利用偶对近似和矩方法对空间性生态学中性比率和有性生殖维持的研究
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摘要
空间生态学和性生态学都是当前理论生态学和数学生态学研究的重要领域。性生态学和空间生态的结合乃是当今研究的前沿和热点。因为大多研究空间生态学忽略了有性生殖,而有性生殖的研究又没考虑空间因素。偶对近似和矩方法是近几年发展起来了的先进空间分析方法。它们是通过空间相关性来反映种群空间分布的两种近似随机空间模型。其优点是可以系统地进行数学分析处理,克服了空间模拟耗时和随机性带来的缺陷。本论文选题正是利用偶对近似和矩方法来研究具有空间结构的有性生殖种群中两个重要的具体问题:性比率和有性生殖的维持。文章主体将分为五部分:第一章介绍了空间生态学和性生态学的概念、理论、模型和应用;第二、三章介绍了偶对近似和矩模型的构造方法;第四章利用偶对近似研究了空间局部作用和生境退化对有性生殖种群和性比率的影响;最后建立了有性生殖和无性生殖种群的空间矩方程,给出了有性种群维持和续存的空间生态条件。研究结果表明:(1)对于均匀混合的有性种群有平凡稳定点。这是由于有性生殖导致的Allee效应使得当种群数量很小时增长率降低而导致灭绝:(2)由于空间空斑块的存在使得对于简单的单双倍性别决定机制有性种群在均匀场条件下的性比率偏雄,而空间的局部相互作用使其偏雄性降低乃至偏雌;(3)有性种群数量在空间相互作用范围适中时达到最大。这说明了适中的空间作用范围有种群水平上的进化意义;(4)生境的退化加大了性比率的偏雄性;(5)由于空间分布的聚集,利用偶对近似模型的条件概率提出了局部性比率概念。真正对种群动态起作用的是局部性比率,发现种群的全局性比率和局部性比率的偏向性并不一致。并且雌性周围的局部性比率大于雄性周围的局部性比率,这可能是种群力求交配机会最大化以使种群最大的适应机制;(6)有性生殖方式和无性生殖方式在非空间的情况下能够共存,这依赖于无性种群对有性种群有较小的作用系数;(7)无性种群的空间聚集能够导致有性和无性种群共存,因为空间聚集能够加剧无性种群的内部竞争;(8)由于假设无性个体与有性个体生殖率的两倍关系,在导致无性种群空间聚集的条件上要求比较严格,适当的增长容纳量和适当的相互作用系数;(9)无性种群的空间局部作用范围对有性种群的维持和续存有很大促进作用。当局部作用范围较小时能够弥补在非空间条件下有性种群被替代的不利;(10)有性种群的扩散能力是补偿其性的双重代价的一个空间机制。综上,本文一方面扩展了偶对近似和矩方法的应用范围,建立了不同背景下的具体模型。另一面实际地研究了性比率和有性生殖维持的生态机制,从机理和方法上发展和丰富了空间性生态学的理论。
Both spatial ecology and sex ecology are the important fields in the international research of theoretical and mathematical ecology. Especially the combination of these is one of the frontiers and hotstops of ecological research. Because almost all papers that focus on spatial ecology have ignored the sexual reproduction of considered population, and the researches on sex ecology often do not take the spatial factors into account. Pair approximation and moment methods are the advanced methods of spatial analysis developed in recent years. They are able to explore the spatial distribution of population by the statistics of spatial correlation and predict the behavior of lattice models when mean-approximation fails. Pair approximation and moment methods have the advantages of overcoming analytical intractability of computer simulation and building a spatially stochastic model. The subject of this dissertation is the sex ratio and maintenance of sexual reproduction on spatially structured population utilized the pair approximation and moment methods.This dissertation consists of six chapters. Chapter one summarizes the essential framework and the frontiers and development of spatial ecology and sex ecology. Chapter two and three respectively provides the ways how to build the pair approximation and moment methods to analytically investigate the spatially structured population. Chapter four focus on the dynamics, spatial distribution and sex ratio of spatially structured sexual reproduction population, exploring the effects of habitat decay and habitat connectivity used by pair approximation. In chapter five we construct the moment model for population including sexual reproduction and asexual reproduction, and study the condition of coexistence for these two reproduction patterns. Finally, In the last chapter, I make the main conclusions and the perspectives about the development of the application of pair approximation and moment method in the sex ecology. We have obtained the following main results: (1) In the mean-field sexual reproduction population there exists stable steady trivial equilibrium, which means the population would be extinct. This results from the Allee effect caused by few probability of mating. (2) The sexual population that sex is determined by haploid-diploid has the male-biased sex rations due to the influence of empty patch in the mean-field approximation. Spatially local interaction will reduce the degree of this bias and even to cause female-biased sex ratios.(3)The abundance of the population will be maximized at intermediate spatial interaction scale, which indicates that certain spatial scale has the implication of evolutionary adaptation to the sexual reproduction population at the level of population. (4) Habitat decay can lead to higher degree of male-biased sex ratios. (5)Based on conditional probability in the pair approximation we provide the concept of local sex ratio, which is not always consistent with traditional sex ratio because of spatial structure and really affects the dynamics of population. It is found that local sex ratio at female is always larger than at male, which maybe maximize the probability of mating. (6) Sexual and asexual reproduction can coexist in non-spatial condition. However, it must depend on that the asexual individual has less impact on the growth of the sexual population. (7) The coexistence of sexual and asexual reproduction can result from spatial clustering of asexual population, which increase the degree of intraspecific competition of asexual population. (8) Because asexual individual has double birth rate to sexual individual, there are strict condition about growth capacity and interaction coefficient to lead to spatial clustering of asexual population. (9) Local dispersal of asexual population can improve the maintenance of sexual population, and compensate the disadvantage of sexual population at expense of sex. (10) The stronger ability of dispersal of sexual individual is the spatial mechanism to recoup the twofold cost of sex. In this dissertation we extend the application of pair approximation and moment method and build the particular model in background of sex ecology. And at the same time we investigate the sex ratio and the ecological mechanism of maintenance of sexual population, which develop theoretically and enrich methodologically the theory of spatial sex ecology.
