Effects of natural selection by fertility on the evolution of the dynamic modes of population number: bistability and multistability

Неверова, Г.П.; Zhdanova, O. L.; Frisman, E. Ya.

doi:10.1007/s11071-020-05745-w

Cited by 4 publications

(7 citation statements)

References 42 publications

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“…With ϕρ ≥ a, a phenomenon known as the "bistability trap" can occur, where a more advantageous genotype cannot displace its genetically weaker competitor [49]. However, population decline resulting from external factors, leading to random processes referred to as "population bottlenecks", can induce random changes in genetic composition, causing transition processes from one monomorphic state to another with greater fitness.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…Such multistability is caused by the system having several attracting solutions simultaneously (Figure 9c-h). In the case of the stability of two monomorphic fixed points, the "bistability trap" occurs, where a more promising genetic form cannot displace a weaker competitor (Figure 9c) [49]. However, a drop in population size due to an external factor effect known as a "population bottleneck" [50] can lead to random changes in genetic composition and the transition of the population from one monomorphic state to another more promising but destabilizing dynamic.…”

Section: Bistability and Multistability In System (6)mentioning

confidence: 99%

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Mathematical Modeling of the Evolutionary Dynamics of a Planktonic Community Using a Discrete-Time Model

Neverova,

Zhdanova

2023

Mathematics

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This study proposes a discrete-time eco-genetic model of a planktonic community that includes zooplankton and two competing phytoplankton haplotypes with and without a toxicity trait. The Holling type II response function describes predator consumption. We use the Ricker model to consider density limitation and regulation. The model is analytically and numerically studied. The loss of stability of fixed points occurs via the Neimark–Sacker scenario and a cascade of period-doubling bifurcations. The model reveals bistability and multistability. Therefore, the initial conditions can determine which of the coexisting dynamic modes will be attracted. If the competition of haplotypes is weaker than their self-regulation, then the variation in the current densities of community components can shift the observed dynamics, while the evolution direction remains unchanged. The ratio of haplotype fitnesses and predator pressure generally determines the asymptotic genetic composition of phytoplankton. If competition of haplotypes is higher than their self-regulation, then the bistability of monomorphic fixed points occurs when the displacement of one haplotype by another depends on initial conditions. The presence of predators can maintain the genetic polymorphism of the prey. This system shows dynamic modes similar to experimental dynamics: oscillation with delay, long-period antiphase fluctuations, and cryptic cycles emerging due to rapid evolution.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Section: Bistability and Multistability In System (6)mentioning

confidence: 99%

Mathematical Modeling of the Evolutionary Dynamics of a Planktonic Community Using a Discrete-Time Model

Neverova,

Zhdanova

2023

Mathematics

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“…On the other hand, as a rule, fluctuations in abundance are caused by changes in the population structure caused by the combined effects of environmental factors and self-regulatory mechanisms [12][13][14]. Therefore, when modeling population dynamics, it is advisable to use an ecological-genetic approach that allows us to study the interconnected changes in the abundance and genetic structure of a population [15][16][17][18][19][20][21][22][23][24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

“…The concepts of density-and frequency-dependent components in the action of natural selection have been developed [32][33][34], as have density-independent forms of natural selection, whose action under ecological limitation can cause a change in the nature of the population abundance dynamics [36][37][38]. Currently, research continues to investigate the relationship between population genetics, stage (age) [23][24][25][26]39], and sex [22] structures. The work [22] derives conditions for protected polymorphism in a population characterized by age-or stage-dependent demography with two sexes.…”

Section: Introductionmentioning

confidence: 99%

“…On the other hand, combining classic population genetic theory and ecological modeling makes it possible to see the effects that are missed when using each of these approaches in isolation, as well as to study the interconnected changes in the abundance and genetic structure of a population under ecological limitation during the influence of natural selection [20][21][22][23][24][25][26][27][49][50][51][52]. Examples include the effects of bottlenecks, evolutionary rescue, or degeneration, in which genotype ratios determine the growth or decline of population abundance.…”

Section: Introductionmentioning

confidence: 99%

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The Evolutionary Dynamics of a Sex-Structured Population with Non-Overlapping Generations

Revutskaya,

Neverova,

Zhdanova

et al. 2023

Mathematics

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This paper proposes and studies a discrete-time model for a sex-structured population with non-overlapping generations under density-dependent regulation of survival. The population is assumed to have genetic variety among individuals in terms of reproductive potential, controlled by a single autosomal diallelic locus. We consider a panmictic population with Mendelian inheritance rules. We examine the stability model and show that increasing the average value of reproductive potential destabilizes the population dynamics. The scenario of stability loss in fixed points via period doubling or Neimark–Sacker bifurcations depends on the intensity of the self-regulation. The growth rate at which the population survives and develops is shown to depend on the fitness of the genotypes and the secondary sex ratio. As a result, the asymptotic genetic composition of the population is determined by the values of the reproductive potentials of the heterozygote and homozygotes, the initial conditions, and the parameter describing the ratio of newborn females to males. With disruptive selection, the influence of external factors changing the current genetic composition of a population can alter the direction of evolution and lead to the extinction of a successful developing population or a gradual population recovery due to evolutionary rescue after a noticeable decline in its abundance.

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Evolutionary dynamics of predator in a community of interacting species

2022

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Effects of natural selection by fertility on the evolution of the dynamic modes of population number: bistability and multistability

Cited by 4 publications

References 42 publications

Mathematical Modeling of the Evolutionary Dynamics of a Planktonic Community Using a Discrete-Time Model

Mathematical Modeling of the Evolutionary Dynamics of a Planktonic Community Using a Discrete-Time Model

The Evolutionary Dynamics of a Sex-Structured Population with Non-Overlapping Generations

Evolutionary dynamics of predator in a community of interacting species

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