The interplay of selection and dormancy in a Moran model can lead to coexistence of types

TL;DR

This paper introduces a Moran model where dormancy allows a less fit type to invade and coexist with a dominant type, revealing new stable coexistence regimes due to frequency-dependent effects.

Contribution

It demonstrates how dormancy can enable invasion and stable coexistence of types in a Moran model, a phenomenon not observed in previous models with symmetric competition.

Findings

Dormancy allows invasion of a less fit type.

Stable coexistence of both types due to frequency dependence.

Coexistence arises from Moran model properties and dormancy dynamics.

Abstract

In this paper we propose a Moran model that describes the population dynamics of two types: While the first type has a selective advantage during reproduction, the second type can avoid replacement during reproduction with some positive probability by switching temporarily into a dormant state. We investigate the interplay of both evolutionary strategies by studying the invasion dynamics of the dormant type into the resident (selectively advantageous) population in the large population limit of the system. It turns out that the dormancy trait can not only invade and subsequently fixate under suitable parameter assumptions despite its selective disadvantage (a phenomenon that has already been observed in a related context in Blath and T\'obi\'as (2020)), but that there is also a novel regime of stable coexistence of both types due to a frequency-dependent balancing effect that did not arise in the previous setup with Lotka--Volterra type symmetric competition. The emergence of a coexistence regime here rests in part on specific properties of the Moran modelling framework, in particular its fixed overall population size that enforces instant re-colonization after death events, as well as on the (positive) mortality and resuscitation rates of the dormant state. We provide heuristic explanations for the observed types of behaviour and the corresponding proofs, which involve comparisons to suitable branching processes, approximations by dynamical systems, and an analysis of asymptotic behaviour of the latter.