausnmSklar/snmfnmFH/fnm/au/augsourceWetlands Ecol Manage/sourcepubdate1998/pubdatevolume5/volumefpage245/fpagelpage264/lpage/biblbibl id="B37"titlepDisturbance-mediated mammal persistence and abundance-area relationships in Amazonian forest fragments/p/titleaugausnmMichalski/snmfnmF/fnm/auausnmPeres/snmfnmCA/fnm/au/augsourceConserv Biol/sourcepubdate2007/pubdatevolume21/volumefpage1626/fpagelpage1640/lpagexrefbibpubid idtype="pmpid" link="fulltext"18173486/pubid/xrefbib/biblbibl id="B38"augausnmMuller/snmfnmS/fnm/au/augsourceAdaptive spatially-distributed water-quality modeling: an application to mechanistically simulate phosphorus conditions in the variable-density surface-waters of coastal Everglades wetlands. PhD Dissertation/sourcepublisherUniversity of Florida, Gainesville/publisherpubdate2010/pubdate/biblbibl id="B39"titlepNeutral metacommunity models predict fish disversity patterns in Mississippi-Missouri basin/p/titleaugausnmMuneepeerakul/snmfnmR/fnm/auausnmBertuzzo/snmfnmE/fnm/auausnmLynch/snmfnmHJ/fnm/auausnmFagan/snmfnmWF/fnm/auausnmRinaldo/snmfnmA/fnm/auausnmRodriguez-Iturbe/snmfnmI/fnm/au/augsourceNature/sourcepubdate2008/pubdatevolume453/volumefpage220/fpagelpage222/lpagexrefbibpubidlistpubid idtype="doi"10.1038nature06813/pubidpubid idtype="pmpid" link="fulltext"18464742/pubid/pubidlist/xrefbib/biblbibl id="B40"titlepModeling hydrology and sediment transport in vegetative filter strips/p/titleaugausnmMuñoz-Carpena/snmfnmR/fnm/auausnmParsons/snmfnmJE/fnm/auausnmGilliam/snmfnmJW/fnm/au/augsourceJ Hydrol/sourcepubdate1999/pubdatevolume214/volumefpage111/fpagelpage129/lpagexrefbibpubid idtype="doi"10.1016S0022-1694(98)00272-8/pubid/xrefbib/biblbibl id="B41"titlepFactors influencing cattail abundance in the northern Everglades/p/titleaugausnmNewman/snmfnmS/fnm/auausnmSchutte/snmfnmJ/fnm/auausnmGrace/snmfnmJ/fnm/auausnmRutchey/snmfnmK/fnm/auausnmFontaine/snmfnmT/fnm/auausnmReddy/snmfnmK/fnm/auausnmPietrucha/snmfnmM/fnm/au/augsourceAquat Bot/sourcepubdate1998/pubdatevolume60/volumefpage265/fpagelpage280/lpagexrefbibpubid idtype="doi"10.1016S0304-3770(97)00089-2/pubid/xrefbib/biblbibl id="B42"titlepWetlands management/p/titleaugausnmOdum/snmfnmHT/fnm/auausnmOdum/snmfnmEC/fnm/auausnmBrown/snmfnmMT/fnm/au/augsourceEnvironment and society in Florida/sourcepublisherCRC Press, Boca Raton/publisherpubdate2000/pubdate/biblbibl id="B43"augausnmOtt/snmfnmRL/fnm/auausnmLongnecker/snmfnmMT/fnm/au/augsourceA first course in statistical methods/sourcepublisherCurt Hinrichs, Belmont, CA/publisherpubdate2004/pubdate/biblbibl id="B44"augausnmParadis/snmfnmE/fnm/au/augsourceMoran’s autocorrelation coefficient in comparative methods/sourcepubdate2010/pubdatenoteurlhttp:cran.r-project.orgwebpackagesapevignettesMoranI.pdf/url. Accessed 7 August 2010/notexrefbibpubid idtype="pmpid"23280820/pubid/xrefbib/biblbibl id="B45"augausnmPerez-Ovilla/snmfnmO/fnm/au/augsourceModeling runoff pollutant dynamics through vegetative filter strips: a flexible numerical approach. PhD Dissertation/sourcepublisherUniversity of Florida, Gainesville/publisherpubdate2010/pubdate/biblbibl id="B46"titlepMacrophyte community responses in the Everglades with an emphasis on cattail (Typha domingensis) and sawgrass (Cladium jamaicense) interactions along a gradient of long-term nutrient additions, altered hydroperiod, and fire/p/titleaugausnmRichardson/snmfnmCJ/fnm/auausnmKing Ryan/snmfnmS/fnm/auausnmVymazal/snmfnmJ/fnm/auausnmRomanowicz Edwin/snmfnmA/fnm/auausnmPahl James/snmfnmW/fnm/au/augsourceEcol Stud/sourcepubdate2008/pubdatevolume201/volumefpage215/fpagelpage260/lpagexrefbibpubid idtype="doi"10.1007978-0-387-68923-4_9/pubid/xrefbib/biblbibl id="B47"titlepIncorporation of spectral data into multivariate geostatistical models to map soil phosphorus variability in a Florida wetland/p/titleaugausnmRivero/snmfnmRG/fnm/auausnmGrunwald/snmfnmS/fnm/auausnmBruland/snmfnmGL/fnm/au/augsourceGeoderma/sourcepubdate2007/pubdatevolume140/volumefpage428/fpagelpage443/lpagexrefbibpubid idtype="doi"10.1016j.geoderma.2007.04.026/pubid/xrefbib/biblbibl id="B48"titlepCharacterization of the spatial distribution of soil properties in Water Conservation Area 2A, Everglades, Florida/p/titleaugausnmRivero/snmfnmRG/fnm/auausnmGrunwald/snmfnmS/fnm/auausnmOsborne/snmfnmTZ/fnm/auausnmReddy/snmfnmKR/fnm/auausnmNewman/snmfnmS/fnm/au/augsourceSoil Sci/sourcepubdate2007/pubdatevolume172/volumefpage149/fpagelpage166/lpagexrefbibpubid idtype="doi"10.109701.ss.0000240550.52175.35/pubid/xrefbib/biblbibl id="B49"augausnmRutchey/snmfnmK/fnm/au/augsourceTypha domingensis maps of WCA2A for the years 1991 and 1995. Personal communication/sourcepublisherSouth Florida Water Management District, West Palm Beach/publisherpubdate2011/pubdate/biblbibl id="B50"titlepDevelopment of vegetation maps for assessing Everglades restoration progress/p/titleaugausnmRutchey/snmfnmK/fnm/auausnmSchall/snmfnmT/fnm/auausnmSklar/snmfnmF/fnm/au/augsourceWetlands/sourcepubdate2008/pubdatevolume172/volumeissue2/issuefpage806/fpagelpage816/lpage/biblbibl id="B51"augaucnmSFWMD/cnm/au/augsourceLand cover land use 1995/sourcepubdate1995/pubdatenoteurlhttp:my.sfwmd.govgisappssfwmdxwebdcdataview.aspquery=unq_id=297/url. Accessed 11 November 2009/note/biblbibl id="B52"augaucnmSFWMD/cnm/au/augsourceLand cover land use 1999/sourcepubdate1999/pubdatenoteurlhttp:my.sfwmd.govgisappssfwmdxwebdcdataview.aspquery=unq_id=1593/url. Accessed 11 November 2009/note/biblbibl id="B53"augaucnmSFWMD/cnm/au/augsourceDocumentation of the South Florida Water Management Model version 5.5/sourcepublisherSouth Florida Water Management District, West Palm Beach, FL/publisherpubdate2005a/pubdate/biblbibl id="B54"augaucnmSFWMD/cnm/au/augsourceRegional Simulation Model (RSM) Hydrologic Simulation Engine (HSE) user’s manual/sourcepublisherSouth Florida Water Management District, West Palm Beach, FL/publisherpubdate2005/pubdate/biblbibl id="B55"augaucnmSFWMD/cnm/au/augsourceRegional Simulation Model (RSM) theory manual/sourcepublisherSouth Florida Water Management District, West Palm Beach, FL/publisherpubdate2005/pubdate/biblbibl id="B56"augaucnmSFWMD/cnm/au/augsourceRSM water quality user manual (draft)/sourcepublisherSouth Florida Water Management District, West Palm Beach, FL/publisherpubdate2008/pubdate/biblbibl id="B57"augaucnmSFWMD/cnm/au/augsourceRSMWQE theory manual (draft)/sourcepublisherSouth Florida Water Management District, West Palm Beach, FL/publisherpubdate2008/pubdate/biblbibl id="B58"augaucnmSFWMD/cnm/au/augsourceWCA2A HSE setup/sourcepublisherSouth Florida Water Management District, West Palm Beach, FL/publisherpubdate2008/pubdate/biblbibl id="B59"augaucnmSFWMD/cnm/au/augsourceDBHYDRO/sourcepubdate2009/pubdatenoteurlhttp:my.sfwmd.govdbhydroplsqlshow_dbkey_info.main_menu/url. Accessed 04 August 2010/note/biblbibl id="B60"augausnmStroustrup/snmfnmB/fnm/au/augsourceThe C++ programming language/sourcepublisherAddison-Wesley, Westford, MA/publishereditionspecial/editionpubdate2000/pubdate/biblbibl id="B61"augausnmTarboton/snmfnmKC/fnm/auausnmIrizarry-Ortiz/snmfnmMM/fnm/auausnmLoucks/snmfnmDP/fnm/auausnmDavis/snmfnmSM/fnm/auausnmObeysekera/snmfnmJT/fnm/au/augsourceHabitat suitability indices for evaluating water management alternatives/sourcepublisherSouth Florida Water Management District, West Palm Beach, FL/publisherpubdate2004/pubdate/biblbibl id="B62"titlepFluctuations in sawgrass and cattail densities in Everglades Water Conservation Area 2A under varying nutrient, hydrologic, and fire regimes/p/titleaugausnmUrban/snmfnmNH/fnm/auausnmDavis/snmfnmSM/fnm/auausnmAumen/snmfnmNG/fnm/au/augsourceAquat Bot/sourcepubdate1993/pubdatevolume46/volumefpage203/fpagelpage223/lpagexrefbibpubid idtype="doi"10.10160304-3770(93)90002-E/pubid/xrefbib/biblbibl id="B63"augaucnmUSACE, S.F.R.O/cnm/au/augsourceCERP: The plan in depth part 1/sourcepubdate2010a/pubdatenoteurlhttp:www.evergladesplan.orgaboutrest_plan_pt_01.aspx/url. Accessed 3 August 2010/note/biblbibl id="B64"augaucnmUSACE, S.F.R.O/cnm/au/augsourceCERP: The plan in depth part 2/sourcepubdate2010b/pubdatenoteurlhttp:www.evergladesplan.orgaboutrest_plan_pt_02.aspx/url. Accessed 3 August 2010/note/biblbibl id="B65"titlepSeed bank composition along a phosphorus gradient in the northern Florida Everglades/p/titleaugausnmvan der Valk/snmfnmAG/fnm/auausnmRosburg/snmfnmTR/fnm/au/augsourceWetlands/sourcepubdate1997/pubdatevolume17/volumeissue2/issuefpage228/fpagelpage236/lpagexrefbibpubid idtype="doi"10.1007BF03161411/pubid/xrefbib/biblbibl id="B66"augausnmWalker/snmfnmWW/fnm/auausnmKadlec/snmfnmRH/fnm/au/augsourceA model for simulating phosphorus concentrations in waters and soils downstream of Everglades stormwater treatment areas. Draft/sourcepublisherUS Department of the Interior Everglades National Park, Homestead, FL/publisherpubdate1996/pubdatenote
urlhttp:publicfiles.dep.state.fl.usDEARGoldAdministrativeRecordItem%2027018752.PDF/url
/note/biblbibl id="B67"augausnmWang/snmfnmN/fnm/au/augsource2003 Vegetation map; dss hydrology input files. Personal communication/sourcepublisherSouth Florida Water Management District, West Palm Beach, FL/publisherpubdate2009/pubdatexrefbibpubidlistpubid idtype="pmcid"2829916/pubidpubid idtype="pmpid" link="fulltext"20207880/pubid/pubidlist/xrefbib/biblbibl id="B68"augausnmWang/snmfnmJD/fnm/auausnmSwain/snmfnmED/fnm/auausnmWolfert/snmfnmMA/fnm/auausnmLangevin/snmfnmCD/fnm/auausnmJames/snmfnmDE/fnm/auausnmTelis/snmfnmPA/fnm/au/augsourceApplication of FTLOADDS to simulate flow, salinity, and surface-water stage in the southern Everglades, Florida. Scientific Investigations Report 2007–2010/sourcepublisherUnited States Geological Survey, Florida/publisherpubdate2007/pubdate/biblbibl id="B69"augausnmWetzel/snmfnmPR/fnm/au/augsourcePlant community parameter estimates and documentation for the Across Trophic Level System Simulation (ATLSS)/sourcepublisherEast Tennessee State University, Johnson City/publisherpubdate2001/pubdate/biblbibl id="B70"augausnmWetzel/snmfnmPR/fnm/au/augsourceNutrient and fire disturbance and model evaluation documentation for the Actoss Trophic level System Simulation (ATLSS)/sourcepublisherEast Tennessee State University, Johnson City/publisherpubdate2003/pubdate/biblbibl id="B71"augausnmWillard/snmfnmDA/fnm/au/augsourceSOFIA FS-146-96/sourcepubdate2010/pubdatenoteurlhttp:sofia.usgs.govpublicationsfs146-96/url. Accessed 3 August 2010/note/biblbibl id="B72"titlepAnalysis and simulation of fragmentation patterns in the Everglades/p/titleaugausnmWu/snmfnmY/fnm/auausnmSklar/snmfnmFH/fnm/auausnmRutchey/snmfnmK/fnm/au/augsourceEcol Appl/sourcepubdate1997/pubdatevolume7/volumeissue1/issuefpage268/fpagelpage276/lpagexrefbibpubid idtype="doi"10.18901051-0761(1997)007[0268:AASOFP]2.0.CO;2/pubid/xrefbib/biblbibl id="B73"augausnmZajac/snmfnmZB/fnm/au/augsourceGlobal sensitivity and uncertainty analysis of spatially distributed watershed models. PhD Dissertation/sourcepublisherUniversity of Florida, Gainesville/publisherpubdate2010/pubdate/bibl/refgrp
/bm
/art


