On a model of evolution of subspecies.

Publisher: Springer Verlag Country of Publication: Germany NLM ID: 7502105 Publication Model: Electronic Cited Medium: Internet ISSN: 1432-1416 (Electronic) Linking ISSN: 03036812 NLM ISO Abbreviation: J Math Biol Subsets: MEDLINE

Publication: Berlin : Springer Verlag
Original Publication: Wien, New York, Springer-Verlag.

Stochastic Processes* ; Models, Genetic*; Genetic Fitness ; Biological Evolution ; Mathematical Concepts ; Mutation Rate ; Mutation ; Viruses/genetics ; Viruses/classification

Ben-Ari and Schinazi (J Stat Phys 162:415-425, 2016) introduced a stochastic model to study 'virus-like evolving population with high mutation rate'. This model is a birth and death model with an individual at birth being either a mutant with a random fitness parameter in [0, 1] or having one of the existing fitness parameters with uniform probability; whereas a death event removes the entire population of the least fitness. We change this to incorporate the notion of 'survival of the fittest', by requiring that a non-mutant individual, at birth, has a fitness according to a preferential attachment mechanism, i.e., it has a fitness f with a probability proportional to the size of the population of fitness f. Also death just removes one individual with the least fitness. This preferential attachment rule leads to a power law behaviour in the asymptotics, unlike the exponential behaviour obtained by Ben-Ari and Schinazi (J Stat Phys 162:415-425, 2016).
Competing Interests: Ethical approval: Ethical approval not needed because no animate object was involved in this study.
(© 2024. The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.)

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JP16H06338 Japan Society for the Promotion of Science London

Keywords: Markov chain; Preferential attachment model; Yule-Simon distribution

Date Created: 20241206 Date Completed: 20241206 Latest Revision: 20241206

20241209

10.1007/s00285-024-02165-x

39641863