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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 MunozCarpenal, 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 outcompeting 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 regionalscale 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 userdefineable 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 1simulated) 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 interspecies 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 boxplots, abundancearea curves, Moran's /, and classified difference. The statistics were summarized using the NashSutcliffe 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, 326110570, 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, slowmoving 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 monocrop 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 userdefineable, 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 "hardcoded" into their programming code. This creates a "fixedform" model, with changes in the functioning coming through extensive code rewrites and careful redesign around logical struc tures. Dynamic "freeform" 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 objectoriented 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 freeform 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 metacode structure such as the eXtensible Markup Language (XML) (Harold 1998). There are a number of fixedform 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 wellknown. 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 postprocess 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 (DukeSylvester 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, speciesspecific, presence/ab sencetype 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 SFWMDdeveloped 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 userdefinable 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, freeform 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 PerezOvilla (2010) during their respective TARSEinfluenced, 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, freeform (userdefinable), quantitative ecological model of cattail dynamics. A signifi cant advantage of this freeform modeling approach is that multiple ecological algorithms of differing complexity can be quickly implemented and tested simultaneously, instead of through timeconsuming 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 interspecies 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 19911995, 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 19912003 (testing 1) and 19952003 (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 "2by2" 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 twodimensional 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 OverlandAquifer Density Dependent System (FTLOADDS) (Wang et al. 2007; Muller 2010) and VFSMOD (MufiozCarpena et al. Page 4 of 21 Lagerwall et al. Ecological Processes 2012, 1:10 http://www.ecologicalprocesses.com/content/1/1/10 1999; PerezOvilla 2010). TARSE solves the advection dispersionreaction 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 twodimensional 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 userdefinable in the XML input file (Jawitz et al. 2008). TARSE equations are com posed of preequations, equations, and postequations. Pre and postequations are used for implementing con ditional ("ifthenelse") statements as part of pre and postprocessing after the main processing in the equa tions. For example, preprocessing 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 > cattailoptimumdepth) Then depthHSI 1 (depth cattailoptimumdepth 109 (cattail optimumdepth 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 freeform dynamic system model has been integrated with a fixedform, spatially distributed, hydro logic model (Muller 2010). This unique coupling, with userdefined 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 waterdepthinfluenced 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 [T1], DepthF is the water depth factor [L/L], K is the carrying capacity or maximum population density [M/L2]. Level 3 is a soilphosphorusinfluenced 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 phosphorus1034 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 densitydependent 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 preequations, 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 windborne or waterborne transportation of seeds and rhizome expansionwhich 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 L35B 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 L35B 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 19792000 (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 19911995, while the soil phosphorus map of 2003 was used for both the testing 1 (19912003) and testing 2 (19952003) 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 totalwhich 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 sidebyside 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 multispecies 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. NashSutcliffe 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 i2 (11) Ell '(yi y)2 Where Ef is the NashSutcliffe 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 NashSutcliffe 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 noncattail 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 cellpairwise distance, as in Marani et al. (2006), to determine the trend in spatial autocorrelation across the entire region. A landscapescale abundancearea 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 100200 200400 400600 I 500800 8001000 10001240 (g/m2) Figure 4 Results for (a) training (19911995), (b) testing 1 (19912003), and (c) testing 2 (19952003) 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 19911995 using the level 1 complexity to es tablish the growth rate (6.7 x 109 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 19912003. This provides an extended forecast based on the original calibration time period and initial data. Finally the 19952003 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) BoxPlot 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 highdensity 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 19952004 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) AbundanceArea 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 (19911995) and all five levels of complexity. (a) Rec initial and final data values), (b) abundancearea (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) BoxPlot 1400 1200 1000 800 600 400 20If Data L1 L2 L3 L4 L5 b) AbundanceArea "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 (19912003) and all five levels of complexity. (a) Regional mean trend (red dots represent initial and final data values), (b) abundancearea (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 19911995 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 abundancearea 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 19912003 and 19952003. When considering the first hypothesis, or level of complexity, that cattail growth is density dependent, we note the following points. For the training (19911995) 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 overpredict the data points. The abundancearea 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 abundancearea statistic (Figures 7b and 8b) shows significant overprediction 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) BoxPlot 1400 r 1200 1000 S800 600 400 200 0 b) AbundanceArea 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 (19952003) and all initial and final data values), (b) abundancearea (the black line represents black line represents the data). cattail may indeed have a densitydependent/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 abundancearea 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 inbetween that for level 1 and level 2. Except for the training period, which slightly underpredicts 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 (19911995), (b) testing 1 (19912003), and (c) testing 2 (19952003) 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 abundancearea 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 abundancearea statistic only slightly underpredicts 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 overprediction 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 interspecies 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 (19911995), (b) testing 1 (19912003), and (c) testing 2 (19952003). 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 interspecies 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 NashSutcliffe 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 NashSutcliffe coeffi cients in Table 3 and can be visually compared in Figure 11, with the box plots (or 1to1 comparisons) located in Figure 11a, abundancearea 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 NashSutcliffe values comparing model and observed data for box plot, Moran's I, and abundancearea statistics (represented by Figures 6, 7, and 8, respectively) for level 1, level 2, level 3, level 4, level 5, training (1991995), testing 1 (19912003), and testing 2 (19952003) simulations Year 1991199, level 1to1 Box plot 1 0.74 2 0.13 Moran's I Abundance 0.98 0.98 9912003 049 9952003 0.14 0.39 Everglades. A coupled freeform/fixedform model was introduced to solve this problem. An added benefit of the freeform nature of the RSM/TARSE coupled model is the userdefinable 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 (19911995), testing (19912003), and blind test (19952003) 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 NashSutcliffe coefficient was used to distinguish the success of different models. Both local and landscapescale indicators were used to perform the comparison between historical and modeled cattail patterns. The average local cattail density was estimated with a boxplot analysis; the pairwisecell 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 abundancearea relationship. The boxplot and the abundancearea 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 AbundanceArea .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 NashSutcliffe 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 BoxPlot Levels of Complexity L4 Lagerwall et al. Ecological Processes 2012, 1:10 http://www.ecologicalprocesses.com/content/1/1/10 in watercontrolled areas in which the anthropicdriven 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 0.51.7 km2 (Wang 2009). This constraint was dictated by the choice of the RSM that simulates hydrological processes. Although the imposed gridunit 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 watercontrolled wetlands. Further investigations would consider the quantifica tion of the importance of watercontrolled 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 neutralbased 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 EulerianLagrangian (gridindependent) 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 326110570, 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 objectoriented scientific programming Comp Phys Comm 105'2036 Cliff AD, Ord K (1970) Spatial autocorrelation a review of existing and new measures with applications Econ Geography 46'269292 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 143'17 DeBusk WF, Reddy KR, Koch MS, Wang Y (1994) Spatial distribution of soil nutrients in a northernEverglades marsh Water Conservation Area 2A Soil Soc Am 58'543552 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 56'145163 Douglas MS (1947) The Everglades river of grass Rinehart, New York DukeSylvester 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)517547 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 762768 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 15811825 Grunwald S, Ozborne TZ, Reddy KR (2008) Temporal trajectories of phosphorus and pedopatterns mapped in Water Conservation Area 2, Everglades, Florida, USA Geoderma 146'113 Guardo M, Fink L, Fontaine Thomas D, Newman S, Chimney M, Bearzotti R, Goforth G (1995) Largescale constructed wetlands for nutrient removal from stormwater runoff an Everglades restoration project Environ Manage 19 (6)879889 Harold ER (1998) XML' Extensible Markup Language, 1st edn IDG, Foster City James AI, Jawitz JW (2007) Modeling twodimensional reactive transport using a Godunovmixed finite element method J Hydrol 3382841 Jawitz JW, MunozCarpena 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)199209 Keen RE, Spain JD (1992) Computer simulation in biology WileyLiss, 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 203225 in Arapis, G, Goncharova, N & Baveye, P Ecotoxicology, Ecological Risk Assessment and Multiple Stressors Netherlands Springer (14020 44755) Kiker, G A, RiversMoore, N A, Kiker, M K & Linkov, I 2006 QnD A modeling game system for integrating environmental processes and practical management decisions pp 151185 in Morel, B & Linkov, I Environmental Security and Environmental Management The Role of Risk Assessment Netherlands Springer (1402038925) 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 1907286 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 10391065 Marani M, Tommaso Z, Belluco E, Silvestri S, Maritan A (2006) Nonneutral 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 82430439 McCuen RH, Knight Z, Cutter