Survival criterion for a population subject to selection and mutations; Application to temporally piecewise constant environments

Costa, Manon; Etchegaray, Christèle; Mirrahimi, Sepideh

doi:10.1016/j.nonrwa.2020.103239

Cited by 3 publications

(6 citation statements)

References 16 publications

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“…Using (13) we know that q t is exponentially bounded, and so is q 2 t . Thus the last term of the above inequality is finite.…”

Section: Proof Of Theorem 23mentioning

confidence: 99%

“…where C q depends only on the bound on q established in (13) and on the dimension. Therefore, T is a well-defined continuous linear form on L 2 (R × R − ).…”

Section: Proof Of Theorem 23mentioning

confidence: 99%

“…According to (13), q is integrable against exponential functions. Therefore, the left hand side is finite (and positive, since q ≡ 0), and so is the right hand side.…”

Section: Proof Of Theorem 24mentioning

confidence: 99%

“…To the best of our knowledge, it cannot lead to explicit transient trajectories of adaptation. Temporally piecewise constant environments have also been studied with the same type of methods in the recent work [13]. Note that the equations that were studied in [1,10,16,17,28] have the general form:…”

Section: Introduction and Main Assumptionsmentioning

confidence: 99%

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Adaptation in general temporally changing environments

Roques¹,

Patout²,

Bonnefon³

et al. 2020

Preprint

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We analyze a nonlocal PDE model describing the dynamics of adaptation of a phenotypically structured population, under the effects of mutation and selection, in a changing environment. Previous studies have analyzed the large-time behavior of such models, with particular forms of environmental changes, either linearly changing or periodically fluctuating. We use here a completely different mathematical approach, which allows us to consider very general forms of environmental variations and to give an analytic description of the full trajectories of adaptation, including the transient phase, before a stationary behavior is reached. The main idea behind our approach is to study a bivariate distribution of two 'fitness components' which contains enough information to describe the distribution of fitness at any time. This distribution solves a degenerate parabolic equation that is dealt with by defining a multidimensional cumulant generating function associated with the distribution, and solving the associated transport equation.We apply our results to several examples, and check their accuracy, using stochastic individual-based simulations as a benchmark. These examples illustrate the importance of being able to describe the transient dynamics of adaptation to understand the development of drug resistance in pathogens.

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“…Using (13) we know that q t is exponentially bounded, and so is q 2 t . Thus the last term of the above inequality is finite.…”

Section: Proof Of Theorem 23mentioning

confidence: 99%

“…where C q depends only on the bound on q established in (13) and on the dimension. Therefore, T is a well-defined continuous linear form on L 2 (R × R − ).…”

Section: Proof Of Theorem 23mentioning

confidence: 99%

“…According to (13), q is integrable against exponential functions. Therefore, the left hand side is finite (and positive, since q ≡ 0), and so is the right hand side.…”

Section: Proof Of Theorem 24mentioning

confidence: 99%

Section: Introduction and Main Assumptionsmentioning

confidence: 99%

See 2 more Smart Citations

Adaptation in general temporally changing environments

Roques¹,

Patout²,

Bonnefon³

et al. 2020

Preprint

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“…Different environmental challenges across large geographic scales promote evolution of specific phenotypes suitable to the local conditions (Crozier, 2004; Hoffmann & Blows, 1994). When environmental conditions change, the individuals with previously maladapted phenotypes can now sustain in the new, specific environment (Costa et al., 2021). To create diverse phenotypes in response to diverse environmental conditions, plasticity plays a crucial role.…”

Section: Introductionmentioning

confidence: 99%

Environment drives color pattern polymorphism in sand lizards beyond the Gloger's rule

Smolinský

Martínková

2023

Journal of Zoology

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Species color and color pattern vary geographically contributing to environmental tolerance of the species to the fluctuating climate. In a constantly changing environment, the population remains polymorphic, when individuals that are not acclimated to the current environment can survive adverse time periods. Factors influencing color morph frequencies in populations affect spatial variation through local adaptation, which is in turn linked to large‐scale environmental gradients. The influence of environmental factors has not been adequately studied in many polymorphic organisms where the influence of sexual selection on the persistence of polymorphisms is widely recognized. We hypothesized that different color morphs of sand lizard are distributed throughout the Palearctic depending on different environmental conditions. The goal of this study was to examine if the range of morph composition in a color polymorphic lizard can be explained by geographic and climatic variation in the Palearctic. We used publicly available data on sand lizard occurrence from the Global Biodiversity Information Facility and environmental variables from WorldClim and SEDAC databases. We categorized sand lizards' photos to 10 discrete color morphs based on color and color pattern variation. We predicted the color morph distribution using maximum entropy models. We found that variations in morph distributions were mostly related to temperature seasonality, precipitation, elevation, and anthropogenic activities. Our findings support the relationship between environmental conditions and color morph distribution, implying that environmental selection acts differently on color morphs, most likely in conjunction with sexual selection.

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Measure framework for the pure selection equation: global well posedness and numerical investigations

Martin

2023

MathematicS in Action

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Survival criterion for a population subject to selection and mutations; Application to temporally piecewise constant environments

Cited by 3 publications

References 16 publications

Adaptation in general temporally changing environments

Adaptation in general temporally changing environments

Environment drives color pattern polymorphism in sand lizards beyond the Gloger's rule

Measure framework for the pure selection equation: global well posedness and numerical investigations

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