On multi-type Cannings models and multi-type exchangeable coalescents

IF 1.2 4区生物学 Q4 ECOLOGY

Theoretical Population Biology Pub Date : 2024-02-15 DOI:10.1016/j.tpb.2024.02.005

Martin Möhle

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引用次数: 0

Abstract

A multi-type neutral Cannings population model with migration and fixed subpopulation sizes is analyzed. Under appropriate conditions, as all subpopulation sizes tend to infinity, the ancestral process, properly time-scaled, converges to a multi-type coalescent sharing the exchangeability and consistency property. The proof gains from coalescent theory for single-type Cannings models and from decompositions of transition probabilities into parts concerning reproduction and migration respectively. The following section deals with a different but closely related multi-type Cannings model with mutation and fixed total population size but stochastically varying subpopulation sizes. The latter model is analyzed forward and backward in time with an emphasis on its behavior as the total population size tends to infinity. Forward in time, multi-type limiting branching processes arise for large population size. Its backward structure and related open problems are briefly discussed.

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关于多类型套合模型和多类型可交换共生体。

本文分析了一个具有迁移和固定子群规模的多类型中性坎宁斯种群模型。在适当的条件下，当所有子种群规模趋于无穷大时，祖先过程在适当的时间尺度下会收敛到具有可交换性和一致性特性的多类型凝聚态。这一证明得益于单类型卡宁斯模型的凝聚理论，以及将过渡概率分解为分别与繁殖和迁移有关的部分。下一节将讨论一个不同但密切相关的多类型康宁斯模型，该模型具有突变和固定的种群总规模，但子种群规模是随机变化的。我们将对后一模型进行时间上的前向和后向分析，重点分析其在种群总数趋于无穷大时的行为。随着时间的推移，在种群规模较大时会出现多类型的极限分支过程。本文还简要讨论了该模型的后向结构和相关的未决问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Theoretical Population Biology 生物-进化生物学

CiteScore

2.50

自引率

14.30%

发文量

审稿时长

6-12 weeks

期刊介绍： An interdisciplinary journal, Theoretical Population Biology presents articles on theoretical aspects of the biology of populations, particularly in the areas of demography, ecology, epidemiology, evolution, and genetics. Emphasis is on the development of mathematical theory and models that enhance the understanding of biological phenomena. Articles highlight the motivation and significance of the work for advancing progress in biology, relying on a substantial mathematical effort to obtain biological insight. The journal also presents empirical results and computational and statistical methods directly impinging on theoretical problems in population biology.