AG (2006) Evaluation of the NashSutcliffe Efficiency Index Hydrol Eng 11597602 Miao S (2004) Rhizome growth and nutrient resorption mechanisms underlying the replacement of two clonal species in Florida Everglades Aquat Bot 785566 Miao SL, Sklar FH (1998) Biomass and nutrient allocation of sawgrass and cattail along a nutrient gradient in the Florida Everglades Wetlands Ecol Manage 5245264 Michalski F, Peres CA (2007) Disturbancemediated mammal persistence and abundancearea relationships in Amazonian forest fragments Conserv Biol 21 16261640 Muller S (2010) Adaptive spatiallydistributed waterquality modeling an application to mechanistically simulate phosphorus conditions in the variabledensity surfacewaters of coastal Everglades wetlands PhD Dissertation University of Florida, Gainesville Muneepeerakul R, Bertuzzo E, Lynch HJ, Fagan WF, Rinaldo A, RodriguezIturbe I (2008) Neutral metacommunity models predict fish diversity patterns in Mississippi Missouri basin Nature 453'220222 MuhozCarpena R, Parsons JE, Gilliam JW (1999) Modeling hydrology and sediment transport in vegetative filter strips J Hydrol 214'111129 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 60265280 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 PerezOvilla 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 longterm nutrient additions, altered hydroperiod, and fire Ecol Stud 201 215260 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 140428443 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 172'149166 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)806816 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, IrizarryOrtiz 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 46'203223 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)'228236 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 surfacewater 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)'268276 Zajac ZB (2010) Global sensitivity and uncertainty analysis of spatially distributed watershed models PhD Dissertation University of Florida, Gainesville doi:10.1186/21921709110 Cite this article as: Lagerwall et al A spatially distributed, deterministic approach to modeling Typha domingensis (cattail) in an Everglades wetland. 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ui 21921709110 ji 21921709 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 MuñozCarpenaRafaelcarpena@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, 326110570, 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 21921709 pubdate 2012 volume 1 issue 1 fpage 10 url http://www.ecologicalprocesses.com/content/1/1/10 xrefbib pubid idtype doi 10.1186/21921709110 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 outcompeting 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 regionalscale 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 userdefineable 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 interspecies 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 boxplots, abundancearea curves, Moran’s I, and classified difference. The statistics were summarized using the NashSutcliffe 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 userdefineable, 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, slowmoving 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 monocrop 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 “hardcoded” into their programming code. This creates a “fixedform” model, with changes in the functioning coming through extensive code rewrites and careful redesign around logical structures. Dynamic “freeform” 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 objectoriented 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 freeform 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 metacode structure such as the eXtensible Markup Language (XML) (Harold B21 1998).There are a number of fixedform 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 wellknown. 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 postprocess 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 (DukeSylvester 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, speciesspecific, presence/absencetype 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 SFWMDdeveloped 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 userdefinable 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, freeform 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 PerezOvilla (B45 2010) during their respective TARSEinfluenced, 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, freeform (userdefinable), quantitative ecological model of cattail dynamics. A significant advantage of this freeform modeling approach is that multiple ecological algorithms of differing complexity can be quickly implemented and tested simultaneously, instead of through timeconsuming 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 interspecies 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 “2by2” 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 twodimensional 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 OverlandAquifer Density Dependent System (FTLOADDS) (Wang et al. B68 2007; Muller 2010) and VFSMOD (MuñozCarpena et al. B40 1999; PerezOvilla 2010). TARSE solves the advectiondispersionreaction 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 twodimensional spatial coordinate x, with components (x sub 1 , x 2 ), and time, t. displayformula M1 m:math name 21921709110i1 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 firstorder 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 userdefinable in the XML input file (Jawitz et al. 2008). TARSE equations are composed of preequations, equations, and postequations. Pre and postequations are used for implementing conditional (“ifthenelse”) statements as part of pre and postprocessing after the main processing in the equations. For example, preprocessing 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 21921709110i2 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 /displayformula /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 freeform dynamic system model has been integrated with a fixedform, spatially distributed, hydrologic model (Muller abbr bid="B38"2010/abbr). This unique coupling, with userdefined 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 Lagrangiantype 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 displayformula id="M3" m:math name="21921709110i3" 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 /displayformula /pp/ pWhere itP/it is the population density [MLsup2/sup], itt/it is time [T], itGF/it is the constant growth rate [Tsup1/sup], and itK/it is the carrying capacity or maximum population density [MLsup2/sup]./ppLevel 2 is a