Genetic architecture and postzygotic reproductive isolation: evolution of Bateson-Dobzhansky-Muller incompatibilities in a polygenic model

The Ecology of Hybrid Incompatibilities

Ecologically mediated selection against hybrids, caused by hybrid phenotypes fitting poorly into available niches, is typically viewed as distinct from selection caused by epistatic Dobzhansky-Muller hybrid incompatibilities. Here, we show how selection against transgressive phenotypes in hybrids manifests as incompatibility. After outlining our logic, we summarize current approaches for studying ecology-based selection on hybrids. We then quantitatively review QTL-mapping studies and find traits differing between parent taxa are typically polygenic. Next, we describe how verbal models of selection on hybrids translate to phenotypic and genetic fitness landscapes, highlighting emerging approaches for detecting polygenic incompatibilities. Finally, in a synthesis of published data, we report that trait transgression-and thus possibly extrinsic hybrid incompatibility in hybrids-escalates with the phenotypic divergence between parents. We discuss conceptual implications and conclude that studying the ecological basis of hybrid incompatibility will facilitate new discoveries about mechanisms of speciation.

Pleiotropy, epistasis and the genetic architecture of quantitative traits

Pleiotropy (whereby one genetic polymorphism affects multiple traits) and epistasis (whereby non-linear interactions between genetic polymorphisms affect the same trait) are fundamental aspects of the genetic architecture of quantitative traits. Recent advances in the ability to characterize the effects of polymorphic variants on molecular and organismal phenotypes in human and model organism populations have revealed the prevalence of pleiotropy and unexpected shared molecular genetic bases among quantitative traits, including diseases. By contrast, epistasis is common between polymorphic loci associated with quantitative traits in model organisms, such that alleles at one locus have different effects in different genetic backgrounds, but is rarely observed for human quantitative traits and common diseases. Here, we review the concepts and recent inferences about pleiotropy and epistasis, and discuss factors that contribute to similarities and differences between the genetic architecture of quantitative traits in model organisms and humans.

Fisher's Geometric Model as a Tool to Study Speciation

Interactions between alleles and across environments play an important role in the fitness of hybrids and are at the heart of the speciation process. Fitness landscapes capture these interactions and can be used to model hybrid fitness, helping us to interpret empirical observations and clarify verbal models. Here, we review recent progress in understanding hybridization outcomes through Fisher's geometric model, an intuitive and analytically tractable fitness landscape that captures many fitness patterns observed across taxa. We use case studies to show how the model parameters can be estimated from different types of data and discuss how these estimates can be used to make inferences about the divergence history and genetic architecture. We also highlight some areas where the model's predictions differ from alternative incompatibility-based models, such as the snowball effect and outlier patterns in genome scans.

Mechanisms of Intrinsic Postzygotic Isolation: From Traditional Genic and Chromosomal Views to Genomic and Epigenetic Perspectives

Intrinsic postzygotic isolation typically appears as reduced viability or fertility of interspecific hybrids caused by genetic incompatibilities between diverged parental genomes. Dobzhansky-Muller interactions among individual genes, and chromosomal rearrangements causing problems with chromosome synapsis and recombination in meiosis, have both long been considered as major mechanisms behind intrinsic postzygotic isolation. Recent research has, however, suggested that the genetic basis of intrinsic postzygotic isolation can be more complex and involves, for example, overall divergence of the DNA sequence or epigenetic changes. Here, we review the mechanisms of intrinsic postzygotic isolation from genic, chromosomal, genomic, and epigenetic perspectives across diverse taxa. We provide empirical evidence for these mechanisms, discuss their importance in the speciation process, and highlight questions that remain unanswered.

Hybridization in late stages of speciation: Strong but incomplete genome-wide reproductive isolation and 'large Z-effect' in a moving hybrid zone

