标题： 祖先谱系与密度依赖相互作用种群中的采样 显示英文标题

标题： Ancestral lineages and sampling in populations with density-dependent interactions

摘要： 我们研究一个密度依赖的马尔可夫跳跃过程，描述一个种群，其中每个个体由一种类型表征，并且其繁殖速率既取决于其类型，也取决于种群类型分布。 首先，通过适当的概率变换，我们展示了一个时变的马尔可夫过程，即辅助过程，该过程能够捕捉种群过程中采样系谱的行为。 这是通过一个多对一公式实现的，该公式将种群过程中对祖先系谱的函数平均值与其在辅助过程中的平均值相关联，从而直接解释了潜在的幸存者偏差。 此外，这种构造允许比文献中之前获得的更一般的采样程序，例如限制在子种群中的采样。 其次，我们考虑大种群情况，当种群规模趋于无穷大时。 在经典假设下，种群类型分布可以通过扩散近似来逼近，该近似捕捉了种群过程在其确定性大种群极限周围的波动。 我们建立了一个多对一公式，使得可以在扩散近似中进行采样，并量化相关的近似误差。 显示英文摘要

摘要： We study a density-dependent Markov jump process describing a population where each individual is characterized by a type, and reproduces at rates depending both on its type and on the population type distribution. First, using an appropriate change in probability, we exhibit a time-inhomogeneous Markov process, the auxiliary process, which allows to capture the behavior of a sampled lineage in the population process. This is achieved through a many-to-one formula, which relates the average of a function over ancestral lineages sampled in the population processes to its average over the auxiliary process, yielding a direct interpretation of the underlying survivorship bias. In addition, this construction allows for more general sampling procedures than what was previously obtained in the literature, such as sampling restricted to subpopulations. Second, we consider the large population regime, when the population size grows to infinity. Under classical assumptions, the population type distribution can then be approached by a diffusion approximation, which captures the fluctuations of the population process around its deterministic large population limit. We establish a many-to-one formula allowing to sample in the diffusion approximation, and quantify the associated approximation error.