waterdepthinfluenced 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 displayformula id="M4" m:math name="21921709110i4" 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 /displayformula /pp/ pWhere itP/it is the population density [MLsup2/sup], itt/it is time [T], itGF/it is a constant growth rate [Tsup1/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 soilphosphorusinfluenced 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 displayformula id="M5" m:math name="21921709110i5" 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 /displayformula /pp/ pWhere itP/it is the population density [MLsup2/sup, itt/it is time [T], itGF/it is a constant growth rate [Tsup1/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 displayformula id="M6" m:math name="21921709110i6" 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 /displayformula /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 displayformula id="M7" m:math name="21921709110i7" 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 /displayformula /pp/ pWhere itP/it is the population density [MLsup2/sup], itt/it is time [T], itGF/it is a constant growth rate [Tsup1/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 displayformula id="M8" m:math name="21921709110i8" 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 /displayformula /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 densitydependent influence on the level 1 sawgrass model, which is represented by Equations 9 and 10, respectively./pp displayformula id="M9" m:math name="21921709110i9" 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 /displayformula /pp/ pWhere itP/it is the population density [MLsup2/sup], itt/it is time [T], itGF/it is a constant growth rate [Tsup1/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 displayformula id="M10" m:math name="21921709110i10" 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 /displayformula /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 preequations, 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 windborne or waterborne 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 L35B 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="219217091101"//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="219217091102"//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 L35B 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="219217091103"//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 sidebyside 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 multispecies 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 NashSutcliffe 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 displayformula id="M11" m:math name="21921709110i11" 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 /displayformula /pp/ pWhere itE/it sub itf/it /sub is the NashSutcliffe coefficient, inlineformula m:math name="21921709110i12" 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 /inlineformula is the predicted variable, ity/it sub iti/it /sub is the observed variable, inlineformula m:math name="21921709110i13" 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 /inlineformula is the mean of the observed variable, and itn/it is the sample size. A NashSutcliffe 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 noncattail 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 displayformula id="M12" m:math name="21921709110i14" 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 /displayformula /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 cellpairwise distance, as in Marani et al. (abbr bid="B32"2006/abbr), to determine the trend in spatial autocorrelation across the entire region./ppA landscapescale abundancearea 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 × 10sup9/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 highdensity 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 abundancearea 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="219217091104"//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="219217091105"//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) abundancearea (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="219217091106"//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) abundancearea (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="219217091107"//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) abundancearea (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="219217091108"//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="219217091109"//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 overpredict the data points. The abundancearea 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 abundancearea statistic (Figures figr fid="F7"7b/figr and figr fid="F8"8b/figr) shows significant overprediction 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 densitydependentlogistic 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 abundancearea 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 inbetween that for level 1 and level 2. Except for the training period, which slightly underpredicts 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 underpredict the observed value. However, element 209 tends to predict the observed value better than either of the previous two levels of complexity. The abundancearea statistic (Figures figr fid="F6"6b/figr, figr fid="F7"7/figrb, figr fid="F8"8/figrb) shows consistent underprediction 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 overpredicts the observed density and in turn raises the regional trend above the observed value as well. The abundancearea statistic only slightly underpredicts 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 overprediction 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 interspecies 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 interspecies 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 NashSutcliffe 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="2192170911010"//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 NashSutcliffe 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 1to1 comparisons) located in Figure figr fid="F11"11a/figr, abundancearea 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 NashSutcliffe values comparing model and observed data for box plot, Moran’s/bb it I/it /bb, and abundancearea 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 b1to1 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" p19911995/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" p19912003/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" p19952003/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/titlecaptionpNashSutcliffe summary of statistics/p/captiontext pbNashSutcliffe 