Dynamics of hybrid incompatibility in gene networks in a constant environment

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.

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.

Meiotic drive, postzygotic isolation, and the Snowball Effect

As populations diverge, they accumulate incompatibilities which reduce gene flow and facilitate the formation of new species. Simple models suggest that the genes that cause Dobzhansky-Muller incompatibilities should accumulate at least as fast as the square of the number of substitutions between taxa, the so-called snowball effect. We show, however, that in the special- but possibly common- case in which hybrid sterility is due primarily to cryptic meiotic (gametic) drive, the number of genes that cause postzygotic isolation may increase nearly linearly with the number of substitutions between species.

Speciation and development

Understanding general principles about the origin of species remains one of the foundational challenges in evolutionary biology. The genomic divergence between groups of individuals can spawn hybrid inviability and hybrid sterility, which presents a tantalizing developmental problem. Divergent developmental programs may yield either conserved or divergent phenotypes relative to ancestral traits, both of which can be responsible for reproductive isolation during the speciation process. The genetic mechanisms of developmental evolution involve cis- and trans-acting gene regulatory change, protein-protein interactions, genetic network structures, dosage, and epigenetic regulation, all of which also have roots in population genetic and molecular evolutionary processes. Toward the goal of demystifying Darwin's "mystery of mysteries," this review integrates microevolutionary concepts of genetic change with principles of organismal development, establishing explicit links between population genetic process and developmental mechanisms in the production of macroevolutionary pattern. This integration aims to establish a more unified view of speciation that binds process and mechanism.

Environment-dependent epistasis increases phenotypic diversity in gene regulatory networks

Mutations to gene regulatory networks can be maladaptive or a source of evolutionary novelty. Epistasis confounds our understanding of how mutations affect the expression patterns of gene regulatory networks, a challenge exacerbated by the dependence of epistasis on the environment. We used the toolkit of synthetic biology to systematically assay the effects of pairwise and triplet combinations of mutant genotypes on the expression pattern of a gene regulatory network expressed in Escherichia coli that interprets an inducer gradient across a spatial domain. We uncovered a preponderance of epistasis that can switch in magnitude and sign across the inducer gradient to produce a greater diversity of expression pattern phenotypes than would be possible in the absence of such environment-dependent epistasis. We discuss our findings in the context of the evolution of hybrid incompatibilities and evolutionary novelties.

The ensemble of gene regulatory networks at mutation-selection balance

The evolution of diverse phenotypes both involves and is constrained by molecular interaction networks. When these networks influence patterns of expression, we refer to them as gene regulatory networks (GRNs). Here, we develop a model of GRN evolution analogous to work from quasi-species theory, which is itself essentially the mutation-selection balance model from classical population genetics extended to multiple loci. With this GRN model, we prove that-across a broad spectrum of selection pressures-the dynamics converge to a stationary distribution over GRNs. Next, we show from first principles how the frequency of GRNs at equilibrium is related to the topology of the genotype network, in particular, via a specific network centrality measure termed the eigenvector centrality. Finally, we determine the structural characteristics of GRNs that are favoured in response to a range of selective environments and mutational constraints. Our work connects GRN evolution to quasi-species theory-and thus to classical populations genetics-providing a mechanistic explanation for the observed distribution of GRNs evolving in response to various evolutionary forces, and shows how complex fitness landscapes can emerge from simple evolutionary rules.

Early effects of gene duplication on the robustness and phenotypic variability of gene regulatory networks

Background

Research on gene duplication is abundant and comes from a wide range of approaches, from high-throughput analyses and experimental evolution to bioinformatics and theoretical models. Notwithstanding, a consensus is still lacking regarding evolutionary mechanisms involved in evolution through gene duplication as well as the conditions that affect them. We argue that a better understanding of evolution through gene duplication requires considering explicitly that genes do not act in isolation. It demands studying how the perturbation that gene duplication implies percolates through the web of gene interactions. Due to evolution’s contingent nature, the paths that lead to the final fate of duplicates must depend strongly on the early stages of gene duplication, before gene copies have accumulated distinctive changes.

Methods

Here we use a widely-known model of gene regulatory networks to study how gene duplication affects network behavior in early stages. Such networks comprise sets of genes that cross-regulate. They organize gene activity creating the gene expression patterns that give cells their phenotypic properties. We focus on how duplication affects two evolutionarily relevant properties of gene regulatory networks: mitigation of the effect of new mutations and access to new phenotypic variants through mutation.