In organisms reproducing sexually, speciation occurs when increasing divergence results in pre- or post-zygotic reproductive isolation between lineages. Studies focusing on reproductive isolation origin in early stages of speciation are common and many rely on genomic scans to infer introgression providing limited information on the genomic architecture of reproductive isolation long-term maintenance. This study analyses a natural hybrid zone between two species in a late stage of speciation. We used ddRADseq genotyping in the contact between Podarcis bocagei and P. carbonelli to examine admixture extent, analyse hybrid zone stability and assess genome-wide variation in selection against introgression. We confirmed strong but incomplete reproductive isolation in a bimodal hybrid zone. New findings revealed population genetic structure within P. carbonelli in the contact zone; geographical and genomic clines analysis suggested strong selection against gene flow, but a relatively small proportion of the loci can introgress, mostly within the narrow contact zone. However, geographical clines revealed that a few introgressed loci show signs of potential positive selection, particularly into P. bocagei. Geographical clines also detected a signal of hybrid zone movement towards P. bocagei distribution. Genomic cline analysis revealed heterogeneous patterns of introgression among loci within the syntopy zone, but the majority maintain a strong association with the genomic background of origin. However, incongruences between both cline approaches were found, potentially driven by confounding effects on genomic clines. Last, an important role of the Z chromosome in reproductive isolation is suggested. Importantly, overall patterns of restricted introgression seem to result from numerous strong intrinsic barriers across the genome.

Meiotic drive is associated with sexual incompatibility in Neurospora

Evolution of Bateson-Dobzhansky-Muller (BDM) incompatibilities is thought to represent a key step in the formation of separate species. They are incompatible alleles that have evolved in separate populations and are exposed in hybrid offspring as hybrid sterility or lethality. In this study, we reveal a previously unconsidered mechanism promoting the formation of BDM incompatibilities, meiotic drive. Theoretical studies have evaluated the role that meiotic drive, the phenomenon whereby selfish elements bias their transmission to progeny at ratios above 50:50, plays in speciation, and have mostly concluded that drive could not result in speciation on its own. Using the model fungus Neurospora, we demonstrate that the large meiotic drive haplotypes, Sk-2 and Sk-3, contain putative sexual incompatibilities. Our experiments revealed that although crosses between Neurospora intermedia and Neurospora metzenbergii produce viable progeny at appreciable rates, when strains of N. intermedia carry Sk-2 or Sk-3 the proportion of viable progeny drops substantially. Additionally, it appears that Sk-2 and Sk-3 have accumulated different incompatibility phenotypes, consistent with their independent evolutionary history. This research illustrates how meiotic drive can contribute to reproductive isolation between populations, and thereby speciation.

A possible genomic footprint of polygenic adaptation on population divergence in seed beetles?

Efforts to unravel the genomic basis of incipient speciation are hampered by a mismatch between our toolkit and our understanding of the ecology and genetics of adaptation. While the former is focused on detecting selective sweeps involving few independently acting or linked speciation genes, the latter states that divergence typically occurs in polygenic traits under stabilizing selection. Here, we ask whether a role of stabilizing selection on polygenic traits in population divergence may be unveiled by using a phenotypically informed integrative approach, based on genome‐wide variation segregating in divergent populations. We compare three divergent populations of seed beetles (Callosobruchus maculatus) where previous work has demonstrated a prominent role for stabilizing selection on, and population divergence in, key life history traits that reflect rate‐dependent metabolic processes. We derive and assess predictions regarding the expected pattern of covariation between genetic variation segregating within populations and genetic differentiation between populations. Population differentiation was considerable (mean F_ST = 0.23–0.26) and was primarily built by genes showing high selective constraints and an imbalance in inferred selection in different populations (positive Tajima's D_NS in one and negative in one), and this set of genes was enriched with genes with a metabolic function. Repeatability of relative population differentiation was low at the level of individual genes but higher at the level of broad functional classes, again spotlighting metabolic genes. Absolute differentiation (d_XY) showed a very different general pattern at this scale of divergence, more consistent with an important role for genetic drift. Although our exploration is consistent with stabilizing selection on polygenic metabolic phenotypes as an important engine of genome‐wide relative population divergence and incipient speciation in our study system, we note that it is exceedingly difficult to firmly exclude other scenarios.

Genetic load: genomic estimates and applications in non-model animals

Genetic variation, which is generated by mutation, recombination and gene flow, can reduce the mean fitness of a population, both now and in the future. This 'genetic load' has been estimated in a wide range of animal taxa using various approaches. Advances in genome sequencing and computational techniques now enable us to estimate the genetic load in populations and individuals without direct fitness estimates. Here, we review the classic and contemporary literature of genetic load. We describe approaches to quantify the genetic load in whole-genome sequence data based on evolutionary conservation and annotations. We show that splitting the load into its two components - the realized load (or expressed load) and the masked load (or inbreeding load) - can improve our understanding of the population genetics of deleterious mutations.

