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1、第八届认证杯数学中国数学建模网络挑战赛承 诺 书我们仔细阅读了第八届认证杯数学中国数学建模网络挑战赛的竞赛规则.我们完全明白,在竞赛开始后参赛队员不能以任何方式包括 、电子、网上咨询等与队外的任何人包括指导教师研究、讨论与赛题有关的问题.我们知道,抄袭别人的成果是违反竞赛规则的, 如果引用别人的成果或其他公开的资料包括网上查到的资料,必须按照规定的参考文献的表述方式在正文引用处和参考文献中明确列出.我们郑重承诺,严格遵守竞赛规则,以保证竞赛的公正、公平性.如有违反竞赛规则的行为,我们接受相应处理结果.我们允许数学中国公布论文,以供网友之间学习交流,数学中国以非商业目的的论文交流不需要提前取得我
2、们的同意.我们的参赛队号为：参赛队员 ：队员1： 队员2：队员3：参赛队教练员 ：参赛队伍组别：本科组第八届认证杯数学中国数学建模网络挑战赛编 号 专 用 页参赛队伍的参赛队号：请各个参赛队提前填写好：#1893竞赛统一编号由竞赛组委会送至评委团前编号：竞赛评阅编号由竞赛评委团评阅前进行编号：2015年第八届认证杯数学中国数学建模网络挑战赛第一阶段论文题 目 荒漠区动植物关系的研究 关 键 词 冗余分析、SEM 模型、敏感性分析、典型相关分析方法、生态指数 摘 要本文针对荒漠区动植物关系的研究问题,通过CCA典型相关分析方法、冗余分析、时间序列、敏感性分析、SEM 模型、生态指数、残差分析法等
3、一系列方法,综合分析了荒漠区不同干扰下植物生物量与啮齿动物生物量之间的关系以与不同干扰生境下啮齿动物稳定性和干扰对于啮齿动物群落的影响机制.针对问题一,根据附件一西北某干旱区植物动物数据整理,对不同干扰下植物地上生物量和啮齿动物生物量进行分析,并建立数学模型,最后得到不同干扰下植物地上生物量和啮齿动物生物量变化趋势.建立 PCA主成分分析模型对6 年中生物量进行分析,证明啮齿动物种群数量在所有干扰区均表现出双峰型格局,轮牧和过牧之间的种群动态表现出类似的波动；各区灌木和草本地上生物量各年间存在明显差别,但较为一致的特点是7月是各区绝大多数灌木地上生物量最高的季节.针对问题二,对附件一中的数据应
4、用 CCA典型相关分析方法分析了啮齿动物群落生物量与其生态指标与植物群落之间的相关性.通过建立CCA模型,结果表明两种生境的第一典型相关变量的累积方差贡献率轮牧区为 68.04,过牧区为 83.75.两种干扰类型均在 0.01 水平下达显著,相关系数均达 0.7 以上.第二典型相关变量的相关系数均在 0.7 以下,轮牧区、过牧区在 0.05 水平下均未达显著.轮牧区和过牧区主要是草本植物与啮齿动物生物量均匀性相关作用较大,二者的不同在于草本盖度的增加、草本生物量的减少在轮牧区会使啮齿动物生物量均匀性增加,而过牧区则使啮齿动物生物量均匀性降低.针对问题三,为了了解不同干扰对荒漠啮齿动物群落稳定性
5、的影响,我们从群落多样性、物种间关联性、变异性等方面对不同干扰下的啮齿动物群落进行了分析,并对不同干扰生境下啮齿动物进行敏感性分析、冗余分析,采用Shannon-Weiner 多样性指数、Pielou 均匀性指数和 Simpson 优势度指数等 7 个生态学变量来描述不同干扰类型下啮齿动物群落的动态特征.最后建立SEM 模型来拟合不同干扰对荒漠啮齿动物群落的影响途径.参数估计使用极大似然法,潜变量与测量指标之间的关系用因素载荷表示；潜变量之间的关系用回归系数表示；用卡方自由度比、RMSEA和 CFI 进行拟合检验.证明不同干扰下啮齿动物优势种的种群数量受到多个过程的共同作用.过牧和轮牧区啮齿动
6、物群落多样性和动物总数量受到植物隐蔽的直接影响较大,而受到季节的间接效应较大.此外气候,土壤等因素对其应该也有不同程度的影响.参赛密码 由组委会填写参赛队号: #1893 所选题目: C 题 英文摘要This paper studies the relationship between plants and animals of the desert zone problem by CCA method, redundancy analysis, time series, sensitivity analysis, SEM model, ecological index, residual a
7、nalysis method and a series of methods, a comprehensive analysis of the desert relationship of plant biomass and biomass rodents interference between different areas and rodents stability and interference under different disturbance habitats for rodents Communities mechanism.One of the problem, acco
8、rding to annex a certain arid northwest area of plant and animal data collation of aboveground biomass and biomass of different rodents interference analysis, and a mathematical model, and finally get under different disturbance aboveground biomass and biological rodents volume trends. Establish PCA
9、 model six years biomass analysis, prove the number of rodent populations in all disturbed areas exhibited a bimodal pattern, population between rotational grazing and over-grazing dynamic exhibit similar fluctuations; district shrubs exist between years and herbaceous aboveground biomass significan
10、t difference, but more consistent feature is the vast majority of the district in July is the highest aboveground biomass shrub season. For the second question, Annex I of data applications CCA method to analyze the relevance of the rodent community biomass and plant communities and ecological indic
11、ators between. Through the establishment of CCA model, results showed that the cumulative variance contribution rate of rotational grazing area two habitats first canonical correlation variable is 68.04%, over the pastoral 83.75%. Two kinds of disturbance at the 0.01 level were issued significant co
12、rrelation coefficient reached more than 0.7. The correlation coefficient of the second canonical correlation variables are below 0.7, rotational grazing area, over pastoral at 0.05 level did not reach significant. Rotational grazing and over-pastoral zone is mainly herbaceous plants with large roden
13、t related to the role of biomass homogeneity, difference between the two is to increase the degree of herbaceous cover, herbaceous biomass will reduce rodent biomass increased uniformity in rotational grazing area, and over pastoral makes rodent biomass decreased uniformity. Three of the problem, in
14、 order to understand the impact of interference on different animal desert rodent community stability, from community diversity, inter-species association, variability and other aspects of rodent communities under different disturbances were analyzed, and the different habitat disturbance Under rode
15、nts sensitivity analysis, redundancy analysis, using Shannon-Weiner diversity index, Pielou evenness index and Simpson dominance index and other seven variables to describe the dynamic characteristics of ecology under different disturbance types of rodent communities. Finally, the establishment of SEM model to fit different interference desert rodent communities affected pathways. Parameter estimation using the maximum likelihood method similar relationship, between the latent variables and measure the load factor is re
