Asymptotic dynamics in populations structured by sensitivity to global warming and habitat shrinking. (English) Zbl 1305.35149
Summary: How to recast effects of habitat shrinking and global warming on evolutionary dynamics into continuous mutation/selection models? Bearing this question in mind, we consider differential equations for structured populations, which include mutations, proliferation and competition for resources. Since mutations are assumed to be small, a parameter \(\varepsilon\) is introduced to model the average size of phenotypic changes. A well-posedness result is proposed and the asymptotic behavior of the density of individuals is studied in the limit \(\varepsilon \to 0\). In particular, we prove the weak convergence of the density to a sum of Dirac masses and characterize the related concentration points. Moreover, we provide numerical simulations illustrating the theorems and showing an interesting sample of solutions depending on parameters and initial data.
MSC:
| 35R09 | Integro-partial differential equations |
| 35Q92 | PDEs in connection with biology, chemistry and other natural sciences |
| 92D10 | Genetics and epigenetics |
| 35B40 | Asymptotic behavior of solutions to PDEs |
Keywords:
structured populations; asymptotic analysis; concentration phenomena; integrodifferential equationsReferences:
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