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

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...

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Bibliographic Details
Published in:Bulletin of mathematical biology 2019-11, Vol.81 (11), p.4675-4700
Main Authors: Kuzenkov, Oleg, Morozov, Andrew
Format: Article
Language:English
Subjects:
Cell Biology
Evolution
Fitness
Function space
Heredity
Life Sciences
Mathematical and Computational Biology
Mathematical models
Mathematics
Mathematics and Statistics
Modelling
Natural selection
Replication
Reproductive fitness
Special Issue: Modelling Biological Evolution: Developing Novel Approaches
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Summary: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.
ISSN:0092-8240
1522-9602
DOI:10.1007/s11538-019-00602-3