| 来源类型 | Article |
| 规范类型 | 其他 |
| DOI | 10.1007/s00285-012-0562-5 |
| A rigorous model study of the adaptive dynamics of Mendelian diploids. | |
| Collet P; Meleard S; Metz JAJ | |
| 发表日期 | 2013 |
| 出处 | Journal of Mathematical Biology 67 (3): 569-607 |
| 出版年 | 2013 |
| 语种 | 英语 |
| 摘要 | Adaptive dynamics (AD) so far has been put on a rigorous footing only for clonal inheritance. We extend this to sexually reproducing diploids, although admittedly still under the restriction of an unstructured population with Lotka-Volterra-like dynamics and single locus genetics (as in Kimura's in Proc Natl Acad Sci USA 54:731-736, 1965 infinite allele model). We prove under the usual smoothness assumptions, starting from a stochastic birth and death process model, that, when advantageous mutations are rare and mutational steps are not too large, the population behaves on the mutational time scale (the "long" time scale of the literature on the genetical foundations of ESS theory) as a jump process moving between homozygous states (the trait substitution sequence of the adaptive dynamics literature). Essential technical ingredients are a rigorous estimate for the probability of invasion in a dynamic diploid population, a rigorous, geometric singular perturbation theory based, invasion implies substitution theorem, and the use of the Skorohod M_1 topology to arrive at a functional convergence result. In the small mutational steps limit this process in turn gives rise to a differential equation in allele or in phenotype space of a type referred to in the adaptive dynamics literature as "canonical equation". |
| 主题 | Evolution and Ecology (EEP) |
| 关键词 | Individual-based mutation-selection model Invasion fitness for diploid populations Adaptive dynamics Canonical equation Polymorphic evolution sequence Competitive Lotka-Volterra system |
| URL | http://pure.iiasa.ac.at/id/eprint/10367/ |
| 来源智库 | International Institute for Applied Systems Analysis (Austria) |
| 引用统计 | |
| 资源类型 | 智库出版物 |
| 条目标识符 | http://119.78.100.153/handle/2XGU8XDN/129703 |
| 推荐引用方式 GB/T 7714 | Collet P,Meleard S,Metz JAJ. A rigorous model study of the adaptive dynamics of Mendelian diploids.. 2013. |
| 条目包含的文件 | 条目无相关文件。 | |||||
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