Influence of mutations in phenotypically-structured populations in time periodic environment

Abstract

We study a parabolic Lotka-Volterra equation, with an integral term representing competition, and time periodic growth rate. This model represents a trait structured population in a time periodic environment. After showing the convergence of the solution to the unique positive and periodic solution of the problem, we study the influence of different factors on the mean limit population. As this quantity is the opposite of a certain eigenvalue, we are able to investigate the influence of the diffusion rate, the period length and the time variance of the environment fluctuations. We also give biological interpretation of the results in the framework of cancer, if the model represents a cancerous cells population under the influence of a periodic treatment. In this framework, we show that the population might benefit from a intermediate rate of mutation.

A Mathematical Dissection of the Adaptation of Cell Populations to Fluctuating Oxygen Levels

“…Building upon the modelling framework that we presented in Ardaševa et al (2020), the model is defined in terms of a system of non-local parabolic partial differential equations (PDEs) for the evolution of the phenotype distributions of two competing cell populations that undergo heritable, spontaneous phenotypic variations at different rates. Similar PDEs modelling the evolutionary dynamics of populations structured by continuous traits in periodically-fluctuating environments have recently received increasing attention from the mathematical community (Lorenzi et al, 2015;Mirrahimi et al, 2015;Iglesias and Mirrahimi, 2018;Carrere and Nadin, 2019).…”

A mathematical dissection of the adaptation of cell populations to fluctuating oxygen levels

“…Building upon the modelling framework that we presented in Ardaševa et al (2019), the model is defined in terms of a system of non-local parabolic partial differential equations (PDEs) for the evolution of the phenotype distributions of two competing cell populations that undergo heritable, spontaneous phenotypic variations at different rates. Similar PDEs modelling the evolutionary dynamics of populations structured by continuous traits in periodically-fluctuating environments have recently received increasing attention from the mathematical community Mirrahimi et al, 2015;Iglesias and Mirrahimi, 2018;Carrere and Nadin, 2019).…”

Selection and mutation in a shifting and fluctuating environment

“…Such expansion is closely related to an asymptotic expansion of the Floquet eigenvalue for the linear problem. Furthermore in a very recent work [11] the authors study a closely related model, but without the linear change of the environment, and study the impact of the different parameters of the model on the final population size.…”