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arXiv · 2012.13382

The coalescent tree of a Markov branching process with generalised logistic growth

David Cheek
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Abstract

We consider a class of density-dependent branching processes which generalises exponential, logistic and Gompertz growth. A population begins with a single individual, grows exponentially initially, and then growth may slow down as the population size moves towards a carrying capacity. At a time while the population is still growing superlinearly, a fixed number of individuals are sampled and their coalescent tree is drawn. Taking the sampling time and carrying capacity simultaneously to infinity, we prove convergence of the coalescent tree to a limiting tree which is in a sense universal over our class of models.

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David Cheek. 2020-12-24. The coalescent tree of a Markov branching process with generalised logistic growth. https://arxiv.org/abs/2012.13382

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