Multilocus Population Genetics with Weak Epistasis. I. Equilibrium Properties of Two-Locus Two-Allele Models

Using perturbation techniques, I determine the equilibrium of two-locus two-allele models with overdominance and weak epistasis. To lowest order, the allele frequencies, the mean fitness and the covariance between heterokaryotic and homokaryotic flies arising in the Sturtevant experimental design are independent of the recombination rate, r. The disequilibrium varies as one divided by the recombination rate, in contrast to neutral models. Although the disequilibrium generated by weak epistasis is small, too small to be experimentally detected, it can be large enough to have biological importance.     

A Two-Locus System with Strong Epistasis Underlies Rapid Parasite-Mediated Evolution of Host Resistance

Parasites are a major evolutionary force, driving adaptive responses in host populations. Although the link between phenotypic response to parasite-mediated natural selection and the underlying genetic architecture often remains obscure, this link is crucial for understanding the evolution of resistance and predicting associated allele frequency changes in the population. To close this gap, we monitored the response to selection during epidemics of a virulent bacterial pathogen, Pasteuria ramosa, in a natural host population of Daphnia magna. Across two epidemics, we observed a strong increase in the proportion of resistant phenotypes as the epidemics progressed. Field and laboratory experiments confirmed that this increase in resistance was caused by selection from the local parasite. Using a genome-wide association study, we built a genetic model in which two genomic regions with dominance and epistasis control resistance polymorphism in the host. We verified this model by selfing host genotypes with different resistance phenotypes and scoring their F1 for segregation of resistance and associated genetic markers. Such epistatic effects with strong fitness consequences in host–parasite coevolution are believed to be crucial in the Red Queen model for the evolution of genetic recombination.     

Genetics of Reproductive Isolation in the Drosophila Simulans Clade: Complex Epistasis Underlying Hybrid Male Sterility

We have analyzed the sterility associated with introgressions of the distal one-fourth of the X chromosome from either Drosophila mauritiana or Drosophila sechellia into the genome of Drosophila simulans using a series of visible and DNA markers. Because in Drosophila hybrids, male sterility is usually complete and is often tightly linked with each of several markers used in crosses, a simple genetic basis has generally been assumed. In our low resolution mapping experiment, we were not able to reject the null hypothesis that a single gene, introgressed from either D. mauritiana or D. sechellia, is the cause of male sterility. High resolution mapping, however, reveals a much more complex picture. At least three distinct factors from D. mauritiana, or two from D. sechellia, were identified that need to be jointly present to confer full sterility. Each individual factor by itself is relatively ineffective in causing sterility, or even a partial spermatogenic defect. Moreover, there appear to be more sterility factors on comparable introgressions from D. mauritiana than from D. sechellia. On the basis of these observations, we propose a model which suggests that multilocus weak allele interactions are a very common cause of reproductive incompatibility between closely related species. We also present theoretical argument and empirical evidence against extrapolating the results of within-species analysis to interpret the genetic basis of species differences. The implications of this model on the theories of evolution of species differences and the attempt to understand the mechanisms of hybrid sterility/inviability at the molecular level are discussed.     

Models of Evolution of Reproductive Isolation

Mathematical models are presented for the evolution of postmating and premating reproductive isolation. In the case of postmating isolation it is assumed that hybrid sterility or inviability is caused by incompatibility of alleles at one or two loci, and evolution of reproductive isolation occurs by random fixation of different incompatibility alleles in different populations. Mutations are assumed to occur following either the stepwise mutation model or the infinite-allele model. Computer simulations by using It?'s stochastic differential equations have shown that in the model used the reproductive isolation mechanism evolves faster in small populations than in large populations when the mutation rate remains the same. In populations of a given size it evolves faster when the number of loci involved is large than when this is small. In general, however, evolution of isolation mechanisms is a very slow process, and it would take thousands to millions of generations if the mutation rate is of the order of 10(-5) per generation. Since gene substitution occurs as a stochastic process, the time required for the establishment of reproductive isolation has a large variance. Although the average time of evolution of isolation mechanisms is very long, substitution of incompatibility genes in a population occurs rather quickly once it starts. The intrapopulational fertility or viability is always very high. In the model of premating isolation it is assumed that mating preference or compatibility is determined by male- and female-limited characters, each of which is controlled by a single locus with multiple alleles, and mating occurs only when the male and female characters are compatible with each other. Computer simulations have shown that the dynamics of evolution of premating isolation mechanism is very similar to that of postmating isolation mechanism, and the mean and variance of the time required for establishment of premating isolation are very large. Theoretical predictions obtained from the present study about the speed of evolution of reproductive isolation are consistent with empirical data available from vertebrate organisms.     