Results

Among other observations, we find that those networks that are better at maintaining the original phenotype after duplication are usually also better at buffering the effect of single interaction mutations and that duplication tends to enhance further this ability. Moreover, the effect of mutations after duplication depends on both the kind of mutation and genes involved in it. We also found that those phenotypes that had easier access through mutation before duplication had higher chances of remaining accessible through new mutations after duplication.

Conclusion

Our results support that gene duplication often mitigates the impact of new mutations and that this effect is not merely due to changes in the number of genes. The work that we put forward helps to identify conditions under which gene duplication may enhance evolvability and robustness to mutations.

Genomic patterns of divergence in the early and late steps of speciation of the deep-sea vent thermophilic worms of the genus Alvinella

Background

The transient and fragmented nature of the deep-sea hydrothermal environment made of ridge subduction, plate collision and the emergence of new rifts is currently acting to separate of vent populations, promoting local adaptation and contributing to bursts of speciation and species specialization. The tube-dwelling worms Alvinella pompejana called the Pompeii worm and its sister species A. caudata live syntopically on the hottest part of deep-sea hydrothermal chimneys along the East Pacific Rise. They are exposed to extreme thermal and chemical gradients, which vary greatly in space and time, and thus represent ideal candidates for understanding the evolutionary mechanisms at play in the vent fauna evolution.

Results

We explored genomic patterns of divergence in the early and late stages of speciation of these emblematic worms using transcriptome assemblies and the first draft genome to better understand the relative role of geographic isolation and habitat preference in their genome evolution. Analyses were conducted on allopatric populations of Alvinella pompejana (early stage of separation) and between A. pompejana and its syntopic species Alvinella caudata (late stage of speciation). We first identified divergent genomic regions and targets of selection as well as their position in the genome over collections of orthologous genes and, then, described the speciation dynamics by documenting the annotation of the most divergent and/or positively selected genes involved in the isolation process. Gene mapping clearly indicated that divergent genes associated with the early stage of speciation, although accounting for nearly 30% of genes, are highly scattered in the genome without any island of divergence and not involved in gamete recognition or mito-nuclear incompatibilities. By contrast, genomes of A. pompejana and A. caudata are clearly separated with nearly all genes (96%) exhibiting high divergence. This congealing effect however seems to be linked to habitat specialization and still allows positive selection on genes involved in gamete recognition, as a possible long-duration process of species reinforcement.

Conclusion

Our analyses highlight the non-negligible role of natural selection on both the early and late stages of speciation in the iconic thermophilic worms living on the walls of deep-sea hydrothermal chimneys. They shed light on the evolution of gene divergence during the process of speciation and species specialization over a very long period of time.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12862-022-02057-y.

Speciation and the developmental alarm clock

New species arise as the genomes of populations diverge. The developmental 'alarm clock' of speciation sounds off when sufficient divergence in genetic control of development leads hybrid individuals to infertility or inviability, the world awoken to the dawn of new species with intrinsic post-zygotic reproductive isolation. Some developmental stages will be more prone to hybrid dysfunction due to how molecular evolution interacts with the ontogenetic timing of gene expression. Considering the ontogeny of hybrid incompatibilities provides a profitable connection between 'evo-devo' and speciation genetics to better link macroevolutionary pattern, microevolutionary process, and molecular mechanisms. Here, we explore speciation alongside development, emphasizing their mutual dependence on genetic network features, fitness landscapes, and developmental system drift. We assess models for how ontogenetic timing of reproductive isolation can be predictable. Experiments and theory within this synthetic perspective can help identify new rules of speciation as well as rules in the molecular evolution of development.

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'.

Population structure promotes the evolution of costly sex in artificial gene networks

We build on previous observations that Hill-Robertson interference generates an advantage of sex that, in structured populations, can be large enough to explain the evolutionary maintenance of costly sex. We employed a gene network model that explicitly incorporates interactions between genes. Mutations in the gene networks have variable effects that depend on the genetic background in which they appear. Consequently, our simulations include two costs of sex-recombination and migration loads-that were missing from previous studies of the evolution of costly sex. Our results suggest a critical role for population structure that lies in its ability to align the long- and short-term advantages of sex. We show that the addition of population structure favored the evolution of sex by disproportionately decreasing the equilibrium mean fitness of asexual populations, primarily by increasing the strength of Muller's Ratchet. Population structure also increased the ability of the short-term advantage of sex to counter the primary limit to the evolution of sex in the gene network model-recombination load. On the other hand, highly structured populations experienced migration load in the form of Dobzhansky-Muller incompatibilities, decreasing the effective rate of migration between demes and, consequently, accelerating the accumulation of drift load in the sexual populations.

