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Towards the Construction of a Mathematically Rigorous Framework for the Modelling of Evolutionary Fitness.

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posted on 2019-06-24, 10:28 authored by Oleg Kuzenkov, Andrew Morozov
Modelling of natural selection in self-replicating systems has been heavily influenced by the concept of fitness which was inspired by Darwin's original idea of the survival of the fittest. However, so far the concept of fitness in evolutionary modelling is still somewhat vague, intuitive and often subjective. Unfortunately, as a result of this, using different definitions of fitness can lead to conflicting evolutionary outcomes. Here we formalise the definition of evolutionary fitness to describe the selection of strategies in deterministic self-replicating systems for generic modelling settings which involve an arbitrary function space of inherited strategies. Our mathematically rigorous definition of fitness is closely related to the underlying population dynamic equations which govern the selection processes. More precisely, fitness is defined based on the concept of the ranking of competing strategies which compares the long-term dynamics of measures of sets of inherited units in the space of strategies. We also formulate the variational principle of modelling selection which states that in a self-replicating system with inheritance, selection will eventually maximise evolutionary fitness. We demonstrate how expressions for evolutionary fitness can be derived for a class of models with age structuring including systems with delay, which has previously been considered as a challenge.

Funding

The research collaboration was made possible via an LMS Scheme 2 Grant (the Grant holder is A. Morozov). O. Kuzenkov was supported by the Ministry of Education and Science of the Russian Federation (Project No. 14.Y26.31.0022).

History

Citation

Bulletin of Mathematical Biology, 2019

Author affiliation

/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of Mathematics

Version

  • VoR (Version of Record)

Published in

Bulletin of Mathematical Biology

Publisher

Springer (part of Springer Nature) for Society for Mathematical Biology

eissn

1522-9602

Acceptance date

2019-03-22

Copyright date

2019

Available date

2019-06-24

Publisher version

https://link.springer.com/article/10.1007/s11538-019-00602-3

Language

en

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