Genetic polymorphism under cyclical selection in long-lived species: The complex effect of age structure and maternal selection
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Section snippets
1. Introduction
The maintenance of genetic polymorphism in heterogeneous environments continues to be a topic of research interest in evolutionary genetics for a long time (e.g. Levene, 1953, Dempster, 1955, Haldane and Jayakar, 1963). Within the framework of the classical theory of population genetics of diploids, overdominance is known to be a necessary condition for maintaining balanced polymorphism in a stationary environment, with genotype fitnesses being constantly expressed in and independent on
Maternal selection in a single diallelic locus: Diploid population with nonoverlapping generations
Considering inheritance type of litter size in arctic foxes, it is reasonable to replace Model (1) by maternal selection model. For deriving such a model, let us consider a breeding scheme with the following assumptions.
- 1.
The trait is autosomal, i.e. progeny genotypes are defined by both parents;
- 2.
Maternal genotype is solely responsible for individual’s fitness (wij), the latter being described as a product of average survivals (vij) and offspring number (lij) by females with ij genotype.
- 3.
Gene
Natural selection in an age-structured population with limited size
The previous population genetic models (Eqs. 1, 2) consider allele frequency changes in the population, assuming that different generations of the population do not overlap. However, this assumption does not hold when the lifetime of each generation is essentially longer than the time between breeding seasons.
We consider the model with the age structure that could be represented as the set of two age classes: junior and elder ones. The junior age class consists of immature individuals, and the
Discussion and conclusions
Maternal selection (Yamamichi and Hoso, 2017) and overlapping generations (Ellner and Hairston,, 1994, Hedrick, 1995, Turelli et al., 2001) can facilitate the stable coexistence of alleles under temporally fluctuating environment. Using mathematical models, we considered the complex effect of these two factors on the maintenance of genetic polymorphism in cyclically changing environments. We focused on asymmetric cyclic selection, which allows us to describe fluctuations of environments similar
CRediT authorship contribution statement
Oksana L. Zhdanova: Conceptualization, Methodology, Software, Visualization, Writing - original draft, Writing - review & editing. Efim Ya. Frisman: Conceptualization, Methodology, Writing - original draft, Writing - review & editing.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
We appreciate the work of two anonymous reviewers for constructive comments and insightful suggestions that improved the paper very much.
Funding: The work was completed within the frameworks of the State tasks of the Institute for Automation and Control Processes FEB RAS and the Institute of Complex Analysis of Regional Problem FEB RAS.
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