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="2192170911011"//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 freeformfixedform model was introduced to solve this problem. An added benefit of the freeform nature of the RSMTARSE coupled model is the userdefinable 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 NashSutcliffe coefficient was used to distinguish the success of different models./ppBoth local and landscapescale indicators were used to perform the comparison between historical and modeled cattail patterns. The average local cattail density was estimated with a boxplot analysis; the pairwisecell 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 abundancearea relationship. The boxplot and the abundancearea 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 watercontrolled areas in which the anthropicdriven 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 gridunit 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 watercontrolled wetlands./ppFurther investigations would consider the quantification of the importance of watercontrolled 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 neutralbased 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 (gridindependent) 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 objectoriented 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/auausnmRodriguezIturbe/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"10.1016S03043800(01)003581/pubid/xrefbib/biblbibl id="B6"titlepSpatial distribution of soil nutrients in a northernEverglades 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"augausnmDukeSylvester/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 pedopatterns 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"titlepLargescale 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 twodimensional reactive transport using a Godunovmixed 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/auausnmMuñozCarpena/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/sourcepublisherWileyLiss, 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/auausnmRiversMoore/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"titlepNonneutral 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 NashSutcliffe 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)10840699(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"titlepDisturbancemediated mammal persistence and abundancearea 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 spatiallydistributed waterquality modeling: an application to mechanistically simulate phosphorus conditions in the variabledensity surfacewaters of coastal Everglades wetlands. PhD Dissertation/sourcepublisherUniversity of Florida, Gainesville/publisherpubdate2010/pubdate/biblbibl id="B39"titlepNeutral metacommunity models predict fish disversity patterns in MississippiMissouri basin/p/titleaugausnmMuneepeerakul/snmfnmR/fnm/auausnmBertuzzo/snmfnmE/fnm/auausnmLynch/snmfnmHJ/fnm/auausnmFagan/snmfnmWF/fnm/auausnmRinaldo/snmfnmA/fnm/auausnmRodriguezIturbe/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/titleaugausnmMuñozCarpena/snmfnmR/fnm/auausnmParsons/snmfnmJE/fnm/auausnmGilliam/snmfnmJW/fnm/au/augsourceJ Hydrol/sourcepubdate1999/pubdatevolume214/volumefpage111/fpagelpage129/lpagexrefbibpubid idtype="doi"10.1016S00221694(98)002728/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"10.1016S03043770(97)000892/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.rproject.orgwebpackagesapevignettesMoranI.pdf/url. Accessed 7 August 2010/notexrefbibpubid idtype="pmpid"23280820/pubid/xrefbib/biblbibl id="B45"augausnmPerezOvilla/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 longterm 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"10.10079780387689234_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/sourcepublisherAddisonWesley, Westford, MA/publishereditionspecial/editionpubdate2000/pubdate/biblbibl id="B61"augausnmTarboton/snmfnmKC/fnm/auausnmIrizarryOrtiz/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"10.101603043770(93)90002E/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 surfacewater 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 FS14696/sourcepubdate2010/pubdatenoteurlhttp:sofia.usgs.govpublicationsfs14696/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"10.189010510761(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 UTF8 REPORT xmlns http:www.fcla.edudlsmddaitss xmlns:xsi http:www.w3.org2001XMLSchemainstance xsi:schemaLocation http:www.fcla.edudlsmddaitssdaitssReport.xsd INGEST IEID E5067APYR_0KR059 INGEST_TIME 20130305T20:20:57Z PACKAGE AA00013656_00001 AGREEMENT_INFO ACCOUNT UF PROJECT UFDC FILES xml version 1.0 encoding utf8 standalone no mets ID sortmets_mets OBJID swordmets LABEL DSpace SWORD Item PROFILE METS SIP Profile xmlns http:www.loc.govMETS xmlns:xlink http:www.w3.org1999xlink xmlns:xsi http:www.w3.org2001XMLSchemainstance xsi:schemaLocation http:www.loc.govstandardsmetsmets.xsd metsHdr CREATEDATE 20130103T16:07:51 agent ROLE CUSTODIAN TYPE ORGANIZATION name BioMed Central dmdSec swordmetsdmd1 GROUPID swordmetsdmd1_group1 mdWrap SWAP Metadata MDTYPE OTHER OTHERMDTYPE EPDCX MIMETYPE textxml xmlData epdcx:descriptionSet xmlns:epdcx http:purl.orgeprintepdcx20061116 xmlns:MIOJAVI http:purl.orgeprintepdcxxsd20061116epdcx.xsd epdcx:description epdcx:resourceId swordmetsepdcx1 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 outcompeting 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 regionalscale 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 userdefineable 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 interspecies 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 boxplots, abundancearea curves, Moran’s I, and classified difference. The statistics were summarized using the NashSutcliffe 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 userdefineable, 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 MuñozCarpena, Rafael Convertino, Matteo James, Andrew Wang, Naiming http:purl.orgeprinttermsisExpressedAs epdcx:valueRef swordmetsexpr1 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 20121101 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/10.1186/21921709110 fileSec fileGrp swordmetsfgrp1 USE CONTENT file swordmetsfgid0 swordmetsfile1 FLocat LOCTYPE URL xlink:href 21921709110.xml swordmetsfgid1 swordmetsfile2 applicationpdf 21921709110.pdf structMap swordmetsstruct1 structure LOGICAL div swordmetsdiv1 DMDID Object swordmetsdiv2 File fptr FILEID swordmetsdiv3 PAGE 1 RESEARCHOpenAccessAspatiallydistributed,deterministicapproach tomodeling Typhadomingensis (cattail)inan EvergladeswetlandGarethLagerwall1,GregoryKiker1*,RafaelMuozCarpena1,MatteoConvertino1,AndrewJames2andNaimingWang3AbstractIntroduction: