Dynamics of lineages in adaptation to a gradual environmental change
Vincent Calvez, Beno\^it Henry, Sylvie M\'el\'eard, Viet Chi Tran

TL;DR
This paper models how populations adapt to gradual environmental changes, analyzing both macroscopic PDE behavior and microscopic lineage histories, revealing how ancestral traits influence current populations with a trait lag.
Contribution
It introduces a stochastic individual-based model combined with PDE analysis to study lineage dynamics under environmental change, highlighting ancestral trait influence.
Findings
Population persists with a trait lag under environmental change.
Lineage paths approximate Ornstein-Uhlenbeck processes in large populations.
Ancestral traits shape current trait distributions with a measurable lag.
Abstract
We investigate a simple quantitative genetics model subjet to a gradual environmental change from the viewpoint of the phylogenies of the living individuals. We aim to understand better how the past traits of their ancestors are shaped by the adaptation to the varying environment. The individuals are characterized by a one-dimensional trait. The dynamics -- births and deaths -- depend on a time-changing mortality rate that shifts the optimal trait to the right at constant speed. The population size is regulated by a nonlinear non-local logistic competition term. The macroscopic behaviour can be described by a PDE that admits a unique positive stationary solution. In the stationary regime, the population can persist, but with a lag in the trait distribution due to the environmental change. For the microscopic (individual-based) stochastic process, the evolution of the lineages can be…
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Taxonomy
TopicsEvolution and Genetic Dynamics · Evolutionary Game Theory and Cooperation · Complex Systems and Time Series Analysis