When Two Rights Make a Wrong: The Evolutionary Genetics of Plant Hybrid Incompatibilities

Hybrids between flowering plant species often exhibit reduced fitness, including sterility and inviability. Such hybrid incompatibilities create barriers to genetic exchange that can promote reproductive isolation between diverging populations and, ultimately, speciation. Additionally, hybrid breakdown opens a window into hidden molecular and evolutionary processes occurring within species. Here, we review recent work on the mechanisms and origins of hybrid incompatibility in flowering plants, including both diverse genic interactions and chromosomal incompatibilities. Conflict and coevolution among and within plant genomes contributes to the evolution of some well-characterized genic incompatibilities, but duplication and drift also play important roles. Inversions, while contributing to speciation by suppressing recombination, rarely cause underdominant sterility. Translocations cause severe F₁ sterility by disrupting meiosis in heterozygotes, making their fixation in outcrossing sister species a paradox. Evolutionary genomic analyses of both genic and chromosomal incompatibilities, in the context of population genetic theory, can explicitly test alternative scenarios for their origins.

A tipping point in parapatric speciation

More than two loci are involved in reproductive isolation in most cases of putative recent speciation. We study the speciation between two geographically isolated populations connected by infrequent migration, in which incompatibility is controlled by quantitative loci. Incompatibility genetic distance is defined as the fraction of compatibility controlling loci that are different between individuals. Speciation is established when genetic distance reaches a threshold level in spite of occasional migration and subsequent hybridization that reduce genetic distance. With stochastic analysis, we investigate how the time to speciation depends on the manner in which the magnitude of incompatibility increases with genetic distance. Results are: (1) The time to speciation is short if the migration rate is smaller than the mutation rate, or if intermediate levels of genetic distance cause mild incompatibility, making migrants less effective in reducing genetic distance. (2) Genetic distance may fluctuate around a positive quasi-equilibrium level for a long time, and suddenly show a quick passage to speciation when it goes beyond a "tipping point." Notably a gradual increase in incompatibility can result in a sudden and rapid formation of a new species. (3) Speciation becomes very slow if incompatibility is effective for individuals differing at only one locus. These findings provide testable predictions on reproductive traits controlled by specific incompatibility accumulation forms that facilitate the speciation process.

Spiraling Complexity: A Test of the Snowball Effect in a Computational Model of RNA Folding

Genetic incompatibilities can emerge as a byproduct of genetic divergence. According to Dobzhansky and Muller, an allele that fixes in one population may be incompatible with an allele at a different locus in another population when the two alleles are brought together in hybrids. Orr showed that the number of Dobzhansky-Muller incompatibilities (DMIs) should accumulate faster than linearly-i.e., snowball-as two lineages diverge. Several studies have attempted to test the snowball effect using data from natural populations. One limitation of these studies is that they have focused on predictions of the Orr model, but not on its underlying assumptions. Here, we use a computational model of RNA folding to test both predictions and assumptions of the Orr model. Two populations are allowed to evolve in allopatry on a holey fitness landscape. We find that the number of inviable introgressions (an indicator for the number of DMIs) snowballs, but does so more slowly than expected. We show that this pattern is explained, in part, by the fact that DMIs can disappear after they have arisen, contrary to the assumptions of the Orr model. This occurs because DMIs become progressively more complex (i.e., involve alleles at more loci) as a result of later substitutions. We also find that most DMIs involve >2 loci, i.e., they are complex. Reproductive isolation does not snowball because DMIs do not act independently of each other. We conclude that the RNA model supports the central prediction of the Orr model that the number of DMIs snowballs, but challenges other predictions, as well as some of its underlying assumptions.

Gene Regulation and Speciation

Understanding the genetic architecture of speciation is a major goal in evolutionary biology. Hybrid dysfunction is thought to arise most commonly through negative interactions between alleles at two or more loci. Divergence between interacting regulatory elements that affect gene expression (i.e., regulatory divergence) may be a common route for these negative interactions to arise. We review here how regulatory divergence between species can result in hybrid dysfunction, including recent theoretical support for this model. We then discuss the empirical evidence for regulatory divergence between species and evaluate evidence for misregulation as a source of hybrid dysfunction. Finally, we review unresolved questions in gene regulation as it pertains to speciation and point to areas that could benefit from future research.