Theemergentwetlandspecies Typhadomingensis (cattail)isanativeFloridaEverglades monocotyledonousmacrophyte.Ithasbecomeinvasiveduetoanthropogenicdisturbancesandisoutcompeting othervegetationintheregion,especiallyinareashistoricallydominatedby Cladiumjamaicense (sawgrass).Thereis aneedforaquantitative,deterministicmodelinordertoaccuratelysimulatetheregionalscalecattaildynamicsin theEverglades. Methods: TheRegionalSimulationModel(RSM),combinedwiththeTransportandReactionSimulationEngine (TARSE),wasadaptedtosimulateecology.Thisprovidesaframeworkforuserdefineableequationsand 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 cattaildensitiesinfluencedthesawgrassdensitiestodeterminetheimpactofinterspeciesinteractionsonthe cattaildynamics. Results: Allthesimulationresultsfromthedifferentlevelsofcomplexitywerecomparedtoobserveddataforthe years1995and2003.Theirperformancewasanalyzedusinganumberofdifferentstatisticsthateachrepresenta differentperspectiveontheecologicaldynamicsofthesystem.Thesestatisticsincludeboxplots,abundancearea curves,Moran s I ,andclassifieddifference.ThestatisticsweresummarizedusingtheNashSutcliffecoefficient.The resultsfromallofthesecomparisonsindicatethatthemorecomplexlevel4andlevel5modelswereableto simulatetheobserveddatawithareasonabledegreeofaccuracy.(Continuedonnextpage) *Correspondence: gkiker@ufl.edu1FrazierRogersHall,UniversityofFlorida,POBox110570,Gainesville,FL 326110570,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: Auserdefineable,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,slowmoving sheetofwaterflowingfreelytotheestuariesofBiscayne Bay,TenThousandIslands,andFloridaBay.ThechannelizationoftheEvergladesaround1948causedthereductionoftheoriginalwetlandareasbyupto50%,with relateddeclinesindependentwildlife.Inadditiontothe changesinhydrology,continuousmining,agriculture, andurbanizationactivitieshaveresultedininvasiveand exoticplantsbecomingestablishedinplaceoftheoriginalvegetation,alteringhabitatsandoftenforming monocropstands(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 hardcoded intotheir programmingcode.Thiscreatesa fixedform model, withchangesinthefunctioningcomingthroughextensive coderewritesandcarefulredesignaroundlogicalstructures.Dynamic freeform simulationmodels,suchas STELLA(CostanzaandVoinov2001),QnD(Kikerand Linkov2006;Kikeretal.2006),andtheKeplersystem (Ludascheretal.2006)aregenerallywrittenusingan objectorientedprogramming(OOP)languagesuchas C++(Stroustrup2000)orJava(ArnoldandGosling1998), asopposedtoalinearlanguagesuchasFORTRAN(Cary etal.1998).Wheninteractingwithfreeformmodelsand theiralgorithms,designersdonotinteractdirectlywiththe programcode.Rather,theyinfluenceobjectsthrough placingdata,storage,andlogicalstructuresintoeithera graphicaluserinterface(STELLA,Kepler)orwithina metacodestructuresuchastheeXtensibleMarkup Language(XML)(Harold1998). Thereareanumberoffixedformecologicalmodels currentlyinuseacrosstheEvergladesregion.Ofthese, theAcrossTrophicLevelSystemSimulation(ATLSS) (Gross1996)andtheEvergladesLandscapeModel (ELM)(FitzandTrimble2006b)areprobablythemost wellknown.Theseandmostothermodelsavailablefor modelingcattailintheEvergladesareentirelyqualitative,thatis,theyinvolveswitchingbetweenonespecies andanother.Themajorityofthesecurrentecological modelsarealsostochastic,thatis,basedonprobabilities andadegreeofrandomnessanduncertainty.Theygenerallyrunaspostprocessmodels,usinghydrological dataoutputbyothermodelssuchastheSouthFlorida WaterManagementModel(SFWMM)(Fitzetal.2011). TheATLSSvegetationsuccessionmodelisusedtodeterminethesuccessionofonehabitattypetoanother (e.g.,sawgrasstocattail).TheATLSSmodelsimulateswith anannualtimesteponsquare500mcellsandusesastochasticcellularautomatamodeltoswitchbetweenvegetationtypes.Currentlythereisnowaytodeterminevegetation densitieswithinvegetationtypes(DukeSylvester2005). 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,speciesspecific,presence/absencetypemodel. 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 SFWMDdevelopedRegionalSimulationModel(RSM) (SFWMD2005c)tosimulatesoilphosphorusdynamics intheEvergladessystem.TheOOPstructureofthis coupledhydrologic/waterqualitymodel,alongwiththe userdefinableinputsandinteractions,allowedforthe extensionofthismodelbeyonditsoriginalpurposeinto ecologicalprocessesandfeatures.ThecoupledRSM/ TARSE(henceforthreferredtoasRTE)model,implementedwiththegoalofmodelingecologicalfeatures withinthesouthernFloridalandscapeandpresentedin thispaper,isaspatiallydistributed,freeformmodelsimulatingcattailbiomassdistributionanddynamicsacross WCA2A.UsingtheRTEmodeltocouplevegetation dynamicswithphosphorusdynamicshasbeenalludedto byJawitzetal.(2008),Muller(2010),andPerezOvilla (2010)duringtheirrespectiveTARSEinfluenced,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,freeform(userdefinable), quantitativeecologicalmodelofcattaildynamics.Asignificantadvantageofthisfreef ormmodelingapproachisthat multipleecologicalalgorith msofdifferingcomplexitycan bequicklyimplementedandtestedsimultaneously,instead ofthroughtimeconsumingcod 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.Whetherinterspeciesinteractionsbetweencattailand 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 2by2 modelforits2mileresolution(SFWMD2005a). TheRSMoperatesoveravariabletriangularmeshgrid,in contrasttothe3.22km(2mile)squaregridofthe SFWMM;thisenableshigherresolutioninareasofconcernaswellastheabilitytodelineatecanals(SFWMD 2005c).TheRSMusesaweighted,implicit,finitevolume methodtosimulatetwodimensionaldiffusionalflowand 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 asFlowandTransportinaLinkedOverlandAquifer DensityDependentSystem(FTLOADDS)(Wangetal. 2007;Muller2010)andVFSMOD(MuozCarpenaetal.Lagerwall etal.EcologicalProcesses 2012, 1 :10 Page4of21 http://www.ecologicalprocesses.com/content/1/1/10 PAGE 5 1999;PerezOvilla2010).TARSEsolvestheadvectiondispersionreactionequations(ADRE)overanunstructuredtriangularmesh(JamesandJawitz2007).TheADRE isrepresentedbyEquation1,andeverytermisafunction ofatwodimensionalspatialcoordinate 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 thetransfersamongthemareuserdefinableintheXML inputfile(Jawitzetal.2008).TARSEequationsarecomposedofpreequations,equations,andpostequations. Preandpostequationsareusedforimplementingconditional( ifthenelse )statementsaspartofpreand postprocessingafterthemainprocessingintheequations.Forexample,preprocessingcouldbeusedtodetermineifthecurrentwaterdepth[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 timethatafreeformdynamicsystemmodelhasbeen integratedwithafixedform,spatiallydistributed,hydrologicmodel(Muller2010).Thisuniquecoupling, withuserdefinedinteractionsoperatingacrossa 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[T1],and K isthe carryingcapacityormaximumpopulationdensity[M/L2]. Level2isawaterdepthinfluencedlevel1complexity. 