Spatial Structure of Two-Locus Genotypes under Isolation by Distance

Extensive Monte Carlo simulations are conducted of spatial distributions of two-locus genotypes in large, continuous populations under isolation by distance models. The results show that substantial patches of double homozygotes are present in the spatial structures, even when loci are unlinked. The stochastic spread of identical two-locus genotypes largely outpowers the tendency for recombination to decouple patterns for separate loci. A spatial patch is a large area containing mostly one double homozygous genotype in a highly contiguous constellation. This patch structure is reflected in high positive spatial autocorrelations and large excesses of pairs, or joins, of identical double homozygotes at short-to-intermediate distances of spatial separation. Although spatial patches of double homozygotes are the dominant spatial feature, and the major contributors to overall high levels of autocorrelations among two-locus genotypes, other substantial features include areas of concentrations of identical genotypes heterozygous at only one locus. One implication of the patch structure is the presence of high levels of linkage disequilibrium, caused by isolation by distance even for unlinked loci, at some spatial scales; yet the disequilibrium in the large total populations is near 0. Thus linkage disequilibrium produced by isolation by distance is highly dependent on spatial scale. Another implication is that high degrees of spatial structuring and autocorrelations are produced for genetic variation controlling quantitative traits, at least when the number of loci is relatively small, under a wide range of situations, even if the trait is selectively neutral. The significance of the results to field studies is also examined.     

Sex Chromosome Translocations in the Evolution of Reproductive Isolation

Haldane's rule states that in organisms with differentiated sex chromosomes, hybrid sterility or inviability is generally expressed more frequently in the heterogametic sex. This observation has been variously explained as due to either genic or chromosomal imbalance. The fixation probabilities and mean times to fixation of sex-chromosome translocations of the type necessary to explain Haldane's rule on the basis of chromosomal imbalance have been estimated in small populations of Drosophila melanogaster. The fixation probability of an X chromosome carrying the long arm of the Y(X·Y^L) is approximately 30% greater than expected under the assumption of no selection. No fitness differences associated with the attached Y^L segment were detected. The fixation probability of a deficient Y chromosome is 300% greater than expected when the X chromosome contains the deleted portion of the Y. It is suggested that sex-chromosome translocations may play a role in the establishment of reproductive isolation.     

Maintenance of Genetic Variability under Strong Stabilizing Selection: A Two-Locus Model

We study a two locus model with additive contributions to the phenotype to explore the relationship between stabilizing selection and recombination. We show that if the double heterozygote has the optimum phenotype and the contributions of the loci to the trait are different, then any symmetric stabilizing selection fitness function can maintain genetic variability provided selection is sufficiently strong relative to linkage. We present results of a detailed analysis of the quadratic fitness function which show that selection need not be extremely strong relative to recombination for the polymorphic equilibria to be stable. At these polymorphic equilibria the mean value of the trait, in general, is not equal to the optimum phenotype, there exists a large level of negative linkage disequilibrium which ``hides' additive genetic variance, and different equilibria can be stable simultaneously. We analyze dependence of different characteristics of these equilibria on the location of optimum phenotype, on the difference in allelic effect, and on the strength of selection relative to recombination. Our overall result that stabilizing selection does not necessarily eliminate genetic variability is compatible with some experimental results where the lines subject to strong stabilizing selection did not have significant reductions in genetic variability.     

A Stochastic Model for Reproductive Isolation Under Asymmetrical Mating Preferences

More and more evidence shows that mating preference is a mechanism that may lead to a reproductive isolation event. In this paper, a haploid population living on two patches linked by migration is considered. Individuals are ecologically and demographically neutral on the space and differ only on a trait, a or A, affecting both mating success and migration rate. The special feature of this paper is to assume that the strengths of the mating preference and the migration depend on the trait carried. Indeed, patterns of mating preferences are generally asymmetrical between the subspecies of a population. I prove that mating preference interacting with frequency-dependent migration behavior can lead to a reproductive isolation. Then, I describe the time before reproductive isolation occurs. To reach this result, I use an original method to study the limiting dynamical system, analyzing first the system without migration and adding migration with a perturbation method. Finally, I study how the time before reproductive isolation is influenced by the parameters of migration and of mating preferences, highlighting that large migration rates tend to favor types with weak mating preferences.     