Why and how genetic canalization evolves in gene regulatory networks

Background

Genetic canalization reflects the capacity of an organism’s phenotype to remain unchanged in spite of mutations. As selection on genetic canalization is weak and indirect, whether or not genetic canalization can reasonably evolve in complex genetic architectures is still an open question. In this paper, we use a quantitative model of gene regulatory network to describe the conditions in which substantial canalization is expected to emerge in a stable environment.

Results

Through an individual-based simulation framework, we confirmed that most parameters associated with the network topology (complexity and size of the network) have less influence than mutational parameters (rate and size of mutations) on the evolution of genetic canalization. We also established that selecting for extreme phenotypic optima (nil or full gene expression) leads to much higher canalization levels than selecting for intermediate expression levels. Overall, constrained networks evolve less canalization than networks in which some genes could evolve freely (i.e. without direct stabilizing selection pressure on gene expression).

Conclusions

Taken together, these results lead us to propose a two-fold mechanism involved in the evolution of genetic canalization in gene regulatory networks: the shrinkage of mutational target (useless genes are virtually removed from the network) and redundancy in gene regulation (so that some regulatory factors can be lost without affecting gene expression).

Electronic supplementary material

The online version of this article (doi:10.1186/s12862-016-0801-2) contains supplementary material, which is available to authorized users.

The Pace of Hybrid Incompatibility Evolution in House Mice

Hybrids between species are often sterile or inviable. This form of reproductive isolation is thought to evolve via the accumulation of mutations that interact to reduce fitness when combined in hybrids. Mathematical formulations of this "Dobzhansky-Muller model" predict an accelerating buildup of hybrid incompatibilities with divergence time (the "snowball effect"). Although the Dobzhansky-Muller model is widely accepted, the snowball effect has only been tested in two species groups. We evaluated evidence for the snowball effect in the evolution of hybrid male sterility among subspecies of house mice, a recently diverged group that shows partial reproductive isolation. We compared the history of subspecies divergence with patterns of quantitative trait loci (QTL) detected in F2 intercrosses between two pairs of subspecies (Mus musculus domesticus with M. m. musculus and M. m. domesticus with M. m. castaneus). We used a recently developed phylogenetic comparative method to statistically measure the fit of these data to the snowball prediction. To apply this method, QTL were partitioned as either shared or unshared in the two crosses. A heuristic partitioning based on the overlap of QTL confidence intervals produced unambiguous support for the snowball effect. An alternative approach combining data among crosses favored the snowball effect for the autosomes, but a linear accumulation of incompatibilities for the X chromosome. Reasoning that the X chromosome analyses are complicated by low mapping resolution, we conclude that hybrid male sterility loci have snowballed in house mice. Our study illustrates the power of comparative genetic mapping for understanding mechanisms of speciation.

Modeling the evolution of complex genetic systems: the gene network family tree

In 1994 and 1996, Andreas Wagner introduced a novel model in two papers addressing the evolution of genetic regulatory networks. This work, and a suite of papers that followed using similar models, helped integrate network thinking into biology and motivate research focused on the evolution of genetic networks. The Wagner network has its mathematical roots in the Ising model, a statistical physics model describing the activity of atoms on a lattice, and in neural networks. These models have given rise to two branches of applications, one in physics and biology and one in artificial intelligence and machine learning. Here, we review development along these branches, outline similarities and differences between biological models of genetic regulatory circuits and neural circuits models used in machine learning, and identify ways in which these models can provide novel insights into biological systems.

Genome-wide mapping in a house mouse hybrid zone reveals hybrid sterility loci and Dobzhansky-Muller interactions

Mapping hybrid defects in contact zones between incipient species can identify genomic regions contributing to reproductive isolation and reveal genetic mechanisms of speciation. The house mouse features a rare combination of sophisticated genetic tools and natural hybrid zones between subspecies. Male hybrids often show reduced fertility, a common reproductive barrier between incipient species. Laboratory crosses have identified sterility loci, but each encompasses hundreds of genes. We map genetic determinants of testis weight and testis gene expression using offspring of mice captured in a hybrid zone between M. musculus musculus and M. m. domesticus. Many generations of admixture enables high-resolution mapping of loci contributing to these sterility-related phenotypes. We identify complex interactions among sterility loci, suggesting multiple, non-independent genetic incompatibilities contribute to barriers to gene flow in the hybrid zone.

