Spatial and Temporal Changes in Tree Islands of the Arthur R.
Marshall Loxahatchee National Wildlife Refuge in Response to
Altered Hydrologies
Prepared by:
Laura A. Brandt
University of Florida
Everglades Research and Education Center
PO Box 8003
Belle Glade, FL 33430
561/996-3062 ext 126
and
Wiley M. Kitchens
USGS/BRD
Florida Coop Unit
PO Box 110450
Gainesville, FL 32611-0450
352/846-0536
Final Report
June 1998
List of Tables
1. Number of tree islands per plot based on classification of satellite imagery (Richardson et al.
1990). Pixels are 9 x 9 m. Statistics are based on 100 resamples representing the listed percentage of
complete plots of that size. True mean, variance, and standard deviation are for all of the plots of that
size. Number of tree islands on imagery = 2144.
2. Mean percent tree island cover per plot based on classification of satellite imagery (Richardson
1990). Pixels are 9 x 9 m. Statistics are based on 100 resamples representing the listed percentage of
-complete plots of that size. True mean, variance, and standard deviation are for all of the plots of that
size. Percent cover of tree islands on imagery = 1.96.
3. Mean size (pixels) of tree islands per plot based on classification of satellite imagery (Richardson
1990). Pixels are 9 x 9m. Statistics are based on 100 resamples representing the listed percentage of
complete plots of that size. True mean, variance, and standard deviation are for all of the plots of that
size. Mean size of tree islands on imagery = 52.6 pixels, variance = 572.3, SD = 23.9.
4. Summary statistics for 1950 photo plots from Loxahatchee National Wildlife Refuge. Orientation
is 0 to 180 degrees with 0 = north and 180 = south.
5. Hydrology data for hydrology zones in Loxhatchee National Wildlife Refuge that contained photo
plots. See Appendix A for relation of hydrology zone to NSM and WMM rows and columns.
6. Correlations between tree island variables and hydrology variables for 1950 photo plots. Top num-
ber is correlation coefficient, bottom number is p value. A p value < 0.05 is considered significant.
7. Summary statistics for 1991 photo plots from Loxahatchee National Wildlife Refuge. Orientation
is 0 to 180 degrees with 0 = north and 180 = south.
8. Correlations between tree island variables and hydrology variables for 1991 photo plots. Top num-
ber is correlation coefficient, bottom number is p value. A p value < 0.05 is considered significant.
9. Differences between variables from 1950 to 1991. N.S. indicates no significant difference. Posi-
tive value for density, percent cover and change in ratio indicate anincrease from 1950 to 1991. Posi-
tive change in orientation magnitude indicates a clockwise change in orientation. A negative change
indicates a counter clockwise shift.
10. Spearman correlations between change in tree island variables and change in-hydrology variables
for 28 photo plots in Loxahatchee. Top number is correlation coefficient, bottom number is p value. A
p value < 0.05 is considered significant.
List of Figures
1. Location of Loxahatchee National Wildlife Refuge within the Everglades Ecosystem. Arrows show
general direction of historic sheet flow. Shaded area indicates the extent of the historic Hillsboro
Marsh. Adapted from Light and Dineen 1994 and Parker 1984.
2. Hydrology zone boundaries overlain on tree islands identified from satellite image classification of
Loxahatchee National Wildlife Refuge. Classification is from Richardson et al. 1990. Hydrology
zones are numbered left to right from 2 to 89. See Brandt 1997 for correspondence with overall NSM
and WMM row and columns.
3. Location of groups resulting from 5 class cluster analysis from satellite image classification using the
tree island variables number per cell, mean size, SD of size, and percent cover.
4. Location of 1800 x 900 m photo plots in Loxahatchee National Wildlife Refuge. Large squares are
the boundaries of the hydrology zones.
5. Histograms of mean orientation of tree islands from 1950 photo plots (top) and orientation of NSM
flow for grid cells containing photo plots (bottom).
6. Frequency distribution from all 1950 photo plots of treeislandsize (top), cumulative area (middle),
and contribution of each size class to overall tree island area. Sizes range from 0.01 to 21.22 ha.
Tree islands < 0.16 ha (rank of 16) make up 50% of the total tree island area.
7. Histograms of mean orientation of tree islands from 1991 photo plots (top) and orientation of WMM
flow for grid cells containing photo plots (bottom).
8. Frequency distribution from all 1991 photo plots of tree island size (top), cumulative area (middle),
and contribution of each size class to overall tree island area.- Sizes range from 0.01 to 11.50 ha.
Tree islands < 0.13 ha (rank of 13) make up 50% of the total tree island area.
9. Location of photo plots showing changes in percent cover. Down arrow indicates a decrease from
1950 to 1991, up arrow indicates <=5% increase and up arrow +5 indicates > 5% increase.
Table of Contents
1. Executive Surmn ary................................. ..... ............... .. 5
2. Introduction......................................... ..................8
3. Study A rea ................. ... .... ........ ... ............... .................. ... ............ 11
4. Selection of Sam pling R egim e......................................................................... ....................... 12
5. Historic and Current Patterns of Tree Islands and Correlation With Hydrology........................... 19
6 R esu lts .............. ................... .............. .. .......... .... ..... .. ................. ............. ...... .. ........ 2 2
7. D discussion ................................... ......... ... .. .. ....................... ..................36
8 L iteratu re C ited .................................... ..............................................................................39
9. Appendix...................... ............ ....................... ................................... .. ........ 44
4
Executive Summary
The Everglades, once a vast dynamic
flow-through wetland extending from the Kissim-
mee chain of lakes south to Florida Bay, has been
severely altered in the last century. The develop-
ment of south Florida has led to the conversion of
portions of the historic system to urban and agri-
culture and the conversion of the once sheet-flow
system into a series of highly regulated impound-
ments and canals. The historic hydrological pat-
terns of the Everglades were vital in creating and
maintaining the heterogeneity of the landscape,
which in turn, contributed to the persistence and
resilience of the system (Holling et al.1994). Hy-
drology, the dominant natural mesoscale process
acting in the Everglades has been seriously altered
and has caused changes to the remaining vegeta-
tion in the system (Davis and Ogden 1994).
Changes in hydrologic patterns have contributed to
the reduction in plant community heterogeneity,
the change and decrease in wildlife populations,
and changes in the historic functioning of the Ever-
glades (see Davis and Ogden 1994). Changes in
vegetation structure and composition have been
noted in many regions of the Everglades (Loveless
1959, Alexander and Crook 1984, Higer and Ko-
lipinski 1987, Parks 1987, Worth 1988,
Richardson et al. 1990) and Davis et al. (1994)
have documented massive loss .or -conversion of
entire landscape types. However, the total extent
of these changes is unknown, and it is unlikely that
the magnitude of the changes will be completely
understood.
Tree islands are a prominent feature of the
Everglades wetlands landscape. They are areas of
slightly higher elevation where non-wetland plants
have been able to colonize. They. are important
ecologically as sites of high botanical species rich-
ness and as habitat for species such as wading
birds, raptors, alligators (Alligator mississippien-
sis, turtles, deer (Odocoileus virginianus ),.and
small mammals. Tree islands are the resultant of
many processes operating over a wide range .of
temporal and spatial scales including hydrologic
processes such as flow volume, inundation depth,
and hydroperiod. Feedbacks between dynamic
flows and water stages and the biotic structure of
tree islands determine the physical structure (size,
shape, orientation) of the islands.
The Arthur R. Marshall Loxahatchee Na-
tional Wildlife Refuge (Loxahatchee), is a 57,324
ha area of northern Everglades wetlands mosaic
consisting of wet prairie, sawgrass, slough, and
tree islands_ Located in Palm Beach County, Flor-
ida, south and east of Lake Okeechobee, it was
once a connected part of the historic Everglades
system. Construction of canals to drain the Ever-
glades Agricultural Area and for flood control ef-
fectively isolated Loxahatchee from it's original
watershed. The system changed from a dynamic
flow-through, sheet-flow driven fluvial system
with flow rates that reached a maximum of ap-
proximately 36 m per h (Holling et al. 1994) to an
impounded marsh with the majority of overland
flow inputs being shunted around the marsh via the
exterior canals. Loxahatchee is an ideal area for
examining the long-term effects of changes in hy-
drologic patterns on the landscape. This study
quantifies the historic (1950) and current (1991)
patterns of tree islands in Loxahatchee. Historic
tree island patterns are related to modeled pre-
drainage hydrologic patterns. Current tree island
patterns are related to post-drainage hydrologic
patterns. Changes.in tree island shape, size, and
distribution are examined in relation to changes in
hydrologic processes to better understand the long-
term influences of hydrologic processes on land-
scape pattern
Because it was not logistically feasible to
quantify tree island patterns through out Loxa-
hatchee using aerial photography a sampling re-
gime was developed so that areas with different
size, shaped, and densities of tree islands would be
sampled and so that samples would be representa-
tive of the overall patterns in the refuge. A land
cover classification of Loxahatchee was used to
represent the overall patterns of tree islands in the
refuge. Sample plot size and shape was deter-
mined by overlaying a grid of various sizes on the
land cover and -randomly sampling 100 times 10
to 50 % of the grid cells. For each group of 100
random samples number, average size, percent
cover, and SD of tree island size were determined.
Selection of the final plot size of 200 x 100 pixels
(1800 x 900m ) was based on consideration of
which sampling regime had both the most precise
and accurate estimates of the tree island variables
when compared to the values of those variables for
the entire study area. Once the plot size was se-
lected, plot locations were determined with strati-
fled random sampling. Strata were determined us-
ing a cluster analysis on the tree island variables,
number, size, percent cover, and SD of size. Plots
were selected proportionally from these strata so
that the total area of the samples was 10% of the
refuge (28 plots).
Tree islands were delineated in each plot
using 1950 1:60,000 black and white aerial pho-
tography and 1991 1:40,000 color infrared pho-
tography. Tree island size, shape, orientation and
distribution were quantified for each plot.
Data on hydroperiod, water depth, flow
direction and magnitude were obtained from the
South Florida Water Management District. Data
were from two models 1) the South Florida Water
Management Model Version 2.10 (WMM) devel-
oped to simulate the hydrology of the water man-
agement system in south Florida (MacVicar et al.
1984) and 2) the Natural Systems Model version
4.4 (NSM), adapted from the WMM to simulate
the hydrologic response of pre-drainage .south
Florida using climatic data from 1965-1990
(Fennema et al. 1994). Both models have a grid
cell size of 3.2 x 3.2 km (2 miles x 2 miles). Grid
cells are referred to as hydrology zones though out
this text. Depth, flow direction and magnitude are
the yearly average values for each grid cell calcu-
lated over the entire period of record (1965-1990).
Tree island variables were compared be-
tween the two dates on a plot by plot basis and in
an analysis of all plots together. Correlation
analysis and canonical correlation analysis were
used to relate tree .island patterns to hydrologic
patterns.
Tree island size, shape, and orientation
varied considerably through out Loxahatchee.
Small tree islands made up a larger percent of the
total area covered by tree islands than did large
tree islands. The orientation of elliptical tree is-
lands was not different from the orientation of
modeled historic water flows. Historically, range
in hydroperiod and flow magnitudes were related
to tree island shape, size, and number. Current
relations between tree islands and hydrologic vari-
ables were very different from historic relations,
with current hydroperiod and ponding depth re-
lated to tree island size. Percent cover of tree is-
lands in plots closer to the canals decreased while
percent cover of tree islands in plots in the interior
part of the refuge increased. -Changes in patterns
of tree islands were correlated with changes in hy-
drologic variables, with larger changes in the hy-
drologic variables correlated with larger changes
in tree island variables.
Historically, in Loxahatchee, there were
more tree islands in areas of longer hydroperiod
and greater depth. These areas also were less vari-
able in hydroperiod range. The multivariate analy-
sis demonstrated that hydroperiod range and flow
magnitudes are important inexplaining the ratio of
elliptical to circular tree islands. Areas that were
less variable with lower flow had lower ratios of
elliptical to circular tree islands (e.g. more circular
than elliptical tree islands). In addition, areas with
less variation in hydroperiod had more tree islands
of larger size that covered a larger area. These
results support the hypotheses that flow is impor-
tant in shaping tree islands and that battery tree
islands form under conditions of greater hydro-
period and depth.
The relation between the tree island vari-
ables and hydrology variables in 1991 is very dif-
ferent from 1950. There were no significant corre-
lations between the individual tree island variables
and hydrology as there were with the 1950 data.
The multivariate. analysis shows that of the vari-
ables used here, hydroperiod and depth were the
most important in explaining tree island size. Ar-
eas of longer hydroperiod and depth had smaller
tree islands.
