The smaller a population is, the faster it looses genetic variation due to genetic drift. Loss of genetic variation can reduce population growth rate, making populations even smaller and more vulnerable to loss of genetic variation, and so on. Ultimately, the population can be driven to extinction by this "eco-evolutionary extinction vortex". So far, extinction vortices due to loss of genetic variation have been mainly described verbally. However, quantitative models are needed to better understand when such vortices arise and to develop methods for detecting them. Here we propose quantitative eco-evolutionary models, both individual-based simulations and analytic approximations, that link loss of genetic variation and population decline. Our models assume stochastic population dynamics and multi-locus genetics with different forms of balancing selection. Using mathematical analysis and simulations, we identify parameter combinations that exhibit strong interactions between population size and genetic variation as populations decline to extinction and match our definition of an eco-evolutionary vortex, i.e. the per-capita population decline rates and per-locus fixation rates increase with decreasing population size and number of polymorphic loci. We further highlight cues and early warning signals that may be useful in identifying populations undergoing an eco-evolutionary extinction vortex.
An important goal for conservation is to define minimum viable population (MVP) sizes for long‐term persistence of a species. There is increasing evidence of the role of genetics in population extinction; thus, conservation practitioners are starting to consider the effects of deleterious mutations (DM), in particular the effects of inbreeding depression on fitness. We sought to develop methods to account for genetic problems other than inbreeding depression in MVP estimates, quantify the effect of the interaction of multiple genetic problems on MVP sizes, and find ways to reduce the arbitrariness of time and persistence probability thresholds in MVP analyses. To do so, we developed ecoevolutionary quantitative models to track population size and levels of genetic diversity. We assumed a biallelic multilocus genome with loci under single or multiple, interacting genetic forces. We included mutation–selection–drift balance (for loci with DM) and 3 forms of balancing selection for loci for which variation is lost through genetic drift. We defined MVP size as the lowest population size that avoids an ecoevolutionary extinction vortex. For populations affected by only balancing selection, MVP size decreased rapidly as mutation rates increased. For populations affected by mutation–selection–drift balance, the MVP size increased rapidly. In addition, MVP sizes increased rapidly as the number of loci increased under the same or different selection mechanisms until even arbitrarily large populations could not survive. In the case of fixed number of loci under selection, interaction of genetic problems did not always increase MVP sizes. To further enhance understanding about interaction of genetic problems, there is need for more empirical studies to reveal how different genetic processes interact in the genome.
1The smaller a population is, the faster it looses genetic variation due to genetic drift. Loss 2 of genetic variation can reduce population growth rate, making populations even smaller and 3 more vulnerable to loss of genetic variation, and so on. Ultimately, the population can be driven 4 to extinction by this "eco-evolutionary extinction vortex". So far, extinction vortices due to 5 loss of genetic variation have been mainly described verbally. However, quantitative models are 6 needed to better understand when such vortices arise and to develop methods for detecting 7 them. Here we propose quantitative eco-evolutionary models, both individual-based simulations 8 and analytic approximations, that link loss of genetic variation and population decline. Our 9 models assume stochastic population dynamics and multi-locus genetics with different forms 10 of balancing selection. Using mathematical analysis and simulations, we identify parameter 11 combinations that exhibit strong interactions between population size and genetic variation as 12 populations decline to extinction and match our definition of an eco-evolutionary vortex, i.e. 13 the per-capita population decline rates and per-locus fixation rates increase with decreasing 14 population size and number of polymorphic loci. We further highlight cues and early warning 15 signals that may be useful in identifying populations undergoing an eco-evolutionary extinction 16 vortex.
An important goal for conservation is to define minimum viable population (MVP) sizes for long-term persistence. Although many MVP size estimates focus on ecological processes, with increasing evidence for the role of genetic problems in population extinction, conservation practitioners have also increasingly started to incorporate inbreeding depression (ID). However, small populations also face other genetic problems such as mutation accumulation (MA) and loss of genetic diversity through genetic drift that are usually factored into population viability assessments only via verbal arguments. Comprehensive quantitative theory on interacting genetic problems is missing. Here we develop eco-evolutionary quantitative models that track both population size and levels of genetic diversity. Our models assume a biallelic multilocus genome whose loci can be under either a single or interacting genetic forces. In addition to mutation-selection-drift balance (for loci facing ID and MA), we include three forms of balancing selection (for loci where variation is lost through genetic drift). We define MVP size as the lowest population size that avoids an eco-evolutionary extinction vortex after a time sufficient for an equilibrium allele frequency distribution to establish. Our results show that MVP size decreases rapidly with increasing mutation rates for populations whose genomes are only under balancing selection, while for genomes under mutation-selection-drift balance, the MVP size increases rapidly. MVP sizes also increase rapidly with increasing number of loci under the same or different selection mechanisms until a point is reached at which even arbitrarily large populations cannot survive anymore. In the case of fixed number of loci under selection, interaction of genetic problems did not necessarily increase MVP sizes. To further enhance our understanding about interaction of genetic problems, there is need for more empirical studies to reveal how different genetic processes interact in the genome.
Recent empirical and theoretical work shows that intraspecific trait variation (ITV) is prevalent and ecologically important, and should thus be taken into account in ecological models. What is lacking, however, is a comprehensive understanding of the joint effects of ITV in two interacting species (two-dimensional ITV). Here we address this gap for the cases where interspecific individual-by-individual interactions are affected by the trait values of both participants. Using nonlinear averaging in two dimensions, we show for several interaction functions how ITV affects average predation rates or competition coefficients. We develop an intuition for the direction and magnitude of this effect by using a Taylor approximation based on the local curvatures of the interaction function, the trait means, and the trait variances and covariances. We then incorporate the estimated average interaction parameters into simple competition and predator-prey models to derive the expected population-dynamic consequences. We show that two-dimensional ITV can have quantitative effects on abundances, as well as qualitative effects, such as stabilizing or destabilizing coexistence. Our approach can straightforwardly be applied to other interaction functions and dynamical systems and thus provides a valuable tool for understanding the joint effect of trait variation in two interacting species.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
customersupport@researchsolutions.com
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.