Multitype branching processes in random environment

Vatutin, Vladimir; Dyakonova, E. E.

doi:10.1070/rm10012

Cited by 3 publications

(3 citation statements)

References 84 publications

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“…A mathematical study of the model and its effects on selection might be done using the theory of multitype branching processes (see e.g. (5; 29; 34; 42; 46; 53; 54; 68; 77)). As a somewhat related example, probability of fixation under weak selection can be mathematically investigated using a continuous-state branching process framework(47).…”

Section: Discussionmentioning

confidence: 99%

Genome-wide fixation under viability selection

Eldon

2022

Preprint

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We investigate through simulations the effect of random sweepstakes, recurrent bottlenecks, dominance, and epistasis on selection a diploid population when the phenotype is determined by the genotype at a number of unlinked sites. We assume there are two types at each site, the wild type and a type conferring selective advantage. The focus is on identifying main trends in how the stated elements impact selection when selection acts on at least two unlinked site. We give examples of fixation trajectories under an array of scenarios, and record corresponding numerical estimates of the probability of fixation of the fit type at all the sites in question each time, and the time to fixation conditional on fixation. The results suggest that joint fixation of the fit type at the sites can occur in a number of scenarios, despite starting with the fit type in a single copy at each site. Random sweepstakes generally reduce both the probability and the time to fixation (conditional on fixation). Recurrent strong bottlenecks generally reduce the probability of fixation, but the effect of bottlenecks on the time to fixation (conditional on fixation), depends on the dominance mechanism in question. We identify an example of epistasis where fixation can occur, when in the absence of epistasis fixation does not occur at all or with much lower probability. Our results, coupled with an extensive analysis of genomic data of Atlantic cod (Arnason et al, 2022), is further evidence for pervasive strong positive selection as being a key driving force in the evolution at least of highly fecund populations.

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Section: Discussionmentioning

confidence: 99%

Genome-wide fixation under viability selection

Eldon

2022

Preprint

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“…An open problem is rigorously verifying the simulation results. Here, multitype branching process theory [62][63][64][65][66][67] may be useful. The mathematical analysis of the model of random sweepstakes given in Equation (7) and applied in the simulations is ongoing.…”

Section: Discussionmentioning

confidence: 99%

Viability Selection at Linked Sites

Eldon

2023

Mathematics

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Evolutionary ecology may be described as explaining ecology through evolution and vice versa, but one may also view it as an integration of the two fields, where one takes the view that ecology and evolution are inseparable, and one can only begin to understand the biology of organisms by synthesizing the two fields. An example of such a synthesis is the biology of high fecundity and the associated concept of sweepstakes reproduction, or skewed individual recruitment success. As an illustration, we consider selection at linked sites under various dominance and epistasis mechanisms in a diploid population evolving according to random sweepstakes and experiencing recurrent bottlenecks. Using simulations, we give a few examples of the impact of the stated elements on selection. We show that depending on the dominance mechanisms, random sweepstakes can shorten the time to fixation (conditional on fixation) of the fit type at all sites. Bottlenecks tend to increase the fixation time, with random sweepstakes counteracting the effects of bottlenecks on the fixation time. Understanding the effect of random sweepstakes, recurrent bottlenecks, dominance mechanisms and epistasis on the fate of selectively advantageous mutations may help with explaining genetic diversity in natural highly fecund populations possibly evolving under sweepstakes reproduction.

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“…An open problem is rigorously verifying the simulation results. Here multi-type branching process theory [60][61][62][63][64][65] may be useful. Mathematical analysis of the model of random sweepstakes given in Eq (7) and applied in the simulations is ongoing.…”

Section: Discussionmentioning

confidence: 99%

Viability Selection at Linked Sites

Eldon¹

2022

Preprint

View full text Add to dashboard Cite

Evolutionary ecology may be described as explaining ecology through evolution and vice versa, but one may also view it as an integration of the two fields, where one takes the view that ecology and evolution are inseparable, and one can only begin to understand the biology of organisms by synthesizing the two fields. An example of such a synthesis is the biology of high fecundity and the associated concept of sweepstakes reproduction, or skewed individual recruitment success. As an illustration we consider selection at linked sites under various dominance and epistasis mechanisms in a diploid population evolving according to random sweepstakes and experiencing recurrent bottlenecks. Using simulations we give a few examples of the impact of the stated elements on selection. We show that depending on the dominance mechanisms random sweepstakes can shorten the time to fixation (conditional on fixation) of the fit type at all sites. Bottlenecks tend to increase the fixation time, with random sweepstakes counteracting the effects of bottlenecks on the fixation time. Understanding the effect of random sweepstakes, recurrent bottlenecks, dominance mechanisms and epistasis on the fate of selectively advantageous mutations may help with explaining genetic diversity in natural highly fecund populations possibly evolving under sweepstakes reproduction.

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Multitype branching processes in random environment

Abstract: A survey of results in the theory of multitype branching processes evolving in a random environment is presented. Bibliography: 104 titles.

Cited by 3 publications

References 84 publications

Genome-wide fixation under viability selection

Genome-wide fixation under viability selection

Viability Selection at Linked Sites

Viability Selection at Linked Sites

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