论文标题
二聚体摩兰模型的遗传学
Genetics of the biparental Moran model
论文作者
论文摘要
我们的目标是研究每个人有2个父母的人群的遗传组成，他们对其OSPRING的基因组也同样贡献。我们使用二元模型，该模型的特征是其XED数字n的个体。我们是一个人，并考虑所有生活时间的人的基因组的比例。我们首先证明，当n进入创新时，这些比例几乎肯定会趋向于相同的随机变量。然后，我们严格地证明，当N然后进入Innity时，该随机变量乘以N（即，在整个人口中任何祖先的固定权重）在法律中收敛于0中DIRAC度量的混合物，而指数定律与参数1/2，而几个给定祖先的权重是独立的。
Our goal is to study the genetic composition of a population in which each individual has 2 parents, who contribute equally to the genome of their ospring. We use a biparental Moran model, which is characterized by its xed number N of individuals. We x an individual and consider the proportions of the genomes of all individuals living n time steps later, that come from this individual. We rst prove that when n goes to innity, these proportions all converge almost surely towards the same random variable. We then rigorously prove that when N then goes to innity, this random variable multiplied by N (i.e. the stationary weight of any ancestor in the whole population) converges in law towards the mixture of a Dirac measure in 0 and an exponential law with parameter 1/2, and that the weights of several given ancestors are independent.