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[T1], DepthF isthe waterdepthfactor[L/L], K isthecarryingcapacityor maximumpopulationdensity[M/L2]. Level3isasoilphosphorusinfluencedlevel2complexity,withthesoilphosphorusfactorbeingincorporatedinasimilarfashiontothedepthfactorandcanbe seeninEquation5. dP dt GF P 1 P K DepthF phosphorusF = 2 5 Where P isthepopulationdensity[M/L2], t is time[T], GF isaconstantgrowthrate[T1], 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[T1], 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 adensitydependentinfluenceonthelevel1sawgrass model,whichisrepresentedbyEquations9and10,respectively. dP dt GF P 1 P K cattailF 9 Where P isthepopulationdensity[M/L2], t istime [T], GF isaconstantgrowthrate[T1], 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 factorsareallcalculatedusingthepreequations,similar tothatpresentedinEquation2.Thesefactorsarethen incorporatedintothemaingrowthequations,presented inEquations4,5,7and9representinglevelsofcomplexity2through5,respectively. InTARSE,componentsarelistedaseithermobileor stabile.Mobilecomponentsaremovedinthewater usingtheADREequations,whilethestabilecomponents donotmoveandonlyundergothereactionpartofthe ADRE.Giventhecomplexitiesassociatedwithsimulatingwindborneorwaterbornetransportationofseeds 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.Itcameintoexistencein1961withtheconstructionoftheL35Bcanalandreceivesinflowfrom 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 operationofcontrolpointsalongtheS10andL35B 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.StatisticalanalysisofsimulatedandmonitoredbiomassBesidesasidebysidevisualcomparisonofthemodel output,therewerethreesetsofstatisticalanalysistechniquesthatwereusedtocomparethemodelresultsand therawdata.Thesemetrics,commonlyusedinliteratureforcomparingbothsingleandmultispeciespatterns(FortinandDale2005;Muneepeerakuletal.2008; Convertinoetal.2009),analyzedthelocal,global,and autocorrelationstructureofobservedandmodeledvegetationpatterns.Allmetricswereaccompaniedbya Table1Cattailclassanddensityvaluesforformatting datamapsVegetationclassCattaildensity value(g/m2) Sawgrassdensity value(g/m2) 1Highdensitycattail1,00010 2Mediumdensitycattail600600 3Lowdensitycattail2001,000 4Other101,600 Lagerwall etal.EcologicalProcesses 2012, 1 :10 Page9of21 http://www.ecologicalprocesses.com/content/1/1/10 PAGE 10 NashSutcliffecoefficient(McCuenetal.2006),representedbyEquation11,whichprovidesasingularnumberforthecomparisonofthemodelstatisticsandhow theycomparetotheobserveddata.Thecoefficientisa comparisonofmodelresultsvwiththemeanofthedata. E f 1 X n i 0 y i y 2 X n i 0 y i y 2 11 Where E f istheNashSutcliffecoefficient, ^ y isthepredictedvariable, y i istheobservedvariable, y isthemean oftheobservedvariable,and n isthesamplesize.A NashSutcliffevalueof1meansthatthemodelcompletelymatchesthedata,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 (representingatypicalnoncattailregion),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 areplottedagainstanincreasingcellpairwisedistance, asinMaranietal.(2006),todeterminethetrendin spatialautocorrelationacrosstheentireregion. Alandscapescaleabundanceareaplot(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 moredispersedpatchesofhighdensitycattail.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 )abundancearea(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 abundanceareaplotinFigure6b,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)trendsoverpredictthedatapoints.The abundanceareastatistic(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.Theabundanceareastatistic (Figures7band8b)showssignificantoverpredictionof 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 )abundancearea(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 cattailmayindeedhaveadensitydependent/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.Theabundanceareastatisticforalltimeperiods (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) forlevel3liessomewhatinbetweenthatforlevel1and level2.Exceptforthetrainingperiod,whichslightly underpredictstheobservedvalues,thetwotestingperiodsappeartomoreaccuratelypredicttheobserved densitydistribution.Thisisconfirmedwiththetrend analysis(Figure5a,b,c),whereatleasttheregionaltrend isatorrelativelyclosetotheobservedvalues.Aswith Figure8 Regionalstatisticsfortesting2period(1995 2003)andallfivelevelsofcomplexity. ( a )Regionalmeantrend(reddotsrepresent initialandfinaldatavalues),( b )abundancearea(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.Theabundancearea 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 abundanceareastatisticonlyslightlyunderpredicts 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 statisticindicatesaslightoverpredictionofthe 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,thatinterspeciesinteractionsbetween 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 interspeciesinteractionsmightwellhaveaneffect withadifferentmodelstructure,thecurrentmodeling arrangementhasshownthebeginningofdiminishing returnswithrespecttomodelcomplexityand predictivecapability. WithregardtotheMoran s I statistic,allthecomplexity levelsfollowedthesamebasictrendasthedata(representedbytheblackline)andwereall0byaroundthe 18,240mmark.Thisdistancecorrespondsapproximately tothewidthoftheregion,whilethetotaldistanceof 36,480mintheplotcorrespondstothelongestnorth southdistanceoftheregion.Itisbelievedthatthestatistic dropsto0bythe18,240mmarkduetooverlappingand boundaryeffectsandthatthiselevatestheNashSutcliffe 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,disprovidedbytheNashSutcliffecoefficientsinTable3andcanbevisuallycomparedinFigure11, withtheboxplots(or1to1comparisons)locatedin Figure11a,abundanceareainFigure11b,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.Acoupledfreeform/fixedformmodelwas introducedtosolvethisproblem.Anaddedbenefitofthe freeformnatureoftheRSM/TARSEcoupledmodelisthe userdefinableequationsofinteraction,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.TheNashSutcliffecoefficient wasusedtodistinguishthesuccessofdifferentmodels. Bothlocalandlandscapescaleindicatorswereusedto performthecomparisonbetweenhistoricalandmodeled cattailpatterns.Theaveragelocalcattaildensitywas estimatedwithaboxplotanalysis;thepairwisecell comparisonoflocalcattaildensitieswasanalyzedwith Moran s I ;and,theregionalincreasewithareaofthe localcattaildensitywasestimatedthroughthe abundancearearelationship.Theboxplotandthe abundanceareawerethemostmeaningfulpatternsto discriminatemodelsintermsoftheirabilitytorepresent