Antagonistic Coevolution Accelerates the Evolution of Reproductive Isolation in Tribolium castaneum

Abstract The evolution of reproductive isolation among populations is often the result of selective forces. Among those, parasites exert strong selection on host populations and can thus also potentially drive reproductive isolation. This hypothesis has yet to be explicitly tested, and here we set up a multigenerational coevolution experiment to explore this possibility. Five lines of Tribolium castaneum were allowed to coevolve with their natural parasite, Nosema whitei; five paired lines of identical origin were maintained in the absence of parasites. After 17 generations, we measured resistance within and reproductive isolation between all lines. Host lines from the coevolution treatment had considerably higher levels of resistance against N. whitei than their paired host lines, which were maintained in the absence of parasites. Reproductive isolation was greater in the coevolved selection regime and correlated with phenotypic differentiation in parasite resistance between coevolved host lines. This suggests the presence of a selection-driven genetic correlation between offspring number and resistance. Our results show that parasites can be a driving force in the evolution of reproductive isolation and thus potentially speciation.     

Reproductive Isolation and Morphogenetic Evolution in Drosophila Analyzed by Breakage of Ethological Barriers

This article reports the breaking of ethological barriers through the constitution of soma-germ line chimeras between species of the melanogaster subgroup of Drosophila, which are ethologically isolated. Female Drosophila yakuba and D. teissieri germ cells in a D. melanogaster ovary produced functional oocytes that, when fertilized by D. melanogaster sperm, gave rise to sterile yakuba-melanogaster and teissieri-melanogaster male and female hybrids. However, the erecta-melanogaster and orena-melanogaster hybrids were lethal, since female D. erecta and D. orena germ cells in a D. melanogaster ovary failed to form oocytes with the capacity to develop normally. This failure appears to be caused by an altered interaction between the melanogaster soma and the erecta and orena germ lines. Germ cells of D. teissieri and D. orena in a D. melanogaster testis produced motile sperm that was not stored in D. melanogaster females. This might be due to incompatibility between the teissieri and orena sperm and the melanogaster seminal fluid. A morphological analysis of the terminalia of yakuba-melanogaster and teissieri-melanogaster hybrids was performed. The effect on the terminalia of teissieri-melanogaster hybrids of a mutation in doublesex, a regulatory gene that controls the development of the terminalia, was also investigated.     

Evolution of Courtship Behaviour Patterns and Reproductive Isolation in the Desmognathus ochrophaeus Complex

The extent to which differences in courtship behaviour patterns act as mechanisms of reproductive isolation is critical to understanding both speciation and the evolution of these behaviour patterns. While numerous studies have investigated intraspecific and interspecific differences in courtship, fewer interpret results in a phylogenetic framework. We describe and analyse geographic variation in the courtship behaviour patterns of the Allegheny Dusky salamander ( Desmognathus ochrophaeus ). We then examine courtship among closely related species in the D. ochrophaeus complex in a phylogenetic context. We found that populations of D. ochrophaeus separated by extensive geographic distances show little variation in courtship behaviour patterns and are sexually compatible. This contrasts with significant levels of sexual isolation between D. ochrophaeus and other species in the complex. Mapping behaviour patterns onto a phylogeny that we generated from cytochrome b sequences indicates that two behaviour patterns present in the courtship sequence of other members in the complex have either been lost in D. ochrophaeus or gained independently in other species in the complex. Loss of these behaviour patterns may result in reproductive isolation between D. ochrophaeus and its sister taxon, D. orestes .     

Additive Variation Maintained under Stabilizing Selection: A Two-Locus Model of Pleiotropy for Two Quantitative Characters

A model with two diallelic loci controlling two additive quantitative characters is suggested. One of the loci has a similar effect on both characters, whereas the second locus has an antagonistic effect on two characters. Both characters experience direct stabilizing selection. The model yields a stable polymorphic state, with both characters maintaining genetic variation. The genetic correlation between the characters at the equilibrium is zero, in spite of the pleiotropic effects of the loci controlling them.     

Epistasis Creates Invariant Sites and Modulates the Rate of Molecular Evolution

Invariant sites are a common feature of amino acid sequence evolution. The presence of invariant sites is frequently attributed to the need to preserve function through site-specific conservation of amino acid residues. Amino acid substitution models without a provision for invariant sites often fit the data significantly worse than those that allow for an excess of invariant sites beyond those predicted by models that only incorporate rate variation among sites (e.g., a Gamma distribution). An alternative is epistasis between sites to preserve residue interactions that can create invariant sites. Through computer-simulated sequence evolution, we evaluated the relative effects of site-specific preferences and site-site couplings in the generation of invariant sites and the modulation of the rate of molecular evolution. In an analysis of ten major families of protein domains with diverse sequence and functional properties, we find that the negative selection imposed by epistasis creates many more invariant sites than site-specific residue preferences alone. Further, epistasis plays an increasingly larger role in creating invariant sites over longer evolutionary periods. Epistasis also dictates rates of domain evolution over time by exerting significant additional purifying selection to preserve site couplings. These patterns illuminate the mechanistic role of epistasis in the processes underlying observed site invariance and evolutionary rates.     