System drift and speciation

Even if a species' phenotype does not change over evolutionary time, the underlying mechanism may change, as distinct molecular pathways can realize identical phenotypes. Here we use linear system theory to explore the consequences of this idea, describing how a gene network underlying a conserved phenotype evolves, as the genetic drift of small changes to these molecular pathways causes a population to explore the set of mechanisms with identical phenotypes. To do this, we model an organism's internal state as a linear system of differential equations for which the environment provides input and the phenotype is the output, in which context there exists an exact characterization of the set of all mechanisms that give the same input-output relationship. This characterization implies that selectively neutral directions in genotype space should be common and that the evolutionary exploration of these distinct but equivalent mechanisms can lead to the reproductive incompatibility of independently evolving populations. This evolutionary exploration, or system drift, is expected to proceed at a rate proportional to the amount of intrapopulation genetic variation divided by the effective population size ( Ne$N_e$ ). At biologically reasonable parameter values this could lead to substantial interpopulation incompatibility, and thus speciation, on a time scale of Ne$N_e$ generations. This model also naturally predicts Haldane's rule, thus providing a concrete explanation of why heterogametic hybrids tend to be disrupted more often than homogametes during the early stages of speciation.

The genomic consequences of hybridization

In the past decade, advances in genome sequencing have allowed researchers to uncover the history of hybridization in diverse groups of species, including our own. Although the field has made impressive progress in documenting the extent of natural hybridization, both historical and recent, there are still many unanswered questions about its genetic and evolutionary consequences. Recent work has suggested that the outcomes of hybridization in the genome may be in part predictable, but many open questions about the nature of selection on hybrids and the biological variables that shape such selection have hampered progress in this area. We synthesize what is known about the mechanisms that drive changes in ancestry in the genome after hybridization, highlight major unresolved questions, and discuss their implications for the predictability of genome evolution after hybridization.

Multi-locus interactions and the build-up of reproductive isolation

All genes interact with other genes, and their additive effects and epistatic interactions affect an organism's phenotype and fitness. Recent theoretical and empirical work has advanced our understanding of the role of multi-locus interactions in speciation. However, relating different models to one another and to empirical observations is challenging. This review focuses on multi-locus interactions that lead to reproductive isolation (RI) through reduced hybrid fitness. We first review theoretical approaches and show how recent work incorporating a mechanistic understanding of multi-locus interactions recapitulates earlier models, but also makes novel predictions concerning the build-up of RI. These include high variance in the build-up rate of RI among taxa, the emergence of strong incompatibilities producing localized barriers to introgression, and an effect of population size on the build-up of RI. We then review recent experimental approaches to detect multi-locus interactions underlying RI using genomic data. We argue that future studies would benefit from overlapping methods like ancestry disequilibrium scans, genome scans of differentiation and analyses of hybrid gene expression. Finally, we highlight a need for further overlap between theoretical and empirical work, and approaches that predict what kind of patterns multi-locus interactions resulting in incompatibilities will leave in genome-wide polymorphism data. This article is part of the theme issue 'Towards the completion of speciation: the evolution of reproductive isolation beyond the first barriers'.

Dispersal Predicts Hybrid Zone Widths across Animal Diversity: Implications for Species Borders under Incomplete Reproductive Isolation

Hybrid zones occur as range boundaries for many animal taxa. One model for how hybrid zones form and stabilize is the tension zone model, a version of which predicts that hybrid zone widths are determined by a balance between random dispersal into hybrid zones and selection against hybrids. Here, we examine whether random dispersal and proxies for selection against hybrids (genetic distances between hybridizing pairs) can explain variation in hybrid zone widths across 131 hybridizing pairs of animals. We show that these factors alone can explain ∼40% of the variation in zone width among animal hybrid zones, with dispersal explaining far more of the variation than genetic distances. Patterns within clades were idiosyncratic. Genetic distances predicted hybrid zone widths particularly well for reptiles, while this relationship was opposite tension zone predictions in birds. Last, the data suggest that dispersal and molecular divergence set lower bounds on hybrid zone widths in animals, indicating that there are geographic restrictions on hybrid zone formation. Overall, our analyses reinforce the fundamental importance of dispersal in hybrid zone formation and more generally in the ecology of range boundaries.

