Wright-Fisher模型向后解的一个分层延拓格式
A hierarchical extension scheme for backward solutions of the Wright-Fisher model
摘要：
本文对群体遗传学Wright-Fisher模型的扩散近似的后向Kolmogorov方程提出了一个迭代整体解方案。该模型从后向角度描述了群体中同一基因座上几个等位基因的随机遗传漂变。我们方案的关键是连接等位基因丢失前后的解。然而，在通过随机过程或偏微分方程的方法中，等位基因的这种丢失导致边界奇点，从生物学或几何学的角度来看，这是可以详细分析的自然过程。边界的作用的澄清解决了某些唯一性问题，并阐明了分层解决方案的建设。
英文摘要：
We develop an iterative global solution scheme for the backward Kolmogorov equation of the diffusion approximation of the Wright-Fisher model of population genetics. That model describes the random genetic drift of several alleles at the same locus in a population from a backward perspective. The key of our scheme is to connect the solutions before and after the loss of an allele. Whereas in an approach via stochastic processes or partial differential equations, such a loss of an allele leads to a boundary singularity, from a biological or geometric perspective, this is a natural process that can be analyzed in detail. A clarification of the role of the boundary resolves certain uniqueness issues and enlucidates the construction of hierarchical solutions.
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