Hybrid incompatibility despite pleiotropic constraint in a sequence-based bioenergetic model of transcription factor binding

Hybrid incompatibility can result from gene misregulation produced by divergence in trans-acting regulatory factors and their cis-regulatory targets. However, change in trans-acting factors may be constrained by pleiotropy, which would in turn limit the evolution of incompatibility. We employed a mechanistically explicit bioenergetic model of gene expression wherein parameter combinations (number of transcription factor molecules, energetic properties of binding to the regulatory site, and genomic background size) determine the shape of the genotype-phenotype (G-P) map, and interacting allelic variants of mutable cis and trans sites determine the phenotype along that map. Misregulation occurs when the phenotype differs from its optimal value. We simulated a pleiotropic regulatory pathway involving a positively selected and a conserved trait regulated by a shared transcription factor (TF), with two populations evolving in parallel. Pleiotropic constraints shifted evolution in the positively selected trait to its cis-regulatory locus. We nevertheless found that the TF genotypes often evolved, accompanied by compensatory evolution in the conserved trait, and both traits contributed to hybrid misregulation. Compensatory evolution resulted in "developmental system drift," whereby the regulatory basis of the conserved phenotype changed although the phenotype itself did not. Pleiotropic constraints became stronger and in some cases prohibitive when the bioenergetic properties of the molecular interaction produced a G-P map that was too steep. Likewise, compensatory evolution slowed and hybrid misregulation was not evident when the G-P map was too shallow. A broad pleiotropic "sweet spot" nevertheless existed where evolutionary constraints were moderate to weak, permitting substantial hybrid misregulation in both traits. None of these pleiotropic constraints manifested when the TF contained nonrecombining domains independently regulating the respective traits.

Interspecific tests of allelism reveal the evolutionary timing and pattern of accumulation of reproductive isolation mutations

Despite extensive theory, little is known about the empirical accumulation and evolutionary timing of mutations that contribute to speciation. Here we combined QTL (Quantitative Trait Loci) analyses of reproductive isolation, with information on species evolutionary relationships, to reconstruct the order and timing of mutations contributing to reproductive isolation between three plant (Solanum) species. To evaluate whether reproductive isolation QTL that appear to coincide in more than one species pair are homologous, we used cross-specific tests of allelism and found evidence for both homologous and lineage-specific (non-homologous) alleles at these co-localized loci. These data, along with isolation QTL unique to single species pairs, indicate that >85% of isolation-causing mutations arose later in the history of divergence between species. Phylogenetically explicit analyses of these data support non-linear models of accumulation of hybrid incompatibility, although the specific best-fit model differs between seed (pairwise interactions) and pollen (multi-locus interactions) sterility traits. Our findings corroborate theory that predicts an acceleration ('snowballing') in the accumulation of isolation loci as lineages progressively diverge, and suggest different underlying genetic bases for pollen versus seed sterility. Pollen sterility in particular appears to be due to complex genetic interactions, and we show this is consistent with a snowball model where later arising mutations are more likely to be involved in pairwise or multi-locus interactions that specifically involve ancestral alleles, compared to earlier arising mutations.

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.

Genomic networks of hybrid sterility

Hybrid dysfunction, a common feature of reproductive barriers between species, is often caused by negative epistasis between loci ("Dobzhansky-Muller incompatibilities"). The nature and complexity of hybrid incompatibilities remain poorly understood because identifying interacting loci that affect complex phenotypes is difficult. With subspecies in the early stages of speciation, an array of genetic tools, and detailed knowledge of reproductive biology, house mice (Mus musculus) provide a model system for dissecting hybrid incompatibilities. Male hybrids between M. musculus subspecies often show reduced fertility. Previous studies identified loci and several X chromosome-autosome interactions that contribute to sterility. To characterize the genetic basis of hybrid sterility in detail, we used a systems genetics approach, integrating mapping of gene expression traits with sterility phenotypes and QTL. We measured genome-wide testis expression in 305 male F2s from a cross between wild-derived inbred strains of M. musculus musculus and M. m. domesticus. We identified several thousand cis- and trans-acting QTL contributing to expression variation (eQTL). Many trans eQTL cluster into eleven 'hotspots,' seven of which co-localize with QTL for sterility phenotypes identified in the cross. The number and clustering of trans eQTL-but not cis eQTL-were substantially lower when mapping was restricted to a 'fertile' subset of mice, providing evidence that trans eQTL hotspots are related to sterility. Functional annotation of transcripts with eQTL provides insights into the biological processes disrupted by sterility loci and guides prioritization of candidate genes. Using a conditional mapping approach, we identified eQTL dependent on interactions between loci, revealing a complex system of epistasis. Our results illuminate established patterns, including the role of the X chromosome in hybrid sterility. The integrated mapping approach we employed is applicable in a broad range of organisms and we advocate for widespread adoption of a network-centered approach in speciation genetics.