Geography is essential for reproductive isolation between florally diversified morning glory species from Amazon canga savannahs

The variety, relative importance and eco-evolutionary stability of reproductive barriers are critical to understanding the processes of speciation and species persistence. Here we evaluated the strength of the biotic prezygotic and postzygotic isolation barriers between closely related morning glory species from Amazon canga savannahs. The flower geometry and flower visitor assemblage analyses supported pollination by the bees in lavender-flowered Ipomoea marabaensis and recruitment of hummingbirds as pollinators in red-flowered Ipomoea cavalcantei. Nevertheless, native bee species and alien honeybees foraged on flowers of both species. Real-time interspecific hybridization underscored functionality of the overlap in flower visitor assemblages, questioning the strength of prezygotic isolation underpinned by diversification in flower colour and geometry. Interspecific hybrids were fertile and produced offspring in nature. No significant asymmetry in interspecific hybridization and hybrid incompatibilities among offspring were found, indicating weak postmating and postzygotic isolation. The results suggested that despite floral diversification, the insular-type geographic isolation remains a major barrier to gene flow. Findings set a framework for the future analysis of contemporary evolution of plant-pollinator networks at the population, community, and ecosystem levels in tropical ecosystems that are known to be distinct from the more familiar temperate climate models.

Limited intrinsic postzygotic reproductive isolation despite chromosomal rearrangements between closely related sympatric species of small ermine moths (Lepidoptera: Yponomeutidae)

In evolutionarily young species and sympatric host races of phytophagous insects, postzygotic incompatibility is often not yet fully developed, but reduced fitness of hybrids is thought to facilitate further divergence. However, empirical evidence supporting this hypothesis is limited. To assess the role of reduced hybrid fitness, we studied meiosis and fertility in hybrids of two closely related small ermine moths, Yponomeuta padella and Yponomeuta cagnagella, and determined the extent of intrinsic postzygotic reproductive isolation. We found extensive rearrangements between the karyotypes of the two species and irregularities in meiotic chromosome pairing in their hybrids. The fertility of reciprocal F1 and, surprisingly, also of backcrosses with both parental species was not significantly decreased compared with intraspecific offspring. The results indicate that intrinsic postzygotic reproductive isolation between these closely related species is limited. We conclude that the observed chromosomal rearrangements are probably not the result of an accumulation of postzygotic incompatibilities preventing hybridization. Alternative explanations, such as adaptation to new host plants, are discussed.

The Effects of Epistasis and Pleiotropy on Genome-Wide Scans for Adaptive Outlier Loci

With the advent of next-generation sequencing approaches, the search for individual loci underlying local adaptation has become a major enterprise in evolutionary biology. One promising method to identify such loci is to examine genome-wide patterns of differentiation, using an FST-outlier approach. The effects of pleiotropy and epistasis on this approach are not yet known. Here, we model 2 populations of a sexually reproducing, diploid organism with 2 quantitative traits, one of which is involved in local adaptation. We consider genetic architectures with and without pleiotropy and epistasis. We also model neutral marker loci on an explicit genetic map as the 2 populations diverge and apply FST outlier approaches to determine the extent to which quantitative trait loci (QTL) are detectable. Our results show, under a wide range of conditions, that only a small number of QTL are typically responsible for most of the trait divergence between populations, even when inheritance is highly polygenic. We find that the loci making the largest contributions to trait divergence tend to be detectable outliers. These loci also make the largest contributions to within-population genetic variance. The addition of pleiotropy reduces the extent to which quantitative traits can evolve independently but does not reduce the efficacy of outlier scans. The addition of epistasis, however, reduces the mean FST values for causative QTL, making these loci more difficult, but not impossible, to detect in outlier scans.

Speciation genes are more likely to have discordant gene trees

Speciation genes are responsible for reproductive isolation between species. By directly participating in the process of speciation, the genealogies of isolating loci have been thought to more faithfully represent species trees. The unique properties of speciation genes may provide valuable evolutionary insights and help determine the true history of species divergence. Here, we formally analyze whether genealogies from loci participating in Dobzhansky-Muller (DM) incompatibilities are more likely to be concordant with the species tree under incomplete lineage sorting (ILS). Individual loci differ stochastically from the true history of divergence with a predictable frequency due to ILS, and these expectations-combined with the DM model of intrinsic reproductive isolation from epistatic interactions-can be used to examine the probability of concordance at isolating loci. Contrary to existing verbal models, we find that reproductively isolating loci that follow the DM model are often more likely to have discordant gene trees. These results are dependent on the pattern of isolation observed between three species, the time between speciation events, and the time since the last speciation event. Results supporting a higher probability of discordance are found for both derived-derived and derived-ancestral DM pairs, and regardless of whether incompatibilities are allowed or prohibited from segregating in the same population. Our overall results suggest that DM loci are unlikely to be especially useful for reconstructing species relationships, even in the presence of gene flow between incipient species, and may in fact be positively misleading.

