Mathematical description of continuous time and space replicator-mutator equations for quadratic fitness landscapes
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912153971195904 |
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| author | Pathiraja, Sahani Wacker, Philipp |
| author_facet | Pathiraja, Sahani Wacker, Philipp |
| contents | The replicator-mutator equation is a model for populations of individuals carrying different traits, with a fitness function mediating their ability to replicate, and a stochastic model for mutation. We derive analytical solutions for the replicator-mutator equation in continuous time and for continuous traits for a quadratic fitness function. Using these results we can explain and quantify (without the need for numerical in-silico simulations) a series of evolutionary phenomena, in particular the flying kite effect, survival of the flattest, and the ability of a population to sustain itself while tracking an optimal feature which may be fixed, moving with bounded velocity in trait space, oscillating, or randomly fluctuating. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_08178 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Mathematical description of continuous time and space replicator-mutator equations for quadratic fitness landscapes Pathiraja, Sahani Wacker, Philipp Populations and Evolution Probability 37N25, 92D25, 34A05, 49N05, 91A22, 60G35 The replicator-mutator equation is a model for populations of individuals carrying different traits, with a fitness function mediating their ability to replicate, and a stochastic model for mutation. We derive analytical solutions for the replicator-mutator equation in continuous time and for continuous traits for a quadratic fitness function. Using these results we can explain and quantify (without the need for numerical in-silico simulations) a series of evolutionary phenomena, in particular the flying kite effect, survival of the flattest, and the ability of a population to sustain itself while tracking an optimal feature which may be fixed, moving with bounded velocity in trait space, oscillating, or randomly fluctuating. |
| title | Mathematical description of continuous time and space replicator-mutator equations for quadratic fitness landscapes |
| topic | Populations and Evolution Probability 37N25, 92D25, 34A05, 49N05, 91A22, 60G35 |
| url | https://arxiv.org/abs/2412.08178 |