title: Dissecting the dynamics of epigenetic changes in phenotype-structured populations exposed to fluctuating environments.
abstract: An enduring puzzle in evolutionary biology is to understand how individuals and populations adapt to fluctuating environments. Here we present an integro-differential model of adaptive dynamics in a phenotype-structured population whose fitness landscape evolves in time due to periodic environmental oscillations. The analytical tractability of our model allows for a systematic investigation of the relative contributions of heritable variations in gene expression, environmental changes and natural selection as drivers of phenotypic adaptation. We show that environmental fluctuations can induce the population to enter an unstable and fluctuation-driven epigenetic state. We demonstrate that this can trigger the emergence of oscillations in the size of the population, and we establish a full characterisation of such oscillations. Moreover, the results of our analyses provide a formal basis for the claim that higher rates of epimutations can bring about higher levels of intrapopulation heterogeneity, whilst intense selection pressures can deplete variation in the phenotypic pool of asexual populations. Finally, our work illustrates how the dynamics of the population size is led by a strong synergism between the rate of phenotypic variation and the frequency of environmental oscillations, and identifies possible ecological conditions that promote the maximisation of the population size in fluctuating environments.
authors.affiliation: Centre de Mathématiques et de Leurs Applications, ENS Cachan, CNRS, Cachan 94230 Cedex, France. Electronic address: lorenzi@cmla.ens-cachan.fr.
authors.forename: Tommaso
authors.initials: T
authors.lastname: Lorenzi
authors.affiliation: School of Biotechnology and Biomolecular Sciences, University of New South Wales, Sydney, NSW 2052, Australia.
authors.forename: Rebecca H
authors.initials: RH
authors.lastname: Chisholm
authors.affiliation: Centre de Mathématiques et de Leurs Applications, ENS Cachan, CNRS, Cachan 94230 Cedex, France.
authors.forename: Laurent
authors.initials: L
authors.lastname: Desvillettes
authors.affiliation: School of Mathematics and Statistics, University of Melbourne, Victoria 3010, Australia.
authors.forename: Barry D
authors.initials: BD
authors.lastname: Hughes
mesh_terms: D000220:Adaptation, Biological / Q000235:genetics; D000818:Animals; D005075:Biological Evolution; D044127:Epigenesis, Genetic; D059647:Gene-Environment Interaction; D008957:Models, Genetic; D009154:Mutation; D010641:Phenotype; D011156:Population Density
keywords: Environmental fluctuations; Epimutations; Integro-differential equations; Periodic solutions; Phenotypic adaption