Wright-Fisher模型解的一个分层延拓格式
A hierarchical extension scheme for solutions of the Wright-Fisher model
摘要：
本文对群体遗传学的Wright-Fisher模型的扩散近似的前向Kolmogorov（Fokker-Planck）方程提出了一个全局的和层次的格式。该模型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。我们的方法依赖于发展方程的时刻的过程和边界通量的仔细分析。
英文摘要：
We develop a global and hierarchical scheme for the forward Kolmogorov (Fokker-Planck) 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. 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. Our method depends on evolution equations for the moments of the process and a careful analysis of the boundary flux.
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