Loxahatchee can be grouped into three
zones according to the patterns of change of tree
islands observed from 1950 to 1991. 1) the edge of
the refuge adjacent to the canals, 2) the eastern in-
terior of the refuge, and 3) the western interior of
the refuge. The general trend is for tree islands
along the edge of the refuge to have decreased in
size, number, and percent cover, while those on the
interior increased in size, number, and percent
cover.
Results from this study illustrate the im-
portance of flow magnitude as well as hydroperiod
and depth in structuring-he patterns of tree islands
within this peat wetland. Restoration of historic
hydroperiods and depths without historic flow pat-
terns may not be sufficient to restore or maintain
the historic pattern and function of the system.
Introduction
The Everglades, once a vast dynamic
flow-through wetland extending from the Kissim-
mee chain of lakes south to Florida Bay, has been
severely altered in the last century. The develop-
ment of south Florida has led to the conversion of
Portions of the historic system to urban and agri-
culture and the conversion of the once sheet-flow
system into a series of highly regulated impound-
ments and canals. The vast mosaic of marsh,
slough, tree islands, and pinelands has been re-
duced to half of the historic 3.6 million ha (Davis
and Ogden 1994). In addition, what remains is
subject to hydrologic regimes that, in places, bear
little resemblance to pre-drainage patterns
(Fennema et al. 1994).
The historic hydrological patterns of the
Everglades were vital in creating and maintaining
the heterogeneity of the landscape, which in turn,
contributed to the persistence and resilience of the
system (Holling et al.1994). The Everglades, like
other ecosystems, is the product of the interaction
of biota and abiotic forces such as climate, hydrol-
ogy, nutrient inputs, and disturbance (DeAngelis
and White 1994). These processes, operating over
a range of spatial and temporal scales, interact to
form the current landscape patterns. Changes in
macroscale processes such as geology and climate
occur over long time scales and are generally not
noticeable within a human lifetime. At the other
extreme, changes in microscale processes such as
nutrient transfer occur very rapidly and the conse-
quences to wetland vegetation can be observed in a
season. In between are mesoscale processes that
act on a scale of kilometers to tens of thousands of
kilometers and over time scales of decades to cen-
turies. Hydrology is the dominant natural meso-
scale process acting in the Everglades. It is also
the process that has been most seriously altered
and has caused the largest changes to the remain-
ing vegetation in the system (Davis and Ogden
1994). Changes in hydrologic patterns have con-
tributed to the reduction in plant community het-
erogeneity, the change and decrease in wildlife
populations, and changes in the historic function-
ing of the Everglades (see Davis and Ogden 1994).
Changes in vegetation structure and composition
have been noted in many regions of the Everglades
(Loveless 1959, Alexander and Crook 1984, Hi-
ger and Kolipinski 1987, Parks 1987, Worth 1988,
Richardson et al. 1990) and Davis et al. (1994)
have documented massive loss or conversion of
entire landscape types. However, the total extent
of these changes is unknown, and it is unlikely that
the magnitude of the changes will be completely
understood.
Tree islands are a prominent feature of the
Everglades wetlands landscape. They are areas of
slightly higher elevation where non-wetland plants
have been able to colonize. They are important
ecologically as sites of high botanical species rich-
ness and as habitat for species such as wading
birds, raptors, alligators (Alligator mississippien-
sis), turtles, deer (Odocoileus virginianus ), and
small mammals.
Tree islands are the resultant of many pro-
cesses operating over a wide range of temporal and
spatial scales. At the microscale, processes such as
the deposition and removal of substrate around the
island, establishment of seedlings, tree growth, and
mortality dominate at time scales ranging from
seconds.to years. These microscale processes are
influenced by higher level mesoscale processes/
driving forces such as fire frequency, hydroperiod,
inundation depth, and water flow that act over a
temporal scale of 1-100 years. These higher level
processes are in turn influenced by events such as
hurricanes, floods, and drought and by still higher
level processes such as climate change and geo-
morphology operating on temporal scales of hun-
dreds of years. Major differences in the magnitude
or frequency of any of these processes will be ex-
pressed by different patterns on the landscape
through changes in physical and biotic mecha-
nisms. The feedbacks between colonization,
growth, competition, death, and decomposition de-
termine the biotic structure of the tree island.
Feedbacks between dynamic flows and water
stages and the biotic structure of tree islands deter-
mine the physical structure (size, shape, orienta-
tion) of the islands.
Tree islands in the Everglades have been
described by their general size, shape, and orienta-
tion as either small and circular; "Circular tree is-
lands... are normally quite small in size, ranging
from only about one-quarter acre to five or six
acres in extent." (Loveless 1959 pp. 4) or large
and elongated and oriented in the direction of flow
(Davis 1943, Jones 1948, Gleason et al.1984). It
: is generally thought that the interaction of topogra-
phy and surface water flow resulted in the charac-
teristic shape and orientation of the larger tree is-
lands (Davis 1943, Jones 1948).
Circular tree islands may form in areas of
lower flow, while elongated tree islands may form
in areas of higher more persistent flow. Changes
in flow patterns may change the distribution and
shape of tree islands and may reflect a change in
structuring processes within the system. Altera-
tions in the hydrology in the Everglades ecosystem
provide an opportunity. to study the effects of
changes in landscape patterns in relation to
changes in structuring forces such as hydrology.
Understanding such relationships will be important
for examining potential impacts of Everglades res-
toration plans on the ecosystems structure and
function.
This study. quantifies the historic (1950)
and current (1991) patterns of tree islands in a
remnant of the northern Everglades where the hy-
drologic regime has been severely altered. Historic
tree island patterns are related to modeled pre-
drainage hydrologic patterns. Current tree island
patterns are related to post-drainage hydrologic
patterns. Changes in tree island shape, size, and
distribution are examined in relation to changes in
hydrologic processes to better understand the long-
term influences of hydrologic processes on land-
scape pattern.
---------------
\,\
I V
0 50km
-N-t
Figure 1. Location of Loxahatchee National Wildlife Refuge within the Everglades Ecosystem. Arrows show
general direction of historic sheetflow. Shaded area indicates the extent of the historic Hillsboro Marsh.
Study Area
The Arthur R. Marshall Loxahatchee Na-
tional Wildlife Refuge (Loxahatchee), is a 57,324
ha area of northern Everglades wetlands. Located
in Palm Beach County, Florida, south and east of
Lake Okeechobee, (Figure 1) it was once a con-
nected part of the historic Everglades system.
Loxahatchee is located over the Loxahatchee
Channel, a shallow peat filled depression extend-
ing from Lake Okeechobee that may have acted as
an overflow valve for Lake Okeechobee shunting
water east and south (Gleason et al. 1984).
Changes to the flow patterns in and around Loxa-
hatchee started as early as the 1800s with the con-
struction of the Caloosahatchee canal, which
moved water from Lake Okeechobee to the west.
Additional changes occurred with the completion
of the Hillsboro Canal in the 1920s, with the com-
pletion of the St. Lucie canal in 1931, and the with
the complete enclosure of the area by the L-7 canal
on the west and the L-40 canal on the east during
the 1950s (Light and Dineen 1994). The construc-
tion of these canals effectively isolated Loxa-
hatchee from it's original watershed. The system
changed from a dynamic flow-through, sheet-flow
driven fluvial system with flow rates that reached
a maximum of approximately 36 m per h (Holling
et al. 1994) to an impounded marsh with the ma-
jority of overland flow inputs being shunted
around the marsh via the exterior canals.
Loxahatchee is a peat-based wetland sys-
tem consisting of a mosaic of aquatic sloughs, ex-
panses of wet prairie, strands of sawgrass
(Cladium jamaicense Crantz), patches of brush,
and tree islands. The- origin of these tree islands is
a topic of much speculation. The discussions focus
on two general mechanisms for tree island forma-
tion. The first is that the tree islands have formed
on peat ridges or bedrock outcrops between the
sloughs (Loveless 1959). The second is that the
tree islands have formed from mats of floating
vegetation or peat "popups." The first is a more
plausible explanation for tree islands in the lower
Everglades where limestone outcrops are more
common and a shallow peat layer makes it unlikely
that floating peat islands could develop. It also
may be a reasonable explanation for the formation
of tree islands in the eastern portion of deeper peat
wetlands such as Loxahatchee, where there are
more pronounced peat ridges. The formation of
tree islands from peat "popups" or floating vegeta-
tion is more likely in areas such as Loxahatchee
where peats are relatively deep (3 to 4 m). Peat
"popups" might form in 3 ways: bulges, free float-
ing batteries, or "gator holes". Bulges are formed
when a surface layer of peat becomes separated
from the deeper peat and rises to the water surface,
but remains attached to the- submerged peat on its
periphery (Cypert 1972). Free-floating batteries
occur where the peat breaks loose from the bottom
and rises to the surface often with the return of
high water following a period of low water. There
is some evidence that this occurs in Loxahatchee
(Gleason et al.1980). Disturbance by alligators
also might result in floating peat mats. As an alli-
gator creates it's wallow the underlying substrate
is pushed out of the way. The result is either a
floating peat mat or a local topographic high, ei-
ther of which could lead to tree island formation.
Once these peat mats reach the surface they can be
colonized first by aquatic vegetation such as saw-
grass and Eleocharis spp., as these plants die, the
mass increases making it possible for larger more
woody plants to become established. The location
and characteristics of a tree island will be deter-
mined by local hydrologic and biotic processes.
Selection of Sampling Re2ime
Conducting fine scale analysis across a
large landscape often is not logistically feasible.
Extrapolating results from a sample to the entire
landscape is a difficult task (Allen and Hoekstra
1992, Meentemeyer and Box 1987, Wiens 1989)
and will depend on the scale of the patterns being
observed and the scale of observation. Determining
appropriate sampling units has been a topic of eco-
logical studies for many years (Greig-Smith 1961,
Kershaw 1957, Turner et al.1991). Different sam-
pling methods emphasize different population
properties, resulting in collection of different kinds
of data. Some methods emphasize estimating spe-
cies composition or inclusion of representative
species. Others strive to minimize the variance in
plot to plot measurements. In all cases, plot size
and shape should be based on the question being
addressed and the size and the spatial distribution
of the entity being studied (Green 1979). Plots that
are too large mask the patterns by averaging the
values within the plot, while plots that are too
small may be large inadequate to accurately rep-
resent the spatial pattern (Meentemeyer and Box
1987, Milne 1991).
The position of the plots in the landscape
influences the interpretation of the results. Sample
sites are usually selected randomly when it is as-
sumed that the spatial distribution of the variables
of interest are homogeneous across the area of
study. Because landscapes are heterogeneous, use
of simple random sample locations often is not ap-
propriate or effective. Whenever possible the area
should be divided into homogeneous (based on the
variables of interest) sub-areas and samples se-
lected at random and in proportion to sub-area size
(Green 1979). Broad scale land cover developed
from satellite imagery provides a method for iden-
tifying homogeneous areas within a landscape and
is a tool for that can be used to select appropriate
sample plot sizes and location.
We used a classified satellite image to de-
termine what plot size, shape, and locations would
accurately and precisely represents the patterns of
tree islands within Loxahatchee.
Tree islands were identified from an exist-
ing land cover classification for Loxahatchee de-
veloped from merged, IHS transformed 10 m pan-
chromatic data and 20 m SPOT data (Richardson
et al. 1990) and referenced to State Plane coordi-
nates. Details of the classification methods are
available in Richardson et al. 1990. The classified
image was converted to Universal Transverse
Mercator (UTM) resulting in a cell size of 9 x 9
m. Two tree island classes described as: "lower
stature tree island community made up of a mix of
wax myrtle (Myrica cerifera), dahoon holly (lex
cassine) and red bay (Persea borbonia)", and "core
of larger tree islands, larger stature trees made up
primarily of dahoon holly and red
bay..." (Richardson et al. 1990 pp. 40) were used
in this analysis (Figure 2). All other classes were
considered background. Two tree island layers
were generated for this analysis; the first was an
3 4 6 6 7 S 9
Kilometers
Figure 2. Hydrology zone boundaries overlain on tree islands
identified from satellite image.classification ofLoxahatchee
National Wildlife Refuge. Classification is from Richardson
et al. 1990. Hydrology zones are numbered left to right from
2 to 89. See Brandt 1997for correspondence with overall
NSM and J'iMM row and columns.
image with tree islands coded as 1, all other vege-
tation classes in Loxahatchee as 2, and the area
outside of Loxahatchee as 3. In the second layer
each tree island was labeled with a unique number
using the Clump command in Erdas Imagine
(Erdas Inc. 1995) which identifies contiguous
groups of pixels of a class.
Two thousand one hundred forty-four tree
islands were identified on the classified image.
Average tree island size ( SD) was 52.6 23.9 pix-
els (0.4 ha) Tree islands comprised 1.96 percent
of Loxahatchee.