xml version 1.0 encoding UTF-8
REPORT xmlns http:www.fcla.edudlsmddaitss xmlns:xsi http:www.w3.org2001XMLSchema-instance xsi:schemaLocation http:www.fcla.edudlsmddaitssdaitssReport.xsd
INGEST IEID E5067APYR_0KR059 INGEST_TIME 2013-03-05T20:20:57Z PACKAGE AA00013656_00001
AGREEMENT_INFO ACCOUNT UF PROJECT UFDC
FILES


xml version 1.0 encoding utf-8 standalone no
mets ID sort-mets_mets OBJID sword-mets LABEL DSpace SWORD Item PROFILE METS SIP Profile xmlns http:www.loc.govMETS
xmlns:xlink http:www.w3.org1999xlink xmlns:xsi http:www.w3.org2001XMLSchema-instance
xsi:schemaLocation http:www.loc.govstandardsmetsmets.xsd
metsHdr CREATEDATE 2013-01-03T16:07:51
agent ROLE CUSTODIAN TYPE ORGANIZATION
name BioMed Central
dmdSec sword-mets-dmd-1 GROUPID sword-mets-dmd-1_group-1
mdWrap SWAP Metadata MDTYPE OTHER OTHERMDTYPE EPDCX MIMETYPE textxml
xmlData
epdcx:descriptionSet xmlns:epdcx http:purl.orgeprintepdcx2006-11-16 xmlns:MIOJAVI
http:purl.orgeprintepdcxxsd2006-11-16epdcx.xsd
epdcx:description epdcx:resourceId sword-mets-epdcx-1
epdcx:statement epdcx:propertyURI http:purl.orgdcelements1.1type epdcx:valueURI http:purl.orgeprintentityTypeScholarlyWork
http:purl.orgdcelements1.1title
epdcx:valueString A spatially distributed, deterministic approach to modeling Typha domingensis (cattail) in an Everglades wetland
http:purl.orgdctermsabstract
Abstract
Introduction
The emergent wetland species Typha domingensis (cattail) is a native Florida Everglades monocotyledonous macrophyte. It has become invasive due to anthropogenic disturbances and is out-competing other vegetation in the region, especially in areas historically dominated by Cladium jamaicense (sawgrass). There is a need for a quantitative, deterministic model in order to accurately simulate the regional-scale cattail dynamics in the Everglades.
Methods
The Regional Simulation Model (RSM), combined with the Transport and Reaction Simulation Engine (TARSE), was adapted to simulate ecology. This provides a framework for user-defineable equations and relationships and enables multiple theories with different levels of complexity to be tested simultaneously. Five models, or levels, of increasing complexity were used to simulate cattail dynamics across Water Conservation Area 2A (WCA2A), which is located just south of Lake Okeechobee, in Florida, USA. These levels of complexity were formulated to correspond with five hypotheses regarding the growth and spread of cattail. The first level of complexity assumed a logistic growth pattern to test whether cattail growth is density dependent. The second level of complexity built on the first and included a Habitat Suitability Index (HSI) factor influenced by water depth to test whether this might be an important factor for cattail expansion. The third level of complexity built on the second and included an HSI factor influenced by soil phosphorus concentration to test whether this is a contributing factor for cattail expansion. The fourth level of complexity built on the third and included an HSI factor influenced by (a level 1–simulated) sawgrass density to determine whether sawgrass density impacted the rate of cattail expansion. The fifth level of complexity built on the fourth and included a feedback mechanism whereby the cattail densities influenced the sawgrass densities to determine the impact of inter-species interactions on the cattail dynamics.
Results
All the simulation results from the different levels of complexity were compared to observed data for the years 1995 and 2003. Their performance was analyzed using a number of different statistics that each represent a different perspective on the ecological dynamics of the system. These statistics include box-plots, abundance-area curves, Moran’s I, and classified difference. The statistics were summarized using the Nash-Sutcliffe coefficient. The results from all of these comparisons indicate that the more complex level 4 and level 5 models were able to simulate the observed data with a reasonable degree of accuracy.
Conclusions
A user-defineable, quantitative, deterministic modeling framework was introduced and tested against various hypotheses. It was determined that the more complex models (levels 4 and 5) were able to adequately simulate the observed patterns of cattail densities within the WCA2A region. These models require testing for uncertainty and sensitivity of their various parameters in order to better understand them but could eventually be used to provide insight for management decisions concerning the WCA2A region and the Everglades in general.
http:purl.orgdcelements1.1creator
Lagerwall, Gareth
Kiker, Gregory
Muñoz-Carpena, Rafael
Convertino, Matteo
James, Andrew
Wang, Naiming
http:purl.orgeprinttermsisExpressedAs epdcx:valueRef sword-mets-expr-1
http:purl.orgeprintentityTypeExpression
http:purl.orgdcelements1.1language epdcx:vesURI http:purl.orgdctermsRFC3066
en
http:purl.orgeprinttermsType
http:purl.orgeprinttypeJournalArticle
http:purl.orgdctermsavailable
epdcx:sesURI http:purl.orgdctermsW3CDTF 2012-11-01
http:purl.orgdcelements1.1publisher
Springer
http:purl.orgeprinttermsstatus http:purl.orgeprinttermsStatus
http:purl.orgeprintstatusPeerReviewed
http:purl.orgeprinttermscopyrightHolder
Gareth Lagerwall et al.; licensee BioMed Central Ltd.
http:purl.orgdctermslicense
http://creativecommons.org/licenses/by/2.0
http:purl.orgdctermsaccessRights http:purl.orgeprinttermsAccessRights
http:purl.orgeprintaccessRightsOpenAccess
http:purl.orgeprinttermsbibliographicCitation
Ecological Processes. 2012 Nov 01;1(1):10
http:purl.orgdcelements1.1identifier
http:purl.orgdctermsURI http://dx.doi.org/10.1186/2192-1709-1-10
fileSec
fileGrp sword-mets-fgrp-1 USE CONTENT
file sword-mets-fgid-0 sword-mets-file-1
FLocat LOCTYPE URL xlink:href 2192-1709-1-10.xml
sword-mets-fgid-1 sword-mets-file-2 applicationpdf
2192-1709-1-10.pdf
structMap sword-mets-struct-1 structure LOGICAL
div sword-mets-div-1 DMDID Object
sword-mets-div-2 File
fptr FILEID
sword-mets-div-3



PAGE 1

RESEARCHOpenAccessAspatiallydistributed,deterministicapproach tomodeling Typhadomingensis (cattail)inan EvergladeswetlandGarethLagerwall1,GregoryKiker1*,RafaelMuoz-Carpena1,MatteoConvertino1,AndrewJames2andNaimingWang3AbstractIntroduction: Theemergentwetlandspecies Typhadomingensis (cattail)isanativeFloridaEverglades monocotyledonousmacrophyte.Ithasbecomeinvasiveduetoanthropogenicdisturbancesandisout-competing othervegetationintheregion,especiallyinareashistoricallydominatedby Cladiumjamaicense (sawgrass).Thereis aneedforaquantitative,deterministicmodelinordertoaccuratelysimulatetheregional-scalecattaildynamicsin theEverglades. Methods: TheRegionalSimulationModel(RSM),combinedwiththeTransportandReactionSimulationEngine (TARSE),wasadaptedtosimulateecology.Thisprovidesaframeworkforuser-defineableequationsand relationshipsandenablesmultipletheorieswithdifferentlevelsofcomplexitytobetestedsimultaneously.Five models,orlevels,ofincreasingcomplexitywereusedtosimulatecattaildynamicsacrossWaterConservationArea 2A(WCA2A),whichislocatedjustsouthofLakeOkeechobee,inFlorida,USA.Theselevelsofcomplexitywere formulatedtocorrespondwithfivehypothesesregardingthegrowthandspreadofcattail.Thefirstlevelof complexityassumedalogisticgrowthpatterntotestwhethercattailgrowthisdensitydependent.Thesecond levelofcomplexitybuiltonthefirstandincludedaHabitatSuitabilityIndex(HSI)factorinfluencedbywaterdepth totestwhetherthismightbeanimportantfactorforcattailexpansion.Thethirdlevelofcomplexitybuiltonthe secondandincludedanHSIfactorinfluencedbysoilphosphorusconcentrationtotestwhetherthisisa contributingfactorforcattailexpansion.ThefourthlevelofcomplexitybuiltonthethirdandincludedanHSIfactor influencedby(alevel1 – simulated)sawgrassdensitytodeterminewhethersawgrassdensityimpactedtherateof cattailexpansion.Thefifthlevelofcomplexitybuiltonthefourthandincludedafeedbackmechanismwherebythe cattaildensitiesinfluencedthesawgrassdensitiestodeterminetheimpactofinter-speciesinteractionsonthe cattaildynamics. Results: Allthesimulationresultsfromthedifferentlevelsofcomplexitywerecomparedtoobserveddataforthe years1995and2003.Theirperformancewasanalyzedusinganumberofdifferentstatisticsthateachrepresenta differentperspectiveontheecologicaldynamicsofthesystem.Thesestatisticsincludebox-plots,abundance-area curves,Moran ’ s I ,andclassifieddifference.ThestatisticsweresummarizedusingtheNash-Sutcliffecoefficient.The resultsfromallofthesecomparisonsindicatethatthemorecomplexlevel4andlevel5modelswereableto simulatetheobserveddatawithareasonabledegreeofaccuracy.(Continuedonnextpage) *Correspondence: gkiker@ufl.edu1FrazierRogersHall,UniversityofFlorida,POBox110570,Gainesville,FL 32611-0570,USA Fulllistofauthorinformationisavailableattheendofthearticle 2012Lagerwalletal.;licenseeSpringer.ThisisanOpenAccessarticledistributedunderthetermsoftheCreativeCommons AttributionLicense(http://creativecommons.org/licenses/by/2.0),whichpermitsunrestricteduse,distribution,andreproduction inanymedium,providedtheoriginalworkisproperlycited.Lagerwall etal.EcologicalProcesses 2012, 1 :10 http://www.ecologicalprocesses.com/content/1/1/10