theobservedpatterns. Table3SummaryofNashSutcliffevaluescomparing modelandobserveddataforboxplot,Moran s I ,and abundanceareastatistics(representedbyFigures6,7, and8,respectively)forlevel1,level2,level3,level4, level5,training(199 1995),testing1(1991 2003),and testing2(1995 2003)simulationsYearlevel1to1BoxplotMoran s I Abundance 1991199510.740.980.98 20.130.99 0.94 30.490.950.23 40.740.980.96 50.740.980.96 199120031 0.750.97 1.89 20.020.86 0.35 30.230.980.44 40.490.980.77 50.490.980.76 199520031 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 NashSutcliffesummaryofstatistics. AgraphicalrepresentationofTable3.Thelevel4and5complexitymodelsperform consistentlywellincomparisonwithalltheothermodels. Lagerwall etal.EcologicalProcesses 2012, 1 :10 Page19of21 http://www.ecologicalprocesses.com/content/1/1/10 PAGE 20 inwatercontrolledareasinwhichtheanthropicdriven variableswouldbeexpectedtodominatethespecies processesandtheresultingpatterns. Limitationsofourcurrentmodelingapproachmayincludetheelement/trianglesize,witharangeof0.5 1.7 km2(Wang2009).Thisconstraintwasdictatedbythe choiceoftheRSMthatsimulateshydrologicalprocesses. Althoughtheimposedgridunithasarelativelycoarse sizeinwhichthereisstillconsiderableheterogeneityof theenvironmentalfeatures(Zajac2010),RTEhas proventobecapableofreproducingthedynamicsof cattailandsawgrassatthelandscapescaleusingthelevel 4andlevel5complexities.Thismakesitavaluabletool forexploringpotentialmanagementscenariosinwater conservationareasintheEvergladesandpossiblyin otherwatercontrolledwetlands. Furtherinvestigationswouldconsiderthequantificationoftheimportanceofwatercontrolleddriversand speciestraits(dispersal)forvegetationpatterns,thestability/instabilitystatesofspeciesundervaryingstressors, thepredictionoffuturemanagementscenarios,andthe comparisonwithneutralbasedmodels. Intermsoffurthermodeldevelopmentandaddedcomplexity,effortshavebeenmadetowardsmoreaccuraterepresentationoffaunamovementthroughtheuseof Eulerian Lagrangian(gridindependent)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.GeologicalSurveyWaterResources ResearchCenterattheUniversityofFlorida. Authordetails1FrazierRogersHall,UniversityofFlorida,POBox110570,Gainesville,FL 326110570,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++andFortran90forobjectorientedscientific programming.CompPhysComm105:20 36 CliffAD,OrdK(1970)Spatialautocorrelation:areviewofexistingandnew measureswithapplications.EconGeography46:269 292 ConvertinoM,MuneepeerakulR,AzaeleS,BertuzzoE,RinaldoA,RodriguezIturbe I(2009)Onneutralmetacommunitypatternsofriverbasinsatdifferent scalesofaggregation.WaterResourRes45:W08424 CostanzaR,VoinovA(2001)Modelingecologicalandeconomicsystemswith STELLA:partIII.EcolModel143:1 7 DeBuskWF,ReddyKR,KochMS,WangY(1994)Spatialdistributionofsoil nutrientsinanorthernEvergladesmarsh:WaterConservationArea2A.Soil SocAm58:543 552 DorenRF,ArmentanoThomasV,WhiteakerLouisD,JonesRonaldD(1999) MarshvegetationpatternsandsoilphosphorusgradientsintheEverglades ecosystem.AquaBot56:145 163 DouglasMS(1947)TheEverglades:riverofgrass.Rinehart,NewYork DukeSylvesterS(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 andpedopatternsmappedinWaterConservationArea2,Everglades, Florida,USA.Geoderma146:1 13 GuardoM,FinkL,FontaineThomasD,NewmanS,ChimneyM,BearzottiR, GoforthG(1995)Largescaleconstructedwetlandsfornutrientremovalfrom stormwaterrunoff:anEvergladesrestorationproject.EnvironManage19 (6):879 889 HaroldER(1998)XML:ExtensibleMarkupLanguage,1stedn.IDG,FosterCity JamesAI,JawitzJW(2007)Modelingtwodimensionalreactivetransportusinga Godunovmixedfiniteelementmethod.JHydrol338:28 41 JawitzJW,MuozCarpenaR,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.WileyLiss,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.203225inArapis,G., Goncharova,N.&Baveye,P.Ecotoxicology,EcologicalRiskAssessmentand MultipleStressors.Netherlands:Springer.(1402044755) Kiker,G.A.,RiversMoore,N.A.,Kiker,M.K.&Linkov,I.2006.QnD:Amodeling gamesystemforintegratingenvironmentalprocessesandpractical managementdecisions.pp.151185inMorel,B.&Linkov,I.Environmental SecurityandEnvironmentalManagement:TheRoleofRiskAssessment. Netherlands:Springer.(1402038925) 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)Nonneutral vegetationdynamics.PLoSOne1(1):e78 MartinTE(1980)Diversityandabundanceofspringmigratorybirdsusinghabitat islandsontheGreatPlains.CooperOrnitholSoc82:430 439 McCuenRH,KnightZ,CutterAG(2006)EvaluationoftheNashSutcliffeEfficiency 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)Disturbancemediatedmammalpersistenceand abundancearearelationshipsinAmazonianforestfragments.ConservBiol 21:1626 1640 MullerS(2010)Adaptivespatiallydistributedwaterqualitymodeling:an applicationtomechanisticallysimulatephosphorusconditionsinthe variabledensitysurfacewatersofcoastalEvergladeswetlands.PhD Dissertation.UniversityofFlorida,Gainesville MuneepeerakulR,BertuzzoE,LynchHJ,FaganWF,RinaldoA,RodriguezIturbeI (2008)Neutralmetacommunitymodelspredictfishdisversitypatternsin MississippiMissouribasin.Nature453:220 222 MuozCarpenaR,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.rproject.org/web/packages/ape/vignettes/MoranI.pdf.Accessed7 August2010 PerezOvillaO(2010)Modelingrunoffpollutantdynamicsthroughvegetative filterstrips:aflexiblenumericalapproach.PhDDissertation.Universityof Florida,Gainesville RichardsonCJ,KingRyanS,VymazalJ,RomanowiczEdwinA,PahlJamesW (2008)MacrophytecommunityresponsesintheEvergladeswithan emphasisoncattail( Typhadomingensis )andsawgrass( Cladiumjamaicense ) interactionsalongagradientoflongtermnutrientadditions,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,IrizarryOrtizMM,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:Theplanindepthpart1.http://www. evergladesplan.org/about/rest_plan_pt_01.aspx.Accessed3August2010 USACE,S.F.R.O(2010b)CERP:Theplanindepthpart2.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,andsurfacewaterstage inthesouthernEverglades,Florida.ScientificInvestigationsReport2007 2010.UnitedStatesGeologicalSurvey,Florida WetzelPR(2001)Plantcommunityparameterestimatesanddocumentationfor theAcrossTrophicLevelSystemSimulation(ATLSS).EastTennesseeState University,JohnsonCity WetzelPR(2003)Nutrientandfiredisturbanceandmodelevaluation documentationfortheActossTrophiclevelSystemSimulation(ATLSS).East TennesseeStateUniversity,JohnsonCity WillardDA(2010)SOFIAFS14696.http://sofia.usgs.gov/publications/fs/14696/. Accessed3August2010 WuY,SklarFH,RutcheyK(1997)Analysisandsimulationoffragmentation patternsintheEverglades.EcolAppl7(1):268 276 ZajacZB(2010)Globalsensitivityanduncertaintyanalysisofspatiallydistributed watershedmodels.PhDDissertation.UniversityofFlorida,Gainesvilledoi:10.1186/21921709110 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 