Robustness of Phylogenetic Inference to Model Misspecification Caused by Pairwise Epistasis

Likelihood-based phylogenetic inference posits a probabilistic model of character state change along branches of a phylogenetic tree. These models typically assume statistical independence of sites in the sequence alignment. This is a restrictive assumption that facilitates computational tractability, but ignores how epistasis, the effect of genetic background on mutational effects, influences the evolution of functional sequences. We consider the effect of using a misspecified site-independent model on the accuracy of Bayesian phylogenetic inference in the setting of pairwise-site epistasis. Previous work has shown that as alignment length increases, tree reconstruction accuracy also increases. Here, we present a simulation study demonstrating that accuracy increases with alignment size even if the additional sites are epistatically coupled. We introduce an alignment-based test statistic that is a diagnostic for pairwise epistasis and can be used in posterior predictive checks.     

Teosinte Branched1 and the Origin of Maize: Evidence for Epistasis and the Evolution of Dominance

Two quantitative trait loci (QTL) controlling differences in plant and inflorescence architecture between maize and its progenitor (teosinte) were analyzed. Complementation tests indicate that one of these, which is on chromosome arm 1L, is the locus for the maize mutant teosinte branched1 (tb1). This QTL has effects on inflorescence sex and the number and length of internodes in the lateral branches and inflorescences. This QTL has strong phenotypic effects in teosinte background but reduced effects in maize background. The second QTL, which is on chromosome arm 3L, affects the same traits as the QTL on 1L. We identify two candidate loci for this QTL. The effects of this QTL on several traits are reduced in both maize and teosinte background as compared to a maize-teosinte F(2) population. Genetic background appears to affect gene action for both QTL. Analysis of a population in which both QTL were segregating revealed that they interact epistatically. Together, these two QTL substantially transform both plant and inflorescence architecture. We propose that tb1 is involved in the teosinte plant's response to local environment to produce either long or short branches and that maize evolution involved a change at this locus to produce short branches under all environments.     

Explaining the Evolution of Warning Coloration: Secreted Secondary Defence Chemicals May Facilitate the Evolution of Visual Aposematic Signals

Several pathways have been postulated to explain the evolution of warning coloration, which is a perplexing phenomenon. Many of these attempt to circumvent the problem of naïve predators by inferring kin selection or neophobia. Through a stochastic model, we show that a secreted secondary defence chemical can provide selective pressure, on the individual level, towards developing warning coloration. Our fundamental assumption is that increased conspicuousness will result in longer assessment periods and divergence from the predators'' searching image, thus reducing the probability of a predator making mistakes. We conclude that strong olfactory signaling by means of chemical secretions can lead to the evolution of warning coloration.     

Epistasis Test in Meta-Analysis: A Multi-Parameter Markov Chain Monte Carlo Model for Consistency of Evidence

Conventional genome-wide association studies (GWAS) have been proven to be a successful strategy for identifying genetic variants associated with complex human traits. However, there is still a large heritability gap between GWAS and transitional family studies. The “missing heritability” has been suggested to be due to lack of studies focused on epistasis, also called gene–gene interactions, because individual trials have often had insufficient sample size. Meta-analysis is a common method for increasing statistical power. However, sufficient detailed information is difficult to obtain. A previous study employed a meta-regression-based method to detect epistasis, but it faced the challenge of inconsistent estimates. Here, we describe a Markov chain Monte Carlo-based method, called “Epistasis Test in Meta-Analysis” (ETMA), which uses genotype summary data to obtain consistent estimates of epistasis effects in meta-analysis. We defined a series of conditions to generate simulation data and tested the power and type I error rates in ETMA, individual data analysis and conventional meta-regression-based method. ETMA not only successfully facilitated consistency of evidence but also yielded acceptable type I error and higher power than conventional meta-regression. We applied ETMA to three real meta-analysis data sets. We found significant gene–gene interactions in the renin–angiotensin system and the polycyclic aromatic hydrocarbon metabolism pathway, with strong supporting evidence. In addition, glutathione S-transferase (GST) mu 1 and theta 1 were confirmed to exert independent effects on cancer. We concluded that the application of ETMA to real meta-analysis data was successful. Finally, we developed an R package, etma, for the detection of epistasis in meta-analysis [etma is available via the Comprehensive R Archive Network (CRAN) at https://cran.r-project.org/web/packages/etma/index.html].