PAGE 2

(Continuedfrompreviouspage)Conclusions: Auser-defineable,quantitative,deterministicmodelingframeworkwasintroducedandtestedagainst varioushypotheses.Itwasdeterminedthatthemorecomplexmodels(levels4and5)wereabletoadequately simulatetheobservedpatternsofcattaildensitieswithintheWCA2Aregion.Thesemodelsrequiretestingfor uncertaintyandsensitivityoftheirvariousparametersinordertobetterunderstandthembutcouldeventuallybe usedtoprovideinsightformanagementdecisionsconcerningtheWCA2AregionandtheEvergladesingeneral. Keywords: Typha,Modeling,Ecology,Dynamics,Modelcomplexity,Waterconservationarea2A,Transportand reactionsimulationengine,RegionalsimulationmodelIntroductionTheEverglades,commonlyknownasthe “ RiverOf Grass ” Douglas(1947),insouthernFlorida,USA,once coveredsome28,500km2.Thiswetlandecosystemwas sustainedbytheKissimmeeRiver,flowingthroughLake Okeechobeeandsouthwardsasashallow,slow-moving sheetofwaterflowingfreelytotheestuariesofBiscayne Bay,TenThousandIslands,andFloridaBay.ThechannelizationoftheEvergladesaround1948causedthereductionoftheoriginalwetlandareasbyupto50%,with relateddeclinesindependentwildlife.Inadditiontothe changesinhydrology,continuousmining,agriculture, andurbanizationactivitieshaveresultedininvasiveand exoticplantsbecomingestablishedinplaceoftheoriginalvegetation,alteringhabitatsandoftenforming mono-cropstands(singlespeciesenvironments)(Odum etal.2000). TheComprehensiveEvergladesRestorationPlan(CERP) wasimplementedin2000(USACE,S.F.R.O2010a)with theexplicitgoalofrestoringsomeoftheEverglades ’ former extentandecosystemfunctioning.Themainfocusof CERPhasbeenonimprovedmanagementofwaterquantityandwaterqualitywiththeassumptionthatifthewater quantityandqualityareadequate,theecologywillfollow suit.Thereis,however,anincreasingfocusontheecologicalimpactsofvariousmanagementdecisions,and theseeffortscenteronimprovingspeciesdiversityandprotectingexistinghabitats(USACE,S.F.R.O2010b).Inan efforttoachievethesegoals,stormwatertreatmentareas (STA)wereconstructedjustsouthoftheEvergladesagriculturalarea(EAA)tofilteroutphosphorusfromthe waterbeforereleasingitintothewaterconservationareas (WCA).TheWCAsactasimpoundmentsforwater storageandfloodcontrolaswellasservingaswildlifehabitat.WaterflowsfromtheseWCAsintotheEverglades NationalPark(Guardoetal.1995).Typhadomingensis asaninvasivespeciesTheemergentwetlandspecies Typhadomingensis (cattail) isanativeEvergladesmonocotyledonousmacrophyte, typicallyoccurringasasparsecomplementalongside Cladiumjamaicense (sawgrass)stands.Thesetwospecies havesignificantlydifferentmorphology,growth,andlife historycharacteristics(MiaoandSklar1998),andthishas enabledthecattailtoexpandprolificallyunderthealtered conditionsintheEverglades.Inthe1980s,thearea coveredbycattailstandsinWCA2Adoubled,expanding southwardintothesawgrassmarshes(Willard2010). Cattailhashencebeenlabeledasanindicatorspecies,or speciesofconcern,anditsdistributionisusedtodeterminetheeffectivenessofvariouswatermanagementdecisions.Cattailexpansionhasbeenstudiedextensively (Miao2004;Wuetal.1997;Newmanetal.1998),andit hasbeendeterminedthattherearefourmainexternalfactorsthataffectitsgrowthandaidincattail ’ sdominance oversawgrass.Thesefactorsincludewaterdepth,hydroperiod,soilphosphorusconcentration,anddisturbance (Newmanetal.1998).Itwasdeterminedthatthe optimumwaterdepthatwhichcattailgrowsisbetween 24and95cm(Grace1989),withahydroperiodof180 – 280days(Wetzel2001).Intermsofsoilphosphorus concentration,cattailhasbeenfoundtobeinvadingthe naturalsawgrasshabitatsofWCA2Aalongasoilphosphorusgradientrunningfromthenorthwest(highconcentrations)tothesoutheast(lowconcentrations).Urban etal.(1993)mentionthat,givenanadequatewaterdepth, soilphosphorusconcentrationisthenextmostimportant factorindeterminingcattailexpansion/invasion.IncreatingtheirwaterqualitymodelforsimulatingsoilphosphorusconcentrationsdownstreamoftheEverglades STAs,WalkerandKadlec(1996)determinedthatthe lowerboundsoilphosphorusconcentrationforthe optimumgrowthofcattailwas540mg/kg.Firesandother disturbancessuchashurricaneswerealsofoundtoaffect thecolonizationofareasbycattailbyalteringlocaltopographyandnutrientconcentrations(Newmanetal.1998).EcologicalmodeldesignstoaddressevergladessystemsInordertoassessthesevariousinfluencesoncattailand otherecologicalcomponents,avarietyofcomputation modelsweredesignedandimplemented.Thesemodels aidourunderstandingofcomplexsystemsandallow scientistsandmanagerstoevaluatedifferentecological outcomesofdecisionsbeforethemorecostlytaskoftheir implementation(Fitzetal.2011).Toensurenumerical efficiency,mostspatiallydistributedmodelshavetheirLagerwall etal.EcologicalProcesses 2012, 1 :10 Page2of21 http://www.ecologicalprocesses.com/content/1/1/10

PAGE 3

equations,laws,andassumptions “ hard-coded ” intotheir programmingcode.Thiscreatesa “ fixed-form ” model, withchangesinthefunctioningcomingthroughextensive codere-writesandcarefulredesignaroundlogicalstructures.Dynamic “ free-form ” simulationmodels,suchas STELLA(CostanzaandVoinov2001),QnD(Kikerand Linkov2006;Kikeretal.2006),andtheKeplersystem (Ludascheretal.2006)aregenerallywrittenusingan object-orientedprogramming(OOP)languagesuchas C++(Stroustrup2000)orJava(ArnoldandGosling1998), asopposedtoalinearlanguagesuchasFORTRAN(Cary etal.1998).Wheninteractingwithfree-formmodelsand theiralgorithms,designersdonotinteractdirectlywiththe programcode.Rather,theyinfluenceobjectsthrough placingdata,storage,andlogicalstructuresintoeithera graphicaluserinterface(STELLA,Kepler)orwithina meta-codestructuresuchastheeXtensibleMarkup Language(XML)(Harold1998). Thereareanumberoffixed-formecologicalmodels currentlyinuseacrosstheEvergladesregion.Ofthese, theAcrossTrophicLevelSystemSimulation(ATLSS) (Gross1996)andtheEvergladesLandscapeModel (ELM)(FitzandTrimble2006b)areprobablythemost well-known.Theseandmostothermodelsavailablefor modelingcattailintheEvergladesareentirelyqualitative,thatis,theyinvolveswitchingbetweenonespecies andanother.Themajorityofthesecurrentecological modelsarealsostochastic,thatis,basedonprobabilities andadegreeofrandomnessanduncertainty.Theygenerallyrunaspost-processmodels,usinghydrological dataoutputbyothermodelssuchastheSouthFlorida WaterManagementModel(SFWMM)(Fitzetal.2011). TheATLSSvegetationsuccessionmodelisusedtodeterminethesuccessionofonehabitattypetoanother (e.g.,sawgrasstocattail).TheATLSSmodelsimulateswith anannualtimesteponsquare500mcellsandusesastochasticcellularautomatamodeltoswitchbetweenvegetationtypes.Currentlythereisnowaytodeterminevegetation densitieswithinvegetationtypes(Duke-Sylvester2005). TheELMmodelusesacountertoswitchbetweenspeciesbyaccumulatingdaysofwaterlevelandsoilphosphorusconcentrationabovecertainlimits.Themodelthen switchesbetweenspeciesbasedontheirpreferredhydroperiodandhistoricalsoilphosphorusconcentrations(Fitz andTrimble2006a).TheELMmodelistheonlycurrently availablesimulationtoolforeva luatingwaterqu alityacross theEvergladeslandscapeand doesnotsimulatedetailed ecologicalfeatures(Fitzetal.2011). AnothermodelingeffortbyWuetal.(1997)used Markovchainprobabilitiestoswitchbetween Cladium and Typha species.Thismodelwasinfactusedtoinformthe ATLSSnutrientandfiredisturbancemodel(Wetzel2003). Again,thisisastochastic,species-specific,presence/absence-typemodel. AmodelingeffortbyTarbotonetal.(2004)developed asetofhabitatsuitabilityindices(HSI)forevaluating watermanagementalternatives.TheseHSIsprovideda rangeofprobabilitiesforaparticularspeciesoccurring acrossthelandscapeandwerebasedpredominantlyon localhydrologicalconditionssuchasdepth(maximum, minimum,andmean),hydroperiod,velocity,andflow direction. Giventhatwaterquantity(depth)andquality(soil phosphorusconcentration)affectcattail(andother plants)growthanddistribution,thereisaneedtointegratethesecomponentstodeterminethemoredetailed biologicaloutcomesofanEvergladesecologicalmodel. Thereisalsoaneedforaquantitativemodeltoprovide continuousdensityvaluesforspecificvegetationrather thansimplypresence/absenceinformation.Giventhat theEvergladesrestorationincludesalargeandongoing researcheffort,thereisaneedtoefficientlytestand explorepotentiallyusefulalgorithmsinanadaptable, ecologicalmodelingengine.TheRSM/TARSEecologicalmodelAcombinedeffortoftheUniversityofFlorida,theSouth FloridaWaterManagementDistrict(SFWMD),andthe USGeologicalSurveycreatedtheTransportandReactionSimulationEngine(TARSE)(Jawitzetal.2008), whichwasoriginallydesignedtoruninlinewiththe SFWMD-developedRegionalSimulationModel(RSM) (SFWMD2005c)tosimulatesoilphosphorusdynamics intheEvergladessystem.TheOOPstructureofthis coupledhydrologic/waterqualitymodel,alongwiththe user-definableinputsandinteractions,allowedforthe extensionofthismodelbeyonditsoriginalpurposeinto ecologicalprocessesandfeatures.ThecoupledRSM/ TARSE(henceforthreferredtoasRTE)model,implementedwiththegoalofmodelingecologicalfeatures withinthesouthernFloridalandscapeandpresentedin thispaper,isaspatiallydistributed,free-formmodelsimulatingcattailbiomassdistributionanddynamicsacross WCA2A.UsingtheRTEmodeltocouplevegetation dynamicswithphosphorusdynamicshasbeenalludedto byJawitzetal.(2008),Muller(2010),andPerez-Ovilla (2010)duringtheirrespectiveTARSE-influenced,WQ simulations.Zajac(2010)usedvegetationtypesto influenceManning ’ s n andevapotranspirationcoefficients. Theseparameterswereinformedbyinitialvegetation typesandnotbychangingvegetationdistributionand densityovertime. ThereisthereforeadefiniteneedfortheRTEmodel, whichallowsonetomodelavegetationspeciesquantitativelyandultimatelydeterminetheecologicalimpactof variousmanagementscenariosfallingundertheCERPinitiative.Thisnewenginewouldaccommodatedifferent algorithmsornewspeciesasavailabledataornewLagerwall etal.EcologicalProcesses 2012, 1 :10 Page3of21 http://www.ecologicalprocesses.com/content/1/1/10

