Evolution of Specialization in Heterogeneous Environments: Equilibrium Between Selection, Mutation and Migration

Mirrahimi, Sepideh; Gandon, Sylvain

doi:10.1534/genetics.119.302868

Cited by 22 publications

(71 citation statements)

References 49 publications

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“…We are interested in the asymptotic behaviour of the trait distribution F ε as ε vanishes. This asymptotic regime was investigated thoroughly for various linear operators B ε associated with asexual reproduction such as for instance the diffusion operator F ε (z)+ε 2 ∆F ε (z), or the convolution operator 1 ε K( z ε ) * F ε (z) where K is a probability kernel with unit variance, see Diekmann et al (2005); Perthame (2007); Barles and Perthame (2007); Barles et al (2009) ;Lorz et al (2011) for the earliest investigations, see further Méléard and Mirrahimi (2015); Mirrahimi (2018); Bouin et al (2018b) for the case of a fractional diffusion operator (or similarly a fat-tailed kernel K), and see further Mirrahimi (2013); Mirrahimi and Perthame (2015); Bouin and Mirrahimi (2015); Lam and Lou (2017); Gandon and Mirrahimi (2017); Mirrahimi (2017); Mirrahimi and Gandon (2018); for the interplay between evolutionary dynamics and a spatial structure. In the linear case, the asymptotic analysis usually leads to a Hamilton-Jacobi equation for the Hopf-Cole transform U ε = −ε log F ε .…”

Section: Introductionmentioning

confidence: 99%

Asymptotic analysis of a quantitative genetics model with nonlinear integral operator

Cálvez¹,

Garnier²,

Patout³

2019

Journal De L’École Polytechnique — Mathématiques

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We study the asymptotic behavior of stationary solutions to a quantitative genetics model with trait-dependent mortality and a nonlinear integral reproduction operator. Our asymptotic analysis encompasses the case when the deviation between the offspring and the mean parental trait is typically small. Under suitable regularity and growth conditions on the mortality rate, we prove existence and local uniqueness of a stationary profile that get concentrated around a critical point of the mortality rate, with a nearly Gaussian distribution having small variance. Our approach is based on perturbative analysis techniques that require to describe accurately the correction to the Gaussian leading order profile. Our contribution extends previous results obtained with linear reproduction operator, but using an alternative methodology.

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Section: Introductionmentioning

confidence: 99%

Asymptotic analysis of a quantitative genetics model with nonlinear integral operator

Cálvez¹,

Garnier²,

Patout³

2019

Journal De L’École Polytechnique — Mathématiques

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“…In contrast to neutral differentiation, selection pressure acts as a stabilising force, which maintains the mean of the populations’ adaptive trait to a fixed value. [74] shows that given Eq. (S14), Eq.…”

Section: Supplementary Methodsmentioning

confidence: 99%

“…Assuming that the variance of the mutation kernel is small, one can use a diffusion approximation for the mutation term [82, 72, 74] …”

Section: Supplementary Methodsmentioning

confidence: 99%

Topology and habitat assortativity drive neutral and adaptive diversification in spatial graphs

Boussange

Pellissier

2021

Preprint

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Biodiversity results from differentiation mechanisms developing within biological populations. Such mechanisms are influenced by the properties of the landscape over which individuals interact, disperse and evolve. Notably, landscape connectivity and habitat heterogeneity constrain the movement and survival of individuals, thereby promoting differentiation through drift and local adaptation. Nevertheless, the complexity of landscape features can blur our understanding of how they drive differentiation. Here, we formulate a stochastic, eco-evolutionary model where individuals are structured over a graph that captures complex connectivity patterns and accounts for habitat heterogeneity. Individuals possess neutral and adaptive traits, whose divergence results in differentiation at the population level. The modelling framework enables an analytical underpinning of emerging macroscopic properties, which we complement with numerical simulations to investigate how the graph topology and the spatial habitat distribution affect differentiation. We show that in the absence of selection, graphs with high characteristic length and high heterogeneity in degree promote neutral differentiation. Habitat assortativity, a metric that captures habitat spatial auto-correlation in graphs, additionally drives differentiation patterns under habitat-dependent selection. While assortativity systematically amplifies adaptive differentiation, it can foster or depress neutral differentiation depending on the migration regime. By formalising the eco-evolutionary and spatial dynamics of biological populations in complex landscapes, our study establishes the link between landscape features and the emergence of diversification, contributing to a fundamental understanding of the origin of biodiversity gradients.

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“…The second term on the right-hand side of the partial integro-differential equation ( 4) models the effect of heritable, spontaneous phenotypic changes, which occur at rate θ > 0. Similar diffusion terms have been used in a number of previous papers to model the effect of spontaneous phenotypic changes (Alfaro and Veruete 2019;Almeida et al 2019;Ardaševa et al 2020b;Bouin et al 2012;Chisholm et al 2015;Iglesias and Mirrahimi 2018;Genieys et al 2006;Lorenzi et al 2016;Mirrahimi and Gandon 2020;Perthame and Génieys 2007) and can be obtained as the deterministic continuum limit of corresponding stochastic individual-based models in the asymptotic regime of large numbers of individuals and small phenotypic changes (Champagnat et al 2006;.…”

Section: Dynamics Of Tumour Cellsmentioning

confidence: 99%

A Mathematical Study of the Influence of Hypoxia and Acidity on the Evolutionary Dynamics of Cancer

2021

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Hypoxia and acidity act as environmental stressors promoting selection for cancer cells with a more aggressive phenotype. As a result, a deeper theoretical understanding of the spatio-temporal processes that drive the adaptation of tumour cells to hypoxic and acidic microenvironments may open up new avenues of research in oncology and cancer treatment. We present a mathematical model to study the influence of hypoxia and acidity on the evolutionary dynamics of cancer cells in vascularised tumours. The model is formulated as a system of partial integro-differential equations that describe the phenotypic evolution of cancer cells in response to dynamic variations in the spatial distribution of three abiotic factors that are key players in tumour metabolism: oxygen, glucose and lactate. The results of numerical simulations of a calibrated version of the model based on real data recapitulate the eco-evolutionary spatial dynamics of tumour cells and their adaptation to hypoxic and acidic microenvironments. Moreover, such results demonstrate how nonlinear interactions between tumour cells and abiotic factors can lead to the formation of environmental gradients which select for cells with phenotypic characteristics that vary with distance from intra-tumour blood vessels, thus promoting the emergence of intra-tumour phenotypic heterogeneity. Finally, our theoretical findings reconcile the conclusions of earlier studies by showing that the order in which resistance to hypoxia and resistance to acidity arise in tumours depend on the ways in which oxygen and lactate act as environmental stressors in the evolutionary dynamics of cancer cells.

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Evolution of Specialization in Heterogeneous Environments: Equilibrium Between Selection, Mutation and Migration

Cited by 22 publications

References 49 publications

Asymptotic analysis of a quantitative genetics model with nonlinear integral operator

Asymptotic analysis of a quantitative genetics model with nonlinear integral operator

Topology and habitat assortativity drive neutral and adaptive diversification in spatial graphs

A Mathematical Study of the Influence of Hypoxia and Acidity on the Evolutionary Dynamics of Cancer

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