Modelling of genetic interactions improves prediction of hybrid patterns--a case study in domestic fowl

A major challenge in complex trait genetics is to unravel how multiple loci and environmental factors together cause phenotypic diversity. Both first (F(1)) and second (F(2)) generation hybrids often display phenotypes that deviate from what is expected under intermediate inheritance. We have here studied two chicken F(2) populations generated by crossing divergent chicken lines to assess how epistatic loci, identified in earlier quantitative trait locus (QTL) studies, contribute to hybrid deviations from the mid-parent phenotype. Empirical evidence suggests that the average phenotypes of the intercross birds tend to be lower than the midpoint between the parental means in both crosses. Our results confirm that epistatic interactions, despite a relatively small contribution to the phenotypic variance, play an important role in the deviation of hybrid phenotypes from the mid-parent values (i.e. multi-locus hybrid genotypes lead to lower rather than higher body weights). To a lesser extent, dominance also appears to contribute to the mid-parent deviation, at least in one of the crosses. This observation coincides with the hypothesis that hybridization tends to break up co-adapted gene complexes, i.e. generate Bateson-Dobzhansky-Muller incompatibilities.

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.

Female mating preferences determine system-level evolution in a gene network model

Environmental patterns of directional, stabilizing and fluctuating selection can influence the evolution of system-level properties like evolvability and mutational robustness. Intersexual selection produces strong phenotypic selection and these dynamics may also affect the response to mutation and the potential for future adaptation. In order to to assess the influence of mating preferences on these evolutionary properties, I modeled a male trait and female preference determined by separate gene regulatory networks. I studied three sexual selection scenarios: sexual conflict, a Gaussian model of the Fisher process described in Lande (in Proc Natl Acad Sci 78(6):3721-3725, 1981) and a good genes model in which the male trait signalled his mutational condition. I measured the effects these mating preferences had on the potential for traits and preferences to evolve towards new states, and mutational robustness of both the phenotype and the individual's overall viability. All types of sexual selection increased male phenotypic robustness relative to a randomly mating population. The Fisher model also reduced male evolvability and mutational robustness for viability. Under good genes sexual selection, males evolved an increased mutational robustness for viability. Females choosing their mates is a scenario that is sufficient to create selective forces that impact genetic evolution and shape the evolutionary response to mutation and environmental selection. These dynamics will inevitably develop in any population where sexual selection is operating, and affect the potential for future adaptation.

Most networks in Wagner's model are cycling

In this paper we study a model of gene networks introduced by Andreas Wagner in the 1990s that has been used extensively to study the evolution of mutational robustness. We investigate a range of model features and parameters and evaluate the extent to which they influence the probability that a random gene network will produce a fixed point steady state expression pattern. There are many different types of models used in the literature, (discrete/continuous, sparse/dense, small/large network) and we attempt to put some order into this diversity, motivated by the fact that many properties are qualitatively the same in all the models. Our main result is that random networks in all models give rise to cyclic behavior more often than fixed points. And although periodic orbits seem to dominate network dynamics, they are usually considered unstable and not allowed to survive in previous evolutionary studies. Defining stability as the probability of fixed points, we show that the stability distribution of these networks is highly robust to changes in its parameters. We also find sparser networks to be more stable, which may help to explain why they seem to be favored by evolution. We have unified several disconnected previous studies of this class of models under the framework of stability, in a way that had not been systematically explored before.

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.

A new development: evolving concepts in leaf ontogeny

Elucidation of gene regulatory networks (GRNs) underlying aspects of leaf development in multiple model species has uncovered surprisingly plastic regulatory architecture. The meticulously mapped network interactions in one model species cannot now be assumed to map directly onto a different species. Despite these overall differences, however, many modules do appear to be almost universal. Extrapolating findings across different model systems will demand great care but promises to reveal a rich tapestry of themes in GRN architecture and regulation. The purpose of this review is to approach the field of leaf development from the perspectives of the evolution of developmental systems that orchestrate leaf development.