PAGE 4

knowledgebecomesavailable.Itwouldallowforinteractionsandfeedbackeffectswithinspeciesaswellasamong differentspeciesandwithotherenvironmentalfactors.ObjectivesandhypothesesTheprimaryobjectiveofthispaperistotestandapplyanew spatiallydistributed,determinis tic,free-form(user-definable), quantitativeecologicalmodelofcattaildynamics.Asignificantadvantageofthisfree-f ormmodelingapproachisthat multipleecologicalalgorith msofdifferingcomplexitycan bequicklyimplementedandtestedsimultaneously,instead ofthroughtime-consumingcod eadditions.Asafirststep ofourobjective,wetestedtheinfluenceofincreasingcattail modelcomplexityonreducinguncertaintyinsimulated output(Lindenschmidt2006).Fivelevelsofincreasing complexitywereselectedtomodelthecattaildensities. Thesefivelevelsofcomplexitywerechosentocorrespond withvarioushypothesesreg ardingthegrowthandspread ofcattailintheEverglades,namely: 1.Whethercattailgrowthisdensitydependent. 2.Whetherwaterdepthisanimportantfactorfor cattailexpansion. 3.Whethersoilphosphorousisacontributingfactor forcattailexpansion. 4.Whethersawgrassdensityimpactstherateofcattail expansion. 5.Whetherinter-speciesinteractionsbetweencattailand sawgrasscontributetotheobservedcattaildynamics. FollowingthemethodologyusedbyJawitzetal. (2008),asimplelogisticfunction(KeenandSpain1992) formedthebaseofthecomplexitieswithwaterdepthand soilphosphorusconcentration[thetwomostimportant factorsinfluencingcattailgrowthaccordingtoNewman etal.(1998)]andsawgrassinteractioninfluencingthe higherlevelsofcomplexity.Asecondstepinourobjective wastouseanexistingecosystemanditsmonitoringdata toanalyzeperformanceofourfivecandidatemodels.The entireWCA2Avegetationdataset(1991,1995,and2003), obtainedfromRutcheyetal.(2008),waschronologically dividedintomodeltrainingandtestingsections.Training ofthemodelwasconductedfortheyears1991 – 1995, wherethegrowthfactor(foundinEquation3)wasfitted tothelevel1complexity.Asathirdstepinourobjective, modeltestingwasconductedonthetwotimeperiodsof 1991 – 2003(testing1)and1995 – 2003(testing2),respectively,withthetesting2timeperiodbeingequivalenttoa blindtest(duetodifferentinitialconditions).The1991 and1995vegetationmapswereusedtoinitializethe training,testing1,andtesting2simulations,respectively. Modeloutputfromthetraining,testing1,andtesting 2simulationswascomparedwiththe1995and2003 vegetationmaps.Modeloutputwascomparedto observedpatterns,andthemostaccuratelevelof complexitythusdetermined.MethodsInordertoreproducetheobservedcattailpatterns,both hydrologicalandwaterqualitydatawereusedasinputs fortheecologicalmodel.Tothisend,itwasdecidedto usetheRegionalSimulationModel(RSM),whichwas developedbytheSouthFloridaWaterManagementDistrict(SFWMD)toreplacethepopularSFWMM,coupled withtheTransportandReactionSimulationEngine (TARSE)toprovidethebasestructureformodeling cattaildynamicsacrossthetestsite.TheRegionalSimulationModel(RSM)DevelopedbySFWMD,theRSMsimulateshydrology overtheSouthFloridaregion.Itisoftenthoughtofasthe successortothesuccessfulSFWMM,referredtoasthe “ 2-by-2 ” modelforits2mileresolution(SFWMD2005a). TheRSMoperatesoveravariabletriangularmeshgrid,in contrasttothe3.22km(2mile)squaregridofthe SFWMM;thisenableshigherresolutioninareasofconcernaswellastheabilitytodelineatecanals(SFWMD 2005c).TheRSMusesaweighted,implicit,finitevolume methodtosimulatetwo-dimensionaldiffusionalflowand henceimplicitlysimulatesgroundwaterflowandsurface waterflow(SFWMD2005c).TheOOPdesignstructureof RSMallowsfortheabstractionandmodularityofvarious components(SFWMD2005b).Aresultofthisisthat therearetwoenginesthatcomprisetheRSM,namelythe HydrologicSimulationEngine(HSE)andtheManagementSimulationEngine(MSE).TheHSEsimulatesallthe hydrologicalprocesses,whiletheMSEsimulatesvarious managementorcontrolregimes.Thesetwoengines interactatruntimetoprovideanaccuraterepresentation ofthehydrodynamicsoftheregion(SFWMD2005c).SimulatingtransportandreactionsusingTARSETheTARSEwasrecentlydevelopedtosimulatewater quality(WQ)componentswithintheRSMmodelforareas intheEvergladessystem(Jawitzetal.2008).TheTARSE modelwasdesignedtobeasgenericaspossible,toallow multiplewaterqualitycomponentstobesimulatedwitha simplechangeintheinputfile.Itwasfirstimplementedas anotherenginetobeincorporatedwithintheRSMframework,alongwiththeHSEandMSE,calledtheWater QualityEngine(WQE).Duetoitsstructure,theWQE doesnotsimulatehydrologyandrequiresahydrologic drivertofeeditvaluesofflowanddepthateverytimestep (SFWMD2008b).TARSEhassincebeendecoupledfrom RSMandimplementedwithotherhydrologicdriverssuch asFlowandTransportinaLinkedOverland-Aquifer DensityDependentSystem(FTLOADDS)(Wangetal. 2007;Muller2010)andVFSMOD(Muoz-Carpenaetal.Lagerwall etal.EcologicalProcesses 2012, 1 :10 Page4of21 http://www.ecologicalprocesses.com/content/1/1/10

PAGE 5

1999;Perez-Ovilla2010).TARSEsolvestheadvectiondispersion-reactionequations(ADRE)overanunstructuredtriangularmesh(JamesandJawitz2007).TheADRE isrepresentedbyEquation1,andeverytermisafunction ofatwo-dimensionalspatialcoordinate x ,withcomponents( x1,x2),andtime, t d hc dt chu hD c hf2c hf1c1 1 Where t istime[T], c(x,t) istheconcentration[M/L3], and (x,t) istheporosityofthemedium(whichmaybe 1forsurfacewater)[L3/L3]. h(x,t) isthewaterdepth[L] orthicknessofthesaturatedzoneingroundwaterflow, u(x,t) isthespecificdischarge[L/T]ofwater(eithersurfaceorgroundwater),and D*=D*(u(x,t)) isthedispersion tensor(afunctionof u ). f1(x,t) isasourcerate[M/L3.T] withassociatedconcentration c1,and f2(x,t) isafirstorderdecayrate[M/L3.T].Thedensity[M/L3]ofthe waterisassumedtobeconstant. ThebasisofTARSEinvolvestransfers(e.g.,settling, diffusion,growth)betweenvariousstores,suchassoil watercolumnsolutes,porewatersolutes,macrophytes, andsuspendedsolids.Thespecificsofthesestores,and thetransfersamongthemareuser-definableintheXML inputfile(Jawitzetal.2008).TARSEequationsarecomposedofpre-equations,equations,andpost-equations. Pre-andpost-equationsareusedforimplementingconditional( “ if-then-else ” )statementsaspartofpre-and post-processingafterthemainprocessingintheequations.Forexample,pre-processingcouldbeusedtodetermineifthecurrentwaterdepth[m]isabovethe thresholdforcattailoptimumgrowthandthusreduce thedepthinfluencefactoraccordingly.Ifthedepthis lessthantheoptimumgrowingdepth,thentheinfluence factordecreasesaccordingly.Thelogicjustdescribedis representedbyEquation2,asdescribedbyGrace(1989), wherecattailoptimumdepthis70cm. Ifdepth > cattail optimum depth Then depthHSI 1 depth cattail optimum depth 109 Else depthHSI 1 cattail optimum depth depth 112 2 Themainequationsarestructuredasordinarydifferentialequations(ODE)(SFWMD2008a). TheRSM/TARSEcouplingrepresentspossiblythefirst timethatafree-formdynamicsystemmodelhasbeen integratedwithafixed-form,spatiallydistributed,hydrologicmodel(Muller2010).Thisuniquecoupling, withuser-definedinteractionsoperatingacrossa spatiallydistributeddomain,lendsitselftosimulating ecologicalbehaviors(growth,death,movement,and feeding)aswellastheoriginalWQinteractions.The modelcancurrentlyonlysolveADREmovementand assuchisinsufficientforecological/animalmovement.AttemptstoincludesomeformofLagrangiantypemovementinthismodelarediscussedby Lagerwall(2011).ModelapplicationInordertotesttheinfluenceofincreasingcomplexityon reducinguncertaintyinmodeloutput(Lindenschmidt 2006),fivelevelsofincreasingcomplexitywereselectedto modelthecattaildensities.Followingthemethodology usedbyJawitzetal.(2008),alogisticfunction(Keenand Spain1992)wasusedforthemostbasic,level1 complexity,duetoitsdensitydependentgrowthandrapid (exponential)earlystagesofgrowth.Thelogisticfunction isrepresentedinEquation3. dP dt GF P 1 P K 3 Where P isthepopulationdensity[M/L2], t istime [T], GF istheconstantgrowthrate[T-1],and K isthe carryingcapacityormaximumpopulationdensity[M/L2]. Level2isawater-depth-influencedlevel1complexity. Awaterdepthfactor(habitatsuitabilityindex)ranging from0to1ismultipliedbythecarryingcapacityinthe logisticfunction.Thedepthfactordecreaseslinearly from1asthecurrentdeptheitherrisesaboveordrops belowtheoptimum(70cm)growingdepth.Thisdepth factorcanbeseeninEquation4. dP dt GF P 1 P K DepthF 4 Where P isthepopulationdensity[M/L2], t istime [T], GF isaconstantgrowthrate[T-1], DepthF isthe waterdepthfactor[L/L], K isthecarryingcapacityor maximumpopulationdensity[M/L2]. Level3isasoil-phosphorus-influencedlevel2complexity,withthesoilphosphorusfactorbeingincorporatedinasimilarfashiontothedepthfactorandcanbe seeninEquation5. dP dt GF P 1 P K DepthF phosphorusF = 2 5 Where P isthepopulationdensity[M/L2], t is time[T], GF isaconstantgrowthrate[T-1], DepthF isthewaterdepthfactor[L/L], phosphorusF isthe soilphosphorusfactor[M/L3/M/L3],and K isthe carryingcapacityormaximumpopulationdensity [M/L2].Thesoilphosphorusfactorbehaveslikealogisticfunction,increasingfrom0to1assoilphosphorusconcentrationincreasesto1,800from200Lagerwall etal.EcologicalProcesses 2012, 1 :10 Page5of21 http://www.ecologicalprocesses.com/content/1/1/10

PAGE 6

mg/kg,asdescribedbyWal kerandKadlec(1996), andcanbeseeninEquation6. phosphorusF 1 e phosphorus 1034 144! 1 6 Where phosphorusF isthesoilphosphorusHSI,rangingfrom0to1,and phosphorus isthecurrentsoil phosphorusconcentration(mg/kg). Level4buildsonalevel3complexitywithanadded sawgrassinteractionfactor,muchlikethesoilphosphorusanddepthfactors.Itdecreaseslinearlyfrom1to 0.16assawgrassdensitiesincreaseto1,958from0g/m2(Dorenetal.1999),whichistheirreportedmaximum density(MiaoandSklar1998).Thesawgrassissetto growaccordingtoalevel1complexityasinEquation4, thusthelevel4complexityisrepresentedbyEquation7. dP dt GF P 1 P KDepthF phosphorusF sawgrassF = 3 7 Where P isthepopulationdensity[M/L2], t istime [T], GF isaconstantgrowthrate[T-1], DepthF isthe waterdepthfactor[L/L], phosphorusF isthesoilphosphorusfactor[M/L3/M/L3], sawgrassF isthesawgrass influencefactor[M/L2/M/L2],and K isthecarryingcapacityormaximumpopulationdensity[M/L2].ThesawgrassfactorvariesaccordingtoEquation8. sawgrassF 1 0 : 84 sawgrass = KSAW 8 Where sawgrassF isthesawgrassHSIrangingfrom0 to1, sawgrass isthecurrentsawgrassdensity,and KSAWisthesawgrasscarryingcapacity. Thelevel5complexityisthesameaslevel4,butwith adensity-dependentinfluenceonthelevel1sawgrass model,whichisrepresentedbyEquations9and10,respectively. dP dt GF P 1 P K cattailF 9 Where P isthepopulationdensity[M/L2], t istime [T], GF isaconstantgrowthrate[T-1], cattailF isthe cattailfactorrangingfrom0to1,and K isthecarrying capacityormaximumpopulationdensity[M/L2]. cattailF 1 0 : 84 cattail = KCAT 10 Where cattailF isthecattailHSIrangingfrom0to1, cattail isthecurrentcattaildensity,and KCATisthecattailcarryingcapacity. Thedepth,soilphosphorus,andsawgrassinteraction factorsareallcalculatedusingthepre-equations,similar tothatpresentedinEquation2.Thesefactorsarethen incorporatedintothemaingrowthequations,presented inEquations4,5,7and9representinglevelsofcomplexity2through5,respectively. InTARSE,componentsarelistedaseithermobileor stabile.Mobilecomponentsaremovedinthewater usingtheADREequations,whilethestabilecomponents donotmoveandonlyundergothereactionpartofthe ADRE.Giventhecomplexitiesassociatedwithsimulatingwind-borneorwater-bornetransportationofseeds andrhizomeexpansion — whichisanothermodeofexpansionnotedbyMiao(2004) — allmeshelementswere initialized(seeded)withcattail,withareasoriginallynot containingcattailbeingseededwiththeminimumvalue of10g(dryweight)/m2.Thisassumptionrepresentsthe presenceofaseedbank,providingcattailtheopportunitytocolonizeanareaassoonasconditionsbecomefavorable.Vegetationthenismodeledasastabile component,withnomeansfordispersal,orinanother wayweassume “ infinitedispersal. ” Thelatterassumptionissupportedbyveryhighvaluesofdispersalfor seedsintheEverglades,enhancedbythediffusedpresenceofbiotic(animals)andabiotic(water,wind)dispersalvectors(MiaoandSklar1998).Also,asaresultof thiscurrentinabilityformodeleddispersal,themaximuminfluencethattheaforementionedfactorssuchas phosphorusF,sawgrassF,andcattailFcanhavehasbeen limitedsothattheyreducethecattailpopulationto1% ofitsmaximumdensity.TestsiteThetestsiteusedforecologicalmodeldevelopmentand testingwastheWCA2A(Figure1).WCA2Aisa547 km2managedwetlandjustsouthofLakeOkeechobee, FL,andaccountsforabout6.5%ofthetotalareaofthe Everglades.Itcameintoexistencein1961withtheconstructionoftheL35-Bcanalandreceivesinflowfrom theStormwaterTreatmentAreas(STAs),beforedischargingintodownstreamwaterconservationareas,and eventuallyintotheEvergladesNationalPark(Urban etal.1993).AccordingtoRiveroetal.(2007b),theregionhasanaverageannualtemperatureof20C,and precipitationbetween1,175and1,550mm.TheelevationrangeinWCA2Aisbetween2.0and3.6mabove sealevel,whichgeneratesaslowsheetflowfromthe northwesttothesouthwestoftheregion.Thehydrology iscontrolledbytheSFWMDatanumberofinletand outletstructures(greensquaresinFigure1)alongthe surroundingcanals(bluelinesinFigure1).Thelandscapeiscomposedofdominantsawgrassmarshes,shrub andtreeislandcommunities,andinvasivecattailcommunities(vanderValkandRosburg1997).WCA2AhasLagerwall etal.EcologicalProcesses 2012, 1 :10 Page6of21 http://www.ecologicalprocesses.com/content/1/1/10

