Invasion and effective size of graph-structured populations

Giaimo, Stefano; Arranz, Jordi; Traulsen, Arne

doi:10.1371/journal.pcbi.1006559

Cited by 17 publications

(13 citation statements)

References 39 publications

(67 reference statements)

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“…Driven by the ubiquity of heterogeneity within populations, there has been growing interest in understanding how it affects selection in simple mathematical models. Much of this work, ranging from earlier models in population genetics [24][25][26][27] to those with more fine-grained spatial structure [28][29][30][31][32][33][34][35], is summarized in a prequel to this study [36] (which deals with well-mixed dispersal structures and spatially-modulated fitness). However, a general understanding of the effects of heterogeneous resource distributions within structured populations is still lacking.…”

Section: Introductionmentioning

confidence: 99%

The Moran process on 2-chromatic graphs

Kaveh¹,

McAvoy²,

Chatterjee³

et al. 2020

PLoS Comput Biol

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Resources are rarely distributed uniformly within a population. Heterogeneity in the concentration of a drug, the quality of breeding sites, or wealth can all affect evolutionary dynamics. In this study, we represent a collection of properties affecting the fitness at a given location using a color. A green node is rich in resources while a red node is poorer. More colors can represent a broader spectrum of resource qualities. For a population evolving according to the birth-death Moran model, the first question we address is which structures, identified by graph connectivity and graph coloring, are evolutionarily equivalent. We prove that all properly two-colored, undirected, regular graphs are evolutionarily equivalent (where “properly colored” means that no two neighbors have the same color). We then compare the effects of background heterogeneity on properly two-colored graphs to those with alternative schemes in which the colors are permuted. Finally, we discuss dynamic coloring as a model for spatiotemporal resource fluctuations, and we illustrate that random dynamic colorings often diminish the effects of background heterogeneity relative to a proper two-coloring.

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Section: Introductionmentioning

confidence: 99%

The Moran process on 2-chromatic graphs

Kaveh¹,

McAvoy²,

Chatterjee³

et al. 2020

PLoS Comput Biol

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“…This is the probability that an initial subset of mutants takes over the population, and is a popular measure to compare different strategies within evolutionary theory (Altrock and Traulsen 2009 ; Broom and Rychtář 2008 ; Czuppon and Traulsen 2018 ; Giaimo et al. 2018 ; Lieberman et al. 2005 ; Traulsen and Hauert 2010 ).…”

Section: The Effect Of Fitness Variation On Bet-hedger Selection Probabilitymentioning

confidence: 99%

Evolutionary bet-hedging in structured populations

Overton

Sharkey

2021

J. Math. Biol.

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As ecosystems evolve, species can become extinct due to fluctuations in the environment. This leads to the evolutionary adaption known as bet-hedging, where species hedge against these fluctuations to reduce their likelihood of extinction. Environmental variation can be either within or between generations. Previous work has shown that selection for bet-hedging against within-generational variation should not occur in large populations. However, this work has been limited by assumptions of well-mixed populations, whereas real populations usually have some degree of structure. Using the framework of evolutionary graph theory, we show that through adding competition structure to the population, within-generational variation can have a significant impact on the evolutionary process for any population size. This complements research using subdivided populations, which suggests that within-generational variation is important when local population sizes are small. Together, these conclusions provide evidence to support observations by some ecologists that are contrary to the widely held view that only between-generational environmental variation has an impact on natural selection. This provides theoretical justification for further empirical study into this largely unexplored area.

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“…[ 26 ] provided a mathematical treatment using coalescence times for graph structures under weak selection. Other work has examined the type of graph structures that lead to amplification of selection [ 27 ], the properties of fixation probability and time for the Moran process [ 10 , 13 , 14 , 16 , 28 ], mathematical models for fixation time for specific k-partite graphs [ 29 ] and approaches to approximate the fixation probability for neutral drift models [ 30 ]. This field of research has emphasized game-theoretic models for behaviour, or used a two-allele haploid model based on the Moran process, with the emphasis on how the evolution of cooperation or fixation of a mutant is altered by population structure.…”

Section: Introductionmentioning

confidence: 99%

“…It is worth noting that these models all use a single population with overlapping generations, normally replacing just one (or occasionally, two) individuals per time step (described as a steady-state model [ 32 ]). The generational model, mainly used in evolutionary biology and specifically in the HR model [ 16 ], replaces an entire population each generation. In the electronic supplementary material, we show that this distinction is crucial in terms of how spatial structure affects both fixation probability and time.…”

Section: Introductionmentioning

confidence: 99%

Graph-structured populations and the Hill–Robertson effect

Whigham

Spencer

2021

R. Soc. open sci.

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The Hill–Robertson effect describes how, in a finite panmictic diploid population, selection at one diallelic locus reduces the fixation probability of a selectively favoured allele at a second, linked diallelic locus. Here we investigate the influence of population structure on the Hill–Robertson effect in a population of size N . We model population structure as a network by assuming that individuals occupy nodes on a graph connected by edges that link members who can reproduce with each other. Three regular networks (fully connected, ring and torus), two forms of scale-free network and a star are examined. We find that (i) the effect of population structure on the probability of fixation of the favourable allele is invariant for regular structures, but on some scale-free networks and a star, this probability is greatly reduced; (ii) compared to a panmictic population, the mean time to fixation of the favoured allele is much greater on a ring, torus and linear scale-free network, but much less on power-2 scale-free and star networks; (iii) the likelihood with which each of the four possible haplotypes eventually fix is similar across regular networks, but scale-free populations and the star are consistently less likely and much faster to fix the optimal haplotype; (iv) increasing recombination increases the likelihood of fixing the favoured haplotype across all structures, whereas the time to fixation of that haplotype usually increased, and (v) star-like structures were overwhelmingly likely to fix the least fit haplotype and did so significantly more rapidly than other populations. Last, we find that small ( N < 64) panmictic populations do not exhibit the scaling property expected from Hill & Robertson (1966 Genet. Res. 8 , 269–294. ( doi:10.1017/S0016672300010156 )).

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Invasion and effective size of graph-structured populations

Cited by 17 publications

References 39 publications

The Moran process on 2-chromatic graphs

The Moran process on 2-chromatic graphs

Evolutionary bet-hedging in structured populations

Graph-structured populations and the Hill–Robertson effect

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