The Research On Sex Ratios And Maintenance Of Sexual Reproduction In Spatial Sex Ecology Utilized Pair Approximation And Moment Method

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.