The selection of plot size, shape, number
and location was sequential process in which the
results from the previous analysis determined the
starting point for the next analysis. First an ap-
propriate plot size was selected. Next the percent-
age of the refuge to sample, and hence the number
of plots was determined. Finally, the plot loca-
tions were selected using stratified random sam-
pling based on the patterns observed in the first
analysis.
Plot size was determined by comparing
values from a series of regular grids. Regular
grids of 50 x 50 pixels, 100 x 100 pixels, 200 x
100, and 200 x 200 pixels (length x width) were
generated in ARC/INFO. These grids were im-
ported into Erdas Imagine and overlain on the
Table 1. Number of tree islands per plot based on classification of satellite imagery (Richardson et al.
1990). Pixels are 9 x 9 m. Statistics are based on 100 resamples representing the listed percentage of
complete plots of-that size. True mean, variance, and standard deviation are for all of the plots of that
size. Number of tree islands on imagery = 2144.
Plot size Sample size Percent Mean Variance SD
(pixels)
14.19
14.36
14.25
14.84
14.19
14.46
7.59
7.36
7.38
7.39
7.46
7.42
4.04
4.04
3.96
3.97
3.97
3.96
100 samples of 11
100 samples of 22
100 samples of 33
100 samples of 44
100 samples of 55
111
100 samples of 25
100 samples of 50
100 samples of 75
100 samples of 100
100 samples of 126
252
100 samples of 45
100 samples of 90
100 samples of 135
100 samples of 180
100 samples of 226
451
100 samples of 188
100 samples of 376
100 samples of 565
100 samples of 753
100 samples of 941
1882
1.14
1.11
1.14
1.13
1.12
1.13
21.36
8.53
4.39
2.26
1.74
4.62
2.92
2.09
1.5
1.32
226.12 15.03
2.86
1.14
0.62
0.52
0.25
86.57
0.59
0.3
0.15
0.09
0.06
30.2
0.019
0.008
0.003
0.003
0.002
3.64
1.69
1.07
0.79
0.72
0.5
9.3
0.77
0.55
0.38
0.31
0.26
5.5
0.14
0.09
0.06
0.05
0.04
1.91
200x200
True values
200x100
True values
100x100
True values
50x50
True values
three class image (background, tree islands, not
tree islands) and the clumped image (layer with
individual tree islands labeled) using the Erdas
Imagine Summary command. Output from these
procedures was three data sets for each grid size:
1) the percent cover of tree islands in each grid
cell, 2) the number of different tree islands in each
grid cell, and 3) the size of each tree island in each
grid cell. Mean, median, variance, and standard
deviation were calculated for percent tree island
cover, number of tree islands and size of tree is-
lands for all grid cells combined at each cell size.
These data were used to detennine an appropriate
plot size.
To examine the effects of different sam-
pling intensity on the accuracy and precision of the
results, estimates of tree island size, variance in
size, number, and percent .cover were calculated
100 times using random samples of grid cells to
represent 10%, 20%, 30%, 40%, and 50% cover-
age of the study area.
Results were compared to the values com-
puted for the entire area (all grid cells of that size)
to determine which plot size and coverage percent-
age were most accurate and precise in representing
the size, percent cover, and number of refuge tree
islands. Estimates also were compared to the pa-
rameter values calculated for the entire refuge
Table 2. Mean percent tree island cover per plot based on classification of s-atellite imagery
(Richardson 1990). Pixels are 9 x 9 m. Statistics are based on 100 resamples representing the
listed percentage of complete plots of that size. True mean, variance, and standard deviation
are for all of the plots of that size. Percent co ver of tree islands on imagery = 1.96.
Plot size Sample size Percent Mean Variance SD
(pixels)
200x200 100 samples of 11 10 1.98 0.3 0.55
100 samples of 22 .20 1.9 0.2 0.44
100 samples of 33 30 1.89 0.09 0.29
100 samples of 44 40 1.9 0.06 0.24
100 samples of 55 50 1.91 0.04 0.19
True values 111 100 1.91 4.01 2.00
200x100 100 samples of 25 10 1.88 0.21 0.46
100 samples of 50 20 1.89 0.15 0.38
100 samples of 75 30 1.85 0.08 0.27
100 samples of 100 40 1.85 0.05 0.22
100 samples of 126 50 1.83 0.03 0.18
True values 252 100 1.85 7.99 2.83
100x100 100 samples of 45 10 1.86 0.42 0.65
100 samples of 90 20 1.82 0.15 -0.39
100 samples of 135 30 1.88 0.09 0.3
100 samples of 180 40 1.82 0.06 0.24
100 samples of 226 50 1.84 0.04 0.20
True values 451 100 1.85 16.23 4.03
50x50 100 samples of 188 10 2.07 0.15 0.38
100 samples of 376 20 2.03 0.1 0.31
100 samples of 565 30 1.96 0.05 0.23
100 samples of 753 40 1.97 0.03 0.17
100 samples of 941 50 1.97 0.02 0.16
without using the grids.
Changing plot size and percentage resulted
in larger changes in precision than in accuracy
(Tables 1 to 3). Sampling more of the refuge re-
sulted in lower variance (higher precision) for all
Variables and all plot sizes. The smallest plot size
(50 x 50) had the smallest variance for all vari-
ables followed by the 200 x 100 plot size. Only
compete grid cells were used in the above analyses
so the amount of the refuge sampled varied slightly
among grid sizes.
In unbiased sampling the mean compiled
from successive resampling should exactly equal
the true mean of the population. The mean and
standard deviation of the mean can be used to de-
termine which sampling regime provides the most
accurate (closest to the true value) and precise
(repeatedly close to the. original value) estimates.
In this study, mean values were similar for each
variable at all percentage samples of Loxahatchee
indicating similar accuracy at all percentage sam-
ples. As expected sampling a greater percentage
of the refuge resulted in a more precise estimate of
the mean. Because of logistical constraints (the
effort and cost of a larger sample) sampling per-
centage was limited to 10% of the refuge. Had a
greater proportion of the refuge been sampled the
results would be 20-40% more precise. This sug-
Table 3. Mean size (pixels) of tree islands per plot based on classification of satellite
imagery (Richardson 1990). Pixels are 9 x 9mn. Statistics are based on 100 resamples
representing the listed percentage of com plete plots of that size. True mean, variance, and
standard deviation are for all of the plots of that size. Meanl size of tr-e islands on im agery
= 52.6 pixels, variance = 572.3, SD = 23.9.
Plot size Sample size Percent Mean Variance SD
(p ix els)
200x200 100 samples of 11 10 71.68 1052.99 32.45
100 samples of 22 20 70.57 572.07 23.92
100 samples of 33 30 74.44 407.28 20.18
100 samples of 44 40 72:93 188.67 13.74
100 samples of 55 50 73.53 132.36 11.5
True values 111 100 73.41 14485.1 120.35
200x100 100 samples of 25 10 55.66 370.14 19.24
100 samples of 50 20 61.58 243.3 15.6
100 samples of 75 30 57.76 130.08 11.4
100 samples of 100 40 59.61 69.03 8.31
100 samples of 126 50 59.9 42.91 6.55
True values 252 100 59.85 12626.47 112.37
100x100 100 samples of 45 10 47.04 497.88 22.31
100 samples of 90 20 52.88 278.377 16.68
100 samples of 135 30 51.81 158.88 12.6
100 samples of 180 40 53.67 89.91 9.48
100 samples of 226 50 52.61 70.42 8.39
True values 451 100 52.57 28449.05 16.867
50x50 100 samples of 188 10 28.56 82.13 9.06
100 samples of 376 20 28.01 30.94 5.56
100 samples of 565 30 27.9 15.48 3.93
100 samples of 753 40 27.76 11.08 3.33
100 samples of 941 50 27.97 8.78 2.96
gests that some caution should be used in extrapo- better than the 200 x 200 or 100 x 100. Likewise,
lating results from a 10% sample to the entire ref- estimates of percent cover using the 200 x 100 plot
uge. size were closer to the mean percent cover and had
Estimates of the total number of tree is- a lower standard deviation than other plot sizes.
lands in Loxahatchee were closer to the true num- As was found by O'Neill et al. 1995, sam-
ber when the smaller plot sizes were used, proba- ple plots of different size and shape resulted in dif-
bly because the amount of area sampled was ferent values of the patch (tree island) statistics.
closer to the actual area of the refuge (only plots Mean tree island size was Iunderestimated in the
completely within the refuge boundaries were small plots because of the plots inability to include
used). Estimates from the 200 x 100 plots were tree islands of the largest sizes. On the other hand,
Scale
I= Kilometers
2 0
Figure 3. Location of groups resulting from 5 class cluster analysis from satellite image classification
using the tree island variables number per cell, mean size, SD of size, and percent cover.
large plots tended to over estimate the mean size.
An explanation for this is that larger plots are
more likely to include all of a large tree island at
the exclusion of more smaller tree islands, result-
ing in an increase in the average tree island size in
each plot. An advantage of smaller plots is that
more plots are needed to sample the same area of
the refuge than are needed with larger plots; there-
4 5
fore, the plots can be spread throughout the refuge.
The disadvantage is that smaller plots may not
represent the spatial distribution of the tree islands
because the scale is too fine.
Based on the above analysis, the fact that
the spatial patterning of the tree islands seems to
be more dominant in the north/south direction, and
the added constraint that plots should be large
8 9
'-44
l__
7
i 35ts I
310
Ti
238
210 215 kw |ke 227
205
173
1 147 1
159
124
Ito
S62 10
Scale ________
82
2 0
1b I
Figure 4. Location of 1800 x 900 m photo plots in Loxahatchee National Wildlife Refiuge. Large
squares are the boundaries of the hydrology zones. Hydrology zones are numbered left to right from 2
to 89. -See Brandt 1997 for.correspondence with overall NSMand WMM row and columns.
ft
f
enough to contain the largest tree islands, a plot
size of 200 x 100 was selected.
To ensure that samples selected for photo-
graphic analysis represented the range of tree is-
land densities and size within the refuge, cluster
analysis using Ward's Cluster Method (SAS Insti-
tute Inc. 1989) was used to group grid cells based
on percent cover of tree islands, number of tree
islands, mean size of tree islands, and the variance
of tree island size. Grid cells with no tree islands
were not included in the cluster analysis, but were
assigned to a cluster of their own. Twenty-seven
grid cells (plot locations) were selected using ran-
dom samples from each strata based on the pro-
portion of grid cells in that strata.
The cluster analysis indicated that grid
cells could be divided into five groups based on the
number, .average. size, and percent tree islands
within the cell (Figure 3). The number of cells and
the proportion of the total cells in each group
were:
Group 1- (lownumber of tree islands, me-
dium average size, low percent cover)- 30 cells ,
12%;
Group 2- (high number of tree islands,
medium average size, high percent cover)-185
cells, 73%; Group 3- (low number of tree islands,
small average size, low percent cover)- 5 cells,
2%;
Group 4- (low number of tree islands,
large average size, high percent cover)-6 cells, 3%;
Group 5- (no tree islands)-26 cells, 10%.
Samples for photographic analysis were
selected proportionally from each group so that
10% of the grid cells were represented. The result
was random selection of 4 plots from group 1, 19
plots from group 2, 1 plot from groups 3 and 4,
and 2 plots from group 5 (Figure 4).
Historic and Current Patterns of Tree Islands and Correlation
With Hydrology
Image sources for photographic analysis
Were twelve 1:60,000 panchromatic diapositives
flown in November or December 1950 and twenty
1:40,000 color-infrared diapositives flown in De-
cember 1990 or January 1991. Each set of photos
was photogrammetrically scanned at the appropri-
ate scanning resolution to result in 2 m ground
resolution. The images were referenced to a 10 m
geocoded SPOT satellite image and mosaiced us-
ing Orthoengine from PCI Remote Sensing Corpo-
ration. The result was two complete images of
Loxahatchee with average residual errors of ap-
proximately 4 m for 1950 and 2 m for 1991. Be-
cause plots not individual tree islands were the unit
being compared this level of error was deemed ac-
ceptable.
Boundaries of tree islands larger than 100
m2 within each if the 27 photo plots were screen
digitized in ARC/INFO using scanned images of
the original photography. The original photogra-
phy was used for reference for both years. Addi-
tional 1:24,000 black and white photography was
used as reference for the 1950 plots. Tree island
identification on the 1991 photography was veri-
fied by field sampling.