PAGE 7

beenusedextensivelyasaresearchsitebythe SFWMD,withextensivetrialandmonitoringprogramsforanumberofbiogeochemicalcomponents, especiallysoilphosphorusandvegetativestructure (Riveroetal.2007a).Thetriangularmeshgridused forsimulationisalsodisplayedinFigure1,withthe greenbordercellsusedforn umericalstabilityofthe hydrologicalRSMcomponent.Anoverviewofthe HSEsetupforWCA2A,whichprovidesthe hydrologicaloperatingconditions,canbefoundin SFWMD(2008c). Initialconditions,boundaryconditions,andtime seriesdata Cattailvegetationmaps(Figure2)areusedfortheinitial conditionsaswellasforcomparingmodeloutputwith measureddata.Hydrologicaltimeseriesareusedforinitial andboundaryconditionsalongthesurroundingcanals. Figure1 Testsite,WaterConservationArea2A(WCA2A),inthenorthernEverglades. Greensquaresrepresentinletandoutletcontrol structures;bluelinesrepresentcanalstructures.Trianglesrepresentthemeshusedforsimulation,withgreentrianglesrepresentingtheborder cellsusedinthecentraldifferencemethod.Theredsquaresfallonzonalelements209,244,and380,representingregionsoftypicallyhigh, medium,andlowcattaildensities,respectively. Lagerwall etal.EcologicalProcesses 2012, 1 :10 Page7of21 http://www.ecologicalprocesses.com/content/1/1/10

PAGE 8

Figure2 Formattingofcattailinputmaps. ( a )1991,( b )1995,( c )2003fromRutcheyetal.(2008).Rasterizedrawdataontheleft,overlaidwith theWCA2Atriangularmeshinthemiddle,andthefinaltriangularmeshcattailinputmapontheright. Lagerwall etal.EcologicalProcesses 2012, 1 :10 Page8of21 http://www.ecologicalprocesses.com/content/1/1/10

PAGE 9

UsingRSM,thehydrologicalboundaryconditionsareconvertedintodepthvaluesacrossthedomain,whicharethen usedasinputsinthelevel2complexityalgorithm.Soil phosphorusconcentrationmapsprovideinitialconditions andaninfluencefactorforthelevel3complexityalgorithm.Sawgrassvegetationmapsareusedasinitialconditionsforthelevel1complexitysawgrassmodel,which servesasaninfluencefactorforthelevel4andlevel5 complexitycattailalgorithms.Thefollowingsectionsprovideadditionaldetailonthesemodelinputs.HydrologicaltimeseriesThehydrologyofWCA2Aiscontrolledprimarilybythe operationofcontrolpointsalongtheS10andL35-B canals.Thehydrologydatawereobtainedfromthe SFWMD,whichusestheWCA2Asiteasatestsiteforthe RSM.Theaveragedepthfortheregionrangesfrom60to 90cm(SFWMD,2008c).Theinputdatasetconsistedofa dailytimeseriesofhydraulicheadvalues(m)attheinlet andoutletcontrolstructuresofWCA2A(representedby thegreensquaresinFigure1)fortheyears1979 – 2000 (Wang2009).Thetimeserieshavesincebeenupdatedto 2008forallcontrolstructuresusingdatacollectedfrom theDBHYDROwebsite(SFWMD2009).SoilphosphorusAgradientofsoilphosphorusexistsalongWCA2A,with ahighconcentrationneartheinletsatthenorth,anda lowconcentrationattheoutletsinthesouth.Thissoil phosphorusgradienthasbeenwidelydocumentedand studied(DeBusketal.1994;Grunwaldetal.2004,2008; Riveroetal.2007a,b;Grunwald2010).Giventheunavailabilityofspatialsoilphosphorusdatabeyondmapclassifications(Grunwald2010),soilphosphorusinputmaps werecreatedbyoverlayingtheWCA2Ameshonthe existingmapsobtainedfromGrunwaldetal.(2004,2008). Thesoilphosphorusmapof1990wasusedforthemodel trainingperiodof1991 – 1995,whilethesoilphosphorus mapof2003wasusedforboththetesting1(1991 – 2003) andtesting2(1995 – 2003)simulationperiods.Duetothe poorqualityofthesesoilphosphorusinputmapsandthe inabilityofTARSEtoadequatelysimulatephosphorusdynamicsintheWCA2Aregion(asitisstillindevelopment),thesoilphosphorusconcentrationitselfwasnot simulated,i.e.,thestaticsoilphosphorusconcentration providedbytheinputmapswasusedtoinformthemodel throughoutthesimulationperiod.CattailandsawgrassVegetationmapsforWCA2Awereobtainedfortheyears 1991,1995(Rutchey2011),and2003(Wang2009),which wereallusedinRutcheyetal.(2008).Thesemapsprovideddensity(g/m2)distributionsacrossthetestsitefor cattail.Thenegativecorrelationbetweensawgrassand cattailhasbeenreportedbyDorenetal.(1999)and Richardsonetal.(2008),andvariousothervegetation mapsofthearea,namely1991(Jensenetal.1995),1995 (SFWMD1995),1999(SFWMD1999),and2003(Wang 2009),confirmthisnegativecorrelation.Althoughsawgrassdensityisrelatedtomoreenvironmentalfactors thanonlycattaildensity(MiaoandSklar1998),asimple negativecorrelationwiththecattailmapswasusedin ordertoassigndensitiestothesawgrassmaps.Forexample,highsawgrassdensityvalues(1,600g/m2)were assignedtoregionswithtypicallylowcattaildensity values,andlowsawgrassdensityvalues(600g/m2)were assignedtoregionswithhighcattaildensityvalues. TheprogramArcMap(ESRIEnvironmentalSystems ResourceInstitute2010)wasusedtocreateauniform rastermapfromtheoriginalimageswhichhadaminimummappingunitof50m2(Rutcheyetal.2008).The vegetationclassvalueswereconvertedtodensityvalues accordingtoTable1,withvegetationclass4(other)relatingtotheabsoluteminimum(residual)cattaildensity, representingtheseedbank.Theinputfilewascreated byoverlayingthemeshgridof385triangles(510trianglestotal — whichincludesarowoftrianglesalongthe border)ontherasterizedvegetationmapandcalculating themeanvalueofallrastercelldensityvalueswithin eachtriangularelement.Thisnewaggregatedmapwas usedtocreatetheinputfile.Agraphicaloverviewofthis processforthedatamapscanbeseeninFigure2. ThefinalsawgrassmapsareviewableinFigure3.The maximumdensitiesof1,240g/m2forcattailand1,958g/m2forsawgrasswerereportedbyMiaoandSklar(1998).An overviewoftheparameterdescriptionsfortheincreasing levelsofcomplexitycanbefoundinTable2.StatisticalanalysisofsimulatedandmonitoredbiomassBesidesaside-by-sidevisualcomparisonofthemodel output,therewerethreesetsofstatisticalanalysistechniquesthatwereusedtocomparethemodelresultsand therawdata.Thesemetrics,commonlyusedinliteratureforcomparingbothsingle-andmulti-speciespatterns(FortinandDale2005;Muneepeerakuletal.2008; Convertinoetal.2009),analyzedthelocal,global,and autocorrelationstructureofobservedandmodeledvegetationpatterns.Allmetricswereaccompaniedbya Table1Cattailclassanddensityvaluesforformatting datamapsVegetationclassCattaildensity value(g/m2) Sawgrassdensity value(g/m2) 1-Highdensitycattail1,00010 2-Mediumdensitycattail600600 3-Lowdensitycattail2001,000 4-Other101,600 Lagerwall etal.EcologicalProcesses 2012, 1 :10 Page9of21 http://www.ecologicalprocesses.com/content/1/1/10

PAGE 10

Nash-Sutcliffecoefficient(McCuenetal.2006),representedbyEquation11,whichprovidesasingularnumberforthecomparisonofthemodelstatisticsandhow theycomparetotheobserveddata.Thecoefficientisa comparisonofmodelresultsvwiththemeanofthedata. E f 1 X n i 0 y i y ˆ 2 X n i 0 y i y 2 11 Where E f istheNash-Sutcliffecoefficient, ^ y isthepredictedvariable, y i istheobservedvariable, y isthemean oftheobservedvariable,and n isthesamplesize.A Nash-Sutcliffevalueof1meansthatthemodelcompletelymatchesthedata,whileavalueof0means thatthemodelperformsnobetterthanthemeanof thedata.Anyvaluelessthan0isinterpretedasa poorrepresentationofthedata. Adirectcomparisonbetweenmodeloutputandthe datawasperformedwiththeuseofaclassifieddifference technique(Kiker1998).Sincethedatamapswereinitializedwithaminimumdensityof10g/m 2 toaccountfor movementbetweentriangularelementsthatisnotsimulatedinthismodelapplication,adifferencebetween modeloutputandthedatavaluefallingwithin20g/m 2 wasconsidereda “ perfect ” match.Thisislooselybasedon thefactthatMiaoandSklar(1998)reportedaroughly 10%errorinmeasurementofthemaximumdensityof 1,240g/m 2 .So,forexample,ifthedatavaluewas10g/m 2 (representingatypicalnon-cattailregion),andthemodel outputwas12g/m 2 ,withadifferenceof2g/m 2 (falling withinthe20g/m 2 range),thenthiswouldbeconsidered a “ perfect ” match.Thenextclassofdifferenceslieswithin the200g/m 2 range,whichisthevalueassignedtothelow cattaildensityclassduringtheformattingandcreationof theinputdatamaps.This200g/m 2 rangeisalsohalfthe rangebetweenthesuccessivelyhighercattaildensity classes.Thethirdclassofdifferenceslieswithin400g/m 2 whichcanbethoughtofasadataclassdifference(e.g.,betweenlowandmediumdensities)oralsoasbeingwithin 40%ofthemaximumpossibledifference(themaximum datadensityissetas1,000g/m 2 ).Finally,anydifference abovethe400g/m 2 thresholdisplacedinthefourthclass ofdifferencesandrepresentsasignificantmisrepresentationofthedatabythemodel. Aboxandwhiskersplot(OttandLongnecker2004) wascreatedwithallmodelelementvaluescompared withtheircorrespondingdataelementvalues.The desiredfigureisaplotwiththemeansandranges Figure3 Sawgrassinputmapsfortheyears1991,1995,and2003,respectively. Table2Parameterdescriptionfortheincreasinglevelsofcomplexitystudied ParameterParameterdescriptionLevels influenced AffectedvariablesParameter equation/logic CattailCattaildensity1,2,3,4,5CattailPopulationdensity CATGFCattailgrowthrate1,2,3,4,5CattailRateofincreaseofpopulation DepthFWaterdepthinfluence2,3,4,5Cattailcarryingcapacity,CattailEquation 2 phosphorusFSoilphosphorusconcentrationinfluence3,4,5Cattailcarryingcapacity,cattailEquation 6 SawgrassSawgrassdensity4,5Sawgrass,cattailcarryingcapacity,cattailPopulationdensity SAWGFSawgrassgrowthrate4,5SawgrassRateofincreaseofpopulation Lagerwall etal.EcologicalProcesses 2012, 1 :10 Page10of21 http://www.ecologicalprocesses.com/content/1/1/10

PAGE 11

correspondingtotheassociateddataranges.Thebox andwhiskersplotscovertheentirerangeofpossible valuesfrom0to1,240g/m 2 Moran ’ s I statistic(CliffandOrd1970;Paradis2010) wasusedtodeterminethespatialautocorrelationbetweencellsseparatedbyanincreasingdistance.Moran ’ s I isrepresentedbyEquation12. I X n i 1 X n j 1 x i x x j x W X n i 1 x i x 2 12 Where x i isthecurrentcellvalue, x j isthevalueofthe cellseparatedbyagivendistance, x (bar)isthemean, and W isthenumberofcellssurroundingthecurrent oneandfoundwithinthegivendistance.Thesevalues areplottedagainstanincreasingcell-pairwisedistance, asinMaranietal.(2006),todeterminethetrendin spatialautocorrelationacrosstheentireregion. Alandscape-scaleabundance-areaplot(Martin1980; MichalskiandPeres2007)wasusedtomeasurethe averagechangeindensityacrossthetestsite.Onehundredrandomlydistributedcellsareusedasbasecells. Fromthese,thedensitiesofallcellsfallingwithina givenradiusaresummed.Thistotalisthendividedby thenumberofbasecellsandplottedagainsttheareaof circleswithanincreasingradiusasinMartin(1980). Atrendintheregionalmeandensitywasplottedwith adailytimestepforavisualcomparisonofthetrendsbetweenthedifferentlevelsofcomplexity.Thiswas repeatedfortheindividuallevelsofcomplexityand selectedzones(elements)withintheregion,foramore detailedviewoftheeffectofexternalparametersondifferentareasoftheregion.Elements209,244,and380, Figure4 Resultsfor(a)training(1991 – 1995),(b)testing1(1991 – 2003),and(c)testing2(1995 – 2003)simulationsforthelevel1,2,3, 4,and5complexities. Thehistoricalpatternstheseresultsarecomparedtoareinthefirstcolumn.Densitieshavebeenaggregatedintoeight classesforvisualcomparisononly. Lagerwall etal.EcologicalProcesses 2012, 1 :10 Page11of21 http://www.ecologicalprocesses.com/content/1/1/10

