How chromosomal inversions reorient the evolutionary process.

Inversions are structural mutations that reverse the sequence of a chromosome segment and reduce the effective rate of recombination in the heterozygous state. They play a major role in adaptation, as well as in other evolutionary processes such as speciation. Although inversions have been studied since the 1920s, they remain difficult to investigate because the reduced recombination conferred by them strengthens the effects of drift and hitchhiking, which in turn can obscure signatures of selection. Nonetheless, numerous inversions have been found to be under selection. Given recent advances in population genetic theory and empirical study, here we review how different mechanisms of selection affect the evolution of inversions. A key difference between inversions and other mutations, such as single nucleotide variants, is that the fitness of an inversion may be affected by a larger number of frequently interacting processes. This considerably complicates the analysis of the causes underlying the evolution of inversions. We discuss the extent to which these mechanisms can be disentangled, and by which approach.

The infinitesimal model with dominance.

The classical infinitesimal model is a simple and robust model for the inheritance of quantitative traits. In this model, a quantitative trait is expressed as the sum of a genetic and an environmental component, and the genetic component of offspring traits within a family follows a normal distribution around the average of the parents' trait values, and has a variance that is independent of the parental traits. In previous work, we showed that when trait values are determined by the sum of a large number of additive Mendelian factors, each of small effect, one can justify the infinitesimal model as a limit of Mendelian inheritance. In this paper, we show that this result extends to include dominance. We define the model in terms of classical quantities of quantitative genetics, before justifying it as a limit of Mendelian inheritance as the number, M, of underlying loci tends to infinity. As in the additive case, the multivariate normal distribution of trait values across the pedigree can be expressed in terms of variance components in an ancestral population and probabilities of identity by descent determined by the pedigree. Now, with just first-order dominance effects, we require two-, three-, and four-way identities. We also show that, even if we condition on parental trait values, the "shared" and "residual" components of trait values within each family will be asymptotically normally distributed as the number of loci tends to infinity, with an error of order 1/M. We illustrate our results with some numerical examples.

Slower-X: reduced efficiency of selection in the early stages of X chromosome evolution.

Differentiated X chromosomes are expected to have higher rates of adaptive divergence than autosomes, if new beneficial mutations are recessive (the "faster-X effect"), largely because these mutations are immediately exposed to selection in males. The evolution of X chromosomes after they stop recombining in males, but before they become hemizygous, has not been well explored theoretically. We use the diffusion approximation to infer substitution rates of beneficial and deleterious mutations under such a scenario. Our results show that selection is less efficient on diploid X loci than on autosomal and hemizygous X loci under a wide range of parameters. This "slower-X" effect is stronger for genes affecting primarily (or only) male fitness, and for sexually antagonistic genes. These unusual dynamics suggest that some of the peculiar features of X chromosomes, such as the differential accumulation of genes with sex-specific functions, may start arising earlier than previously appreciated.

On the origin and structure of haplotype blocks.

The term "haplotype block" is commonly used in the developing field of haplotype-based inference methods. We argue that the term should be defined based on the structure of the Ancestral Recombination Graph (ARG), which contains complete information on the ancestry of a sample. We use simulated examples to demonstrate key features of the relationship between haplotype blocks and ancestral structure, emphasizing the stochasticity of the processes that generate them. Even the simplest cases of neutrality or of a "hard" selective sweep produce a rich structure, often missed by commonly used statistics. We highlight a number of novel methods for inferring haplotype structure, based on the full ARG, or on a sequence of trees, and illustrate how they can be used to define haplotype blocks using an empirical data set. While the advent of new, computationally efficient methods makes it possible to apply these concepts broadly, they (and additional new methods) could benefit from adding features to explore haplotype blocks, as we define them. Understanding and applying the concept of the haplotype block will be essential to fully exploit long and linked-read sequencing technologies.

The "New Synthesis".

