Genealogical constructions of population models

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Genealogical constructions of population models

Representations of population models in terms of countable systems of particles are constructed, in which each particle has a ‘type’, typically recording both spatial position and genetic type, and a level. For finite intensity models, the levels are distributed on [0, λ], whereas in the infinite intensity limit λ→∞, at each time t, the joint distribution of types and levels is conditionally Po...

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Inferring population history from genealogical trees.

Inference about population history from DNA sequence data has become increasingly popular. For human populations, questions about whether a population has been expanding and when expansion began are often the focus of attention. For viral populations, questions about the epidemiological history of a virus, e.g., HIV-1 and Hepatitis C, are often of interest. In this paper I address the following...

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Genetic genealogical models in rare event analysis

We present in this article a genetic type interacting particle systems algorithm and a genealogical model for estimating a class of rare events arising in physics and network analysis. We represent the distribution of a Markov process hitting a rare target in terms of a Feynman–Kac model in path space. We show how these branching particle models described in previous works can be used to estima...

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Line-of-descent and genealogical processes, and their applications in population genetics models.

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ژورنال

عنوان ژورنال: The Annals of Probability

سال: 2019

ISSN: 0091-1798

DOI: 10.1214/18-aop1266