Evolvability and robustness: A paradox restored

Evolvability and robustness are crucial for the origin and maintenance of complex organisms, but may not be simultaneously achievable as robust traits are also hard to change. Andreas Wagner has proposed a solution to this paradox by arguing that the many-to-few aspect of genotype-phenotype maps creates neutral networks of genotypes coding for the same phenotype. Phenotypes with large networks are genetically robust, but they may also have more neighboring phenotypes and thus higher evolvability. In this paper, we explore the generality of this idea by sampling large numbers of random genotype-phenotype maps for Boolean genotypes and phenotypes. We show that there is indeed a preponderance of positive correlations between the evolvability and robustness of phenotypes within a genotype-phenotype map, but also that there are negative correlations between average evolvability and robustness across maps. We interpret this as predicting a positive correlation across the phenotypic states of a character, but a negative correlation across characters. We also argue that evolvability and robustness tend to be negatively correlated when phenotypes are measured on ordinal or higher scale types. We conclude that Wagner's conjecture of a positive relation between robustness and evolvability is based on strict and somewhat unrealistic biological assumptions.

Signatures of Dobzhansky-Muller Incompatibilities in the Genomes of Recombinant Inbred Lines

In the construction of recombinant inbred lines (RILs) from two divergent inbred parents certain genotype (or epigenotype) combinations may be functionally "incompatible" when brought together in the genomes of the progeny, thus resulting in sterility or lower fertility. Natural selection against these epistatic combinations during inbreeding can change haplotype frequencies and distort linkage disequilibrium (LD) relations between loci on the same or on different chromosomes. These LD distortions have received increased experimental attention, because they point to genomic regions that may drive a Dobzhansky-Muller type of reproductive isolation and, ultimately, speciation in the wild. Here we study the selection signatures of two-locus epistatic incompatibility models and quantify their impact on the genetic composition of the genomes of two-way RILs obtained by selfing. We also consider the biases introduced by breeders when trying to counteract the loss of lines by selectively propagating only viable seeds. Building on our theoretical results, we develop model-based maximum-likelihood (ML) tests that can be applied to multilocus RIL genotype data to infer the precise mode of incompatibility as well as the relative fitness of incompatible loci. We illustrate this ML approach in the context of two published Arabidopsis thaliana RIL panels. Our work lays the theoretical foundation for studying more complex systems such as RILs obtained by sibling mating and/or from multiparental crosses.

Long distance linkage disequilibrium and limited hybridization suggest cryptic speciation in atlantic cod

Hybrid zones provide unprecedented opportunity for the study of the evolution of reproductive isolation, and the extent of hybridization across individuals and genomes can illuminate the degree of isolation. We examine patterns of interchromosomal linkage disequilibrium (ILD) and the presence of hybridization in Atlantic cod, Gadus morhua, in previously identified hybrid zones in the North Atlantic. Here, previously identified clinal loci were mapped to the cod genome with most (∼70%) occurring in or associated with (<5 kb) coding regions representing a diverse array of possible functions and pathways. Despite the observation that clinal loci were distributed across three linkage groups, elevated ILD was observed among all groups of clinal loci and strongest in comparisons involving a region of low recombination along linkage group 7. Evidence of ILD supports a hypothesis of divergence hitchhiking transitioning to genome hitchhiking consistent with reproductive isolation. This hypothesis is supported by Bayesian characterization of hybrid classes present and we find evidence of common F1 hybrids in several regions consistent with frequent interbreeding, yet little evidence of F2 or backcrossed individuals. This work suggests that significant barriers to hybridization and introgression exist among these co-occurring groups of cod either through strong selection against hybrid individuals, or genetic incompatibility and intrinsic barriers to hybridization. In either case, the presence of strong clinal trends, and little gene flow despite extensive hybridization supports a hypothesis of reproductive isolation and cryptic speciation in Atlantic cod. Further work is required to test the degree and nature of reproductive isolation in this species.

