Polygenic Adaptation in a Population of Finite Size

Polygenic dynamics underlying the response of quantitative traits to directional selection

We study the response of a quantitative trait to exponential directional selection in a finite haploid population, both at 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 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 non-extinction until n, is described accurately by the deterministic increase from an initial distribution with mean 1. This distribution is related to the absolutely continuous part W+ of the random variable, typically denoted W, that characterizes the stochasticity accumulating during the mutant's sweep. A suitable transformation yields the approximate dynamics of the mutant frequency distribution in a Wright-Fisher population of size N. Our expression provides a very accurate approximation except when mutant frequencies are close to 1. On this basis, 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 approximations for all times, even for the quasi-stationary phase when the expected per-generation response and the trait variance have equilibrated. The latter refine classical results. In addition, we find that Θ is the main determinant of the pattern of adaptation at the genetic level, i.e., whether the initial allele-frequency dynamics are best described by sweep-like patterns at few loci or small allele-frequency shifts at many. The number of segregating sites is an appropriate indicator for these patterns. The selection strength determines primarily the rate of adaptation. The accuracy of our results is tested by comprehensive simulations in a Wright-Fisher framework. We argue that our results apply to more complex forms of directional selection.

Polygenic response of sex chromosomes to sexual antagonism

Sexual antagonism occurs when males and females differ in their phenotypic fitness optima but are constrained in their evolution to these optima because of their shared genome. The sex chromosomes, which have distinct evolutionary "interests" relative to the autosomes, are theorized to play an important role in sexually antagonistic conflict. However, the evolutionary responses of sex chromosomes and autosomes have usually been considered independently, that is, via contrasting the response of a gene located on either an X chromosome or an autosome. Here, we study the coevolutionary response of the X chromosome and autosomes to sexually antagonistic selection acting on a polygenic phenotype. We model a phenotype initially under stabilizing selection around a single optimum, followed by a sudden divergence of the male and female optima. We find that, in the absence of dosage compensation, the X chromosome promotes evolution toward the female optimum, inducing coevolutionary male-biased responses on the autosomes. Dosage compensation obscures the female-biased interests of the X, causing it to contribute equally to male and female phenotypic change. We further demonstrate that fluctuations in an adaptive landscape can generate prolonged intragenomic conflict and accentuate the differential responses of the X and autosomes to this conflict.

A theory of oligogenic adaptation of a quantitative trait

Rapid phenotypic adaptation is widespread in nature, but the underlying genetic dynamics remain controversial. Whereas population genetics envisages sequential beneficial substitutions, quantitative genetics assumes a collective response through subtle shifts in allele frequencies. This dichotomy of a monogenic and a highly polygenic view of adaptation raises the question of a middle ground, as well as the factors controlling the transition. Here, we consider an additive quantitative trait with equal locus effects under Gaussian stabilizing selection that adapts to a new trait optimum after an environmental change. We present an analytical framework based on Yule branching processes to describe how phenotypic adaptation is achieved by collective changes in allele frequencies at the underlying loci. In particular, we derive an approximation for the joint allele-frequency distribution conditioned on the trait mean as a comprehensive descriptor of the adaptive architecture. Depending on the model parameters, this architecture reproduces the well-known patterns of sequential, monogenic sweeps, or of subtle, polygenic frequency shifts. Between these endpoints, we observe oligogenic architecture types that exhibit characteristic patterns of partial sweeps. We find that a single compound parameter, the population-scaled background mutation rate Θbg, is the most important predictor of the type of adaptation, while selection strength, the number of loci in the genetic basis, and linkage only play a minor role.

Redundancy analysis, genome-wide association studies and the pigmentation of brown trout (Salmo trutta L.)

The association of molecular variants with phenotypic variation is a main issue in biology, often tackled with genome-wide association studies (GWAS). GWAS are challenging, with increasing, but still limited, use in evolutionary biology. We used redundancy analysis (RDA) as a complimentary ordination approach to single- and multitrait GWAS to explore the molecular basis of pigmentation variation in brown trout (Salmo trutta) belonging to wild populations impacted by hatchery fish. Based on 75,684 single nucleotide polymorphic (SNP) markers, RDA, single- and multitrait GWAS allowed the extraction of 337 independent colour patterning loci (CPLs) associated with trout pigmentation traits, such as the number of red and black spots on flanks. Collectively, these CPLs (i) mapped onto 35 out of 40 brown trout linkage groups indicating a polygenic genomic architecture of pigmentation, (ii) were found to be associated with 218 candidate genes, including 197 genes formerly mentioned in the literature associated to skin pigmentation, skin patterning, differentiation or structure notably in a close relative, the rainbow trout (Onchorhynchus mykiss), and (iii) related to functions relevant to pigmentation variation (e.g., calcium- and ion-binding, cell adhesion). Annotated CPLs include genes with well-known pigmentation effects (e.g., PMEL, SLC45A2, SOX10), but also markers associated with genes formerly found expressed in rainbow or brown trout skins. RDA was also shown to be useful to investigate management issues, especially the dynamics of trout pigmentation submitted to several generations of hatchery introgression.

Genome-wide evolutionary response of European oaks during the Anthropocene

The pace of tree microevolution during Anthropocene warming is largely unknown. We used a retrospective approach to monitor genomic changes in oak trees since the Little Ice Age (LIA). Allelic frequency changes were assessed from whole-genome pooled sequences for four age-structured cohorts of sessile oak (Quercus petraea) dating back to 1680, in each of three different oak forests in France. The genetic covariances of allelic frequency changes increased between successive time periods, highlighting genome-wide effects of linked selection. We found imprints of parallel linked selection in the three forests during the late LIA, and a shift of selection during more recent time periods of the Anthropocene. The changes in allelic covariances within and between forests mirrored the documented changes in the occurrence of extreme events (droughts and frosts) over the last 300 years. The genomic regions with the highest covariances were enriched in genes involved in plant responses to pathogens and abiotic stresses (temperature and drought). These responses are consistent with the reported sequence of frost (or drought) and disease damage ultimately leading to the oak dieback after extreme events. They provide support for adaptive evolution of long-lived species during recent climatic changes. Although we acknowledge that other sources (e.g., gene flow, generation overlap) may have contributed to temporal covariances of allelic frequency changes, the consistent and correlated response across the three forests lends support to the existence of a systematic driving force such as natural selection.

Rapid Evolutionary Adaptation in Response to Selection on Quantitative Traits

Evolutionary adaptation after sudden environmental changes can occur very rapidly. The mechanisms facilitating rapid adaptation range from strong positive directional selection leading to large shifts in the allele frequencies at a few loci (selective sweeps) to polygenic selection causing small changes in allele frequencies at many loci. In addition, combinations of these two extreme mechanisms may also result in fast evolution. In recent years, following reports of new case studies of rapid adaptation, population genetic models have been proposed to explain these observations. In these models, the role of the major selective forces (positive directional and stabilizing selection) is highlighted as well as the genetic architecture of quantitative traits. Furthermore, the factors limiting the speed of adaptation are analyzed, in particular, the effects of random genetic drift and demography due to finite population size.