群体遗传学中的一个非标准进化问题

A negative answer to a conjecture arising in the study of selection-migration models in population genetics

We deal with the study of the evolution of the allelic frequencies, at a single locus, for a population distributed continuously over a bounded habitat. We consider evolution which occurs under the joint action of selection and arbitrary migration, that is independent of genotype, in absence of mutation and random drift. The focus is on a conjecture, that was raised up in literature of population genetics, about the possible uniqueness of polymorphic equilibria, which are known as clines, under particular circumstances. We study the number of these equilibria, making use of topological tools, …

Transition probabilities for degenerate diffusions arising in population genetics

We provide a detailed description of the structure of the transition probabilities and of the hitting distributions of boundary components of a manifold with corners for a degenerate strong Markov process arising in population genetics. The Markov processes that we study are a generalization of the classical Wright-Fisher process. The main ingredients in our proofs are based on the analysis of the regularity properties of solutions to a forward Kolmogorov equation defined on a compact manifold with corners, which is degenerate in the sense that it is not strictly elliptic and the coefficients …

The best of both worlds: Combining population genetic and quantitative genetic models

Numerous traits under migration-selection balance are shown to exhibit complex patterns of genetic architecture with large variance in effect sizes. However, the conditions under which such genetic architectures are stable have yet to be investigated, because studying the influence of a large number of small allelic effects on the maintenance of spatial polymorphism is mathematically challenging, due to the high complexity of the systems that arise. In particular, in the most simple case of a haploid population in a two-patch environment, while it is known from population genetics that polymor…

具有有性繁殖和选择的种群遗传学模型向稳态的指数收敛

Exponential convergence to a steady-state for a population genetics model with sexual reproduction and selection

该研究针对有性繁殖和选择的种群遗传学模型，在选择强度较小时，通过Wasserstein距离不等式结合尾部估计，证明其解指数收敛到局部唯一稳态，为相关种群动力学分析提供了理论支撑。

群体遗传学中一类不定谱问题的均匀化

Homogenization of an indefinite spectral problem arising in population genetics

研究渐近细圆柱中二阶自伴椭圆算子的不定谱问题，推导出谐振子形式的一维有效谱问题并证明谱收敛性，为群体遗传学中带变号权重的谱问题提供理论支持。