A history of phenotypic plasticity accelerates adaptation to a new environment

Can a history of phenotypic plasticity increase the rate of adaptation to a new environment? Theory suggests it can be through two different mechanisms. Phenotypically plastic organisms can adapt rapidly to new environments through genetic assimilation, or the fluctuating environments that result in phenotypic plasticity can produce evolvable genetic architectures. In this article, I studied a model of a gene regulatory network that determined a phenotypic character in one population selected for phenotypic plasticity and a second population in a constant environment. A history of phenotypic plasticity increased the rate of adaptation in a new environment, but the amount of this increase was dependent on the strength of selection in the original environment. Phenotypic variance in the original environment predicted the adaptive capacity of the trait within, but not between, plastic and nonplastic populations. These results have implications for invasive species and ecological studies of rapid adaptation.

Genetic variation and co-variation for fitness between intra-population and inter-population backgrounds in the red flour beetle, Tribolium castaneum

Hybrids from crosses between populations of the flour beetle, Tribolium castaneum, express varying degrees of inviability and morphological abnormalities. The proportion of allopatric population hybrids exhibiting these negative hybrid phenotypes varies widely, from 3% to 100%, depending upon the pair of populations crossed. We crossed three populations and measured two fitness components, fertility and adult offspring numbers from successful crosses, to determine how genes segregating within populations interact in inter-population hybrids to cause the negative phenotypes. With data from crosses of 40 sires from each of three populations to groups of five dams from their own and two divergent populations, we estimated the genetic variance and covariance for breeding value of fitness between the intra- and inter-population backgrounds and the sire × dam population interaction variance. The latter component of the variance in breeding values estimates the change in genic effects between backgrounds owing to epistasis. Interacting genes with a positive effect, prior to fixation, in the sympatric background but a negative effect in the hybrid background cause reproductive incompatibility in the Dobzhansky-Muller speciation model. Thus, the sire × dam population interaction provides a way to measure the progress towards speciation of genetically differentiating populations on a trait by trait basis using inter-population hybrids.

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

The Bateson-Dobzhansky-Muller model predicts that postzygotic isolation evolves due to the accumulation of incompatible epistatic interactions, but few studies have quantified the relationship between genetic architecture and patterns of reproductive divergence. We examined how the direction and magnitude of epistatic interactions in a polygenic trait under stabilizing selection influenced the evolution of hybrid incompatibilities. We found that populations evolving independently under stabilizing selection experienced suites of compensatory allelic changes that resulted in genetic divergence between populations despite the maintenance of a stable, high-fitness phenotype. A small number of loci were then incompatible with multiple alleles in the genetic background of the hybrid and the identity of these incompatibility loci changed over the evolution of the populations. For F(1) hybrids, reduced fitness evolved in a window of intermediate strengths of epistatic interactions, but F(2) and backcross hybrids evolved reduced fitness across weak and moderate strengths of epistasis due to segregation variance. Strong epistatic interactions constrained the allelic divergence of parental populations and prevented the development of reproductive isolation. Because many traits with varying genetic architectures must be under stabilizing selection, our results indicate that polygenetic drift is a plausible hypothesis for the evolution of postzygotic reproductive isolation.

Genetics and ecological speciation

Species originate frequently by natural selection. A general mechanism by which this occurs is ecological speciation, defined as the evolution of reproductive isolation between populations as a result of ecologically-based divergent natural selection. The alternative mechanism is mutation-order speciation in which populations fix different mutations as they adapt to similar selection pressures. Although numerous cases now indicate the importance of ecological speciation in nature, very little is known about the genetics of the process. Here, we summarize the genetics of premating and postzygotic isolation and the role of standing genetic variation in ecological speciation. We discuss the role of selection from standing genetic variation in threespine stickleback (Gasterosteus aculeatus), a complex of species whose ancestral marine form repeatedly colonized and adapted to freshwater environments. We propose that ecological speciation has occurred multiple times in parallel in this group via a "transporter" process in which selection in freshwater environments repeatedly acts on standing genetic variation that is maintained in marine populations by export of freshwater-adapted alleles from elsewhere in the range. Selection from standing genetic variation is likely to play a large role in ecological speciation, which may partly account for its rapidity.