Number, area, perimeter, and centroid lo-
cations (X and Y coordinates) for all tree islands
were obtained directly from ARC/INFO. Length
of long axis and secondary axis were calculated
using a program developed in S-plus (Statistical
Sciences, Inc. 1995). Tree islands were classified
as circular, elliptical (shaped) or irregular (no
shape) using a combination of a circularity index
(Miller 1953) and ellipse index. These indices are
the ratio of the area of the tree island to the area of
a circle, or ellipse, respectively given the same
long axis and secondary axis. An index of 1 indi-
cates complete agreement (an exact circle or el-
lipse). Values above or below 1 indicate deviation
from the ideal shape. Index thresholds were deter-
mined by randomly selecting tree islands and visu-
ally categorizing them as- circular, elliptical, or ir-
regular. The calculated index values and the vis-
ual categorization were used to determine the cut-
off criteria for each type of tree island. Tree is-
lands with a circularity index of 0.85 or larger
were considered circular. Tree islands with a cir-
cularity index < 0.85 were elliptical if their ellipse
index was < 6. All remaining tree islands were
classified as irregular. Orientation was determined
for elliptical tree islands by calculating the direc-
tion of the long axis using a program developed in
S-plus (Statistical Sciences, Inc. 1995). Orienta-
tion ranges from 0 to 180 with 0 as north and 180
as south. No attempt was made to distinguish be-
tween the leading and trailing edge of the tree is-
land.
Data on hydroperiod, water depth, flow
direction and magnitude were obtained from the
South Florida Water Management District. Data
are from two models 1) the South Florida Water
Management Model Version 2.10 (WMM) devel-
oped to simulate the hydrology of the water man-
agement system in south Florida (MacVicar et al.
1984) and 2) the Natural Systems Model version
4.4 (NSM), adapted from the WMM to simulate
the hydrologic response of pre-drainage south
Florida using climatic data from 1965-1990
(Fennema et al. 1994). Both models have a grid
cell size of 32 x 3.2 km.(2 miles x 2 miles). Grid
cells are referred to as hydrology zones though out
this text. Depth, flow direction and magnitude are
the yearly average values for each grid cell calcu-
lated over the entire period of record (1965-1990).
Direction of flow was standardized to 0-180 de-
grees to match the range used for the tree island
orientation and then transformed using tan
(theta /2). Two variables were used to represent
hydroperiod: the first was the 90% hydroperiod or
the hydroperiod that was exceeded in 90% of the
26 years. The second hydroperiod variable was
range in hydroperiod. Range in hydroperiod was
Table 4. Summary statistics for 1950 photo plots from Loxahatchee National Wildlife Refuge. Orientation is
and 180 = south.
tree is- Percent Mean ttee Median Standard Number of Number Ratio of Mean ellipti-
landden- tree is- island area tree island deviation of circular of ellipti- elliptical cal tree island
sity (#/ha) land (m2) area (12) area tree is- cal tree to circular orientation t
cover lands islands tree is- (degrees)
lands
jkle 1.1 10.0 542.4 287.9 1688.1 47 100 2.1 1
jklw 0.8 11.9 963.8 273.1 6845.8 59 46 0.8 180
llw 1.2 31.8 318.7 247.8 284.6 85 86 1.0 176
110 1.0 8.7 517.5 253.7 1793.0 77 55 0.7 19
173 0.8 9.5 589.2 269.4 1999.6 60 44 0.7 10
210 0.1 4.0 1819.5 674.7 2275.0 6 5 0.8 165
S215 0.6 6.1 648.8 384.9 963.3 40 31 0.8 168
257 0.5 12.8 1279.6 360.2 3086.3 22 43 2.0 174
260 0.9 6.4 426.1 259.1 764.3 60 58 1.0 160
306 1.0 8.8 521.5 440.8 300.7 98 36 0.4 146
310 2.2 11.8 259.2 215.4 171.2 164 139 0.8 157
325 0.7 10.7 874.8 262.3 1619.2 18 62 3.4 156
328 0.7 5.3 453.7 346.3 386.5 49 35 0.7 145
5576 0.4 4.1 1429.1 593.0 2130.7 1 25 25.0 169
5577 0.2 2.3 10711.6 310.9 45070.7 3 15 5.0 173
6278 0.1 0.2 285.1 202.7 192.1 1 5 5.0 34
6279 0.7 2.6 661.5 390.5 820.7 11 22 2.0 9
12460 0.5 1.4 330.3 187.1 388.8 11 21 1.9 179
12461 0.3 1.2 487.1 242.5 624.8 5 16 3.2 177
14460 0.3 7.6 570.1 224.8 854.0 13 14 1.1 173
15964 0.7 20.4 1256.6 538.8 2013.4 25 52 2.1 8
20556 0.8 10.0 1239.5 755.0 1366.8 16 42 2.6 5
22748 1.6 33.7 1419.3 752.0 2803.7 111 62 0.6 179
23836 0.8 7.4 968.6 451.4 3254.8 51 17 0.3 164
Table 4 Continued.
Tree island
density (#/tr
ha)
37712 0.9
37713 0.8
le55 1.5
ce38 1.7
min 0.08
max 2.16
mean 0.81
Stdev 0.49
Percent Mean tree Median Standard Number ofNumber of
eeislandisland area tree island deviation of circular elliptical
cover (m2) ) area () aea tree is- tree is-
lands lands
9.4
6.0
14.6
13.3
0.3
33.7
9.7
7.9
1501.4
790.1
,654.7
496.0
259.24
10711.6
1143.42
1922.43
491.0
539.2
258.1
342.5
187.10
755.04
376.97
165.36
6452.5
734.2
4241.8
741.7
171.23
45070.75
3352.45
8354.22
30
43
111
156
1
164
49.04
45.43
24
26
45
46
5
139
41.86
29.53
Ratio of
elliptical
to circular
tree is-
lands
0.8
0.6
0.4
0.3
0.29
25
2.36
4.62
Mean ellipti
cal tree islar
orientation
(degrees)
151
154
175
175
1
180
127.93
68.88
Results
used to reflect the variability among the hydrology photo plots
zones. The assumption is that tree islands are the
resultant of processes operating over time and that
tree islands in 1950 and the NSM output reflect
pre-drainage hydrology. Likewise, the assumption /
is made that 1991 tree islands and WMM output 27* i -
reflect the last 40 years of post drainage patterns. /
The topographic surface generated by
Richardson et al. 1990 for Loxahatchee was used
for this analysis. The grid cell resolution of this
surface was 183 x 183 m. The 3.2 x 3.2 km cell
180
boundaries for the hydrology models were overlain N
on the elevation surface and average elevation and -
elevation gradient calculated for each cell of the
hydrology model. Because the relation between
current and historic elevation is unknown the topo-
graphic information was used only with the 1991 \2
photo plots.
Plot Comparisons and Relations to Hy-
drology
Because initial plot selection was done in-
dependent of the hydrological analysis, all of the I--
plots did not fall completely in one hydrology
zone. In cases where the plots were in more than Figure5. Histograms ofmean orientation of tree islands
one zone, analysis was done for each zone sepa- from 1950 photo plots (top) and orientation ofNSM flow for
grid cells containing photo plots (bottom).
R 'e: sisn
; I-
40o
21
Figure 6. Frequency distribution from all 1950photo plots of tree island size (top), cumulative area (middle), and contribu-
tion of each size class to overall tree island area. Sizes range from 0.01 to 21.22 ha. Tree islands < 0.16 ha (rank of 16)
make up 50% of the total tree island area.
Table 5. Hydrology data for hydrology zones in Loxhatchee National Wildlife Refuge that contained photo p
Plots Hydrology NSM hy- WMM NSM WMM NSM WMM NSM orien- WMM ori- NSM f
zone dro- hydro- range in range in mean mean station entation magnit
period period hydro- hydro- ponding ponding (degrees) (degrees) (m3xl
(days) (days) period period depth depth
(days) (days) (m) (m)
37712 12 283 205 129 188 0.25 0.09 127 95 4984
37713 13 297 228 109 171 0.34 0.14 133 0 5924
325 19 287 195 103 159 0.27 0.08 158 160 5795
328 20 262 183 121 169 0.21 0.07 158 155 4016
306 28 270 203 101 190 0.23 0.10 170 155 4644
310 29 276 210 106 139 0.25 0.11 174 135 4764
U 257 35 272 204 118 184 0.26 0.12 172 22 6285
23836, 36 264 213 125 148 0.23 0.12 178 171 5288
260
le 38 291 243 104 171 0.31 0.17 8 160 7728
210 43 274 218 119 181 0.24 0.14 176 18 6425
23836 44 243 229 148 167 0.22 0.15 8 3 6691
jke, 46 294 258 95 170 0.32 0.20 16 170 7612
jkw,215
227 48 320 269 49 151 0.40 0.24 7 180 1106'
173 53 289 287 100 176 0.31 0.26 28 25 8246
lw 54 293 285 110 170 0.30 0.22 20.5 175 5672
le 55 299 289 -97 170 0.32 0.22 10 11 8673
20556 56 314 274 62 147 0.37 0.26 5 180 10321
12460, 60 275 280 168 166 0.25 0.32 21 18 9690
14460,
147
12461 61 263 275 185 182 0.24 0.26 25 25 7755
15964 64 329 294 47 118 0.39 0.31 7 180 9061
Table 5 Continued.
Plots Hydrology
zone
NSM
hydro-
period
(days)
WMM NSM WMM NSM WMM NSMori-
hydro-
period
(days)
range in range in mean mean ettatibn
hydro- hydro- pondingponding (degrees)
period period depth depth
(days) (days) (m) (m)
WMM ori- NSM
entation flow m;
(degrees) nitudi
(m3xl(
313
240
261
248
299
344
319
290
84
256
175
272
147
53
100
171
0.34
0.23
0.26
0.20
0.31
0.73
0.61
0.37
79 267 273 225 200 0.23 0.25
240 183 47 53 0.20
329 344 272 200 0.40
254.68
43.30
128.32
57.46
159.52
31.41
0.28
0.06
mean 280.96
stdev 23.39
0.07
0.73
0.23
0.16
62434
12952
9537:
6645!
34 3561,
0 35613.
180 129521
5.4
42.1
3.0
58.6
71838.
23292.
110
5576
5577
6278,
36
6279
min
max
rately. At least one third of the plot had to be in
the hydrology zone for it to be considered. Tree
island numbers were converted to densities to al-
low comparison among plots of different sizes.
Median area and median long axis were used as
size variables for. the plot comparisons because
individual area and long axis of tree islands within
the plots were not distributed normally, and could
not be normalized using simple transformations.
Partial plots did not have significantly different
median tree island size or densities than full plots.
The following analysis was done on the resulting
28 plots.
Density, percent cover of tree islands, me-
dian area, median long axis, ratio of elliptical to
circular tree islands, ratio of non-shaped to shaped
tree islands, and mean orientation of tree islands
were compared between the two years. Data that
were non normally distributed were transformed
prior to .analysis. Hydroperiod, mean ponding
depth, range in hydroperiod, flow magnitude, and
flow orientation data from the NSM and WMM
also were compared.
The relations between tree island variables
and hydrologic variables were examined using ca-
nonical correlation analysis for the 1950 and NSM
data, the 1991 and WMM data, the 1950 tree is-
land data, the 1991 tree island data, and the NSM
Table 6. Correlations between tree island variables and hydrology variables for 1950 photo plots. Top
number is correlation coefficient, bottom number is p value. A p value < 0.05 is considered significant.
Flow magnitude
NSM 90% hydro-
period
NSM mean ponding NSM range in hydro-
depth period
Tree island density
Percent tree island cover
Mean tree island area
Median tree island area
Density of circular tree is-
lands
Density of elliptical tree is-
lands
-0.148
0.453
0.221
0.259
0.363
0.058
0.205
0.295
-0.177
0.368
-0.037
0.852
Mean tree island long axis 0.418
0.027
Median tree island long axis -0.275
0.156
Ratio of elliptical to circular 0.527
tree islands 0.004
0.456
0.015
0.661
0.000
0.055
0.782
0.229
0.241
0.384
0.044
0.422
0.025
0.169
0.390
-0.177
0.367
-0.404
0.033
0.417
0.027
0.653
0.000
0.171
0.384
0.284
0.042
0.352
0,066
0.400
0.035
0.256
0.189
-0.240
0.219
-0.238
0.222
-0.526
.0.004
-0.665
0.000
-0.095
0.630
-0.373
0.050
-0.461
0.014
-0.418
0.027
-0.233
0.231
0.287
0.139
0.450
0.016
Table 7. Summary statistics for 1991 photo plots from Loxahatchee National
and 180 = south.
density (#/ tree island island size
ha) cover (m2)
jkle
jklw
llw
110
173
210
215
257
260
306
310
325
328
5576
5577
6278
6279
12460
12461
14460
15964
20556
22748
23836
37712
37713
1.5
1.6
1.8
1.3
1.2
0.1
0.7
0.2
0.7
0.8
2.3
0.3
0.8
0.0
0.1
0.0
0.3
0.2
0.3
0.2
0.9
1.4
1.9
1.1
0.9
1.1
22.6
26.2
39.8
17.6
23.8
3.8
9.1
6.5
10.1
9.8
25.8
9.6
11.6
0.06
0.2
0.04
1.6
1.4
2.3
7.4
13.5
8.2
29.3
11.8
13.5
13.2
852.1
964.6
463.8
764.8
1037.6
2314.0
697.3
1687.0
813.1
724.9
521.7
1563.8
848.5
207.4
281.8
363.6
1034.8
736.7
672.0
667.9
1216.9
577.8
976.7
1090.8
2021.2
1183.4
island area
(m2)
425.8
345.8
342.1
423.6
573.9
1429.4
465.2
518.6
536.3
601.8
333.6
790.0
659.2
132.5
159.4
363.6
478.3
449.1
458.7
289.9
365.3
384.7
620.0
619.7
977.1
871.2
deviation of
area
1678.2
6851.8
433.3
1830.5
1679.2
2263.9
961.8
3387.4
1102.9
531.4
704.9
2137.9
744.5
153.7
260.6
1160.6
903.4
603.0
899.9
7212.9
594.2
1332.2
3185.6
6313.9
872.6
circular
tree is-
lands
41
39
83
109
49
2
35
16
44
80
117
11
58
1
2
1
5
4
3
10
39
48
125
55
41
61
Wildlife Refuge. Orientation i
elliptical
tree is-
lands
130
128
158
79
80
8
48
11
52
32
197
25
50
2
5
0
9
7
20
16
42
59
82
35
12
23
elliptical cal tree is
to circu- land orieni
lar tree tion
islands
--
Table 7 Continued.
