Polygenic adaptation: From sweeps to subtle frequency shifts

Abstract

Evolutionary theory has produced two conflicting paradigms for the adaptation of a polygenic trait. While population genetics views adaptation as a sequence of selective sweeps at single loci underlying the trait, quantitative genetics posits a collective response, where phenotypic adaptation results from subtle allele frequency shifts at many loci. Yet, a synthesis of these views is largely missing and the population genetic factors that favor each scenario are not well understood. Here, we study the architecture of adaptation of a binary polygenic trait (such as resistance) with negative epistasis among the loci of its basis. The genetic structure of this trait allows for a full range of potential architectures of adaptation, ranging from sweeps to small frequency shifts. By combining computer simulations and a newly devised analytical framework based on Yule branching processes, we gain a detailed understanding of the adaptation dynamics for this trait. Our key analytical result is an expression for the joint distribution of mutant alleles at the end of the adaptive phase. This distribution characterizes the polygenic pattern of adaptation at the underlying genotype when phenotypic adaptation has been accomplished. We find that a single compound parameter, the population-scaled background mutation rate Θ bg , explains the main differences among these patterns. For a focal locus, Θ bg measures the mutation rate at all redundant loci in its genetic background that offer alternative ways for adaptation. For adaptation starting from mutation-selection-drift balance, we observe different patterns in three parameter regions. Adaptation proceeds by sweeps for small Θ bg ≲ 0.1, while small polygenic allele frequency shifts require large Θ bg ≳ 100. In the large intermediate regime, we observe a heterogeneous pattern of partial sweeps at several interacting loci.

Polygenic Adaptation to an Environmental Shift: Temporal Dynamics of Variation Under Gaussian Stabilizing Selection and Additive Effects on a Single Trait

“…The total mutation rate per diploid, U , was 2μ. These mutation rates corresponded to Θ=4Nμ values of 5, 20, and 100, respectively, meaning sweeps were expected to be high frequency, mixes of partial and complete sweeps, and adaptation primarily by allele frequency changes, respectively, as the population approached the new optimum (Höllinger et al 2019). The three postshift optima used were zo=0.1, 0.5, and 1.…”

“…Under a model of a trait with a small number of phenotypic classes, Höllinger et al (2019) describe the dynamics of mutations following an optimum shift for traits with low mutation rates and for highly polygenic traits. The key parameter in their model is Θ=4Nμ, where μ is the mutation rate relevant to the trait.…”

“…In general, the standard model of a single trait with additive-effect mutations and Gaussian stabilizing selection assumes linkage equilibrium (or quasi-linkage equilibrium) (Turelli 1984; Barton 1986; de Vladar and Barton 2014; Jain and Stephan 2015, 2017b). Höllinger et al (2019) were able to accommodate partial linkage by simplifying how mutations affect phenotype and focusing on the dynamics up until a particular mean trait value was first reached. In their simplest model, an individual is either mutant or nonmutant, and therefore there are only two phenotypes possible.…”

Important role of genetic drift in rapid polygenic adaptation

“…Here, we examine to what extent these deterministic results may be generalized to populations of finite size, in which genetic drift plays an important role. We focus on polygenic adaptation involving a large number of weakly selected loci, since this type of adaptation is not nearly as well studied as the case of strong selection and selective sweeps (with the exception of the very recent work by Simons, Bullaughey, Hudson, and Sella (2018) and Höllinger, Pennings, and Hermisson (2019)). Furthermore, we describe the effect of demography (population size bottlenecks) on polygenic adaptation.…”

The Linked Selection Signature of Rapid Adaptation in Temporal Genomic Data

“…However, most adaptation on ecological timescales likely involves selection on phenotypes with polygenic architecture and abundant standing variation (Endler 1986;Hendry and Kinnison 1999;Kinnison and Hendry 2001;Kopp and Hermisson 2009b). We know from theory that adaptation on such traits can result from very subtle allele frequency changes across the many loci that underlie the trait (Bulmer 1980), at least for the short-term evolutionary response (Hermisson and Pennings 2005;Chevin and Hospital 2008;Stephan 2015, 2017;Thornton 2018;Höllinger et al 2019). These changes may be individually indistinguishable from genetic drift in temporal data.…”