Evolutionary dynamics of complex traits in sexual populations in a heterogeneous environment: how normal? - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Journal of Mathematical Biology Year : 2022

Evolutionary dynamics of complex traits in sexual populations in a heterogeneous environment: how normal?

Abstract

When studying the dynamics of trait distribution of populations in a heterogeneous environment, classical models from quantitative genetics choose to look at its system of moments, specifically the first two ones. Additionally, in order to close the resulting system of equations, they often assume that the trait distribution is Gaussian (see for instance Ronce and Kirkpatrick 2001). The aim of this paper is to introduce a mathematical framework that follows the whole trait distribution (without prior assumption) to study evolutionary dynamics of sexually reproducing populations. Specifically, it focuses on complex traits, whose inheritance can be encoded by the infinitesimal model of segregation (Fisher 1919). We show that it allows us to derive a regime in which our model gives the same dynamics as when assuming a Gaussian trait distribution. To support that, we compare the stationary problems of the system of moments derived from our model with the one given in Ronce and Kirkpatrick 2001 and show that they are equivalent under this regime and do not need to be otherwise. Moreover, under this regime of equivalence, we show that a separation bewteen ecological and evolutionary time scales arises. A fast relaxation toward monomorphism allows us to reduce the complexity of the system of moments, using a slow-fast analysis. This reduction leads us to complete, still in this regime, the analytical description of the bistable asymmetrical equilibria numerically found in Ronce and Kirkpatrick 2001. More globally, we provide explicit modelling hypotheses that allow for such local adaptation patterns to occur.
Fichier principal
Vignette du fichier
JOMB_hal_revised_version_20211015.pdf (1.12 Mo) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-03073813 , version 1 (16-12-2020)
hal-03073813 , version 2 (15-10-2021)

Identifiers

Cite

Léonard Dekens. Evolutionary dynamics of complex traits in sexual populations in a heterogeneous environment: how normal?. Journal of Mathematical Biology, 2022, ⟨10.1007/s00285-021-01712-0⟩. ⟨hal-03073813v2⟩
100 View
383 Download

Altmetric

Share

Gmail Mastodon Facebook X LinkedIn More