Tree island Percent Mean tree Median tree Standard Number ofNumber of Ratio of Mean ellip
density (#/ tree island island size island area deviation of circular elliptical elliptical cal tree is
ha) cover (m2) (m2) area tree is- tree is- to circu- land orient
lands lands lar tree tion
islands
le55 2.0 22.2 777.3 387.2 3730.7 73 139 1.9 151
ce38 1.8 42.6 858.6 594.1 1185.9 139 61 0.4 168
Min 0.01 0.04 207.41 132.45 153.70 1. 0 0.00 1.00
Max 2.31 42.6 2314.01 1429.44 7212.92 139 197 6.67 177.00
Mean 0.92 13.7 925.71 521.29 1952.48 46 54 1.65 113.11
SD 0.69 11.6 486.90 260.54 1976.01 41 53 1.38 72.39
i-...
_-_ photoots and WMM data. Canonical correlation analysis is
S -i ---.-.. used to investigate the relations between two sets
of variables by deriving a linear combination of
the X variables (U=aX1 + aX2 + ... +aXi) and a
linear combination of the Y variables (V=aY1 +
S2" aY2 + ... +aYi) such that the correlation between
U and V is as large as possible (Manly 1994). A
S'/ non-significant result indicates that the largest ca-
nonical correlation can be accounted for by sam-
pling variation alone. Canonical correlation com-
180 l bines the multiple variables into a single index
variable (U or V). Examination of the coefficients
Sof the individual variables that make up U or V
indicates the contribution of that variable to the
overall index. Variables with higher coefficients
are more important.
180
Figure 7. Histograms of mean orientation of tree islands from
1991 photo plots (top) and orientation of OviAIflowfor grid
cells containing photo plots (bottom).
900
700
100
o100 . .- -. .
Rank of size
S400
300
2 200
(4 0) 1 ( 0
i 100 -
6
Rank of size
Figure 8. Frequency distribution from all 1991 photo plots of tree island size (top), cumulative area r(middle), and contribu-
tion of each size class to overall tree island area. Sizes range from 0.01 to 11.50 ha. Tree islands < 9.13 ha (rank of 13)
make up 50% of the total tree island area.
1950 Plots and NSM Hydrology
Density of tree islands per plot ranged
from 0.08 tree islands/ha to 2.16 tree islands/ha.
Percent cover ranged from 0.2 to 26.7%. Median
tree island size ranged from 187 m2 to 755 m2 and
median long axis from 20 to 46 m. The ratio of
elliptical to circular tree islands varied from 0.3 to
25 (Table 4) and the ratio of non-shaped to shaped
from 0.15 to 8.12. Mean orientation of elliptical
tree islands ranged from 1 to 180 degrees with
most between 1 to 30 or 150 to 180 degrees
(Figure 5). Density of tree islands was correlated
with location (X-Y coordinates of plot centroid).
Higher densities of tree islands occurred in the
northern and eastern plots. There was no correla-
tion between the area or long axis of tree islands
and location. The ratio of elliptical to circular tree
islands increased from north to south indicating
relatively fewer elliptical tree islands in the more
northern plots.
The distribution of tree island sizes from
all plots combined showedmany small tree islands
and few larger tree islands (Figure 6). Fifty per-
cent of the tree island area was made up of tree
islands < 0.16 ha. Ninety-four percent of the 3769
Table 8. Correlations between tree island variables and hydrology variables for 1991 photo plots. Top
number is correlation coefficient, bottom number is p value. A p value < 0.05 is considered significant.
Flow magni-
tude
WMM 90%
hydroperiod
WMM mean
ponding depth
WMM range in Elevation
hydroperiod gradient
Free island den- -0.160
3ity 0.416
Percent cover
-0.115
0.464
Mean tree island-0.296
area 0.126
Median tree is- -0.252
Land area 0.195
Density of cir- -0.196
:ular tree is- 0.317
lands
Density of ellip- -0.118
tical tree islands 0.548
Ratio of ellipti- 0.043
cal to circular 0.827
tree islands
Mean long axis
Median long
axis
-0.235
0,229
-0.281
0.147
Mean cell
elevation
-0.079
0.688
-0.115
0.561
-0.559
0.002
-0.728
0.000
-0.201
0.305
0.024
0.902
0.190
0.333
-0.608
0.001
-0.665
0.000
-0.224
0.251
-0.256
0.189
-0.558
0.002
-0.749
0.000
-0.303
0.117
-0.122
0.539
0.198
0.314
-0.610
0.001
-0.655
0.000
0.091
0.645
0.191
0.331
0.443
0.018
0.684
0.000
0.085
0.667
0.044
0.825
0.026
0.896
0.584
0.001
0.547
0.003
-0.626
0.000
0.352
0.066
-0.405
0.032
-0.554
0.002
-0.600
0.000
-0.508
0.006
0.027
0.893
-0.436
0.020
-0.465
0.013
0.313
0.105
-0.519
0.005
0.562
0.002
0.799
0.000
0.387
0.042
0.187
0.342
-0.212
0.279
0.636
0.000
0.669
0.000
Table 9. Differences between variables from 1950 to 1991.
and change in ratio indicate an increase from 1950 to 1991.
tion. A negative change indicates a counter clockwise Shift.
N.S. indicates no significant difference. Positive
Positive change in orientation magnitude indicate
Plot Median Significance tested with Wil-
tree island coxon Ratk Sum Test
area (m2)
jke
jkw
1lw
110
173
210
215
257
260
306
310
325
328
5576
5577
6278
6279
12460
12461
14460
15964
20556
22748
23836
37712
Percent Density (tree Orientation
cover islaids/ha)
137.8
72.7
94.4
169.9
304.4
754.7
80.4
158.4
277.2
161.0
118.2
527.8
312.9
-460.6
-151.4
160.9
87.8
262.0
216.2
65.2
-173.5
-370.4
-132.1
168.2
486.1
Z=-5.54, p<0.001
Z=-2.63, p=0.008
Z=-4.91, p<0.001
Z=-5.99, p< 0.001
Z=-6.74, p<0.001
N.S.
N.S.
N.S.
Z=-5.80, p<0.001
Z-3.56, p<0.001
Z=-6.71, p<0.001
Z=-3.41, p<0.001
Z-6.60, p<0.001
N.S.
N.S.
N.S.
N.S.
N.S.
N.S.
N.S.
Z=4.60, p<0.001
Z=5.36, p< 0.001
Z=3.29, p=0.001
Z=-2.52, p=0.011
Z=-5.20, p< 0.001
7.8
8.8
4.9
5.5
8.8
-0.1
1.8
-3.9
2.3
0.7
8.6
-0.7
3.9
-5.7
-2.4
-0.2
-1.9
0.1
1.2
-0.1
-5.4
-1.8
-3.5
4.4
5.7
Significance tested
Test for detennini
circular means.
N.S.
N.S.
F=54.85, p=0.00,
F=20.88, p=0.00,
N.S.
N.S.
N.S.
N.S.
F=9.66, p=0.00, d
F-12.58, p=0.00,
F=7.23, p=0.00, d
N.S.
F=5.88, p=0.00, d
N.S.
N.S,
F=5.70, p=0.02, d
F=5.56, p=0.03, d
F=6.77, p=0.01, d
F=10.15, p=0.00,
N.S.
N.S.
N.S.
0.5
0.8
0.6
0.4
0.4
-0.1
0.1
-0.3
-0.1
-0.2
0.2
-0.4
0.1
-0.4
-0.2
-0.1
-0.5
-0.4
0.0
0.0
0.1
0.6
0.3
0.3
0.0
0.0
4.0
-27.0
-22.0
9.0
6.0
-11.0
-13.0
16.0
23.0
-11.0
7.0
15.0
0.0
8.0
23.0
21.0
-16.0
-17.0
-2.0
-6.0
3.0
Table 9 Continued.
Plot Median
tree island
area (m2)
37713 331.9
le55 129.1
cle38 251.6
max 754.70
min -460.57
mean 144.32
stdev 250.46
Significance tested with Wil- Percent
coxon Rank Sum Test cover
Z=-4.61, p< 0.001
Z=-4.93,p< 0.001
Z=-8.07, p< 0.001
8.0
5.6
20.8
20.83
-5.73
2.61
5.66
Density (tree Orientation
islands/ha)
-2.0
-24.0
-7.0
Significance tested
Test for determinii
circular means.
N.S.
F=23.83, p-0.00,
N.S.
0.81
-0.47
0.10
0.34
__I__ __ ~_
observed tree islands were < 0.16 ha.
Mean hydroperiod for the NSM in the
cells in which photo plots occurred ranged from
240 to 329 days and mean ponding depth from 0.2
m to 0.4 m. Range in hydroperiod was as little as
47 days and as great as 272 days (Table 5). Den-
sity of all tree islands and circular and elliptical
tree islands were positively correlated with hydro-
period and negatively correlated with hydroperiod
range (Table 6). Overall density of tree islands
and density of elliptical tree islands were corre-
lated with mean depth. Median area of tree islands
was positively correlated with mean ponding depth
and negatively correlated with range in hydro-
period. Median long axis was not correlated with
any of the hydrology variables. Mean tree island
orientation was not significantly different from ori-
entation of NSM flow.
Canonical correlation analysis was per-
formed with the tree island variables density, area,
and ratio of elliptical to circular tree islands and
the hydrology variables NSM magnitude, hydro-
period, mean ponding depth, and hydroperiod
range. It was performed again replacing area with
long axis. In both instances only the first canoni-
cal correlation was significant (p=0.0002, r=0.85;
p=0.0003, r=0.85 respectively). In both analyses
the hydrology variables NSM hydroperiod range
and NSM magnitude (coefficients of -0.82 and -
0.62 and 0.78 and 0.61 for hydroperiod range and
magnitude in the two analyses respectively) were
the most important, as was the tree island variable
ratio of elliptical to circular tree islands
(coefficients of -0.74 and 0.77). Eighty-eight and
eighty-seven percent of the variation between the
linear combinations were explained.
1991 Plots and WMM Hydrology
Density of tree islands per plot ranged
from 0.01 tree islands/ha to 2.31 tree islands/ha.
Percent cover ranged from 0.03 to 30.2%. Median
tree island size ranged from 132 m2 to 1429 m2
and median long axis from 18 m to 59 m. Ratio of
elliptical to circular tree islands from 0 to 6.7
(Table 7) and ratio of non-shaped to shaped from
0.16 to 17.00. Mean orientation of elliptical tree
islands ranged from 1 to 180 degrees with most
between 1 to 30 or 150 to 180 degrees (Figure 7).
Density of tree islands was correlated with loca-
tion, with.a trend of higher densities in the east
than in the west. Median tree island area and long
axis were correlated with location, with larger tree
islands in the north and tree islands with shorter
long axis in the south and east. The ratio of ellip-
tical to circular tree islands was not significantly
correlated with location.
As with the 1950 photo plots, the distribu-
tion of tree island sizes showed many small tree
islands and few larger tree islands (Figure 8). Fifty
percent of the tree island area was made up of tree
islands < 0.13 ha. Eighty-seven percent of the
4392 identified tree islands fell into this category.
Mean WMM hydroperiod in the cells
within which photo plots occurred ranged from
183 to 344 days with a range between 47 and 272
days. Mean ponding depth ranged between 0.07 m
and 0.73 m. Density of tree islands, and density of
circular and elliptical tree islands were correlated
with elevation gradient (Table 8). Density of cir-
cular tree islands also was correlated with mean
cell elevation. Median tree island area and median
long axis were negatively correlated with hydro-
period, mean ponding depth, and elevation gradient
and positively correlated with hydroperiod range
and mean elevation. Mean tree island orientation
was not significantly different from WMM flow
orientation or NSM flow orientation.
