Genetic polymorphism under cyclical selection in long-lived species: The complex effect of age structure and maternal selection

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Highlights

  • Maintenance of genetic polymorphism in cyclically changing environments.

  • Complex effect of maternal selection and overlapping generations is considered.

  • Odd and even external cycles produce different types of polymorphism regions.

  • Model case is like those demonstrated by natural populations of arctic foxes.

Abstract

Maternal selection and overlapping generations can facilitate the stable coexistence of alleles under temporally fluctuating environment. Using mathematical models, we considered the complex effect of both factors on the maintenance of genetic polymorphism in cyclically changing environments. We concentrated on asymmetric cyclic selection, which allows describing fluctuations of environments by analogy of food resources cycles with rare peaks and prolonged decline of prey abundance.

The complex effect of maternal selection and overlapping generations turned out to work as follows: although overlapping generations always tend to dilate the polymorphism region, odd and even external cycles produce different types of polymorphism regions. Maternal selection under external odd cycles extends the coexistence region comparing with classic selection. Even cycles produce a part of parameter region, where the picture changes radically, and classic selection becomes more effective in maintaining polymorphism.

Our models have clear biological interpretation, because we tried to model a situation demonstrated by natural populations of arctic foxes. The litter size being a major life history trait is a sex-limited female trait. It is influenced by maternal selection with cyclical fluctuations because of oscillations in food abundance. Arctic fox is a long-lived species having an age structure. The obtained results showed that compared with the simple Mendelian inheritance in the classic model, this trait inheritance allows polymorphism to be maintained in a wider range of the parameter that characterizes the advantage of survival in a small litter. Besides, adding overlapping generations to the model further broadens the parameter space for the protected polymorphism. Thus, this study shows that maternal selection and overlapping generations increases the chances of maintaining polymorphism in populations of arctic foxes.

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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