When Mendel's work was rediscovered in 1900, and extended to establish classical genetics, it was initially seen in opposition to Darwin's theory of evolution by natural selection on continuous variation, as represented by the biometric research program that was the foundation of quantitative genetics. As Fisher, Haldane, and Wright established a century ago, Mendelian inheritance is exactly what is needed for natural selection to work efficiently. Yet, the synthesis remains unfinished. We do not understand why sexual reproduction and a fair meiosis predominate in eukaryotes, or how far these are responsible for their diversity and complexity. Moreover, although quantitative geneticists have long known that adaptive variation is highly polygenic, and that this is essential for efficient selection, this is only now becoming appreciated by molecular biologists-and we still do not have a good framework for understanding polygenic variation or diffuse function.

Effects of fine-scale population structure on the distribution of heterozygosity in a long-term study of Antirrhinum majus.

Many studies have quantified the distribution of heterozygosity and relatedness in natural populations, but few have examined the demographic processes driving these patterns. In this study, we take a novel approach by studying how population structure affects both pairwise identity and the distribution of heterozygosity in a natural population of the self-incompatible plant Antirrhinum majus. Excess variance in heterozygosity between individuals is due to identity disequilibrium, which reflects the variance in inbreeding between individuals; it is measured by the statistic g2. We calculated g2 together with FST and pairwise relatedness (Fij) using 91 SNPs in 22,353 individuals collected over 11 years. We find that pairwise Fij declines rapidly over short spatial scales, and the excess variance in heterozygosity between individuals reflects significant variation in inbreeding. Additionally, we detect an excess of individuals with around half the average heterozygosity, indicating either selfing or matings between close relatives. We use 2 types of simulation to ask whether variation in heterozygosity is consistent with fine-scale spatial population structure. First, by simulating offspring using parents drawn from a range of spatial scales, we show that the known pollen dispersal kernel explains g2. Second, we simulate a 1,000-generation pedigree using the known dispersal and spatial distribution and find that the resulting g2 is consistent with that observed from the field data. In contrast, a simulated population with uniform density underestimates g2, indicating that heterogeneous density promotes identity disequilibrium. Our study shows that heterogeneous density and leptokurtic dispersal can together explain the distribution of heterozygosity.

Why did the Wolbachia transinfection cross the road? drift, deterministic dynamics, and disease control.

Maternally inherited Wolbachia transinfections are being introduced into natural mosquito populations to reduce the transmission of dengue, Zika, and other arboviruses. Wolbachia-induced cytoplasmic incompatibility provides a frequency-dependent reproductive advantage to infected females that can spread transinfections within and among populations. However, because transinfections generally reduce host fitness, they tend to spread within populations only after their frequency exceeds a critical threshold. This produces bistability with stable equilibrium frequencies at both 0 and 1, analogous to the bistability produced by underdominance between alleles or karyotypes and by population dynamics under Allee effects. Here, we analyze how stochastic frequency variation produced by finite population size can facilitate the local spread of variants with bistable dynamics into areas where invasion is unexpected from deterministic models. Our exemplar is the establishment of wMel Wolbachia in the Aedes aegypti population of Pyramid Estates (PE), a small community in far north Queensland, Australia. In 2011, wMel was stably introduced into Gordonvale, separated from PE by barriers to A. aegypti dispersal. After nearly 6 years during which wMel was observed only at low frequencies in PE, corresponding to an apparent equilibrium between immigration and selection, wMel rose to fixation by 2018. Using analytic approximations and statistical analyses, we demonstrate that the observed fixation of wMel at PE is consistent with both stochastic transition past an unstable threshold frequency and deterministic transformation produced by steady immigration at a rate just above the threshold required for deterministic invasion. The indeterminacy results from a delicate balance of parameters needed to produce the delayed transition observed. Our analyses suggest that once Wolbachia transinfections are established locally through systematic introductions, stochastic "threshold crossing" is likely to only minimally enhance spatial spread, providing a local ratchet that slightly-but systematically-aids area-wide transformation of disease-vector populations in heterogeneous landscapes.

Dynamic maximum entropy provides accurate approximation of structured population dynamics.