Canonical correlation analysis was per-
formed with the tree island variables density, area,
and ratio of elliptical to circular tree islands and
the hydrology variables WMM magnitude, hydro-
period, mean ponding depth, and hydroperiod
range. The analysis was performed again replac-
ing area with long axis and a iird and fourth time
with the addition of mean elevation and elevation
gradient. In all cases, there were two significant
canonical correlations.
In the first two analyses (without eleva-
tion), the first significant correlation (p=0.001,
r=0.85 and p=0.0003, r-0.79) was between the
hydrology variables WMM hydroperiod range and
mean ponding depth (coefficients of 0.49 and 0.43
and 0.58 and -0.41 respectively) and the tree is-
land variable representing size (coefficients of -
0.98 and -0.96 for area and long axis respec-
tively). Seventy-seven and sixty-seven percent of
the variability was explained by the first signifi-
cant correlation. The second significant correla-
tions explained an additional 21 and 20% of the
variability respectively. The important variables
in the second correlations were mean ponding
depth and hydroperiod (coefficients of 4.96 and -
4.56 and 4.93 and -4.60 for analysis using area
and long axis respectively). In both cases, the im-
portant tree island variable was tree island density
(coefficients of -0.98 and -0.94 respectively).
When the elevation variables were added
to the analysis, mean elevation and mean ponding
depth (coefficients of 1.54 and.9.73) were the most
Figure 9. Location ofphoto plots showing changes in percent cover. Down arrow indicates a decrease from 1950 to 1991,
up arrow indicates <=5% increase and up arrow +5 indicates > 5% increase.
important hydrology variables in the first signifi-
cant correlations (p=0.0001, r=0.91 and
p=0.0001, r-0.86). Median area was the most inm-
portant tree island variable when size was repre-
sented as area (coefficient of 0.82). Both tree is-
land density and long axis (coefficients of -0.77
and -0.70) were important when length was used.
Seventy-six and sixty-nine percent of the variabil-
ity was explained by the first sets of correlations.
An additional 20 and 27% of the variability was
explained by the second significant correlations.
The most important hydrology variables in the sec-
ond set of correlations were hydroperiod
(coefficients of -3.10 and -3.29 for analysis using
area and long axis respectively). Tree island den-
sity (coefficient of -0.84) was the most important
variable when area was used to represent size.
Both long axis and density (coefficients of 0.72
and -0.63 respectively) were important when long
axis was used to represent size.
Comparison Between Individual Plots
Twenty of the twenty, eight plots showed
significant differences between the median size of
tree islands between years (Table 9). Seventeen
increased in percent cover and eleven decreased
(Figure 9) Density of tree islands in ten plots de-
Table 10. Spearman correlations between change in tree island variables and change in hydrology vari-
ables for 28 photo plots in Loxahatchee. Top number is correlation coefficient, bottom number is p value.
A p value < 0.05 is considered significant.
Flow magnitude 90% hydroperiod
Mean ponding
depth
Range in hydroperiod
Free island density
Percent tree island cover
Mean tree island area
Median tree island area
Density of circular tree
islands
Density of elliptical tree
islands
-0.123
0.531
0.315
0.103
0.528
0.004
0.499
0.007
-0.160
0.414
-0.046
0.814
Mean tree island long axis 0.457
0.014
Median tree island long
axis
0.436
0.020
Ratio of elliptical to circu-0.236
tar tree islands 0.227
-0.074
0.708
-0.229
0.241
-0.529
0.004
-0.511
0.006
-0.052
0.972
-0.046
0.816
-0.340
0.077
-0.370
0.053
-0.258
0.184
-0.230
0.239
-0.314
0.104
-0.415
0.028
-0.392
0.039
-0.035
0.859
-0.164
0.403
-0.252
0.195
-0.272
0.161
-0.295
0.128
0.610
0.001
0.286
0.140
0.070
0.723
0.017
0.931
-0.030
0.881
0.522
0.004
0.018
0,927
-0.029
0.884
0.326
0:090
creased, in three plots stayed the same and in-
creased in fifteen plots. Eleven plots had signifi-
cant changes in mean tree island orientation, four-
teen did not. Sample size in the remaining plots
was too small for comparison. The ratio of num-
ber of elliptical to circular tree islands in 1991 was
larger in fourteen plots, smaller in twelve plots and
the same in two plots. The ratio of non-shaped to
shaped tree islands was larger in 20 plots and
smaller in eight plots.
All Plots Together
When analyzed together in a pair-wise
analysis, median tree island area, median long
axis, and ratio of non-shaped to shaped tree is-
lands were significantly different between years
(Wilcoxon signed-rank W=240, p=0.006; W=225,
p=0.01; W=248, p=0.0001 respectively). Density
of tree islands were not significantly different, nor
was the number of elliptical and circular tree is-
lands per plots, ratio of elliptical to circular tree
islands, or the orientation of the tree islands.
Canonical correlation analysis was per-
formed using the tree island variables density,
area, and ratio of elliptical to circular tree islands
for 1950 and 1991 to examine changes in the rela-
tion of the variables between the time periods.
Only the first canonical correlation was significant
(p=0.0001 r=0.94). Ninety percent of the varia-
tion was explained by this analysis. Density and
area from 1950 and 1991 had similar coefficients
(0.82 and 0.90 for density and 0.22 and 0.29 for
area respectively). The coefficient for ratio of el-
liptical to circular tree islands was slightly more
important in the 1950 data than in the 1991 data (-
0.37 and 0.14 respectively).
A similar analysis was performed using
the hydrology data for the two sample periods. In
this analysis the first two correlations were signifi-
cant (p=0.0001, r=0.88 and p=0.020, r=0.67 for
the first and second correlations respectively). Un-
like the pattern for the tree island variables, the
coefficients between the two years were not simi-
lar. In the first correlation, hydroperiod range
(coefficient of 1.10) was the most important NSM
hydrology variable followed by NSM depth
(coefficient of 0.71), NSM magnitude (coefficient
of 0.61), and hydroperiod (coefficient of 0.18).
WMM depth (coefficient of 1.06) was the most
important WMM hydrology variable with hydro-
period range (coefficient of 0.06), hydroperiod
(coefficient, of -0.03), and magnitude (coefficient
of 0.01) contributing little. The order of impor-
tance for the second correlation was similar to the
first for the NSM data (coefficients of 1.28, 1.05,
0.91, and -0.75 for hydroperiod range, depth, hy-
droperiod, and magnitude respectively). The im-
portance of the WMM variables was not similar to
that seen in the first correlation and was not simi-
lar to that of the NSM data (coefficients of 2.56, -
1.96, 0.87, -0.29 for hydroperiod, depth, hydro-
period range, and magnitude).
All hydrology variables except for flow
orientation were significantly different between the
two time periods (hydroperiod- t=-2.8, p=0.01;
hydroperiod range- W=176.0, p=0.02; mean pond-
ing depth- W=-169.0, p=0.02; flow magnitude-
t=14.0, p<0.0001). Mean water depths were gen-
erally shallower and hydroperiods shorter for the
WMM than for the NSM. Depth and hydroperiod
were more variable under WMM, while hydro-
period range and flow magnitude were less vari-
able (Table 5).
A decrease in flow magnitude was corre-
lated with a decrease in tree island area and long
axis. Decreases in hydroperiod and depth were
correlated with increases in area. Decreases in hy-
droperiod range were correlated with decreases in
the number of tree islands (Table 10).
Change in density was positively corre-
lated with location, with a greater change in den-
sity in the east than the west.: Change in area and
change in long axis were not correlated with loca-
tion. The change in the ratio of elliptical to circu-
lar tree islands increased from north to south.
Discussion
Historically, in Loxahatchee, there were
more tree islands in areas of longer hydroperiod
and greater depth. These areas also were less vari-
able in hydroperiod range. The multivariate analy-
sis demonstrated that hydroperiod range and flow
magnitudes are important in explaining the ratio of
elliptical to circular tree islands. Areas that were
less variable with lower flow had lower ratios of
elliptical to circular tree islands (e.g. more circular
than elliptical tree islands). In addition, areas with
less variation in hydroperiod had more tree islands
of larger size.that covered a larger area. These
results support the hypotheses that flow is impor-
tant in shaping tree islands and that battery tree
islands form under conditions of greater hydro-
period and depth.
The relation between the tree island vari-
ables and hydrology variables in 1991 is very dif-
ferent from 1950. There were no significant corre-
lations between the individual tree island variables
and hydrology as there were with the 1950 data.
The multivariate analysis shows that of the vari-
ables used here, hydroperiod and depth were the
most important in explaining tree island size. Ar-
eas of longer hydroperiod and depth had smaller
tree islands.
Loxahatchee can be grouped into three
zones according to the patterns of change of tree
islands observed from 1950 to 1991. 1)the edge of
the refuge adjacent to the canals, 2) the eastern in-
terior of the refuge, and 3) the western interior of
the refuge. The general trend is for tree islands
along the edge of the refuge to have decreased in
size, number, and percent cover, while those on the
interior increased in size, number, and percent
cover.
The patterns of change are what is ex-
pected given the changes in hydrology. Areas of
extreme hydroperiod and increased ponding depth
should have a decrease in tree island area due to
drowning of the vegetation on the tree islands. This
is seen primarily along the southern boundary of
the refuge. The plots along the Hillsboro Canal
have obvious remnants of drowned tree islands.
These plots also are the plots that did not show a
significant difference in median tree island area
between 1950 and 1991, possibly because the
greatest changes in tree islands in these areas oc-
curred after the construction -of the canal in 1915.
Areas of shorter hydroperiod and shallower pond-
ing depth should show an increase in tree island
area as woody vegetation colonizes the drier sites.
In this analysis,. decreases in hydroperiod and
depth were correlated with increases in tree island
area. The ultimate consequence of these changes
are to change a heterogeneous wetland into a more
homogeneous upland.
Hagenbuck et al. (1974) expressed con-
cern that an increase in the aquatic setting in
Loxahatchee (e.g. extended hydroperiod and
greater depth) might lead to arl increase in the for-
mation of battery islands. These islands form in
areas where hydroperiods are longer and detritus
settles to the bottom and forms loose peat mats.
Dislodged peat can become floating peat mats that
are colonized by woody vegetation. The cumula-
tive effect is to diminish the total water storage ca-
pacity of the area and reduce the amount of avail-
able wetland habitat (Hagenbuck et al. 1974).
This may be happening in portions of Loxa-
hatchee; however, because ofthe coarseness of the
hydrology data, it is not possible to determine if
the increase in the number of small circular tree
islands thought to be battery tree islands within a
plot, is due to increases in -hydroperiod or other
factors. In some of the plots, especially those
along the edge of the refuge, where there has been
an increase in the number of circular tree islands
there has been a decrease in the median area of the
tree islands. It may be that tree islands that were
not circular in 1950 are circular in 1991 due to
loss of area.
In other areas of the refuge, particularly in
the northern interior, an increase in the percent
cover. and.size of tree islands indicates that tree
islands are expanding in size. Much of this area
has had shorter hydroperiods and lower mean
ponding depths in the recent past, both of which
would seem to promote tree: island growth. This
pattern of increase in percent cover of tree islands
in the northern areas was noted by Richardson et
al. (1990), Silveira 1996, and Hagenbuck et al. in
1974. Hagenbuck et al.(1974) hypothesized that
this expansion would continue to occur in areas of
shorter hydroperiod. Data presented here support
that. It may not be the changes in the mean hy-
drology variables themselves that result in the
changes, but the loss of the dynamic pulsing nature
of the historic processes.
The relation between the hydrology vari-
ables is very different now than it was historically
indicating a potential change in the structuring
processes. Flow, which was important in describ-
ing the historic patterns of tree islands, now is vir-
tually non existent. Processes such as nutrient
transport, seed dispersal, and soil accretion and
deccretion are influenced by flow magnitudes. The
results of removal of this structuring force from
the system may be more subtle than changing hy-
droperiods, but just as important.
These analyses provide evidence that
changes in flow magnitudes as well as other hydro-
logic variables contribute to the changes in the na-
ture of tree islands in Loxahatchee. Several as-
sumptions made in these analyses now should be
considered. It has been assumed that tree islands
are the resultant of processes operating in previous
years and that these processes are related to the
average values of structuring forces of flow, hy-
droperiod, and depth. Another assumption is that
the relationship between the hydrologic variables
in the 26 years averaged by the NSM are similar
to the hydrologic variables that the landscape ex-
perienced in the 26 years prior to 1950. Because
historic data do not exist, this represents the best
available information. Because of the magnitude
of changes that have occurred in terms of hydrol-
.ogy, the model outputs probably give a good rela-
tive idea of the magnitude of the changes that have
occurred. As long as the errors in the model are
similar across the refuge, and between the two
time periods, the associations between the tree is-
lands and hydrology should be valid. From this
study it can be concluded that: 1) the relations be-
tween the hydrology variables is different pre and
post drainage; 2) patterns of tree islands have
changed from 1950 to 1991; 3) the patterns of
change in tree islands is different throughout the
refuge; and 4) greater changes in hydrology lead to
greater changes in the patterns of tree islands.