PAGE 12

Figure5 Regionalandzonaltrendsfor(a)training,(b)testing1,and(c)testing2simulationperiods,forallfivelevelsofcomplexity. Thepointsatthebeginningandendofthetrendsrepresenttheobserveddatadensities. Lagerwall etal.EcologicalProcesses 2012, 1 :10 Page12of21 http://www.ecologicalprocesses.com/content/1/1/10

PAGE 13

locatedinthenortheast,central,andsouthwest,were selectedasrepresentativeelementsfortypicallyhigh, medium,andlowcattaildensities,respectively.These elementsaremarkedbyredsquaresinFigure1andare usefulforevaluatinglocalvegetationindicators. Modeltrainingandtesting Therewerethreetimeperiodsoverwhichthemodel wassimulatedusingtheavailabledatamapsof1991, 1995,and2003.Trainingwasperformedforthetime period1991 – 1995usingthelevel1complexitytoestablishthegrowthrate(6.710 -9 g/g s),andresults fromtheotherlevelswillbeduesolelytotheeffect oftheirincludedexternalp arameters.Itistherefore expectedthattheresultsoftheotherlevelsofcomplexitywillnotbeasaccurateasthelevel1complexityforthistimeperiod.Testingofthemodel wasperformedforthetimeperiod1991 – 2003.This providesanextendedforecastbasedontheoriginal calibrationtimeperiodandinitialdata.Finallythe 1995 – 2003timeperiodwasusedasablindtestof themodel,usingdifferentinitialconditionsanddeterminingitsabilitytoaccu ratelypredictthedensity distributionofthe2003cattailmap. Resultsanddiscussion FromthecattailmapsofFigure2andthoseinRutchey etal.(2008),atrendincattaildistributionovertheyears isobservable.Itappearsthatcattaildensityanddistributionincreasedfrom1991to1995.From1995to2003 thegeneraldistributioncontinuedtoincreasebutwith moredispersedpatchesofhigh-densitycattail.Thismay berelatedtoareductionintheoveralldispersalortoan increasedlocalspeciation.Throughtheuseofbest managementpractices,thetotalphosphorusload enteringWCA2Afortheperiod1995 – 2004wasreduced byroughly36%(Richardsonetal.2008),whichmayhave alsohadaroleinthedispersalnotedabove. TheresultsofthesimulationsandanalysesaredisplayedinFigures4,5,6,7,and8.Figure4showsthe modeloutputmapsforthedifferentsimulationperiods, andallfivelevelsofcomplexity,comparedtothefinal datamaps.Thesedensitymapshavehadtheirvalues aggregatedintoeightclassesforvisualcomparisononly. AbetterdepictionofthesetrendsisfoundintheclassifieddifferencemapsofFigure9below.Figure5showsa timeseriesplotforthefivelevelsofcomplexityacross allthreesimulationperiods.Itprovidesaddedinsight intothetrendsofthemodel,withoutrelyingpurelyon Figure6 Regionalstatisticsfortrainingperiod(1991 – 1995)andallfivelevelsofcomplexity. ( a )Regionalmeantrend(reddotsrepresent initialandfinaldatavalues),( b )abundance-area(theblacklinerepresentsthedata),( c )boxplot(dataplotontheleft),and( d )Moran ’ s I (the blacklinerepresentsthedata). Lagerwall etal.EcologicalProcesses 2012, 1 :10 Page13of21 http://www.ecologicalprocesses.com/content/1/1/10

PAGE 14

theendpoints.Theplotsarefortheregionalmean density(R),inred,andelements209(blue),244(green), and380(cyan).Thethreestatisticsandcomparisontime seriesforthecalibrationperiod1991 – 1995canbefound inFigure6.Theregionalmeantimeseriesplotforall fivelevelsofcomplexitycanbefoundinFigure6a,the abundance-areaplotinFigure6b,theboxplotin Figure6cenablesacomparisonofthespreadofmodel densitieswiththatoftheobserveddata,andtheMoran ’ s I plotisfoundinFigure6d.Figures7and8displaythe samethreestatisticsandregionalmeandensitytrendsas inFigure6fortheothertwosimulationperiods,namely 1991 – 2003and1995 – 2003. Whenconsideringthefirsthypothesis,orlevelof complexity,thatcattailgrowthisdensitydependent,we notethefollowingpoints.Forthetraining(1991 – 1995) timeperiod,thelevel1complexity ’ sspatialdensitydistribution(Figures4and9)isthemostsimilartothe observed1995data.Thedensitytrend(Figure5)is smoothandslowlyincreasingforallobservedpoints (reddots).Theregionaltrendendsdirectlyonthedata density.Thesouthwest(element380)andcentral (element244)trendsover-predictthedatapoints.The abundance-areastatistic(Figure6b)followsthedata trend(blackline)theclosest.Themeananddistribution ofdensities(Figure6c)arerelativelyclosetothedata. TheMoran ’ s I statisticfollowsthedata(blackline)trend relativelyclosely(Figure6d).Alloftheseresultsfrom thetrainingperiodareexpectedbecausethislevelof complexitywasusedforcalibrationoverthistime period.Forthetwotestingsimulationperiods,thelevel 1complexityclearlyoverestimatesthehistoricaldata (Figures4and9).Thedensitytrend(Figure5b,c) remainssmoothbutoverestimatestheobserveddata,exceptforelement380inFigure5cwhichremainslow, possiblyduetothelowinitialstartingdensityandrelativelyshorttimeperiod.Theabundance-areastatistic (Figures7band8b)showssignificantover-predictionof thedatatrend(blackline).Themeandensityisstilllow, butthedistributionissignificantlyskewedtowardthe higherdensities(Figures7cand8c).Thisisevidence thataspatialdistributionofdensitiesismoreinformativethansimplyusingthemeanfortheareaorapresence/absencetypemodel.Moran ’ s I statisticfollowsthe data(blackline)trendrelativelyclosely(Figures7dand 8d).Theresultsoftheseanalysesconfirmthatalthough Figure7 Regionalstatisticsfortesting1period(1991 – 2003)andallfivelevelsofcomplexity. ( a )Regionalmeantrend(reddotsrepresent initialandfinaldatavalues),( b )abundance-area(theblacklinerepresentsthedata),( c )boxplot(dataplotontheleft),and( d )Moran ’ s I (the blacklinerepresentsthedata). Lagerwall etal.EcologicalProcesses 2012, 1 :10 Page14of21 http://www.ecologicalprocesses.com/content/1/1/10

PAGE 15

cattailmayindeedhaveadensity-dependent/logistic growthpatternasweareabletosimulateobserveddata duringthetrainingperiod,ourinabilitytosimulate observeddataforthetwotrainingperiodsindicatesthat therearecertainlyotherparametersaffectingthegrowth anddistributionofthisspecies. Whenconsideringthesecondhypothesis,orlevelof complexity,thatcattailgrowth/expansionisdependent onwaterdepth,wenotethefollowingpoints.Forall timeperiods(training,testing1,andtesting2),thelevel 2complexity ’ sspatialdensitydistrib ution(Figures4and9) isconsistentlylowerthantheobservedvalues.Thisis confirmedinthetrendanalysis(Figure5a,b,c),whereall theobservedelements(209,244,and380)andtheregionaltrendareconsistentlybelowtheobservedvalues. Theonlyexceptioniselement380inFigure5a,where thereishardlyanychangeintheelement ’ sdensity,and thisispossiblyduetothelowinitialdensityvalueofthat element.Theabundance-areastatisticforalltimeperiods (Figures6b,7b,8b)issignificantlylowerthanthe observedtrend.Similarly,thedistributionofdensitiesfor alltimeperiods(Figures6c,7c,8c)ismuchreduced.For theMoran ’ s I statistic,themodelisrelativelyclosetothe datatrendbutconsistentlyhasalonger(thelongest)tail. Thisimpliesthatcellsfurtherawayhaveanobservable impactonthedensityofanyothercell.Thiswouldbe duetothefactthatthewaterdepthineverycellhasan effect/influenceoneveryothercellintheregion.We knowthatwaterdepthisaninfluentialfactorincattail growth(Newmanetal.1998;MiaoandSklar1998),howevertheresultsoftheseanalysesindicatethatthecurrent model(level2complexity)isoverlyinfluencedbythis parameter.Itisexpectedthattheinfluenceofthisparameterwillbereducedasitis “ diluted ” withotherparametersinthehighercomplexitymodels. Whenconsideringthethirdhypothesis,orlevelof complexity,thatcattailgrowth/expansionisdependent onsoilphosphorusconcentration,wenotethefollowing points.Thespatialdensitydistribution(Figures4and9) forlevel3liessomewhatin-betweenthatforlevel1and level2.Exceptforthetrainingperiod,whichslightly under-predictstheobservedvalues,thetwotestingperiodsappeartomoreaccuratelypredicttheobserved densitydistribution.Thisisconfirmedwiththetrend analysis(Figure5a,b,c),whereatleasttheregionaltrend isatorrelativelyclosetotheobservedvalues.Aswith Figure8 Regionalstatisticsfortesting2period(1995 – 2003)andallfivelevelsofcomplexity. ( a )Regionalmeantrend(reddotsrepresent initialandfinaldatavalues),( b )abundance-area(theblacklinerepresentsthedata),( c )boxplot(dataplotontheleft),and( d )Moran ’ s I (the blacklinerepresentsthedata). Lagerwall etal.EcologicalProcesses 2012, 1 :10 Page15of21 http://www.ecologicalprocesses.com/content/1/1/10

PAGE 16

thelevel2complexity,element380tendstounderpredicttheobservedvalue.However,element209tends topredicttheobservedvaluebetterthaneitherofthe previoustwolevelsofcomplexity.Theabundance-area statistic(Figures6b,7b,8b)showsconsistentunderpredictionoftheobservedtrend,butalsoshowsconsistentlyhighervaluesthanthelevel2trendandiscloserto thedatathanthelevel1trend.Thedistributionofdensitiesforalltimeperiods(Figures6c,7c,8c),although greaterthanthelevel2complexity,isstillsignificantly lowerthantheobserveddistribution.TheMoran ’ s I trendisfollowedcloselyforalltimeperiods(Figures6d, 7d,8d).Theresultsoftheseanalysesconfirmthatsoil phosphorusisasignificantinfluencingfactorinthedistributionofcattail,althoughthewaterdepthparameter remainshighlyinfluential.Thelevel3complexityis betterabletopredictcattailinareasoftypicallyhigh phosphorusorofhighcattaildensitythantheprevious twolevelsofcomplexity. Whenconsideringthefourthhypothesis,orlevelof complexity,thatsawgrassdensitymayimpacttherate ofcattailexpansion,wenotethefollowingpoints. Thespatialdensitydistribution(Figures4and9)is closertotheobservedvaluesthanthepreviouslevels ofcomplexity.Thisisconfirmedinthetrendanalysis (Figure5a,b,c),wheremostnotablyalloftheelementstendtobetterpredicttheobservedvalues, exceptforelement244inFigure5c,whichoverpredictstheobserveddensityandinturnraisesthe regionaltrendabovetheobservedvalueaswell.The abundance-areastatisticonlyslightlyunder-predicts theobservedtrendduringthetrainingtimeperiod Figure9 Classifieddifferencemapsfor(a)training(1991 – 1995),(b)testing1(1991 – 2003),and(c)testing2(1995 – 2003)simulations forthelevel1,2,3,4,and5complexities. Theclassifieddifferencesofthedatamapstheseresultsarecomparedtoareinthefirstcolumn (historicalpatterns). Lagerwall etal.EcologicalProcesses 2012, 1 :10 Page16of21 http://www.ecologicalprocesses.com/content/1/1/10

