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Title: Towards the Construction of a Mathematically Rigorous Framework for the Modelling of Evolutionary Fitness.
Authors: Kuzenkov, Oleg
Morozov, Andrew
First Published: 4-Apr-2019
Publisher: Springer (part of Springer Nature) for Society for Mathematical Biology
Citation: Bulletin of Mathematical Biology, 2019
Abstract: 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.
DOI Link: 10.1007/s11538-019-00602-3
eISSN: 1522-9602
Version: Publisher Version
Status: Peer-reviewed
Type: Journal Article
Rights: Copyright © the authors, 2019. This is an open-access article distributed under the terms of the Creative Commons Attribution License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Appears in Collections:Published Articles, Dept. of Mathematics

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