On Λ-Fleming–Viot processes with general frequency-dependent selection
| Autor: | Adrián González Casanova, Charline Smadi |
|---|---|
| Přispěvatelé: | Universidad Nacional Autónoma de México (UNAM), Laboratoire des EcoSystèmes et des Sociétés en Montagne (UR LESSEM), Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Institut Fourier (IF), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA), Centre National de la Recherche Scientifique (CNRS), European Commission, Chair 'Modelisation Mathematique et Biodiversite' of VEOLIA-Ecole Polytechnique-MNHN-F.X, Consejo Nacional de Ciencia y Tecnologia (CONACyT) : A1-S-14615 |
| Rok vydání: | 2020 |
| Předmět: |
Statistics and Probability
General Mathematics Population Frequency-dependent selection 01 natural sciences Lambda-Fleming-Viot process 010104 statistics & probability Stochastic differential equation Quantitative Biology::Populations and Evolution Limit (mathematics) Statistical physics 0101 mathematics education Selection (genetic algorithm) Mathematics education.field_of_study Generality multidimensional SDEs with jumps 010102 general mathematics population genetics [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] frequency-dependent selection Fixation (population genetics) Population model Statistics Probability and Uncertainty ancestral process |
| Zdroj: | Journal of Applied Probability Journal of Applied Probability, Cambridge University press, 2020, 57 (4), pp.1162-1197. ⟨10.1017/jpr.2020.55⟩ |
| ISSN: | 1475-6072 0021-9002 |
| DOI: | 10.1017/jpr.2020.55 |
| Popis: | We construct a multitype constant-size population model allowing for general selective interactions as well as extreme reproductive events. Our multidimensional model aims for the generality of adaptive dynamics and the tractability of population genetics. It generalises the idea of Krone and Neuhauser [39] and González Casanova and Spanò [29], who represented the selection by allowing individuals to sample several potential parents in the previous generation before choosing the ‘strongest’ one, by allowing individuals to use any rule to choose their parent. The type of the newborn can even not be one of the types of the potential parents, which allows modelling mutations. Via a large population limit, we obtain a generalisation of$\Lambda$-Fleming–Viot processes, with a diffusion term and a general frequency-dependent selection, which allows for non-transitive interactions between the different types present in the population. We provide some properties of these processes related to extinction and fixation events, and give conditions for them to be realised as unique strong solutions of multidimensional stochastic differential equations with jumps. Finally, we illustrate the generality of our model with applications to some classical biological interactions. This framework provides a natural bridge between two of the most prominent modelling frameworks of biological evolution: population genetics and eco-evolutionary models. |
| Databáze: | OpenAIRE |
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