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. 2014 Jan 21;9(1):e86125.
doi: 10.1371/journal.pone.0086125. eCollection 2014.

The Interaction Between Selection, Demography and Selfing and How It Affects Population Viability

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Free PMC article

The Interaction Between Selection, Demography and Selfing and How It Affects Population Viability

Diala Abu Awad et al. PLoS One. .
Free PMC article

Erratum in

  • PLoS One. 2014;9(2):e91627. Awad, Diala Abu [corrected to Abu Awad, Diala]

Abstract

Population extinction due to the accumulation of deleterious mutations has only been considered to occur at small population sizes, large sexual populations being expected to efficiently purge these mutations. However, little is known about how the mutation load generated by segregating mutations affects population size and, eventually, population extinction. We propose a simple analytical model that takes into account both the demographic and genetic evolution of populations, linking population size, density dependence, the mutation load, and self-fertilisation. Analytical predictions were found to be relatively good predictors of population size and probability of population viability when verified using an explicit individual based stochastic model. We show that initially large populations do not always reach mutation-selection balance and can go extinct due to the accumulation of segregating deleterious mutations. Population survival depends not only on the relative fitness and demographic stochasticity, but also on the interaction between the two. When deleterious mutations are recessive, self-fertilisation affects viability non-monotonically and genomic cold-spots could favour the viability of outcrossing populations.

Conflict of interest statement

Competing Interests: The authors have declared that no competing interests exist.

Figures

Figure 1
Figure 1. Demographic and genetic evolution of populations.
A) Typical evolution of population size formula image with time for a viable population (formula image), one that reaches equilibrium but goes extinct due to stochasticity (formula image), and one that is not viable (formula image). formula image, formula image, formula image, formula image, formula image and formula image. formula image follows the same pattern. B) Population size at equilibrium, formula image as a function of mean population fitness formula image for different values of formula image. The dashed line represents the expected population size formula image from Equation 3, and the points represent simulation results for all viable populations for all parameter sets with formula image and formula image. C) Probability of population extinction from simulations run for all sets of parameter values for formula image and formula image as a function of the average population's mean relative fitness formula image. The grey line represents the population fitness above which the probability of population extinction in less than formula image generations due to demographic stochasticity alone is almost null. D) Standard deviation of population size over time at population equilibrium formula image as a function of the relative fitness formula image from simulations run for all sets of parameter values for formula image and formula image. The light grey points each represent formula image of a single simulation, the open circles represent the mean standard deviation across simulations per group of parameter values formula image and the full circles represent results from simulations run that take into account only demographic stochasticity.
Figure 2
Figure 2. Population extinction and equilibrium.
A) Probability of population extinction calculated from the 1000 simulations run (formula image and formula image), from black (0% extinction) to white (100% extinction), as a function of formula image. The circles indicate that more than formula image of populations went extinct. The horizontal lines indicate that deterministic extinction was predicted (Equation 3). B) Mean values of the observed population fitness at equilibrium across simulations formula image of viable populations as a function of formula image for formula image and formula image. The grey lines represent the expected mean fitness formula image for (from top to bottom) formula image, formula image, formula image, formula image, formula image and formula image. Top row formula image and below formula image. Missing points indicate parameter values for which none of the 1000 simulations run were viable. C) Standard deviation of population size over time at population equilibrium across simulations formula image with a logarithmic scale as a function of formula image, with formula image and formula image. Note that this variable is underestimated for parameter sets with less than formula image population survival, as the standard deviation of extinct populations is not taken into account. For B and C: ▪ formula image, formula image formula image, ▴ formula image, formula image formula image, formula image formula image.
Figure 3
Figure 3. Accumulation and fixation of deleterious mutations.
A) Mean number of mutations per chromosome equilibrium across simulations as a function of formula image. formula image, formula image, formula image and formula image. Missing points present parameter values for which no populations were viable. B) Mean population size at first fixation of deleterious mutations for populations greater than formula image individuals as a function of formula image. formula image in grey, formula image in black. formula image, formula image and formula image.
Figure 4
Figure 4. Mutational meltdown and time to extinction.
A) Median value of acceleration in the rate of decrease of formula image, formula image and formula image, noted formula image, for non-viable populations from formula image until extinction as a function of formula image. formula image, formula image, formula image, formula image, formula image and formula image. B) Mean time to extinction as a function of formula image. formula image, formula image and formula image.

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Publication types

Grant support

This work benefited from the support of the Chair “Modélisation Mathémathique et Biodiversité” of Veolia Environnement - École Polytechnique - Muséum National d'Histoire Naturelle - Fondation X and the French Agence Nationale de la Recherche ANR-11-BSV7- 013-03. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
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