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Sensitivity Analysis of a Spatially Explicit Fish Population Model Applied to Everglades Restoration
René A. Salinas and Louis J. Gross
The Institute for Environmental Modeling, University of Tennessee, Knoxville, Tennessee 37996
INTRODUCTION
HYDROLOGY
The ATLSS Landscape Fish Model (ALFISH)* is a spatially-explicit, size
structured functional group model that estimates freshwater fish densities across
the south Florida Restudy area (Fig. 1) for a given hydrological scenario
associated with Everglades restoration.
Fish densities are vital for the
survival of endangered wading bird
species. ALFISH divides the
landscape into 500m X 500m cells
and runs on 5-day increments. Two
important aspects of the model are
alligator hole and other pond type
densities and lower trophic level
resource concentration. Ponds act
as refuges for fish as water level
decreases (drydowns). Ponds are
assumed to be 50m2 in area. Our
model assumes 5% of fish in a cell
can enter ponds during a drydown,
5% can enter an adjacent cell, and
90% die. ALFISH assumes
seasonal cycles of lower trophic
level concentrations.
ABSTRACT
ALFISH is a spatially explicit population level model for freshwater fish in the south Florida Everglades.
The model divides the region into 500m x 500m cells. The models objective is to predict fish biomass for
wading birds under different hydrological scenarios associated with Everglades restoration. Determining model
parameter sensitivity is critical to its reliability in assessing alternative scenarios. Two important model
components are pond distribution and available lower trophic level resources. Pond distribution is important in
providing fish refuges during periods when water level is low. Initial estimates suggest 34% of cells have ponds.
ALFISH's sensitivity to pond distribution was assessed using alternative pond distributions and the same
hydrologic data. Pond spatial distribution was varied to include spatial Poisson, uniform and clustered. Pond
density was also varied. Food resources for the fish were varied using constant maxima and minima across
season as well as two alternative, seasonally varying cases. Results suggest that ALFISH is more sensitive to
pond spatial distribution than density, but lower trophic level concentration interacts with this.
•Determine the effects of density and spatial distribution of alligator holes and other
pond types to freshwater fish under a specific hydrologic regime in a spatially-explicit
model of south Florida.
•Determine the effects of various concentrations of lower trophic level resources on
freshwater fish under a specific hydrologic regime in a spatially-explicit model of
south Florida.
Fig. 5.
A) 100%
B) 50%
Fig. 2:
Pond maps used in
sensitivity analysis.
A) 100% of cells
with a pond
B) 50% of cells with
a pond(Poisson)
C) 0% (No ponds)
D) 25% of cells with
a pond (Poisson)
E) 25% of cells with
a pond (Uniform)
F) 25% of cells with
a pond (clustered
Poisson)
C) 0%
A)
C)
Time series graphs of fish density averaged yearly. The three graphs are defined as follows: 1) 1st
Scenario, 2) (1st Scenario - 2nd Scenario), 3) 2nd Scenario.
100%
50%
difference
difference
0%
25%
B)
100%
D) 25% Poisson
difference
difference
25%
25% Clustered
1.6
300
1.4
250
1.2
200
150
g/m^2
g/m^2
1
Periphyton
Aquatic Macrophytes
Detritus
Aquatic Mesoinvertebrates
0.8
Aquatic Macroinvertebrates
0.6
•Table 1 shows the percent difference, (difference/2nd
Scenario)*100, at three distinct years that involve fish density
recovery from a drydown.
•Fig. 5 shows time series graphs comparing fish densities averaged
over each year.
•Fig. 6 shows the spatial distribution of fish during a drydown.
Table 1
Comparison
1983
1988
1993
100% vs. 0
77.0%
200.0%
600.0%
50% vs. 0
46.0%
150.0%
500.0%
100% vs. 25%
40%
42%
37%
100% vs. 50%
22%
26%
18%
50% vs. 25%
22.0%
19.0%
17.0%
25% Uniform vs.
2.0%
2.8%
3.7%
6.0%
33.0%
72.0%
Constant Max LTL vs.
Seasonal LTL
14.6%
14.6%
15.0%
Constant Max LTL vs.
32.0%
33.0%
30.0%
-1.3%
-2.3%
-1.4%
25% Clustered
Constant Min LTL
difference
Minimum LTL
F) Maximum LTL
difference
Seasonal LTL
Seasonal LTL vs.
Inverse Seasonal LTL
CONCLUSIONS
Fig. 6
Lower Trophic Level Resources
B)
Because ALFISH is designed as a qualitative tool, it is most useful
when comparing two scenarios.
25% Poisson vs.
ALFISH divides lower trophic level resources into five categories and assumes
a seasonal cycle for each (Fig. 3). We tested three alternative scenarios:
1) Constant with the maximum value for each type,
2) Constant with the minimum value for each type, and
3) Inverse seasonal cycle for each type.
Lower Trophic Level Resources
B) Yearly
Averages
25% Poisson
E) Maximum LTL
D) 25% Poisson E) 25% Uniform F) 25% Clustered
A) 5 - Day
increments
RESULTS
OBJECTIVES
the restudy area of south Florida
An important analysis of a model is its sensitivity to parameters. In the
case of ALFISH, there is no pond map for the entire restudy region. We wanted
to know what aspects of pond densities the model was most sensitive to. We
looked at variations in pond number and pond spatial distribution (Fig 2).
Fig. 4
A)
Fig. 1. ATLSS subregions associated with
SENSITIVITY ANALYSIS
The Calibration Validation hydrology data set (Fig. 4) was used for the
analysis. This data set, which runs from 1979 through 1995, most accurately
reflects the history of actual water levels determined by the South Florida
Management District.
Spatial difference map of the 25% Clustered and 25% Poisson pond scenarios showing total fish densities
on October 13, 1993.
Our results suggest that the model must have ponds for the
fish to survive (Fig 5A, Table 1). Within the range of 25% and 100%
pond density, the percent difference, although significant, does not
increase exponentially through time (Fig 5B and 5C, Table 1). This
is important since in the absence of ponds the percent difference
increases over time. This suggests that deviations from our
current estimate of 34% pond density will not significantly affect
qualitative results.
Our results also show that pond spatial distribution can have a
major effect on fish density (Fig. 5D, Fig. 6, Table 1). These results
suggests that it is important that we understand where there may
be large gaps in pond distribution.
100
0.4
50
0.2
0
30
0
20
0
10
300
150
0
5 - Day Increments
0
0
0
5 - Day Increm ents
Fig. 3. Lower trophic level seasonal cycles used by ALFISH.
*Gaff, H. et al. 2000. A dynamic landscape model for fish in the Everglades and its
application to restoration. Ecological Modelling 127: 33-52.
Finally, within the range of lower trophic level resource
concentrations that we are using, the effects on fish densities are
uniform through time and thus qualitatively similar (Figs. 5E and 5F,
Table 1). Therefore, unless we intend to change the resource
densities by an order of magnitude, the present seasonal cycle
need not be changed.