2015第八届数学建模认证杯网络挑战赛 C题优秀论文4348队

2015 年第八届“认证杯”数学中国

（由组委会填写）

Abstract

We analyze stability rodent community, based on a total of 12 kinds of variables ，depending on the factor of 3 kinds of rodents species per clip capture rate and the effect of 2 kinds of plants. We did the correlation analysis and significant test, qualitative analysis of the influencing factors ,finding that the stability of rodent community are significant, and then by means of linear regression analysis, we get the quantitative result in the different interference conditions the significant factors to influence the stability of the rodent community.

According to graphs of the preprocessed data of 2 kinds of plant biomass and 3 rodent species dominant species per clip capture rate, we get the trend of the rodent desert plants under different disturbance on biomass; using the Pearson correlation coeffic ient test and Spearman rank correlation test of 2 kinds of plant biomass and the total capture rate of rodents, and the significant test, we get the positively herbaceous biomass with rodents, negatively correlated with shrub biomass and rodents.

When we analyzing stability rodent community, we take advantage of the correlation analysis and significant test, where a total of 12 kinds of variables on the factor of 3 kinds of rodents species per clip capture rate and the effect of 2 kinds of plants, and we a nalyze the influencing factors of the stability of rodent community with significance in qualitative, and then by using linear regression analysis, we get the quantitative result in the different interference conditions the significant factors to influence the stability of the rodent community.

Finally, we make application of principal component analysis, which reveals the influence mechanism of interference for the rodent community: Compared to grazing in turns, overgrazing is the vegetation coverage of economical grazing ,making the shrub coverage significantly decrease, and indirectly making the rodent hidden reduce, so that it is more easily to be found when exposed to natural enemy. At the same time ,as the increasing of grazing intensity, after grazing the rodents habitat quality variation, the biomass of rodent community decreased due to lack of food. Therefore, there are indications of grazing disturbance intensity of the capture of desert rodent.

Key words：Significant test、Correlation analysis、PCA、Stepwise regression analysis 、SPSS

10 月的比较即可代指夏秋季节气候变化。我们将啮齿动物优势种作为啮齿动物的代表，

? ? = ? ?

xy ?

S 三、模型假设

1、除附表干扰因素与生物因子，忽略其他因子的影响

2、附表给出的数据都是正确合理的。

3、在未来的较短时间内，没有很大的人为灾害与自然灾害。

1、 y k —第

k 对观测值的因变量值 四、符号说明

2、 x jk —第

k 对观测值第 j 个自变量值 3、 εk —随机误差项

4、 a k , a ijk —第 k 对观测值第 j 个自变量相对于第 i 个因变量的回归系数

5、 a ?0 , a ?ij —最小二乘法估计得第 j 个因变量相对于第 i 个自变量的回归系数

6、 r xyj —相关系数

7、 S x , S y — x ij , y i 的均方差

8、m —第 i 个因变量对应多元回归自变量元数 9、n —观测值个数

10、k —每百夹捕获率对应的啮齿动物生物量

m

N (0,σ 2

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k =1

m

a

?0 = y - ∑a ? j x j j =1

r = S

x a ?

?r xy 1 ? 记 相 关 系 数 矩阵 ： R = ? ?r xyn ? xyj j

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，其自由度为 1 22 ∑

k k

SSE =

( y - y ? k =1

)2 ，其自由度为(n-2) 显著性检验使用的统计量为 F 统计：

F =

2)

spearman 秩相关系数检验：将两变量 X 、Y 成对的观察值分别从小到大顺序编秩，用 p i 表示 x i 的秩次；用 q i 表示 y i 的秩次。若观察值相同取平均秩次。 r s =

l

pearson 相关系数：

r p

F 检验：

S 2 =

∑( x - x )2 n -1

Y

Ⅰ鼠：三趾跳鼠；Ⅱ鼠：子午沙鼠；Ⅲ鼠：小毛足鼠

x13 =x4 +x8 ，y13 =y4 +y8 啮齿动物生物量即为三趾跳鼠生物量，子午沙鼠生物量与小毛足鼠生物量之和：

x12 =x9 +x10 +x11，y12 =y9 +y10 +y11 啮齿动物百夹捕获率即为三趾跳鼠百夹捕获率，子午沙鼠百夹捕获率与小毛足鼠百夹捕

x17 =k ?x12 ，x14 =k ?x9 ，x15 =k ?x10 ，x16 =k ?x11 (其中

k 为正数)。

1、灌木植物Th物量与干扰Th境关系

（a）不同干扰生境对灌木植物生物量影响：

（b）不同季节对灌木植物生物量影响：

2、植物Th物量与干扰Th境关系

3、啮齿动物Th物量与季节关系

N =k ?M

N :啮齿类动物优势种生物量；

k :啮齿类动物优势种与捕获率之间比例系数；

M :啮齿类动物优势种捕获率；我们在考虑啮齿类动物优势种生物量是通过分析捕获率获得其变化趋势关系。在过

4、啮齿动物Th物量与干扰Th境关系

5、植物Th物量与啮齿动物Th物量关系

1、不同干扰下植物地上生物量变化趋势：

(1）人为干扰下植物地上生物量变化趋势：

2、不同干扰下啮齿动物生物量变化趋势：

（1）人为干扰下啮齿动物生物量变化趋势：轮

（2）自然干扰下啮齿动物群落生物量变化趋势：秋季相

3、不同干扰情况下植物地上生物量与啮齿动物生物量间变化关系：

1、多元线性回归模型 基础模型为前述多元线性回归模型，考虑不同干扰因素下动物生物

z jk = x jk - x j

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∑(x

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k =1

j n s 2 = k =1

,

j

n -1

R = ??r ij ??m xm =

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Z ， n - 1

r ij

=

∑ z jp z pk n - 1 ，

w ∑ λ j j =1

m

λ j

≥ 0.85

λI m = 0

j =1

T o

U jk = z j b j

2

3.1

3.2 过牧干扰生境灌木植物因子随季节变化关系

3.3 轮牧干扰生境草本植物因子随季节变化关系

3.4 轮牧干扰生境灌木植物因子随季节变化关系