Both spatial ecology and sex ecology are the important fields in the international research of theoretical and mathematical ecology. Especially the combination of these is one of the frontiers and hotstops of ecological research. Because almost all papers that focus on spatial ecology have ignored the sexual reproduction of considered population, and the researches on sex ecology often do not take the spatial factors into account. Pair approximation and moment methods are the advanced methods of spatial analysis developed in recent years. They are able to explore the spatial distribution of population by the statistics of spatial correlation and predict the behavior of lattice models when mean-approximation fails. Pair approximation and moment methods have the advantages of overcoming analytical intractability of computer simulation and building a spatially stochastic model. The subject of this dissertation is the sex ratio and maintenance of sexual reproduction on spatially structured population utilized the pair approximation and moment methods.This dissertation consists of six chapters. Chapter one summarizes the essential framework and the frontiers and development of spatial ecology and sex ecology. Chapter two and three respectively provides the ways how to build the pair approximation and moment methods to analytically investigate the spatially structured population. Chapter four focus on the dynamics, spatial distribution and sex ratio of spatially structured sexual reproduction population, exploring the effects of habitat decay and habitat connectivity used by pair approximation. In chapter five we construct the moment model for population including sexual reproduction and asexual reproduction, and study the condition of coexistence for these two reproduction patterns. Finally, In the last chapter, I make the main conclusions and the perspectives about the development of the application of pair approximation and moment method in the sex ecology. We have obtained the following main results: (1) In the mean-field sexual reproduction population there exists stable steady trivial equilibrium, which means the population would be extinct. This results from the Allee effect caused by few probability of mating. (2) The sexual population that sex is determined by haploid-diploid has the male-biased sex rations due to the influence of empty patch in the mean-field approximation. Spatially local interaction will reduce the degree of this bias and even to cause female-biased sex ratios.(3)The abundance of the population will be maximized at intermediate spatial interaction scale, which indicates that certain spatial scale has the implication of evolutionary adaptation to the sexual reproduction population at the level of population. (4) Habitat decay can lead to higher degree of male-biased sex ratios. (5)Based on conditional probability in the pair approximation we provide the concept of local sex ratio, which is not always consistent with traditional sex ratio because of spatial structure and really affects the dynamics of population. It is found that local sex ratio at female is always larger than at male, which maybe maximize the probability of mating. (6) Sexual and asexual reproduction can coexist in non-spatial condition. However, it must depend on that the asexual individual has less impact on the growth of the sexual population. (7) The coexistence of sexual and asexual reproduction can result from spatial clustering of asexual population, which increase the degree of intraspecific competition of asexual population. (8) Because asexual individual has double birth rate to sexual individual, there are strict condition about growth capacity and interaction coefficient to lead to spatial clustering of asexual population. (9) Local dispersal of asexual population can improve the maintenance of sexual population, and compensate the disadvantage of sexual population at expense of sex. (10) The stronger ability of dispersal of sexual individual is the spatial mechanism to recoup the twofold cost of sex. In this dissertation we extend the application of pair approximation and moment method and build the particular model in background of sex ecology. And at the same time we investigate the sex ratio and the ecological mechanism of maintenance of sexual population, which develop theoretically and enrich methodologically the theory of spatial sex ecology.
引文
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