性生态学中两个基本问题的空间结构模型及机理研究
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摘要
空间生态学研究和性生态学研究近年来一直是理论生态学和数学生态学研究的热点问题,两者的结合更是当今研究的前沿领域。然而大多数空间结构下的研究都忽略了性,而关于性的大多数研究又都没有考虑空间因素的因素。本篇论文就是在性生态学的两个基本问题(性比率的1：1稳定维持机制及有性生殖和无性生殖的共存)的研究中考虑了空间结构的影响。我们利用常微分方程、偶对近似方法和元胞自动机方法建立了数学模型,利用数学分析和数值模拟的方法从理论角度回答了空间结构的影响。同时,扩散作为生物生活史的一个重要特征,其对生物自组织的影响一直是生态学工作者的关注的核心问题之一。我们在以上研究的基础上还研究了扩散对生态系统的影响。研究得到了许多有意义的结果：(1).空间结构下的Allee效应有利于种群性比率稳定在1：1附近,空间结构越明显,Allee效应的影响越强；(2).斑块之间的联通度过低会导致偏雌的进化维持策略；(3).空间联通度的改善,对雌雄性的影响并不相同,其导致雄性更加聚集,雌性更加离散,使得雄性局域性比率减小,而却不会影响雌性局域性比率；(4).迁移并不会影响两性种群的进化维持性比,但是,个体的迁移对有性集合种群的时空动态的影响差异明显,雄性的迁移以有利于整个集合种群的繁殖,然而雌性迁移几乎没有影响；雄性的迁移增大了两性的局域性比率,而雌性的迁移减少了两性的局域性比率；而且,雄性局域性比率总是大于雌性局域性比率,这可能是由于雌性种希望得到更多的交配机会的原因；(5).空间结构可以从根本上解释雌核发育种群和其依附种群的共存问题,其共存可能有两种情况：1.在集合种群模式下,其共存于同一斑块,这是由于配对歧视或者生态位的分化导致雌核发育对有性生殖的危害比较小；2.在集合种群框架下,类似于宿主-寄生系统的共存,即雌核发育个体导致斑块上有性生殖灭绝,从而使自身灭绝,形成新的空斑块,有利于有性生殖个体的繁殖和再次侵占；(6).雌核发育过高的繁殖率会导致整个有性生殖的灭绝,进而自身也灭绝；(7).雌核发育的繁殖率和其导致有性生殖的灭绝率对系统空间结构的影响,在两个共存区间是不同的,因此,在研究具体物种时应该予以重视；(8).当雌核发育对有性生殖的影响适中时,雌核发育的灭绝率的增大在一定范围之内反而有利于雌核发育种群密度的提高；(9).空间联通程度亦会影响到雌核发育的空间分布,联通越低,雌核发育越易聚集分布：(10).虽然有性生殖和雌核发育的迁移都有利于雌核发育的增长,减少了有性生殖斑块的密度,但是,其强度有明显的差异,雌核发育的迁移比有性生殖的迁移影响要强得多,即迁移对系统作用的不对称性,这是因为雌核发育的类似于寄生的特点决定的。
综上,本文的研究丰富和发展了空间结构下的性生态学理论,同时,也丰富了扩散生态学中关于扩散对集合种群的时空动态的影响。
Spatial ecology and sex ecology are both important fields in the international research of theoretical and mathematical ecology, especially the combination of those is one of the frontiers and hotspots in ecology. However, almost all papers that focus on spatial ecology have ignored the sex reproduction in population, and the research on sex often do not take the spatial factors into account. In this PhD thesis, the effect of spatial structure on the two basic problems in sex ecology, the stability of 1:1 sex ratio and the coexistence of sexual and asexual modes of reproduction, are considered. Ordi-nary differential equations, Pair-approximation and computer simulation model (Cellu-lar Automaton) are used to built spatial structured models, with the help of which we can find how the spatial structure influence on the upon two problems. Two approaches are used, mathematical analysis and numerical simulation. Meanwhile, the effect of migration on the two system are also investigated. The main results are as follows:
1. The stability of 1:1 sex ratio may be strongly enhanced by the Allee effect. The effect became more severe when the spatial structure is considered explicitly.
2. The small scale of ecological interactions will lead to female biased EMS;
3. The impact on female and male are not the same when the spatial scale becomes larger. Male becomes more aggregated, but female more discreted. The increase of spatial scale also causes male sex local ratio decreasing, while has no effect on female local sex ratio.
