Joint effect of changing selection and demography on the site frequency spectrum

Jain, Kavita; Kaushik, Sachin

doi:10.1016/j.tpb.2022.07.001

Cited by 5 publications

(7 citation statements)

References 44 publications

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“…Towards this end, PGFT is not a priori necessary; there have been many attempts at describing nonequilibrium dynamics in a number of ways, ranging from a focus on fixation probability in a changing population size [38,39] or changing environment [40] (or both simultaneously [37]), integral solutions to neutral non-equilibrium dynamics of the allele frequency spectrum [41], exact solutions for the transition density in the form of an infinite series (for constant population size [42] and variable population size [43]), a system of ODEs for the moments of the allele frequency distribution [44,46], numerical solutions to the time-dependent diffusion equations [44][45][46], analysis of the stochastic dynamics of traveling waves of fitness [52], amongst many others. Several approaches involve the use of path integrals [47][48][49][50][51]65], which is a natural way to characterize the trajectory that an allele takes through a population over time, also employed in the present manuscript.…”

Section: Discussionmentioning

confidence: 99%

“…From a modeling standpoint, this class of demographies provides a convenient example for the application of PGFT to a relatively complex demography that can be defined using a relatively simple deterministic function for the population size. Cyclical demographies can be parameterized in a number of ways (see, e.g., [37] for a recent example), which do not all describe equivalent demographies, as the shape of the population size trajectory over the course of each oscillation may differ in different models. Here, I will analyze one class of cyclical demographies as an example, which are defined by the following three-parameter function representing the time-dependence of the diploid population size N (t).…”

Section: Cyclical Demography With Oscillatory Population Sizementioning

confidence: 99%

“…However, the majority of the mathematics developed to model population genetics is, by construction, restricted to equilibrium or pseudo-equilibrium regimes. This is for both analytic and intuitive simplicity, but, additionally, forays far beyond equilibrium population genetics are notoriously difficult to describe mathematically, particularly when more than one parameter can temporally vary (see, e.g., [37] for a recent paper on co-varying parameters). There are, of course, a number of exceptions (i.e., non-equilibrium models [27,[37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52]), some of which are highlighted in the Discussion.…”

Section: Introductionmentioning

confidence: 99%

“…This is for both analytic and intuitive simplicity, but, additionally, forays far beyond equilibrium population genetics are notoriously difficult to describe mathematically, particularly when more than one parameter can temporally vary (see, e.g., [37] for a recent paper on co-varying parameters). There are, of course, a number of exceptions (i.e., non-equilibrium models [27,[37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52]), some of which are highlighted in the Discussion. Non-equilibrium descriptions in the literature are often constructed using ad hoc techniques suited to model a specific demography or phenomena of interest (e.g., models presented in [27,37]).…”

Section: Introductionmentioning

confidence: 99%

“…There are, of course, a number of exceptions (i.e., non-equilibrium models [27,[37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52]), some of which are highlighted in the Discussion. Non-equilibrium descriptions in the literature are often constructed using ad hoc techniques suited to model a specific demography or phenomena of interest (e.g., models presented in [27,37]). Instead, this manuscript aims to describe a distinct and generalizable formalism that is flexible enough to characterize a wide range of behavior in non-equilibrium populations in a unified framework.…”

Section: Introductionmentioning

confidence: 99%

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A field theoretic approach to non-equilibrium population genetics in the strong selection regime

Balick

2023

Preprint

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Natural populations are virtually never observed in equilibrium, yet equilibrium approximations comprise the majority of our understanding of population genetics. Using standard tools from statistical physics, a formalism is presented that re-expresses the stochastic equations describing allelic evolution as a partition functional over all possible allelic trajectories (i.e.,paths) governed by selection, mutation, and drift. A perturbative field theory is developed for strong additive selection, relevant to disease variation, that facilitates the straightforward computation of closed-form approximations for time-dependent moments of the allele frequency distribution across a wide range of non-equilibrium scenarios; examples are presented for constant population size, exponential growth, bottlenecks, and oscillatory size, all of which align well to simulations and break down just above the drift barrier. Equilibration times are computed and, even for static population size, generically extend beyond the order 1/stimescale associated with exponential frequency decay. Though the mutation load is largely robust to variable population size, perturbative drift-based corrections to the deterministic trajectory are readily computed. Under strong selection, the variance of a new mutation's frequency (related to homozygosity) is dominated by drift-driven dynamics and a transient increase in variance often occurs prior to equilibrating. The excess kurtosis over skew squared is roughly constant (i.e., independent of selection, provided 2Ns≈5 or larger) for static population size, and thus potentially sensitive to deviation from equilibrium. These insights highlight the value of such closed-form approximations, naturally generated from Feynman diagrams in a perturbative field theory, which can simply and accurately capture the parameter dependences describing a variety of non-equilibrium population genetic phenomena of interest.

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Section: Discussionmentioning

confidence: 99%

Section: Cyclical Demography With Oscillatory Population Sizementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A field theoretic approach to non-equilibrium population genetics in the strong selection regime

Balick

2023

Preprint

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Polygenic dynamics underlying the response of quantitative traits to directional selection

Götsch,

Bürger

2024

Theoretical Population Biology

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Polygenic dynamics underlying the response of quantitative traits to directional selection

Götsch¹,

Bürger²

2023

Preprint

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We study the response of a quantitative trait to exponential directional selection in a finite haploid population, both on the genetic and the phenotypic level. We assume an infinite sites model, in which the number of new mutations per generation in the population follows a Poisson distribution (with mean Θ) and each mutation occurs at a new, previously monomorphic site. Mutation effects are beneficial and drawn from a distribution. Sites are unlinked and contribute additively to the trait. Assuming that selection is stronger than random genetic drift, we model the initial phase of the dynamics by a slightly supercritical Galton-Watson process. This enables us to obtain time-dependent results. We show that the copy-number distribution of the mutant in generation n, conditioned on survival until n, is described accurately by the deterministic increase from an initial distribution with mean 1. This distribution corresponds to the absolutely continuous part W+ of the random variable, typically denoted W, that characterizes the stochasticity accumulating during the mutant's sweep. In bypassing, we prove the folklore result that W+ is approximately exponentially distributed, but in general not exactly so by deriving its second and third moment. A proper transformation yields the approximate mutant frequency dynamics in a Wright-Fisher population of size N. Then we derive explicitly the (approximate) time dependence of the expected mean and variance of the trait and of the expected number of segregating sites. Unexpectedly, we obtain highly accurate expressions even for the quasi-stationary phase, when the expected per-generation response has equilibrated. These refine classical results, and they are derived from first principles. We find that Θ is the main determinant of the pattern of adaptation at the genetic level, i.e., whether the response is mainly due to sweeps or to small allele-frequency shifts, and the number of segregating sites is an appropriate indicator for it. The selection strength determines primarily the rate of adaptation. The accuracy of our results is tested for a Poisson offspring distribution by comprehensive simulations in a Wright-Fisher framework.

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Joint effect of changing selection and demography on the site frequency spectrum

Cited by 5 publications

References 44 publications

A field theoretic approach to non-equilibrium population genetics in the strong selection regime

A field theoretic approach to non-equilibrium population genetics in the strong selection regime

Polygenic dynamics underlying the response of quantitative traits to directional selection

Polygenic dynamics underlying the response of quantitative traits to directional selection

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