Tree islands and changes in tree islands
not only reflect the nature of historic processes and
changes in macroscale processes such as hydro-
logic flows, but also are a potential indicator of
changes in lower level processes such as system
productivity, heterogeneity, and connectivity that
are associated with flows. Additionally, tree is-
lands are habitat patches for a wide range of wild-
life (Gunderson and Loftus 1993) and changes to
the pattern of tree islands have the potential to
change the dynamics of wildlife populations.
The shape of a landscape feature can indi-
cate it's origin and it's current function (Forman
1995). Streamlined shapes such as the elongated
tree islands in this study indicate the action of con-
stant or repeated processes. The maintenance of
patterns of defined shapes.reqqires the input of en-
ergy. In the absence of energy inputs a system will
tend toward randomness. The change in tree is-
lands from more defined shapes to what appears to
be more irregular shapes may well be a reflection
of the change in the energy inputs to the system.
Associated with this change in energy may be a
change in primary productivity, decomposition,
nutrient cycling, and import-and export of organic
matter, etc.. Heinselman (1970) found that as
flow-through conditions increased in northern
peatlands that plant species diversity increased.
Additionally, Mitsch and Gosselink (1986) demon-
strated that primary production in wetlands was
enhanced by flowing conditions and a pulsing hy-
droperiod -and that stagnant conditions often de-
pressed these processes. In a low energy system
such as the Everglades, small decreases in energy
inputs through the suppression of flow, may have
major long term effects by changing the nutrient
dynamics. The result is an even more nutrient
poor system that can not support the range of spe-
cies that it did historically, and a system that is
more susceptible to invasion by non-native species.
Water and energy flows provide topo-
graphic heterogeneity and create channels and
pathways for the movement of materials. Topo-
graphic heterogeneity is an important feature in the
Everglades landscape. High spots provide the
base for the start of tree islands while depressions
provide pools that retain water for longer periods
during the dry season and provide habitat for fish
and other aquatic animals. Transitional wetland
areas, such as those that occur in Loxahatchee
have been shown to be extremely important for
wading birds (Hoffman et al. 1994).
Results from this study illustrate the un-
coupling of hydrology and landscape patterns that
has occurred within the impoundment of the ref-
uge. They also show that variations in hydroperi-
ods and flow magnitudes were important variables
associated with tree island patterns and suggest
that in the absence of historic flows the once het-
erogeneous marsh may be becoming more homoge-
neous. In attempts to restore the Everglades it will
be important to consider the importance of flow as
well as hydroperiod in future management scenar-
ios.
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Appendix 1
Meta data for photos and imagery used in this report
Photoplot Scanning and Referencing
bata documentation for Loxahatchee photo plot .txt files
Procedures for digitizing tree islands
Post plot digitizing procedure (assumes plot cleaned, built, with labels, and projection)
Plot number, who digitized it, and what additional photo sources were used for reference
pdatabak.cpp- C++ program Takes an ungenerate file from Arc/Info and puts ids on all verticies.
findaxv2- Splus function that finds the longaxis of each tree island and calculates orientation data.
Photodat.txt- Splus function that will bring data from arc/info unload (id, x, y,area, perimeter, edge,
matrx- no matrix for 1950 plots) together with data calculated with findaxes program (azlong, longaxis,
secaxis) and puts orientation in range of 0-180.
Addvar50.txt
Addvar91 .txt- Splus function that creates variables for circle, ellipse, shidx(shape index indicating circle,
ellipse, irregular, or no shape) for files with id,x,y, area, perimeter, edge,
longaxis, secaxis.
Plotsum.txt- Splus function that will print out summary stats for a plot.
Photoplot Scanning and Referencing- done by Jack Makemson, Image and Mapping Technologies,
Inc. 2320 SW 131 Terrace, Davie, FL 33325. 954/916-9296.
Image sources were 21 1:40,000 NAP Color-IR diapositives flown in December 1990, January 1991, and
March 1991 (see photometa.xls for sources) and 12 1:60,000 panchromatic diapositives flown in Novem-
ber 1950 and January 1951. Side and end overlap was optimal in the NAP photos and marginal in the
1950/51 photos. Each set of photos was sent to Image Scans in Denver, CO to be photogramettrically
scanned at the appropriate scanning resolutions to result in 2 m ground resolution. The NAP CIR's were
scanned at 50 microns in gray scale. The 1950/51 photos were scanned at 33 microns.
In order to perform comparative spatial analysis, it would be necessary to rectify and georeference each
set of images to a common coordinate system (UTM). Polynomial rectification would require a minimum
of 4 photo identifiable ground survey control points for each image. A traditional field ground control
survey was ruled out because of lack of photo identifiable man-made features and accessibility in the
study area. Since absolute geographic accuracy is not as important as relative spatial accuracy for the
study, it was decided to use a 10 m resolution UTM geocoded Spot satellite image (Silveira 1996- file
623rect.lan and 623rect.sta) to extract coordinates from natural features such as the tips or centers of the
tree islands that were uniquely photo-identifiable in all 3 images.
The program chosen to perform the image rectification was ORTHOENGINE from PCI Remote Sensing
Corporation. The capability of ORTHOENGINE to perform Bundle Block adjustment model calcula-
tions is an important feature in multiple photo projects. Substantially fewer GCP's are needed, since a
single model is created for the entire set of photos. Tie points(photo identifiable points common to 2 or
more images) are collected and calculated into the model resulting in much better mosaic edge matching.
Ordinarily, a DEM is needed to perform a digital ortho rectification, but ORTHOENGINE also allows
the user to choose a constant elevation. Since the study area has very little elevation differential, this
made collection of a DEM unnecessary in this case. However, camera model created in ORTHOEN-
GINE would correct for other factors such as radial distortion due to focal length, and the output digital
image will have a more constant scale and residual error. A higher order polynomial rectification (rubber
sheeting) model would result in higher error in areal measurements.
The ortho images were generated after model calculations of average residual error was acceptable
(approximately 2 meters- 1990 and 4 meters 1950). ORTHOENGINE was then used to generate a UTM
geocoded mosaic of each set of ortho images for the study area, and files output in LAN format of ap-
proximately 250 MB each ((Provided on CD- lox50mos.img and lox91mos.img). Marginal side and end
overlap in the 1950/51 photos resulted in a few small "zero data" holes in the final mosaic.
Data documentation for Loxahatchee photo plot .txt files
The name of the file indicates which plot it is as follows:
p=plot
110=plot number
30 or 91 indicates the year
additional digits indicate a partial plot. The last 2 digits represent the hydrology zone. A key to hydrol-
ogy zone correspondence to WMM hydrology zones is given in Appendix B of Brandt, L. A. 1997. Spa-
tial and temporal changes in tree islands of the Arthur R. Marshall Loxahatchee National Wildlife Refuge.
Dissertation. University of Florida. See Appendix A of the same document for plot names and locations.
Examples:
p5550= plot 55 from 1950
p559176 = plot 55 from 1991, only that part within hydrology zone 76.
Fields within each file are as follows:
id Tree island number from Arc/Info coverage
10 UTM X coordinate of centroid of tree islands
y UTM X coordinate of centroid of tree islands
area- Area in square meters of tree island
perimeter- Perimeter in meters of tree island
edge- Code indicating if the tree island touches the edge of the plot. 1 = tree island touches the edge. 0 =
tree island does not touch the edge.
matrx- In 1991 plots only. Indicates the predominant type of vegetation within an approximate 100 m ra-
dius around each tree island. Codes are as follows:
0= open (not sawgrass or brush)
1= brush matrix/ associated with brush
2= sawgrass/brush mix
3= sawgrass
4= old tree island
azlong- Orientaion of long axis of the tree island. 0= North, 180 = South. Calculated using Splus.
longaxis- Length in meters of long axis. Calculated using Splus.
secaxis- Length in meters of secondary axis perpendicular to the long axis and at the mid point of the long
axis. Calculated using Splus.
circl- Circularity index
ellipse- Ellipse index
shidx- Indicates if the tree island is circular (1), elliptical (2), or no shape (0) based on criteria outlined in
Brandt 1997.
Procedures for digitizing tree islands
Log into Pulsar or Enos as lab
Change directories to your directory.
On Pulsar: cd directory name
On Enos: cd /castle/lab/directory name
Make sure the .img file of the plot you are going to work on is in your directory.
Start Arc/Info by typing in arc.
At the arc prompt enter display 9999
Get into Arcedit by typing ae.
Set the map extent to the bounds of the .img file by typing mape image filename.img
Set the image to the above file by typing image filename.img.
Display the image by typing draw.
Set the draw environment to arcs and tics by typing de arc tic
Set the input type for coordinates to keyboard sing coord keyboard.
Create the cover using createcover covemame.
You will be prompted for tics as follows:
TIC- enter 1 for the first then 2, 3, 4
X,Y- enter the X and Y coordinates for the comer of the plot you are working on. The upper left
is tic 1, upper right is 2, lower left is 3, and lower right is 4.
You will now be prompted to define a box outside of the tic area. Do this by putting the mouse some-
where in the upper left hand comer and dragging it diagonally to the bottom right comer to create the box.
You can move tics using the editfeature tic command.
Set the arcsnap and nodesnap features on by typing:
arcsnap on 2
nodesnap first
Create a boundary around the image y connecting the tics
coord keyboard
ef arc
add
you will be prompted for the coordinates you want to go from and to. Use thp comer coordinates.
Connect 1 to 2, 2 to 4, 4 to 3, and 3 to 1.
Set the coordinate input back to the mouse using coord mouse.
Since you have already specified the feature you want to edit (arcs), you do not have to specify it again,
you can begin digitizing by using add. You will see a menu appear on the screen. You must start and end
each polygon with a node. You create a node using the second mouse button. After you create your start-
ing node use the first mouse button to create verticies. The verticies define the shape of the polygon.
When you have completely digitized the polygon create another node using the second mouse button.
Typing 9 from the keyboard when in the image window will exit you out of digitizing mode.
You can zoom in and out by typing zi or zo and then clicking in the image window. Each time you click
you will zoom in or out. To exit zoom type 9 in the image window. The same procedure works for the
pan command.
The oops command will undo your last actionss.
After you have been working for a while save your work by issuing the save command. Issue the save
command before you exit.
After you have digitized your first set of tree islands and saved the file you will need to define the coordi-
nate system. Do this from the arc prompt using the projectdefine command. Enter each of the following
lines at the.prompts followed by a carriage return:
projection UTM
units meters
zone 17
datum nad27
spheroid clarke 1866
parameters
When you have finished digitizing all of the tree islands in the plot you need to clean the coverage using
the following command:
clean filename cleanfilename # #
For the cleanfilename use the same name as the original filename followed by cl.
Post plot digitizing procedure (assumes plot cleaned, built, with labels, and projection)
1 Check position with other plot (compare 1950 and 1991)
2- ADD ITEM FOR MATRIX CODE:
additem
matrx 2 2 n
3- Fill in values for matrx
0 = open water
1 = brush matrix
2 = sawgrass/brush matrix
3 = sawgrass
4 = old tree island
Pull up the image and the cover to add code to.
Set the ef and de to poly
Select many
Click on polygons to get the same code
At the prompt type calc matrx = codenumber
calc $symbol = 4 will change the color of the selected polygons (different number are different colors)
Make a backup of this file
4 Move labels to centroid. centroidlabel inside
5 Add xy coordinates- addxy
6- Delete the large polygon created by the boundary lines.
Find the area of the largest polygon (it will be a lot bigger than the others)
select this polygon
delete it
Another way to do this is in arcedit- click in the interior of the bounding box- this should select
that polygon. Now delete it.
7 Build
8- SELECT POLYGONS > MINIMUM MAPPING UNIT (100M2)
At the arc prompt:
reselect
: res area >= 100
enter a blank line after this and answer no to the questions about adding additional selections.