4. Migration does no effect on EMS, but can largely change the spatial-temporary dynamic:migration of male increases the local sex ratio, which are benefit for the growth of the population, while the migration of female decreases the local sex ratio and has no influence on the population. in addition, male local sex ratio is always greater than the ratio of female-locality, this may because females want more opportunities to mate with males.
5. spatial dynamics can be essential for explanting the coexistence of Genogenesis and the sexual species which offers sperm. coexistence may occurs in two sit-uation:1. Niche differentiation and mate discrimination keep local extinction rate low, most patches contain both species; 2. In metapopulation, the system re- sembles host-parasite dynamics where parasite frequently drive the host locally extinct, and host reinvade the empty patches again.
6. The good colonization rate of Genogenesis is not always beneficial for its persis-tence. The high colonization rate can cause extinction of the whole metapopula-tion.
7. The effect of colonization rate of sexual patches by Genogenesis and the extinc-tion rate of patches with both species on the spatial distribution of the metapop-ulation are not the same in the two coexistence regions. So it is worth paying attention when the field study is done.
8. When the effect of Genogenesis on sexual species is intermediate, high Genogenesis-only extinction can increase the equilibrium frequency of patches that Genogenesis is able to occupy.
9. When the spatial interaction scale is small, Genogenesis tend to be more aggre-gated. 10. Both migration can be beneficial for Genogenesis, and destructive for sexual species. However, the influence of migration of Genogenesis are much stronger than that of sexual, The asymmetric effect is determined by the parasite feature of genogenesis.
In all, Our research has enriched and developed the theories in spatial sex ecology, and enriched content that the effect of migration on spatial-temporal dynamics in metapop-ulation.
综上,本文的研究丰富和发展了空间结构下的性生态学理论,同时,也丰富了扩散生态学中关于扩散对集合种群的时空动态的影响。
Spatial ecology and sex ecology are both important fields in the international research of theoretical and mathematical ecology, especially the combination of those is one of the frontiers and hotspots in ecology. However, almost all papers that focus on spatial ecology have ignored the sex reproduction in population, and the research on sex often do not take the spatial factors into account. In this PhD thesis, the effect of spatial structure on the two basic problems in sex ecology, the stability of 1:1 sex ratio and the coexistence of sexual and asexual modes of reproduction, are considered. Ordi-nary differential equations, Pair-approximation and computer simulation model (Cellu-lar Automaton) are used to built spatial structured models, with the help of which we can find how the spatial structure influence on the upon two problems. Two approaches are used, mathematical analysis and numerical simulation. Meanwhile, the effect of migration on the two system are also investigated. The main results are as follows:
1. The stability of 1:1 sex ratio may be strongly enhanced by the Allee effect. The effect became more severe when the spatial structure is considered explicitly.
2. The small scale of ecological interactions will lead to female biased EMS;
3. The impact on female and male are not the same when the spatial scale becomes larger. Male becomes more aggregated, but female more discreted. The increase of spatial scale also causes male sex local ratio decreasing, while has no effect on female local sex ratio.
4. Migration does no effect on EMS, but can largely change the spatial-temporary dynamic:migration of male increases the local sex ratio, which are benefit for the growth of the population, while the migration of female decreases the local sex ratio and has no influence on the population. in addition, male local sex ratio is always greater than the ratio of female-locality, this may because females want more opportunities to mate with males.
5. spatial dynamics can be essential for explanting the coexistence of Genogenesis and the sexual species which offers sperm. coexistence may occurs in two sit-uation:1. Niche differentiation and mate discrimination keep local extinction rate low, most patches contain both species; 2. In metapopulation, the system re- sembles host-parasite dynamics where parasite frequently drive the host locally extinct, and host reinvade the empty patches again.
6. The good colonization rate of Genogenesis is not always beneficial for its persis-tence. The high colonization rate can cause extinction of the whole metapopula-tion.
7. The effect of colonization rate of sexual patches by Genogenesis and the extinc-tion rate of patches with both species on the spatial distribution of the metapop-ulation are not the same in the two coexistence regions. So it is worth paying attention when the field study is done.
8. When the effect of Genogenesis on sexual species is intermediate, high Genogenesis-only extinction can increase the equilibrium frequency of patches that Genogenesis is able to occupy.
9. When the spatial interaction scale is small, Genogenesis tend to be more aggre-gated. 10. Both migration can be beneficial for Genogenesis, and destructive for sexual species. However, the influence of migration of Genogenesis are much stronger than that of sexual, The asymmetric effect is determined by the parasite feature of genogenesis.
In all, Our research has enriched and developed the theories in spatial sex ecology, and enriched content that the effect of migration on spatial-temporal dynamics in metapop-ulation.
引文
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