Polymorphic evolution sequence and evolutionary branching
Polymorphic evolution sequence and evolutionary branching
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DOI：
10.1007/s00440-010-0292-9
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发表时间：
2011-10-01
影响因子：
2
通讯作者：
Meleard, Sylvie
中科院分区：
文献类型：
--
作者：
Champagnat, Nicolas;Meleard, Sylvie
我们感兴趣的是在适应动力学的生物框架的特定尺度上描述具有突变和选择的多态种群的进化模型的研究。假定种群规模大，突变率小。证明了在这两个尺度的良好组合下，种群过程在突变的长时间尺度上近似为描述种群连续性状平衡的马尔可夫纯跳跃过程。这一过程概括了所谓的性状替代序列（TSS），称为多态性进化序列（PES）。然后引入了突变大小的尺度，并研究了小突变极限下的PES。通过对进化奇点邻域的研究，我们得到了进化分支现象的一个启发式判据的充分数学证明。这种现象对应于这样一种情况，即最初基本上是单一模态的种群，在选择性力量的驱使下分成两个独立的亚种群。为此，我们细致地分析了三维竞争Lotka-Volterra系统的渐近行为。
We are interested in the study of models describing the evolution of a polymorphic population with mutation and selection in the specific scales of the biological framework of adaptive dynamics. The population size is assumed to be large and the mutation rate small. We prove that under a good combination of these two scales, the population process is approximated in the long time scale of mutations by a Markov pure jump process describing the successive trait equilibria of the population. This process, which generalizes the so-called trait substitution sequence (TSS), is called polymorphic evolution sequence (PES). Then we introduce a scaling of the size of mutations and we study the PES in the limit of small mutations. From this study in the neighborhood of evolutionary singularities, we obtain a full mathematical justification of a heuristic criterion for the phenomenon of evolutionary branching. This phenomenon corresponds to the situation where the population, initially essentially single modal, is driven by the selective forces to divide into two separate subpopulations. To this end we finely analyze the asymptotic behavior of three-dimensional competitive Lotka-Volterra systems.