PAGE 17

(Figure6b).Duringthetwotestingtimeperiods,the statisticindicatesaslightover-predictionofthe observedtrend,butresultsshowbetterpredictions thananyofthepreviouslevelsofcomplexity.The densitydistribution(Figures6c,7c,8c)issignificantly higherthanthelevel2andlevel3complexities,and equalto(Figure6c;training)orlessthan(Figures7c, 8c;testing)thelevel1complexity.Thismeansthat thelevel4complexityconsistentlyapproximatesthe observeddensitiesfortheregionbetterthantheother levelsofcomplexityforalltimeperiods,albeitwith slightlyelevatedminimumdensities.TheMoran ’ s I statistic(Figures6d,7d,8d)followstheobserved trendrelativelywellforalltimeperiods.Althoughthe level4complexitytendstohaveslightlyelevated minimumdensities,likethelevel1complexity,the generalresultfromtheseanalysesisthatthelevel4 complexityisabletosimula tethecattaildensities throughtheregionconsistentlybetterthananyofthe previouslevelsofcomplexity.Wecanthusconclude thatincludingasimulatedsawgrassdensitydoesindeedimpacttherateofcattailexpansionandimprove simulationresults. Whenconsideringthefifthhypothesis,orlevelof complexity,thatinter-speciesinteractionsbetween cattailandsawgrasscontributetotheobservedcattail dynamics,wefindthefollowing:Thespatialdensity distribution(Figures4and9)doesnotpredictthe Figure10 Classifieddifferencesummary. Percentageofcellsoccurringwithineachclass,foralllevelsofcomplexityandtimeperiods( a ) training(1991 – 1995),( b )testing1(1991 – 2003),and( c )testing2(1995 – 2003). Lagerwall etal.EcologicalProcesses 2012, 1 :10 Page17of21 http://www.ecologicalprocesses.com/content/1/1/10

PAGE 18

observedvaluessignificantlybetterthanthelevel4 complexity.Thetrendanalysis(Figure5a,b,c)isalmostidenticaltothatofthelevel4complexityin everyrespect.Allofthestati sticalanalysesanddistributionsforalltimeperiods(Figures6b,c,d;7b,c,d;8b, c,d)arealmostidenticaltothoseofthelevel4complexity.Theresultoftheseanalysesisthatthelevel5 complexitydoesnotpredicttheobservedvalueswith greatersuccessthanthelevel4complexity.While inter-speciesinteractionsmightwellhaveaneffect withadifferentmodelstructure,thecurrentmodeling arrangementhasshownthebeginningofdiminishing returnswithrespecttomodelcomplexityand predictivecapability. WithregardtotheMoran ’ s I statistic,allthecomplexity levelsfollowedthesamebasictrendasthedata(representedbytheblackline)andwereall0byaroundthe 18,240mmark.Thisdistancecorrespondsapproximately tothewidthoftheregion,whilethetotaldistanceof 36,480mintheplotcorrespondstothelongestnorth – southdistanceoftheregion.Itisbelievedthatthestatistic dropsto0bythe18,240mmarkduetooverlappingand boundaryeffectsandthatthiselevatestheNash-Sutcliffe coefficientforalllevelsofcomplexityinthisstatistic. AsummaryoftheFigure9classifieddifferencemaps canbefoundinthebarchartofFigure10,whichshows thepercentageoftriangularelementsfallingwithineach classforallfivelevelsofcomplexityandsimulationperiods.Uponfurtherinspectionoftheseplots,thelevel 4andlevel5complexitiesconsistentlyoutperformthe otherlevelsofcomplexity,witheitherthehighest percentageofcombinedclasses0(<20g/m2)and1 (<200g/m2),orthelowestpercentageofcombined classes2(<400g/m2)and3(>400g/m2). AsummaryofthethreestatisticsfoundinFigures6b,c,d; 7b,c,d;and8b,c,disprovidedbytheNash-SutcliffecoefficientsinTable3andcanbevisuallycomparedinFigure11, withtheboxplots(or1-to-1comparisons)locatedin Figure11a,abundance-areainFigure11b,andMoran ’ s I in Figure11c.FromFigure11itcanbenotedthatthelevel4 and5complexities,whichincl udedepth,soilphosphorus, andsawgrassinteractions,consistentlyperformbetterthan theotherlevelsofcomplexity.Apointtonoteregarding thelevel5complexityisthatdespitethefactthatitdoes notofferasignificantimprovementinpredictivecapability overthelevel4complexity,itdoesnotpredicttheobserved valuesanyworsethanthelevel4complexityeither.ConclusionsThemethodsofmodelingcattailforecologicalmodelscurrentlyinusewerecompared,theirsimilaritiesanddifferenceswerenoted,andaknowledgegapidentified:there doesn ’ tyetexistamethodofquantitativelyanddeterministicallydeterminingthespatialdistributionofcattailinthe Everglades.Acoupledfree-form/fixed-formmodelwas introducedtosolvethisproblem.Anaddedbenefitofthe free-formnatureoftheRSM/TARSEcoupledmodelisthe user-definableequationsofinteraction,whichcanbe modifiedasdataand/ornewtheoriesbecomeavailable. Thisnewecologicalimplementationofthemodel(RTE) wassuccessfullyappliedtowardsmodelingcattaildynamics acrosstheWCA2Atestsitefortraining(1991 – 1995), testing(1991 – 2003),andblindtest(1995 – 2003)simulationperiods.Fivealgorithms,withincreasingcomplexity,wereusedtomatchthehistoricaldata.Upon analysisoftheperformanceofthesedifferentlevels,it canbeconcludedthatthelevel4and5complexities, whichincludedepth,soilphosphorus,andsawgrass interactionparameters,arethemostsuitablemodelsfor matchingthehistoricaldata.TheNash-Sutcliffecoefficient wasusedtodistinguishthesuccessofdifferentmodels. Bothlocalandlandscape-scaleindicatorswereusedto performthecomparisonbetweenhistoricalandmodeled cattailpatterns.Theaveragelocalcattaildensitywas estimatedwithabox-plotanalysis;thepairwise-cell comparisonoflocalcattaildensitieswasanalyzedwith Moran ’ s I ;and,theregionalincreasewithareaofthe localcattaildensitywasestimatedthroughthe abundance-arearelationship.Thebox-plotandthe abundance-areawerethemostmeaningfulpatternsto discriminatemodelsintermsoftheirabilitytorepresent theobservedpatterns. Table3SummaryofNash-Sutcliffevaluescomparing modelandobserveddataforboxplot,Moran ’ s I ,and abundance-areastatistics(representedbyFigures6,7, and8,respectively)forlevel1,level2,level3,level4, level5,training(199 – 1995),testing1(1991 – 2003),and testing2(1995 – 2003)simulationsYearlevel1-to-1BoxplotMoran ’ s I Abundance 1991-199510.740.980.98 20.130.99 0.94 30.490.950.23 40.740.980.96 50.740.980.96 1991-20031 0.750.97 1.89 20.020.86 0.35 30.230.980.44 40.490.980.77 50.490.980.76 1995-20031 0.950.99 0.80 20.140.94 0.29 30.360.970.51 40.390.990.77 50.390.990.77 Lagerwall etal.EcologicalProcesses 2012, 1 :10 Page18of21 http://www.ecologicalprocesses.com/content/1/1/10

PAGE 19

Theautocorrelationstructureofthecattailpatternswere wellrepresentedbyallthemod elsateachcomplexitylevel. Thisispossiblyduetothefactthatthroughoverlapping andboundaryeffects,cattaildensitiesleveledoffafter roughlyhalfthedistance(toptobottom)thatwasusedto calculatethestatistic.Itmaybemorerepresentativeiffuturecalculationsconsideredonlyhalfthismaximumdistance,wherethevariationswouldcarryagreaterweighting. Oursimulationresultswouldbeinagreementwiththe studiesofNewmanetal.(1998)andMiaoandSklar (1998),inwhichwaterdepthandsoilphosphorusconcentrationwerethemostimportantfactorsaidingincattailexpansion.Ourresultsalsoincludeaninteractionparameter withsawgrass,whichisofinterestintheregion.Thus,we confirmtheimportanceofconsideringspeciesdependenciesorinteractionsinreproducingthecattailpatternseven Figure11 Nash-Sutcliffesummaryofstatistics. AgraphicalrepresentationofTable3.Thelevel4and5complexitymodelsperform consistentlywellincomparisonwithalltheothermodels. Lagerwall etal.EcologicalProcesses 2012, 1 :10 Page19of21 http://www.ecologicalprocesses.com/content/1/1/10

PAGE 20

inwater-controlledareasinwhichtheanthropic-driven variableswouldbeexpectedtodominatethespecies processesandtheresultingpatterns. Limitationsofourcurrentmodelingapproachmayincludetheelement/trianglesize,witharangeof0.5 – 1.7 km2(Wang2009).Thisconstraintwasdictatedbythe choiceoftheRSMthatsimulateshydrologicalprocesses. Althoughtheimposedgrid-unithasarelativelycoarse sizeinwhichthereisstillconsiderableheterogeneityof theenvironmentalfeatures(Zajac2010),RTEhas proventobecapableofreproducingthedynamicsof cattailandsawgrassatthelandscapescaleusingthelevel 4andlevel5complexities.Thismakesitavaluabletool forexploringpotentialmanagementscenariosinwater conservationareasintheEvergladesandpossiblyin otherwater-controlledwetlands. Furtherinvestigationswouldconsiderthequantificationoftheimportanceofwater-controlleddriversand speciestraits(dispersal)forvegetationpatterns,thestability/instabilitystatesofspeciesundervaryingstressors, thepredictionoffuturemanagementscenarios,andthe comparisonwithneutral-basedmodels. Intermsoffurthermodeldevelopmentandaddedcomplexity,effortshavebeenmadetowardsmoreaccuraterepresentationoffaunamovementthroughtheuseof Eulerian – Lagrangian(grid-independent)particlemovement(Lagerwall2011),aswellasusingvegetationtypes/ densitiestoinfluencethehydrologywithadynamically linkedManning ’ s n parameter(Zajac2010).Whilecreating moredynamicallylinkedparametersisanongoingtask, theselinkagesremainachallengetoimplementduetothe difficultiesassociatedwithparameterizing(training)a modelwithfeedbackeffects.Thisfeedbackrelationshipbetweenecologicalandhydrologicalmodelcomponentsmay bequiteimportanttothefunctionandresilienceofthese ecosystemsandiscertainlyasubjectoffurtherresearch.Competinginterests Theauthorsdeclarethattheyhavenocompetinginterests. Authors ’ contributions GLconductedthemajorityoftheresearch,modeladaptationforecology, andwritingofthepaper.GKprovidedecologicalmodelingexpertise, generalguidance,helpindevelopingthefivelevelsofcomplexity,paper writing,andreviewcontributions.RMCprovidedstatisticalinsights,provided criticalreviewonmodeldesign,andensuredthatthegenerallogicofthe paperwasmaintained.MCprovidedexpertiseintheecologicalstatisticsand contributedtopaperwriting,formatting,andreview.AJprovidedRSM/ TARSEmodelexpertise.NWprovidedRSMandWCA2Aexpertise,supplied rawvegetationmaps,andprovidedcriticalreviewonmodeldesign.All authorsreadandapprovedthefinalmanuscript. Acknowledgements FinancialsupportforthisresearchwasprovidedbytheSouthFloridaWater ManagementDistrictandtheU.S.GeologicalSurvey-WaterResources ResearchCenterattheUniversityofFlorida. Authordetails1FrazierRogersHall,UniversityofFlorida,POBox110570,Gainesville,FL 32611-0570,USA.2SoilandWaterEngineeringTechnology,Inc.,3960 MagnoliaLeafL,SuwaneeGA30024,USA.3HydrologicandEnvironmental SystemsModeling,SouthFloridaWaterManagementDistrict,3301GunClub Rd,WestPalmBeach,FL33406,USA. Received:2July2012Accepted:7October2012 Published:1November2012 ReferencesArnoldK,GoslingJ(1998)TheJavaprogramminglanguage,2ndedn.Prentice Hall,UpperSaddleRiver,NJ CaryJR,ShasharinaSG,CummingsJC,ReyndersJVW,HinkerPJ(1998) ComparisonofC++andFortran90forobject-orientedscientific programming.CompPhysComm105:20 – 36 CliffAD,OrdK(1970)Spatialautocorrelation:areviewofexistingandnew measureswithapplications.EconGeography46:269 – 292 ConvertinoM,MuneepeerakulR,AzaeleS,BertuzzoE,RinaldoA,Rodriguez-Iturbe I(2009)Onneutralmetacommunitypatternsofriverbasinsatdifferent scalesofaggregation.WaterResourRes45:W08424 CostanzaR,VoinovA(2001)Modelingecologicalandeconomicsystemswith STELLA:partIII.EcolModel143:1 – 7 DeBuskWF,ReddyKR,KochMS,WangY(1994)Spatialdistributionofsoil nutrientsinanorthern-Evergladesmarsh:WaterConservationArea2A.Soil SocAm58:543 – 552 DorenRF,ArmentanoThomasV,WhiteakerLouisD,JonesRonaldD(1999) MarshvegetationpatternsandsoilphosphorusgradientsintheEverglades ecosystem.AquaBot56:145 – 163 DouglasMS(1947)TheEverglades:riverofgrass.Rinehart,NewYork Duke-SylvesterS(2005)Initialperformancemeasuresandinformationrelatedto theATLSSvegetationsuccessionmodel.http://atlss.org/VSMod.Accessed31 July2010 ESRI(EnvironmentalSystemsResourceInstitute)(2010)ArcMap10.0.ESRI, Redlands,CA FitzCH,TrimbleB(2006a)DocumentationoftheEvergladesLandscapeModel: ELMv2.5.SouthFloridaWaterManagementDistrict,WestPalmBeach,FL FitzCH,TrimbleB(2006b)EvergladesLandscapeModel(ELM).http://my.sfwmd.gov/ portal/page/portal/xweb%20-%20release%202/elm.Accessed31July2010 FitzHC,KikerGA,KimJB(2011)Integratedecologicalmodelinganddecision analysiswithintheEvergladeslandscape.CritRevEnvironSciTechnol41 (S1):517 – 547 FortinMJ,DaleMRT(2005)Spatialanalysis,aguideforecologists.Cambridge UniversityPress,Cambridge GraceJBL(1989)Effectsofwaterdepthon Typhalatifolia and Typhadomingensis AmJBot76:762 – 768 GrossLJ(1996)ATLSShomepage.http://atlss.org/.Accessed31July2010 GrunwaldS(2010)PhosphorusdataforWCA2A.PersonalCommunication. UniversityofFlorida,Gainesville GrunwaldS,ReddyKR,NewmanS,DeBuskWF(2004)Spatialvariability, distributionanduncertaintyassessmentofsoilphosphorusinaSouthFlorida wetland.Environmetrics15:811 – 825 GrunwaldS,OzborneTZ,ReddyKR(2008)Temporaltrajectoriesofphosphorus andpedo-patternsmappedinWaterConservationArea2,Everglades, Florida,USA.Geoderma146:1 – 13 GuardoM,FinkL,FontaineThomasD,NewmanS,ChimneyM,BearzottiR, GoforthG(1995)Large-scaleconstructedwetlandsfornutrientremovalfrom stormwaterrunoff:anEvergladesrestorationproject.EnvironManage19 (6):879 – 889 HaroldER(1998)XML:ExtensibleMarkupLanguage,1stedn.IDG,FosterCity JamesAI,JawitzJW(2007)Modelingtwo-dimensionalreactivetransportusinga Godunov-mixedfiniteelementmethod.JHydrol338:28 – 41 JawitzJW,Muoz-CarpenaR,MullerS,GraceKA,JamesAI(2008)Development, testing,andsensitivityanduncertaintyanalysesofaTransportandReaction SimulationEngine(TaRSE)forspatiallydistributedmodelingofphosphorus inSouthFloridapeatmarshwetlands.ScientificInvestigationsReport2008 – 5029.UnitedStatesGeologicalSurvey,Reston,VA JensenJR,RutcheyK,KochMS,NarumalaniS(1995)Inlandwetlandchange detectionintheEvergladesWaterConservationArea2Ausingatimeseries ofremotelysenseddata.PhotogrammEngRemSens61(2):199 – 209 KeenRE,SpainJD(1992)Computersimulationinbiology.Wiley-Liss,NewYork KikerGA(1998)Developmentandcomparisonofsavannaecosystemmodelsto exploretheconceptofcarryingcapacity.PhDDissertation.Cornell University,IthacaLagerwall etal.EcologicalProcesses 2012, 1 :10 Page20of21 http://www.ecologicalprocesses.com/content/1/1/10