Hybrid incompatibility arises in a sequence-based bioenergetic model of transcription factor binding

Postzygotic isolation between incipient species results from the accumulation of incompatibilities that arise as a consequence of genetic divergence. When phenotypes are determined by regulatory interactions, hybrid incompatibility can evolve even as a consequence of parallel adaptation in parental populations because interacting genes can produce the same phenotype through incompatible allelic combinations. We explore the evolutionary conditions that promote and constrain hybrid incompatibility in regulatory networks using a bioenergetic model (combining thermodynamics and kinetics) of transcriptional regulation, considering the bioenergetic basis of molecular interactions between transcription factors (TFs) and their binding sites. The bioenergetic parameters consider the free energy of formation of the bond between the TF and its binding site and the availability of TFs in the intracellular environment. Together these determine fractional occupancy of the TF on the promoter site, the degree of subsequent gene expression and in diploids, and the degree of dominance among allelic interactions. This results in a sigmoid genotype-phenotype map and fitness landscape, with the details of the shape determining the degree of bioenergetic evolutionary constraint on hybrid incompatibility. Using individual-based simulations, we subjected two allopatric populations to parallel directional or stabilizing selection. Misregulation of hybrid gene expression occurred under either type of selection, although it evolved faster under directional selection. Under directional selection, the extent of hybrid incompatibility increased with the slope of the genotype-phenotype map near the derived parental expression level. Under stabilizing selection, hybrid incompatibility arose from compensatory mutations and was greater when the bioenergetic properties of the interaction caused the space of nearly neutral genotypes around the stable expression level to be wide. F2's showed higher hybrid incompatibility than F1's to the extent that the bioenergetic properties favored dominant regulatory interactions. The present model is a mechanistically explicit case of the Bateson-Dobzhansky-Muller model, connecting environmental selective pressure to hybrid incompatibility through the molecular mechanism of regulatory divergence. The bioenergetic parameters that determine expression represent measurable properties of transcriptional regulation, providing a predictive framework for empirical studies of how phenotypic evolution results in epistatic incompatibility at the molecular level in hybrids.

Epistasis and natural selection shape the mutational architecture of complex traits

The evolutionary trajectories of complex traits are constrained by levels of genetic variation as well as genetic correlations among traits. As the ultimate source of all genetic variation is mutation, the distribution of mutations entering populations profoundly affects standing variation and genetic correlations. Here we use an individual-based simulation model to investigate how natural selection and gene interactions (that is, epistasis) shape the evolution of mutational processes affecting complex traits. We find that the presence of epistasis allows natural selection to mould the distribution of mutations, such that mutational effects align with the selection surface. Consequently, novel mutations tend to be more compatible with the current forces of selection acting on the population. These results suggest that in many cases mutational effects should be seen as an outcome of natural selection rather than as an unbiased source of genetic variation that is independent of other evolutionary processes.

Cryptic genetic variation: evolution's hidden substrate

Cryptic genetic variation (CGV) is invisible under normal conditions, but it can fuel evolution when circumstances change. In theory, CGV can represent a massive cache of adaptive potential or a pool of deleterious alleles that are in need of constant suppression. CGV emerges from both neutral and selective processes, and it may inform about how human populations respond to change. CGV facilitates adaptation in experimental settings, but does it have an important role in the real world? Here, we review the empirical support for widespread CGV in natural populations, including its potential role in emerging human diseases and the growing evidence of its contribution to evolution.

The evolution of genetic architectures underlying quantitative traits

In the classic view introduced by R. A. Fisher, a quantitative trait is encoded by many loci with small, additive effects. Recent advances in quantitative trait loci mapping have begun to elucidate the genetic architectures underlying vast numbers of phenotypes across diverse taxa, producing observations that sometimes contrast with Fisher's blueprint. Despite these considerable empirical efforts to map the genetic determinants of traits, it remains poorly understood how the genetic architecture of a trait should evolve, or how it depends on the selection pressures on the trait. Here, we develop a simple, population-genetic model for the evolution of genetic architectures. Our model predicts that traits under moderate selection should be encoded by many loci with highly variable effects, whereas traits under either weak or strong selection should be encoded by relatively few loci. We compare these theoretical predictions with qualitative trends in the genetics of human traits, and with systematic data on the genetics of gene expression levels in yeast. Our analysis provides an evolutionary explanation for broad empirical patterns in the genetic basis for traits, and it introduces a single framework that unifies the diversity of observed genetic architectures, ranging from Mendelian to Fisherian.

