A general multi-scale description of metastable adaptive motion across fitness valleys
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2021
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866913299820445696 |
|---|---|
| author | Esser, Manuel Kraut, Anna |
| author_facet | Esser, Manuel Kraut, Anna |
| contents | We consider a stochastic individual-based model of adaptive dynamics on a finite trait graph $G=(V,E)$. The evolution is driven by a linear birth rate, a density dependent logistic death rate an the possibility of mutations along the (possibly directed) edges in $E$. We study the limit of small mutation rates for a simultaneously diverging population size. Closing the gap between the works of Bovier, Coquille and Smadi (2019) and Coquille, Kraut and Smadi (2021), we give a precise description of transitions between evolutionary stable conditions (ESC), where multiple mutations are needed to cross a valley in the fitness landscape. The system shows a metastable behaviour on several divergent time scales associated to a degree of stability. We develop the framework of a meta graph that is constituted of ESCs and possible metastable transitions between those. This allows for a concise description of the multi-scale jump chain arising from concatenating several jumps. Finally, for each of the various time scale, we prove the convergence of the population process to a Markov jump process visiting only ESCs of sufficiently high stability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_12675 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | A general multi-scale description of metastable adaptive motion across fitness valleys Esser, Manuel Kraut, Anna Probability Populations and Evolution 37N25, 60J27, 60J80, 92D15, 92D25 We consider a stochastic individual-based model of adaptive dynamics on a finite trait graph $G=(V,E)$. The evolution is driven by a linear birth rate, a density dependent logistic death rate an the possibility of mutations along the (possibly directed) edges in $E$. We study the limit of small mutation rates for a simultaneously diverging population size. Closing the gap between the works of Bovier, Coquille and Smadi (2019) and Coquille, Kraut and Smadi (2021), we give a precise description of transitions between evolutionary stable conditions (ESC), where multiple mutations are needed to cross a valley in the fitness landscape. The system shows a metastable behaviour on several divergent time scales associated to a degree of stability. We develop the framework of a meta graph that is constituted of ESCs and possible metastable transitions between those. This allows for a concise description of the multi-scale jump chain arising from concatenating several jumps. Finally, for each of the various time scale, we prove the convergence of the population process to a Markov jump process visiting only ESCs of sufficiently high stability. |
| title | A general multi-scale description of metastable adaptive motion across fitness valleys |
| topic | Probability Populations and Evolution 37N25, 60J27, 60J80, 92D15, 92D25 |
| url | https://arxiv.org/abs/2112.12675 |