Realistic models of biological processes typically involve interacting components on multiple scales, driven by changing environment and inherent stochasticity. Such models are often analytically and numerically intractable. We revisit a dynamic maximum entropy method that combines a static maximum entropy with a quasi-stationary approximation. This allows us to reduce stochastic non-equilibrium dynamics expressed by the Fokker-Planck equation to a simpler low-dimensional deterministic dynamics, without the need to track microscopic details. Although the method has been previously applied to a few (rather complicated) applications in population genetics, our main goal here is to explain and to better understand how the method works. We demonstrate the usefulness of the method for two widely studied stochastic problems, highlighting its accuracy in capturing important macroscopic quantities even in rapidly changing non-stationary conditions. For the Ornstein-Uhlenbeck process, the method recovers the exact dynamics whilst for a stochastic island model with migration from other habitats, the approximation retains high macroscopic accuracy under a wide range of scenarios in a dynamic environment.

Haplotype tagging reveals parallel formation of hybrid races in two butterfly species.

Genetic variation segregates as linked sets of variants or haplotypes. Haplotypes and linkage are central to genetics and underpin virtually all genetic and selection analysis. Yet, genomic data often omit haplotype information due to constraints in sequencing technologies. Here, we present "haplotagging," a simple, low-cost linked-read sequencing technique that allows sequencing of hundreds of individuals while retaining linkage information. We apply haplotagging to construct megabase-size haplotypes for over 600 individual butterflies (Heliconius erato and H. melpomene), which form overlapping hybrid zones across an elevational gradient in Ecuador. Haplotagging identifies loci controlling distinctive high- and lowland wing color patterns. Divergent haplotypes are found at the same major loci in both species, while chromosome rearrangements show no parallelism. Remarkably, in both species, the geographic clines for the major wing-pattern loci are displaced by 18 km, leading to the rise of a novel hybrid morph in the center of the hybrid zone. We propose that shared warning signaling (Müllerian mimicry) may couple the cline shifts seen in both species and facilitate the parallel coemergence of a novel hybrid morph in both comimetic species. Our results show the power of efficient haplotyping methods when combined with large-scale sequencing data from natural populations.

Homage to Felsenstein 1981, or why are there so few/many species?

If there are no constraints on the process of speciation, then the number of species might be expected to match the number of available niches and this number might be indefinitely large. One possible constraint is the opportunity for allopatric divergence. In 1981, Felsenstein used a simple and elegant model to ask if there might also be genetic constraints. He showed that progress towards speciation could be described by the build-up of linkage disequilibrium among divergently selected loci and between these loci and those contributing to other forms of reproductive isolation. Therefore, speciation is opposed by recombination, because it tends to break down linkage disequilibria. Felsenstein then introduced a crucial distinction between "two-allele" models, which are subject to this effect, and "one-allele" models, which are free from the recombination constraint. These fundamentally important insights have been the foundation for both empirical and theoretical studies of speciation ever since.

Polygenic local adaptation in metapopulations: A stochastic eco-evolutionary model.

This article analyzes the conditions for local adaptation in a metapopulation with infinitely many islands under a model of hard selection, where population size depends on local fitness. Each island belongs to one of two distinct ecological niches or habitats. Fitness is influenced by an additive trait which is under habitat-dependent directional selection. Our analysis is based on the diffusion approximation and accounts for both genetic drift and demographic stochasticity. By neglecting linkage disequilibria, it yields the joint distribution of allele frequencies and population size on each island. We find that under hard selection, the conditions for local adaptation in a rare habitat are more restrictive for more polygenic traits: even moderate migration load per locus at very many loci is sufficient for population sizes to decline. This further reduces the efficacy of selection at individual loci due to increased drift and because smaller populations are more prone to swamping due to migration, causing a positive feedback between increasing maladaptation and declining population sizes. Our analysis also highlights the importance of demographic stochasticity, which exacerbates the decline in numbers of maladapted populations, leading to population collapse in the rare habitat at significantly lower migration than predicted by deterministic arguments.

Mating system variation in hybrid zones: facilitation, barriers and asymmetries to gene flow.

Plant mating systems play a key role in structuring genetic variation both within and between species. In hybrid zones, the outcomes and dynamics of hybridization are usually interpreted as the balance between gene flow and selection against hybrids. Yet, mating systems can introduce selective forces that alter these expectations; with diverse outcomes for the level and direction of gene flow depending on variation in outcrossing and whether the mating systems of the species pair are the same or divergent. We present a survey of hybridization in 133 species pairs from 41 plant families and examine how patterns of hybridization vary with mating system. We examine if hybrid zone mode, level of gene flow, asymmetries in gene flow and the frequency of reproductive isolating barriers vary in relation to mating system/s of the species pair. We combine these results with a simulation model and examples from the literature to address two general themes: (1) the two-way interaction between introgression and the evolution of reproductive systems, and (2) how mating system can facilitate or restrict interspecific gene flow. We conclude that examining mating system with hybridization provides unique opportunities to understand divergence and the processes underlying reproductive isolation.

