另一种具有均匀祖先记忆的可解种群动态
Another solvable population dynamic with uniform ancestral memory
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中文总结 AI 辅助
该研究提出一种具有均匀祖先记忆的可解种群模型，通过分析大世代种群确定马尔萨斯参数并估计特定子种群期望规模，丰富了种群动态研究的可解模型类别。
中文摘要 AI 辅助
我们研究一种具有不重叠世代的种群模型，其中个体具有类型并保留所有祖先类型的记忆。与经典多类型分支过程仅依赖亲本类型不同，我们假设每个个体的繁殖规律取决于祖先类型的经验分布。我们进一步假设平均繁殖矩阵的秩为1。基于与Bastien Mallein合作的前期工作中的技术（这些技术本身借鉴了Philippe Flajolet及其合作者在解析瓮领域的基础贡献），我们分析大世代时的种群情况。特别地，我们确定了马尔萨斯参数，并估计了其祖先类型经验分布属于给定集合的子种群的期望规模。
英文摘要
We study a population model with non-overlapping generations, where individuals have a type and retain the memory of the types of all their ancestors. We assume that for each individual, the reproduction law depends on the empirical distribution of ancestral types, unlike for a classical multi-type branching process where it hinges on the parental type only. We further assume the mean reproduction matrix has rank one. Building on techniques from previous works with Bastien Mallein, which themselves draw on foundational contributions by Philippe Flajolet and collaborators in the context of analytic urns, we analyze the population at large generations. In particular, we determine the Malthusian parameter and estimate the expected size of the sub-population whose empirical distribution of ancestral types lies within a given set.
