The mathematical theory of group selection. I. Full solution of a nonlinear Levins E = E(x) model
| Autor: | Paul R. Levitt |
|---|---|
| Rok vydání: | 1978 |
| Předmět: |
education.field_of_study
Population Mathematical analysis Metapopulation Locus (genetics) Genetics Behavioral Models Biological Mathematical theory Nonlinear system Fixation (population genetics) Group selection Genetics Population Statistics Animals Humans Selection Genetic education Ecology Evolution Behavior and Systematics Open interval Mathematics |
| Zdroj: | Theoretical population biology. 13(3) |
| ISSN: | 0040-5809 |
| Popis: | The first complete overtime solution is obtained for a group selection model of Levins E = E(x) type with recolonization but no other gene flow between islands. Assuming a subdivided population at carrying capacity, the model describes selection at a biallelic locus (A, a) where a is opposed by Mendelian selection but is favored by a lower rate of extinction of demes having high a frequency. By contrast to the linear diffusion equations encountered in classical mathematical genetics, the PDE governing the dynamics is now nonlinear in the metapopulation gene frequency distribution φ(x, t); furthermore, the initial conditions now heavily influence the equilibrium distribution φ∞(x). A fully explicit formula (20) expressing this dependence is derived. The results indicate that a fixation is never reached, but (A, a) polymorphism in the metapopulation will result if E(0) − E(1)s > B(1 − h), where s ⪡ 1 parametrizes the strength of Mendelian selection, E(x) is the Levins extinction operator, h (typically in the open interval (0, 1)) is the dominance of a, and B is a parameter measuring the flatness of the initial distribution f(x) in the x → 1 limit. |
| Databáze: | OpenAIRE |
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