Or: go to arcedit
sel area < 100
delete
The resulting file will have only tree islands >= 0.01ha (100sq meters)
9 Add verticies at every 6 m so that there are enough points all the way around to calculate longest axis.
At arc prompt: densifyarc 6 vertex
10 Build
11 ungenerate poly plqtname plotname.gen
12 tables
13 sel plotname.pat
14 unload plotname.txt plotnam-ID, x-coord, y-coord, area, perimeter, matrx, edge. (NOTE: no matrx in
1950 photos)
4/22/97
Once files are in .gen and .txt format on FIREBALL (FIREBALL is Laura's home computer)
Remove final end in the .gen file (d:\loxdata\phdata\ungen)
Run C++ (pdatabak.cpp) file on .gen- output will be .txt in above directory
move .gen file to rancprog directory
FTP new .txt files to Jade (computer with Unix version of Splus) using DOS ftp
move .txt file to onjade directory
Create batch file as follows:
vi goll11050
p 11050ax<-findaxv2("P 11050.TXT") note capitalization
Run batch file:
Splus BATCH g911050 goll050.out
Check to make sure it started
more gol 1050.out
After the batch file has finished:
From Splus create a .dat file
dput(p11050ax, "p11050ax.dat")
FTP .dat files to FIREBALL (d:Apxdata\phdata\spdat)
remove .dat and .txt files from jade
In Splus access the spphoto dir
attach("d:\\spluswin\\home\\spphoto", pos = 1)
Run photodat.50 or photodat.91 to bring data into Splus
p 11050f<-photodat.50("d:\\loxdata\\phdata\\unload\\pl 11050.txt", "d:\\loxdata\\phdata\\spdat\
\pll050ax.dat")
Run addvar50 or addvar91 to add circle, ellipse, spindx and correct orientation
p 11050f<-addvar50(p 11050f)
Run plotsum to get means, medians etc for plot
p1 1050sum<-plotsum(p 11050f)
//pdatabak.cpp- L.A. Brandt 2/3/97
// Takes an ungenerate file from ARC/INFO and puts ids on all verticies
// output is id, x, y
#include
#include
include
#include
#include
#include
void main(void)
{
int id, test, testl;
float cx,cy, vx, vy;
ifstream fin;
ofstream fout;
fin.open("d:\\loxdata\\Mngen\\j 14750.gen");
if (fin.fail())
{cerr << "couldn't open file";
exit(l);
}
fout.open("d:\\loxdata\\ungea\\p l4750.txt");
fout << "id" << << "x" << << "y" << '\n';
do
{
fin >> id >> cx >> cy;
do
{ fin >> vx >> vy;
fout << id << "<< vx << << vy << '\n';
testl=-fin.get();
test=fin.get();
}while(test != 69);
fin.ignore(80, '\n');
}while(Ifin.eof());
fout.closeO;
fin.close();
}
#Splus program that finds longaxis and calculates orientation for data in id,x,y matrix
#J. Harrison- IFAS statistics 1996
findaxv2<-function(a)
{
mtx
squarepatch <- NULL
patchpoints <- as.matrix(mtx)
idtable <- table(patchpoints[, 1])
idvalues <- as.numeric(labpls(idtable)$.Names)
idfreqs <- as.numeric(idtable)
index <- 1:(dim(patchpoints)[1])
finallist <- matrix(rep(-9, 4 length(idvalues)), ncol = 4)
for(lp in 1:length(idvalues)) {
numpoints <- idfreqs[lp]
{
extract <- index[patchpointsj, 1] = idvalues[pp]]
plist <- patchpoints[extract, 2:3]
numpoints2 <- dim(plist)[1]
testdist <- round(dist(plist, metric = "euclidean"))
longdist <- max(testdist)
cat("\nFound long axis for ID number", idvalues[lp])
index2 <- i;length(testdist)
locmax <- index2[longdist = testdist]
# If there are 2 or more pairs with the samp maximum distance,
# keep track of their id numbers in a vector called squarepatch.
# For now, arbitrarily choose the first such pair.
if(length(locmax) >= 2)
squarepatch <- c(squarepatch, idvalues[lp])
locmax <- min(locmax)
Indexl <- NULL
Index2 <- NULL
for(ii in 1 :(numpoints2 1)) {
for(jj in (ii + 1):numpoints2) {
Indexl <- c(Indexl, ii)
Index2 <- c(Index2, jj)
}
}
whchl <- Indexl[locmax]
whch2 <- Index2[locmax]
whmchxyl <- plist[whchl, ]
whchxy2 <- plist[whch2, ]
whchxy <- rbind(whchxyl, whchxy2)
along <- (((atan((whchxy[l, 2] whchxy[2, 2])/(whchxy[1, 1] whchxy[
2, 1])))/pi) 180)
slope <- (whchxy[l, 2] whchxy[2, 2])/(whchxy[l, 1] whchxy[2, 1])
newslope <- (-1)/slope
midx <- round((min(whchxy[, 1])) + abs((whchxy[2, 1] whchxy[1, 1])/2)
)
midy <- round((min(whchxy[, 2])) + abs((whchxy[2, 2] whchxy[l, 2])/2)
)
# calculates middle of the line- take min and abs of diff to get correct value
newy <- NULL
xlist <- NULL
ylist <- NULL
for(m in l:(abs(midx max(plist[, 1])) + 1)) {
newy <- round(newslope m) + midy
xlist <- c(xlist, midx + m)
ylist <- c(ylist, newy)
newy <- round(newslope m) + midy + 1
xlist <- c(xlist, midx + m)
ylist <- c(ylist, newy)
newy <- round(newslope m) + midy + 2
list <- c(xlist, midx + m)
ylist <- c(ylist, newy)
newy <- round(newslope m) + midy + 3
xlist <- c(xlist, midx + m)
ylist <- c(ylist, newy)
newy <- round(newslope m) + midy 1
xlist <- c(xlist, midx + m)
ylist <- c(ylist, newy)
newy <- round(newslope m) + midy 2
xlist <- c(xlist, midx + m)
list <- c(ylist, newy)
newy <- round(newslope m) + midy 3
xlist <- c(xlist, midx + m)
ylist <- c(ylist, newy)
}
form in -1 :(midx max(plist[, 1])) 1) {
newy <- round(newslope m + midy)
xlist <- c(xlist, midx + m)
ylist <- c(ylist, newy)
newy <- round(newslope m + midy + 1)
xlist <- c(xlist, midx + m)
ylist <- c(ylist, newy)
newy <- round(newslope m) + midy + 2
list <- c(xlist, midx + m)
ylist <- c(ylist, newy)
newy <- round(newslope m) + midy + 3
xlist <- c(xlist, midx + m)
ylist <- c(ylist, newy)
newy <- round(newslope m + midy 1)
xlist <- c(xlist, midx + m)
list <- c(ylist, newy)
newy <- round(newslope m) + midy 2
xlist <- c(xlist, midx + m)
ylist <- c(ylist, newy)
newy <- round(newslope m) + midy 3
list <- c(xlist, midx + m)
ylist <- c(ylist, newy)
}
candidates <- cbind(xlist, ylist)
xymatches <- NULL
plist <- round(plist)
for(kkin 1:dim(candidates)[l]) {
for(ll in l:dim(plist)[l]) {
bothmatch <- as.numeric(all(candidates[kk, ] = (plist[ll,
])))
if(bothmatch = 1)
xymatches <- rbind(xymatches, as.vector(candidates[kk, ]))
if(bothmatch = 1)
break
}
}
#See if the list includes at least 2 points in the patch along the
#secondary diagonal.
checkvector <- as.numeric(xymatches)
if(length(checkvector) <= 2)
finallist[lp, ] <- c(azlong,-longdist, -11, idvalues[lp])
if(length(checkvector) <= 2)
next
horizdist <- dist(xymatches, metric = "euclidean")
maxhdist <- max(horizdist)
finallist[lp, 1] <- along
finallist[lp, 2] <- longdist
finllistPlp, 3] <- maxhdist
finallist[lp, 4] <- idvalues[lp]
}
}
#end small
retum(finallist, squarepatch)
}
#Splus program that will bring data from arc/info unload (id, x, y,area, perimeter, edge, matrx-
# no matrix for 1950 plots) together with data calculated with findaxes
#program alongn, longaxis, secaxis) and puts orientation in range of 0-180.
photodat.9 <-function(z,w) {
a<-read.table(z, header = F, sep=",")
#z='"d:\\loxdata\\phdata\\unload\\plot3650.txt"- file with size info
S#w="d:\\spluswin\\home\\spphoto\\p3650ax.dat"-dumped file from jade
b<-dget(w)
a<-merge(a,b$finallist, by.x=l, by.y = 4, all.x = T)
#merges file with area and perimeter with file with orientation and axis data
names(a)<-c("id","x","y","area","perimeter", "edge","matrx", alongng, 'longaxis", "secaxis")
a$azlong<-90-a$azlong
#puts orientation angle on range of 0 t9 180 with 0 = north
retun(a)
}
#4/22/97 LAB
#This program creates variables for circle, ellipse, shidx(shape index indicating
#circle, ellipse, irregular, or no shape) for files with id,x,y,area,perimeter,edge,
#longaxis,secaxis.
addvar50<-function(a) {
#a= pxxxxf file
radius<-a$perimneter/(2*pi)
idarea<-pi*(radiusA2)
circ 1 <-as.matrix(a$area/idarea)
ellipse<-as.matrix(a$area/(pi*(.5*a$longaxis)*(.5*a$secaxis)))
shidx<-rep(0,(length(a$id)))
out<-cbind(p,circl,ellipse, shidx)
names(out)<-c("id","x","y","area","perimeter", "edge", alongng, "longaxis", "secaxis", circle" "ellipse",
"shidx")
out$shid*[out$circl >=. 85]<-1
#codes for circles
out$shidx[out$shidx != 1 & out$ellipse < 6]<-2
#codes for ellipses
out$shidxfout$shidx !=1 & out$ellipse >=6]<-3
#codes for irregular
out$shidx[out$secaxis = -11]<-0
#codes patches with no sec axis
out$shidx[out$edge = 1]<-0
#codes edge tree island shape as 0
retum(out)
}
#4/22/97 LAB
#This program creates variables for circle, ellipse, shidx(shape index indicating
#circle, ellipse, irregular, or no shape) for files with id,x,y,area,perimeter,edge,
#longaxis,secaxis.
addvar91<-function(a) {
#a= pxxxxf file
radius<-a$perimeter/(2*pi)
idarea<-pi*(radius^2)
circle <-as.matrix(a$area/idarea)
ellipse<-as.matrix(a$area/(pi*(.5*a$1ongaxis)*(.5*a$secaxis)))
shidx<-rep(,(length(a$id)))
out<-cbind(4,circl,ellipse, shidx)
names(out)<-c("id","x","y","area","perimeter", "edge", "matrx", alongng, "longaxis", "secaxis", circle" ,
"ellipse", "shidx")
out$shidx[out$circ 1>=. 85]<-1
#codes for circles
out$shidx[out$shidx != 1 & out$ellipse < 6]<-2
#codes for ellipses
out$shidx[out$shidx !=1 & out$ellipse >=6]<-3
#codes for irregular
out$shidx[out$secaxis = -11]<-0
#codes patches with no sec axis
out$shidx[out$edge = 1]<-0
#codes edge tree island shape as 0
retum(out)
}
#4/22/97 LAB
# This Splus function will print out summary stats for a plot
plotsum<-function(a) {
#a= pxxxxf file
numti<-length(a$id)
numedge<-length(a$edge[a$edge = 1])
nosec<-length(a$secaxis[a$secaxis = -11])
noseced<-length(a$secaxis[a$secaxis = r11 & a$edge = 1])
armeanall<-mean(a$area)
armenoe<-mean(a$area[a$edge !=1])
armedall<-median(a$area)
armednoe<-median(a$area[a$edge != 1])
arallsd<-sqrt(var(a$area))
arsdnoe<-sqrt(var(a$area[a$edge != 1]))
numcir<-length(a$shidx[a$shidx = 1])
if(numcir = 0) {
marcir<- NA
medcir<- NA
sdcir<-NA
}
if(numcir > 0)
marcir<-mean(a$arpa[a$shidx = 1])
medcir<-median(a$area[a$shidx = 1])
sdcir<-sqrt(var(a$4rea[a$shidx = 1]))
}
numellip<-length(a$area[a$shidx = 2])
if(numellip = 0){
marellip<- NA
medelip<- NA
sdellip<-NA
}
if(numellip > 0)
marellip<-mean(a$arpa[a$shidx = 2])
medellip<-median(a$area[a$shidx = 2])
sdellip<-sqrt(var(a$area[a$shidx = 2]))
}
numirr<-length(a$shidx[a$shidx = 3])
if(numirr = 0)
marirr<-NA
medirr<-NA
sdirr<-NA
}
if(numirr > 0) {
marirr<-mean(a$aTra[a$shidx = 3])
medirr<-median(a$area[a$shidx = 3])
sdirr<-sqrt(var(a$area[a$shidx = 3]))
}
out<-cbind(numti, numedge, nosec, noseced, armeanall, armenoe,armedall,
armednoe, arallsd,arsdnoenumcir,marcir,medcir,sdcir, numellip,marellip,medellip,
sdllip, numirr, medirr,sdirr)
retum(out)
}
