A mathematical formalism for natural selection with arbitrary spatial and genetic structure

Allen, Benjamin; McAvoy, Alex

doi:10.1007/s00285-018-1305-z

Cited by 40 publications

(107 citation statements)

References 187 publications

(393 reference statements)

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“…To calculate the zeroth-and first-order coefficients, ρ � and ρ 0 respectively, in the weak-selection expansion, Eq (3), we apply methods developed in previous works [14,33,45]. We address the zeroth-order (neutral drift) and first-order (weak selection) terms separately.…”

Section: Calculating Fixation Probabilitymentioning

confidence: 99%

Fixation probabilities in graph-structured populations under weak selection

et al. 2021

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A population’s spatial structure affects the rate of genetic change and the outcome of natural selection. These effects can be modeled mathematically using the Birth-death process on graphs. Individuals occupy the vertices of a weighted graph, and reproduce into neighboring vertices based on fitness. A key quantity is the probability that a mutant type will sweep to fixation, as a function of the mutant’s fitness. Graphs that increase the fixation probability of beneficial mutations, and decrease that of deleterious mutations, are said to amplify selection. However, fixation probabilities are difficult to compute for an arbitrary graph. Here we derive an expression for the fixation probability, of a weakly-selected mutation, in terms of the time for two lineages to coalesce. This expression enables weak-selection fixation probabilities to be computed, for an arbitrary weighted graph, in polynomial time. Applying this method, we explore the range of possible effects of graph structure on natural selection, genetic drift, and the balance between the two. Using exhaustive analysis of small graphs and a genetic search algorithm, we identify families of graphs with striking effects on fixation probability, and we analyze these families mathematically. Our work reveals the nuanced effects of graph structure on natural selection and neutral drift. In particular, we show how these notions depend critically on the process by which mutations arise.

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Section: Calculating Fixation Probabilitymentioning

confidence: 99%

Fixation probabilities in graph-structured populations under weak selection

et al. 2021

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“…Formally, this gene's-eye framework is mathematically equivalent to the framework based on haploid individuals [54]. All of our results therefore carry over to sexually reproducing populations without any additional mathematical assumptions.…”

Section: Marginal Distributions and Stationary Frequenciesmentioning

confidence: 79%

Stationary frequencies and mixing times for neutral drift processes with spatial structure

et al. 2018

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We study a general setting of neutral evolution in which the population is of finite, constant size and can have spatial structure. Mutation leads to different genetic types (traits), which can be discrete or continuous. Under minimal assumptions, we show that the marginal trait distributions of the evolutionary process, which specify the probability that any given individual has a certain trait, all converge to the stationary distribution of the mutation process. In particular, the stationary frequencies of traits in the population are independent of its size, spatial structure and evolutionary update rule, and these frequencies can be calculated by evaluating a simple stochastic process describing a population of size one (i.e. the mutation process itself). We conclude by analysing mixing times, which characterize rates of convergence of the mutation process along the lineages, in terms of demographic variables of the evolutionary process.

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“…In a process with sufficiently rare mutation, the quotient ρ C / (ρ C + ρ D ) represents the amount of time spent in the all-producer state; the remaining time is spent in the all-non-producer state [56,57]. Thus, condition R 0 is a measure of C relative to D, and its point of comparison is neutral drift.…”

Section: Quantifying the Effects Of Selectionmentioning

confidence: 99%

Intriguing effects of selection intensity on the evolution of prosocial behaviors

McAvoy

Rao

Hauert

2021

Preprint

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In many models of evolving populations, genetic drift has an outsized role relative to natural selection, or vice versa. While there are many scenarios in which one of these two assumptions is reasonable, intermediate balances between these forces are also biologically relevant. In this study, we consider some natural axioms for modeling intermediate selection intensities, and we explore how to quantify the long-term evolutionary dynamics of such a process. To illustrate the sensitivity of evolutionary dynamics to drift and selection, we show that there can be a "sweet spot" for the balance of these two forces, with sufficient noise for rare mutants to become established and sufficient selection to subsequently spread. In particular, this balance allows prosocial traits to evolve in evolutionary models that were previously thought to be unconducive to the emergence and spread of altruistic behaviors. Furthermore, the effects of selection intensity on long-run evolutionary outcomes in these settings, such as when there is global competition for reproduction, can be highly non-monotonic. Although intermediate selection intensities (neither weak nor strong) are notoriously difficult to study analytically, they are often biologically relevant; and the results we report here suggest that they can elicit novel and rich dynamics in the evolution of prosocial behaviors.

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A mathematical formalism for natural selection with arbitrary spatial and genetic structure

Cited by 40 publications

References 187 publications

Fixation probabilities in graph-structured populations under weak selection

Fixation probabilities in graph-structured populations under weak selection

Stationary frequencies and mixing times for neutral drift processes with spatial structure

Intriguing effects of selection intensity on the evolution of prosocial behaviors

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