PAGE 21

Kiker,G.A.&Linkov,I.2006.TheQnDModel/GameSystem:Integrating QuestionsandDecisionsforMultipleStressors.pp.203-225inArapis,G., Goncharova,N.&Baveye,P.Ecotoxicology,EcologicalRiskAssessmentand MultipleStressors.Netherlands:Springer.(1-4020-4475-5) Kiker,G.A.,Rivers-Moore,N.A.,Kiker,M.K.&Linkov,I.2006.QnD:Amodeling gamesystemforintegratingenvironmentalprocessesandpractical managementdecisions.pp.151-185inMorel,B.&Linkov,I.Environmental SecurityandEnvironmentalManagement:TheRoleofRiskAssessment. Netherlands:Springer.(1-4020-3892-5) LagerwallGL(2011)Modeling Typhadomingensis inanEvergladeswetland. Dissertation.UniversityofFlorida,Gainesville LindenschmidtKE(2006)Theeffectofcomplexityonparametersensitivityand modeluncertaintyinriverwaterqualitymodeling.EcolModel190:72 – 86 LudascherB,AltintasI,BerkleyC,HigginsD,JaegerE,JonesM,LeeEdwardA, TaoJ,ZhaoY(2006)ScientificworkflowmanagementandtheKeplersystem. ConcurrCompPractExper18:1039 – 1065 MaraniM,TommasoZ,BellucoE,SilvestriS,MaritanA(2006)Non-neutral vegetationdynamics.PLoSOne1(1):e78 MartinTE(1980)Diversityandabundanceofspringmigratorybirdsusinghabitat islandsontheGreatPlains.CooperOrnitholSoc82:430 – 439 McCuenRH,KnightZ,CutterAG(2006)EvaluationoftheNash-SutcliffeEfficiency Index.HydrolEng11:597 – 602 MiaoS(2004)Rhizomegrowthandnutrientresorption:mechanismsunderlying thereplacementoftwoclonalspeciesinFloridaEverglades.AquatBot 78:55 – 66 MiaoSL,SklarFH(1998)Biomassandnutrientallocationofsawgrassandcattail alonganutrientgradientintheFloridaEverglades.WetlandsEcolManage 5:245 – 264 MichalskiF,PeresCA(2007)Disturbance-mediatedmammalpersistenceand abundance-arearelationshipsinAmazonianforestfragments.ConservBiol 21:1626 – 1640 MullerS(2010)Adaptivespatially-distributedwater-qualitymodeling:an applicationtomechanisticallysimulatephosphorusconditionsinthe variable-densitysurface-watersofcoastalEvergladeswetlands.PhD Dissertation.UniversityofFlorida,Gainesville MuneepeerakulR,BertuzzoE,LynchHJ,FaganWF,RinaldoA,Rodriguez-IturbeI (2008)Neutralmetacommunitymodelspredictfishdisversitypatternsin Mississippi-Missouribasin.Nature453:220 – 222 Muoz-CarpenaR,ParsonsJE,GilliamJW(1999)Modelinghydrologyand sedimenttransportinvegetativefilterstrips.JHydrol214:111 – 129 NewmanS,SchutteJ,GraceJ,RutcheyK,FontaineT,ReddyK,PietruchaM (1998)FactorsinfluencingcattailabundanceinthenorthernEverglades. AquatBot60:265 – 280 OdumHT,OdumEC,BrownMT(2000)Wetlandsmanagement.In:Environment andsocietyinFlorida.CRCPress,BocaRaton OttRL,LongneckerMT(2004)Afirstcourseinstatisticalmethods.CurtHinrichs, Belmont,CA ParadisE(2010)Moran ’ sautocorrelationcoefficientincomparativemethods. http://cran.r-project.org/web/packages/ape/vignettes/MoranI.pdf.Accessed7 August2010 Perez-OvillaO(2010)Modelingrunoffpollutantdynamicsthroughvegetative filterstrips:aflexiblenumericalapproach.PhDDissertation.Universityof Florida,Gainesville RichardsonCJ,KingRyanS,VymazalJ,RomanowiczEdwinA,PahlJamesW (2008)MacrophytecommunityresponsesintheEvergladeswithan emphasisoncattail( Typhadomingensis )andsawgrass( Cladiumjamaicense ) interactionsalongagradientoflong-termnutrientadditions,altered hydroperiod,andfire.EcolStud201:215 – 260 RiveroRG,GrunwaldS,BrulandGL(2007a)Incorporationofspectraldatainto multivariategeostatisticalmodelstomapsoilphosphorusvariabilityina Floridawetland.Geoderma140:428 – 443 RiveroRG,GrunwaldS,OsborneTZ,ReddyKR,NewmanS(2007b) CharacterizationofthespatialdistributionofsoilpropertiesinWater ConservationArea2A,Everglades,Florida.SoilSci172:149 – 166 RutcheyK(2011) Typhadomingensis mapsofWCA2Afortheyears1991and 1995.Personalcommunication.SouthFloridaWaterManagementDistrict, WestPalmBeach RutcheyK,SchallT,SklarF(2008)Developmentofvegetationmapsforassessing Evergladesrestorationprogress.Wetlands172(2):806 – 816 SFWMD(1995)Landcoverlanduse1995.http://my.sfwmd.gov/gisapps/ sfwmdxwebdc/dataview.asp?query=unq_id=297.Accessed11November2009 SFWMD(1999)Landcoverlanduse1999.http://my.sfwmd.gov/gisapps/ sfwmdxwebdc/dataview.asp?query=unq_id=1593.Accessed11November2009SFWMD(2005a)DocumentationoftheSouthFloridaWaterManagementModel version5.5.SouthFloridaWaterManagementDistrict,WestPalmBeach,FL SFWMD(2005b)RegionalSimulationModel(RSM)HydrologicSimulationEngine (HSE)user ’ smanual.SouthFloridaWaterManagementDistrict,WestPalm Beach,FL SFWMD(2005c)RegionalSimulationModel(RSM)theorymanual.SouthFlorida WaterManagementDistrict,WestPalmBeach,FL SFWMD(2008a)RSMwaterqualityusermanual(draft).SouthFloridaWater ManagementDistrict,WestPalmBeach,FL SFWMD(2008b)RSMWQEtheorymanual(draft).SouthFloridaWater ManagementDistrict,WestPalmBeach,FL SFWMD(2008c)WCA2AHSEsetup.SouthFloridaWaterManagementDistrict, WestPalmBeach,FL SFWMD(2009)DBHYDRO.http://my.sfwmd.gov/dbhydroplsql/show_dbkey_info. main_menu.Accessed04August2010 StroustrupB(2000)TheC++programminglanguage,specialthedn.AddisonWesley,Westford,MA TarbotonKC,Irizarry-OrtizMM,LoucksDP,DavisSM,ObeysekeraJT(2004) Habitatsuitabilityindicesforevaluatingwatermanagementalternatives. SouthFloridaWaterManagementDistrict,WestPalmBeach,FL UrbanNH,DavisSM,AumenNG(1993)Fluctuationsinsawgrassandcattail densitiesinEvergladesWaterConservationArea2Aundervaryingnutrient, hydrologic,andfireregimes.AquatBot46:203 – 223 USACE,S.F.R.O(2010a)CERP:Theplanindepth-part1.http://www. evergladesplan.org/about/rest_plan_pt_01.aspx.Accessed3August2010 USACE,S.F.R.O(2010b)CERP:Theplanindepth-part2.http://www. evergladesplan.org/about/rest_plan_pt_02.aspx.Accessed3August2010 vanderValkAG,RosburgTR(1997)Seedbankcompositionalongaphosphorus gradientinthenorthernFloridaEverglades.Wetlands17(2):228 – 236 WalkerWW,KadlecRH(1996)Amodelforsimulatingphosphorusconcentrations inwatersandsoilsdownstreamofEvergladesstormwatertreatmentareas. Draft.USDepartmentoftheInteriorEvergladesNationalPark,Homestead, FL,http://publicfiles.dep.state.fl.us/DEAR/GoldAdministrativeRecord/Item% 2027/018752.PDF WangN(2009)2003Vegetationmap;dsshydrologyinputfiles.Personal communication.SouthFloridaWaterManagementDistrict,WestPalmBeach,FL WangJD,SwainED,WolfertMA,LangevinCD,JamesDE,TelisPA(2007) ApplicationofFTLOADDStosimulateflow,salinity,andsurface-waterstage inthesouthernEverglades,Florida.ScientificInvestigationsReport2007 – 2010.UnitedStatesGeologicalSurvey,Florida WetzelPR(2001)Plantcommunityparameterestimatesanddocumentationfor theAcrossTrophicLevelSystemSimulation(ATLSS).EastTennesseeState University,JohnsonCity WetzelPR(2003)Nutrientandfiredisturbanceandmodelevaluation documentationfortheActossTrophiclevelSystemSimulation(ATLSS).East TennesseeStateUniversity,JohnsonCity WillardDA(2010)SOFIA-FS-146-96.http://sofia.usgs.gov/publications/fs/146-96/. Accessed3August2010 WuY,SklarFH,RutcheyK(1997)Analysisandsimulationoffragmentation patternsintheEverglades.EcolAppl7(1):268 – 276 ZajacZB(2010)Globalsensitivityanduncertaintyanalysisofspatiallydistributed watershedmodels.PhDDissertation.UniversityofFlorida,Gainesvilledoi:10.1186/2192-1709-1-10 Citethisarticleas: Lagerwall etal. : Aspatiallydistributed,deterministic approachtomodeling Typhadomingensis (cattail)inanEverglades wetland. EcologicalProcesses 2012 1 :10.Lagerwall etal.EcologicalProcesses 2012, 1 :10 Page21of21 http://www.ecologicalprocesses.com/content/1/1/10