Why epistasis is important for selection and adaptation

Organisms are built from thousands of genes that interact in complex ways. Still, the mathematical theory of evolution is dominated by a gene-by-gene perspective in which genes are assumed to have the same effects regardless of genetic background. Gene interaction, or epistasis, plays a role in some theoretical developments such as the evolution of recombination, reproductive isolation, and canalization, but is strikingly missing from our standard accounts of phenotypic adaptation. This absence is most puzzling within the field of quantitative genetics, which, despite its polygenic perspective and elaborate statistical representation of epistasis, has not found a single important role for gene interaction in evolution. To the contrary, there is a widespread consensus that epistasis is evolutionary inert, and that all we need to know to predict evolutionary dynamics is the additive component of the genetic variance. This view may have roots in convenience, but also in theoretical results showing that the response to selection derived from epistatic variance components is not permanent and will decay when selection is relaxed. I show that these results are tied to a conceptual confusion, and are misleading as general statements about the significance of epistasis for the selection response and adaptation.

The evolution of hybrid incompatibilities along a phylogeny

The Dobzhansky-Muller model of speciation posits that defects in hybrids between species are the result of negative epistatic interactions between alleles that arose in independent genetic backgrounds. Tests of one important prediction from this model, that incompatibilities "snowball," have relied on comparisons of the number of incompatibilities between closely related pairs of species separated by different divergence times. How incompatibilities accumulate along phylogenies, however, remains poorly understood. We extend the Dobzhansky-Muller model to multispecies clades to describe the mathematical relationship between tree topology and the number of shared incompatibilities among related pairs of species. We use these results to develop a statistical test that distinguishes between the snowball and alternative incompatibility accumulation models, including nonepistatic and multilocus incompatibility models, in a phylogenetic context. We further demonstrate that patterns of incompatibility sharing across species pairs can be used to estimate the relative frequencies of different types of incompatibilities, including derived-derived versus derived-ancestral incompatibilities. Our results and statistical methods should motivate comparative genetic mapping of hybrid incompatibilities to evaluate competing models of speciation.

Current applications of models of genetic effects with interactions across the genome

Models of genetic effects integrate the action of genes, regulatory regions and interactions among alleles across the genome. Such theoretical frameworks are critical for applied studies in at least two ways. First, discovering genetic networks with specific effects underlying traits in populations requires the development of models that implement those effects as parameters-adjusting the implementation of epistasis parameters in genetic models has for instance been a requirement for properly testing for epistasis in gene-mapping studies. Second, studying the properties and implications of models of genetic effects that involve complex genetic networks has proven to be valuable, whether those networks have been revealed for particular organisms or inferred to be of interest from theoretical works and simulations. Here I review the current state of development and recent applications of models of genetic effects. I focus on general models aiming to depict complex genotype-to-phenotype maps and on applications of them to networks of interacting loci.

A stochastic model for the development of Bateson-Dobzhansky-Muller incompatibilities that incorporates protein interaction networks

Speciation is characterized by the development of reproductive isolating barriers between diverging groups. Intrinsic post-zygotic barriers of the type envisioned by Bateson, Dobzhansky, and Muller are deleterious epistatic interactions among loci that reduce hybrid fitness, leading to reproductive isolation. The first formal population genetic model of the development of these barriers was published by Orr in 1995, and here we develop a more general model of this process by incorporating finite protein-protein interaction networks, which reduce the probability of deleterious interactions in vivo. Our model shows that the development of deleterious interactions is limited by the density of the protein-protein interaction network. We have confirmed our analytical predictions of the number of possible interactions given the number of allele substitutions by using simulations on the Saccharomyces cerevisiae protein-protein interaction network. These results allow us to define the rate at which deleterious interactions are expected to form, and hence the speciation rate, for any protein-protein interaction network.

