Models for Eco-Evolutionary Extinction Vortices under Balancing Selection

Nabutanyi, Peter; Wittmann, Meike J.

doi:10.1086/712805

Cited by 20 publications

(27 citation statements)

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“…For the MCA with equilibrium assumptions, a quasi-extinction threshold of absolute fitness 1 was used. The absolute fitness of 1 acts as a boundary between population persistence ( W > 1) and rapid population decline ( W < 1) in an eco-evolutionary extinction vortex (Nabutanyi & Wittmann, 2021).…”

Section: Discussionmentioning

confidence: 99%

“…Also, we show how estimates of minimum viable population size depend on fitness per locus (Appendix S6) and how equilibrium fitness and critical number of loci can be estimated (Appendix S4). Briefly, FS was derived as follows (see Nabutanyi & Wittmann (2021) for a detailed description).…”

Section: Supporting Informationmentioning

confidence: 99%

“…The diffusion approximation involved numerically solving the diffusion equation for f ( x, t ) in each generation subject to some initial and boundary conditions (Zhao et al, 2013; Xu et al, 2019; Nabutanyi & Wittmann, 2021), where a ( x, t ) and b ( x, t ) are the mean and variance of the change in allele frequency during an infinitesimal time interval, derived for each selection mechanism (Appendix S2.1).…”

Section: General Modelmentioning

confidence: 99%

“…Briefly, FS was derived as follows (see Nabutanyi & Wittmann (2021) for a detailed description). The relative fitnesses of the genotypes were and , where s A,t = s A · sin(2 π · t/κ ) and s a,t = s a · sin( π + 2 π · t/κ ) are temporally fluctuating selection coefficients and h t = 0.5 − c · sin(2 π · t/κ ) is the temporally fluctuating dominance coefficient.…”

Section: Figure S21mentioning

confidence: 99%

“…For example, assuming s a and s A are very small that higher order terms involving and above are negligible, for HA, ID and MA, The three mechanisms differed in h, s a and s A . For FS (see Nabutanyi & Wittmann (2021) supplementary Section A.3), and for FD, where, h t , h, μ a , μ A , s A , s a , s a,t , and s A,t are as defined under ”Selection Mechanisms” subsection. We adopted the numerical scheme in Zhao et al (2013); Xu et al (2019) to solve Equation (1) subject to the initial condition f ( x, 0) = x 0 and the boundary condition that conserves probability at all times. The scheme basically discretizes both time t and allele frequency x over the interval 0 and 1 inclusive.…”

Section: Figure S21mentioning

confidence: 99%

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Modeling minimum viable population size with multiple genetic problems of small populations

Nabutanyi

Wittmann

2021

Preprint

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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.

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Section: Discussionmentioning

confidence: 99%

Section: Supporting Informationmentioning

confidence: 99%

Section: General Modelmentioning

confidence: 99%

Section: Figure S21mentioning

confidence: 99%

Section: Figure S21mentioning

confidence: 99%

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Modeling minimum viable population size with multiple genetic problems of small populations

Nabutanyi

Wittmann

2021

Preprint

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Plastic and quantitative genetic divergence mirror environmental gradients among wild, fragmented populations of Impatiens capensis

Toczydlowski

Waller

2022

American J of Botany

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Premise Habitat fragmentation generates molecular genetic divergence among isolated populations, but few studies have assessed phenotypic divergence and fitness in populations where the genetic consequences of habitat fragmentation are known. Phenotypic divergence could reflect plasticity, local adaptation, and/or genetic drift. Methods We examined patterns and potential drivers of phenotypic divergence among 12 populations of jewelweed (Impatiens capensis) that show strong molecular genetic signals of isolation and drift among fragmented habitats. We measured morphological and reproductive traits in both maternal plants within natural populations and their self‐fertilized progeny grown together in a common garden. We also quantified environmental divergence between home sites and the common garden. Results Populations with less molecular genetic variation expressed less maternal phenotypic variation. Progeny in the common garden converged in phenotypes relative to their wild mothers but retained among‐population differences in morphology, survival, and reproduction. Among‐population phenotypic variance was 3–10× greater in home sites than in the common garden for 6 of 7 morphological traits measured. Patterns of phenotypic divergence paralleled environmental gradients in ways suggestive of adaptation. Progeny resembled their mothers less as the environmental distance between their home site and the common garden increased. Conclusions Despite strong molecular signatures of isolation and drift, phenotypic differences among these Impatiens populations appear to reflect both adaptive quantitative genetic divergence and plasticity. Quantifying the extent of local adaptation and plasticity and how these covary with molecular and phenotypic variation help us predict when populations may lose their adaptive capacity.

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Multi‐scale effects of habitat loss and the role of trait evolution

Bagawade,

van Benthem,

Wittmann

2024

Ecology and Evolution

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Habitat loss (HL) is a major cause of species extinctions. Although the effects of HL beyond the directly impacted area have been previously observed, they have not been modelled explicitly, especially in an eco‐evolutionary context. To start filling this gap, we study a two‐patch deterministic consumer‐resource model, with one of the patches experiencing loss of resources as a special case of HL. Our model allows foraging and mating within a patch as well as between patches. We then introduce heritable variation in consumer traits related to resource utilization and patch use to investigate eco‐evolutionary dynamics and compare results with constant and no trait variation scenarios. Our results show that HL in one patch can indeed reduce consumer densities in the neighbouring patch but can also increase consumer densities in the neighbouring patch when the resources are overexploited. Yet at the landscape scale, the effect of HL on consumer densities is consistently negative. Patch isolation increases consumer density in the patch experiencing HL but has generally negative effects on the neighbouring patch, with context‐dependent results at the landscape scale. With high cross‐patch dependence and coupled foraging and mating preferences, local HL can sometimes even lead to landscape‐level consumer extinction. Eco‐evolutionary dynamics can rescue consumers from such extinction in some cases if their death rates are sufficiently small. More generally, trait evolution had positive or negative effects on equilibrium consumer densities after HL, depending on the evolving trait and the spatial scale considered. In summary, our findings show that HL at a local scale can affect the neighbouring patch and the landscape as a whole, where heritable trait variation can, in some cases, alleviate the impact of HL. We thus suggest joint consideration of multiple spatial scales and trait variation when assessing and predicting the impacts of HL.

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Models for Eco-Evolutionary Extinction Vortices under Balancing Selection

Cited by 20 publications

References 53 publications

Modeling minimum viable population size with multiple genetic problems of small populations

Modeling minimum viable population size with multiple genetic problems of small populations

Plastic and quantitative genetic divergence mirror environmental gradients among wild, fragmented populations of Impatiens capensis

Multi‐scale effects of habitat loss and the role of trait evolution

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