数学兀2002年国际大学生数学建模竞赛ICM题

2020年11月22日发(作者：陶碧)
ICM: The Interdisciplinary Contest in Modeling

2002 Contest Problem

If we SCRUB our land too much, we may lose the LIZARDs
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.
Picture by Grant Hokit


You will find a fact sheet on the Florida Scrub Lizard at
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 F
a
(the average fecundity
of adult lizards); S
j
(the survivorship of juvenile lizards- between birth and the first reproductive
season); and S
a
(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
1
2
3
0
1
2
972
180
20
495
92
11
Avg. Female Size
(mm)
30.3
45.8
55.8