Thinking About the Evolution of Complex Traits in the Era of Genome-Wide Association Studies.

Many traits of interest are highly heritable and genetically complex, meaning that much of the variation they exhibit arises from differences at numerous loci in the genome. Complex traits and their evolution have been studied for more than a century, but only in the last decade have genome-wide association studies (GWASs) in humans begun to reveal their genetic basis. Here, we bring these threads of research together to ask how findings from GWASs can further our understanding of the processes that give rise to heritable variation in complex traits and of the genetic basis of complex trait evolution in response to changing selection pressures (i.e., of polygenic adaptation). Conversely, we ask how evolutionary thinking helps us to interpret findings from GWASs and informs related efforts of practical importance.

An integrative genomic analysis of the Longshanks selection experiment for longer limbs in mice.

Evolutionary studies are often limited by missing data that are critical to understanding the history of selection. Selection experiments, which reproduce rapid evolution under controlled conditions, are excellent tools to study how genomes evolve under selection. Here we present a genomic dissection of the Longshanks selection experiment, in which mice were selectively bred over 20 generations for longer tibiae relative to body mass, resulting in 13% longer tibiae in two replicates. We synthesized evolutionary theory, genome sequences and molecular genetics to understand the selection response and found that it involved both polygenic adaptation and discrete loci of major effect, with the strongest loci tending to be selected in parallel between replicates. We show that selection may favor de-repression of bone growth through inactivating two limb enhancers of an inhibitor, Nkx3-2. Our integrative genomic analyses thus show that it is possible to connect individual base-pair changes to the overall selection response.

Replicability of Introgression Under Linked, Polygenic Selection.

We study how a block of genome with a large number of weakly selected loci introgresses under directional selection into a genetically homogeneous population. We derive exact expressions for the expected rate of growth of any fragment of the introduced block during the initial phase of introgression, and show that the growth rate of a single-locus variant is largely insensitive to its own additive effect, but depends instead on the combined effect of all loci within a characteristic linkage scale. The expected growth rate of a fragment is highly correlated with its long-term introgression probability in populations of moderate size, and can hence identify variants that are likely to introgress across replicate populations. We clarify how the introgression probability of an individual variant is determined by the interplay between hitchhiking with relatively large fragments during the early phase of introgression and selection on fine-scale variation within these, which at longer times results in differential introgression probabilities for beneficial and deleterious loci within successful fragments. By simulating individuals, we also investigate how introgression probabilities at individual loci depend on the variance of fitness effects, the net fitness of the introduced block, and the size of the recipient population, and how this shapes the net advance under selection. Our work suggests that even highly replicable substitutions may be associated with a range of selective effects, which makes it challenging to fine map the causal loci that underlie polygenic adaptation.

Introgression of a Block of Genome Under Infinitesimal Selection.

Adaptive introgression is common in nature and can be driven by selection acting on multiple, linked genes. We explore the effects of polygenic selection on introgression under the infinitesimal model with linkage. This model assumes that the introgressing block has an effectively infinite number of loci, each with an infinitesimal effect on the trait under selection. The block is assumed to introgress under directional selection within a native population that is genetically homogeneous. We use individual-based simulations and a branching process framework to compute various statistics of the introgressing block, and explore how these depend on parameters such as the map length and initial trait value associated with the introgressing block, the genetic variability along the block, and the strength of selection. Our results show that the introgression dynamics of a block under infinitesimal selection are qualitatively different from the dynamics of neutral introgression. We also find that, in the long run, surviving descendant blocks are likely to have intermediate lengths, and clarify how their length is shaped by the interplay between linkage and infinitesimal selection. Our results suggest that it may be difficult to distinguish the long-term introgression of a block of genome with a single, strongly selected, locus from the introgression of a block with multiple, tightly linked and weakly selected loci.