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

TL;DR
This paper analyzes the coalescent tree structure of a broad class of density-dependent branching processes, including logistic and Gompertz growth, showing convergence to a universal limiting tree as population parameters grow large.
Contribution
It introduces a unified framework for the coalescent trees of various density-dependent growth models and proves their convergence to a universal limiting tree.
Findings
Coalescent trees converge to a universal limit as population size and sampling scale increase.
The model generalizes classical exponential, logistic, and Gompertz growth processes.
The limiting tree is robust across different density-dependent growth dynamics.
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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Taxonomy
TopicsStochastic processes and statistical mechanics