Selection against accumulating mutations in niche-preference genes can drive speciation

Our current understanding of sympatric speciation is that it occurs primarily through disruptive selection on ecological genes driven by competition, followed by reproductive isolation through reinforcement-like selection against inferior intermediates/heterozygotes. Our evolutionary model of selection on resource recognition and preference traits suggests a new mechanism for sympatric speciation. We find speciation can occur in three phases. First a polymorphism of functionally different phenotypes is established through evolution of specialization. On the gene level, regulatory functions have evolved in which some alleles are conditionally switched off (i.e. are silent). These alleles accumulate harmful mutations that potentially may be expressed in offspring through recombination. Second mating associated with resource preference invades because harmful mutations in parents are not expressed in the offspring when mating assortatively, thereby dividing the population into two pre-zygotically isolated resource-specialist lineages. Third, silent alleles that evolved in phase one now accumulate deleterious mutations over the following generations in a Bateson-Dobzhansky-Muller fashion, establishing a post-zygotic barrier to hybridization.

What do we need to know about speciation?

Speciation has been a major focus of evolutionary biology research in recent years, with many important advances. However, some of the traditional organising principles of the subject area no longer provide a satisfactory framework, such as the classification of speciation mechanisms by geographical context into allopatric, parapatric and sympatry classes. Therefore, we have asked where speciation research should be directed in the coming years. Here, we present a distillation of questions about the mechanisms of speciation, the genetic basis of speciation and the relationship between speciation and diversity. Our list of topics is not exhaustive; rather we aim to promote discussion on research priorities and on the common themes that underlie disparate speciation processes.

Measurement and meaning in biology

Measurement--the assignment of numbers to attributes of the natural world--is central to all scientific inference. Measurement theory concerns the relationship between measurements and reality; its goal is ensuring that inferences about measurements reflect the underlying reality we intend to represent. The key principle of measurement theory is that theoretical context, the rationale for collecting measurements, is essential to defining appropriate measurements and interpreting their values. Theoretical context determines the scale type of measurements and which transformations of those measurements can be made without compromising their meaningfulness. Despite this central role, measurement theory is almost unknown in biology, and its principles are frequently violated. In this review, we present the basic ideas of measurement theory and show how it applies to theoretical as well as empirical work. We then consider examples of empirical and theoretical evolutionary studies whose meaningfulness have been compromised by violations of measurement-theoretic principles. Common errors include not paying attention to theoretical context, inappropriate transformations of data, and inadequate reporting of units, effect sizes, or estimation error. The frequency of such violations reveals the importance of raising awareness of measurement theory among biologists.

Genes versus phenotypes in the study of speciation

Despite persistent debate on the nature of species, the widespread adoption of Mayr's biological species concept has led to a heavy emphasis on the importance of reproductive isolation to the speciation process. Equating the origin of species with the evolution of reproductive isolation has become common practice in the study of speciation, coincident with an increasing focus on elucidating the specific genetic changes (i.e.-speciation genes) underlying intrinsic reproductive barriers between species. In contrast, some have recognized that reproductive isolation is usually a signature effect rather than a primary cause of speciation. Here we describe a research paradigm that shifts emphasis from effects to causes in order to resolve this apparent contradiction and galvanize the study of speciation. We identify major elements necessary for a balanced and comprehensive investigation of the origin of species and place the study of so-called "speciation genes" into its appropriate context. We emphasize the importance of characterizing diverging phenotypes, identifying relevant evolutionary forces acting on those phenotypes and their role in the causal origins of reduced gene flow between incipient species, and the nature of the genetic and phenotypic boundaries that results from such processes. This approach has the potential to unify the field of speciation research, by allowing us to make better "historical" predictions about the fate of diverging populations regardless of taxon.

Directionality of epistasis in a murine intercross population

Directional epistasis describes a situation in which epistasis consistently increases or decreases the effect of allele substitutions, thereby affecting the amount of additive genetic variance available for selection in a given direction. This study applies a recent parameterization of directionality of epistasis to empirical data. Data stems from a QTL mapping study on an intercross between inbred mouse (Mus musculus) strains LG/J and SM/J, originally selected for large and small body mass, respectively. Results show a negative average directionality of epistasis for body-composition traits, predicting a reduction in additive allelic effects and in the response to selection for increased size. Focusing on average modification of additive effect of single loci, we find a more complex picture, whereby the effects of some loci are enhanced consistently across backgrounds, while effects of other loci are decreased, potentially contributing to either enhancement or reduction of allelic effects when selection acts at single loci. We demonstrate and discuss how the interpretation of the overall measurement of directionality depends on the complexity of the genotype-phenotype map. The measure of directionality changes with the power of scale in a predictable way; however, its expected effect with respect to the modification of additive genetic effects remains constant.