mcm2002C If we SCRUB our land too much, we may lose the LIZARDs - matlab数学建模

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标题：mcm2002C If we SCRUB our land too much, we may lose the LIZARDs
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所属分类: 数学建模资源类型：文档文件大小: 18.99 KB 上传时间: 2019-08-19 20:41:47 下载次数: 58 资源积分：1分提供者: jiqiren 20190819084240123

内容：
(MCM 2002C)

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.

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.

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

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.

如果我们过分扫荡自己的土地，将会失去各种各样的蜥蜴(美国竞赛2002年C题)

佛罗里达灌木蜥蜴是一种灰色或灰褐色小蜥蜴，遍布于佛罗里达中部和大西洋沿岸地区的沙质高地上。Florida濒危动植物委员会把这种灌木蜥蜴归类为濒危的生物。

佛罗里达灌木蜥蜴的长期存活，有赖于保留适当的空间搭配和灌木丛生地带的规模。

任务1：讨论在佛罗里达州促使灌木蜥蜴丧失适当栖息地的各种因素。为了保留这些栖息地，你会提出哪些建议？并且论述实现你的建议的各种障碍。

任务2：利用表1中提供的数据估计数值Fa(成年蜥蜴平均产卵量)；Sj(处在出生和第一个繁殖季节之间的幼年蜥蜴存活率)；Sa(成年蜥蜴平均存活率)。

表1 摘要数据是关于一群灌木蜥蜴的，它们先被捕捉尔后连续跟踪四年。幼小蜥蜴(0岁)在出生当年夏季不产卵。所有其他雌蜥蜴的平均孵卵量与身体尺寸成比例，正如线性函数 y=0.21×SVL−7.5 所表示的，其中 y 是孵卵量，而 SVL 是鼻子到肛门以mm为单位的长度。

(年度年龄存活总数雌蜥蜴存活数平均雌蜥蜴身长(mm) )

任务3：人们推测，参数Fa, Sj 和 Sa 与一片灌木地带的露天沙质区的规模和总量有关联。利用提供在表2中的数据构造若干函数来针对不同地带估计 Fa, Sj 和 Sa。此外，构造函数对给定地带评估其承载灌木蜥蜴的能力 C。

表2 关于8个灌木地带的摘要数据，包括灌木蜥蜴的生命变化速率。对于每个地带，雌蜥蜴的年产卵量(Fa), 幼小蜥蜴存活率(Sj), 以及成年蜥蜴存活率(Sa), 连同地带规模和露天沙质栖息地的总量列在一起。

灌木地带地带规模 (公顷) 沙质栖息地 (公顷) Fa Sj Sa 密度(蜥蜴数/公顷)

任务4：已有许多动物研究表明，在一个栖息地带中，食物，空间，掩蔽地，抑或繁殖配偶可能受限制的，这就导致动物个体在各个地带之间迁徙。有关灌木蜥蜴的迁徙原因缺少明确的证据。不过，确有百分之十的幼年蜥蜴在各个地带之间游走，而这种迁徙会影响一个地带中群体规模。成年蜥蜴显然不迁徙。利用下面直方图中给出的数据估计在任何两个地带i和j之间经迁徙而存活的蜥蜴的概率。

表3 直方图

幼年蜥蜴的迁徙数据，是经由个体标记，释放，再捕获直到6个月后获取的。对于再捕捉的测量工作是在距离释放地点方圆750m内进行。

任务5：对于表3中给出的地表形貌，建立模型估计灌木蜥蜴的整个群体规模。而且，确定哪些地带适于灌木蜥蜴栖息，哪些地带会不支持一个有生存力的群体。

对于一个展布在Avon Park Air Force Range上面的具有29个地带的地表形貌，下面的表格列出了各个地带规模和露天沙质栖息地。

任务6：空中摄影业已确定，在佛罗里达灌木区域内，植被密度一年增长6%左右。请针对一个可控燃烧政策提出建议。

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mcm2002C If we SCRUB our land too much, we may lose the LIZARDs .doc