ICM:
The Interdisciplinary Contest in Modeling
2002 Contest Problem
If
we SCRUB our land too much, we may lose the LIZARDs
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The Florida scrub lizard is a small, gray
or gray-brown lizard that lives throughout upland sandy
areas in the Central and Atlantic coast regions of Florida.
The Florida Committee on Rare and Endangered Plants classified
the scrub lizard as endangered.
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Picture by Grant Hokit |
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You will find a fact sheet on the Florida
Scrub Lizard at scrublizard.pdf
The long-term survival of the Florida scrub
lizard is dependent upon preservation of the proper spatial
configuration and size of scrub habitat patches.
Task 1: Discuss factors
that may contribute to the loss of appropriate habitat for scrub
lizards in Florida. What recommendations would you make to
the state of Florida to preserve these habitats and discuss
obstacles to the implementation of your recommendations?
Task 2: Utilize the data provided in Table
1 to estimate the value for Fa (the average
fecundity of adult lizards); Sj (the survivorship of juvenile
lizards- between birth and the first reproductive season); and
Sa (the average adult survivorship).
Table 1
Summary data for a cohort of scrub lizards captured and followed
for 4 consecutive years. Hatchling lizards (age 0) do not produce
eggs during the summer they are born. Average clutch size for
all other females is proportional to body size according to
the function y = 0.21*(SVL)-7.5, where y
is the clutch size and SVL is the snout-to-vent length
in mm.
Year
|
Age
|
Total Number Living
|
Number of Living Females
|
Avg. Female Size (mm)
|
1
|
0
|
972
|
495
|
30.3
|
2
|
1
|
180
|
92
|
45.8
|
3
|
2
|
20
|
11
|
55.8
|
4
|
3
|
2
|
2
|
56.0
|
Task 3: It
has been conjectured that the parameters Fa
, Sj , and Sa
, are related to the size and amount of open sandy area
of a scrub patch. Utilize the data provided in Table 2 to develop
functions that estimate Fa, Sj
, and Sa for different patches. In
addition, develop a function that estimates C, the carrying
capacity of scrub lizards for a given patch.
Table 2
Summary data for 8 scrub patches including vital rate data
for scrub lizards. Annual female fecundity (Fa),
juvenile survivorship (Sj), and adult survivorship
(Sa) are presented for each patch along with
patch size and the amount of open sandy habitat.
Patch
|
Patch Size (ha)
|
Sandy Habitat (ha)
|
Fa
|
Sj
|
Sa
|
Density (lizards/ha)
|
a
|
11.31
|
4.80
|
5.6
|
0.12
|
0.06
|
58
|
b
|
35.54
|
11.31
|
6.6
|
0.16
|
0.10
|
60
|
c
|
141.76
|
51.55
|
9.5
|
0.17
|
0.13
|
75
|
d
|
14.65
|
7.55
|
4.8
|
0.15
|
0.09
|
55
|
e
|
63.24
|
20.12
|
9.7
|
0.17
|
0.11
|
80
|
f
|
132.35
|
54.14
|
9.9
|
0.18
|
0.14
|
82
|
g
|
8.46
|
1.67
|
5.5
|
0.11
|
0.05
|
40
|
h
|
278.26
|
84.32
|
11.0
|
0.19
|
0.15
|
115
|
Task 4: There
are many animal studies that indicate that food, space, shelter,
or even reproductive partners may be limited within a habitat
patch causing individuals to migrate between patches. There is no conclusive evidence on why scrub lizards
migrate. However, about 10 percent of juvenile lizards do migrate
between patches and this immigration can influence the size
of the population within a patch. Adult lizards apparently
do not migrate. Utilizing the data provided in the histogram
below estimate the probability
of lizards surviving the migration between any two patches i
and patch j.
Table 3
Histogram
Migration data for juvenile lizards marked, released, and recaptured
up to 6 months later. Surveys for recapture were conducted
up to 750m from release sites.
Task 5: Develop
a model to estimate the overall population size of scrub lizards
for the landscape given in Table 3. Also, determine which patches
are suitable for occupation by scrub lizards and which patches
would not support a viable population.
Patch size and amount of open sandy habitat for a landscape
of 29 patches located on the Avon Park Air Force Range. See:
map.jpg
for a map of the landscape.
Patch Identification
|
Patch Size (ha)
|
Sandy Habitat (ha)
|
1
|
13.66
|
5.38
|
2
|
32.74
|
11.91
|
3
|
1.39
|
0.23
|
4
|
2.28
|
0.76
|
5
|
7.03
|
3.62
|
6
|
14.47
|
4.38
|
7
|
2.52
|
1.99
|
8
|
5.87
|
2.49
|
9
|
22.27
|
8.44
|
10
|
19.25
|
7.58
|
11
|
11.31
|
4.80
|
12
|
74.35
|
19.15
|
13
|
21.57
|
7.52
|
14
|
15.50
|
2.82
|
15
|
35.54
|
11.31
|
16
|
2.93
|
1.15
|
17
|
47.21
|
10.73
|
18
|
1.67
|
0.13
|
19
|
9.80
|
2.23
|
20
|
39.31
|
7.15
|
21
|
2.23
|
0.78
|
22
|
3.73
|
1.02
|
23
|
8.46
|
1.67
|
24
|
3.89
|
1.89
|
25
|
1.33
|
1.11
|
26
|
0.85
|
0.79
|
27
|
8.75
|
5.30
|
28
|
9.77
|
6.22
|
29
|
13.45
|
4.69
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TASK 6: It has been determined
from aerial photographs that vegetation density increases by
about 6% a year within the Florida scrub areas. Please make
a recommendation on a policy for controlled burning.