Genetics of male nuptial colour divergence between sympatric sister species of a Lake Victoria cichlid fish

The hypothesis of sympatric speciation by sexual selection has been contentious. Several recent theoretical models of sympatric speciation by disruptive sexual selection were tailored to apply to African cichlids. Most of this work concludes that the genetic architecture of female preference and male trait is a key determinant of the likelihood of disruptive sexual selection to result in speciation. We investigated the genetic architecture controlling male nuptial colouration in a sympatric sibling species pair of cichlid fish from Lake Victoria, which differ conspicuously in male colouration and female mating preferences for these. We estimated that the difference between the species in male nuptial red colouration is controlled by a minimum number of two to four genes with significant epistasis and dominance effects. Yellow colouration appears to be controlled by one gene with complete dominance. The two colours appear to be epistatically linked. Knowledge on how male colouration segregates in hybrid generations and on the number of genes controlling differences between species can help us assess whether assumptions made in simulation models of sympatric speciation by sexual selection are realistic. In the particular case of the two sister species that we studied a small number of genes causing major differences in male colouration may have facilitated the divergence in male colouration associated with speciation.     

The additive genetic variance after bottlenecks is affected by the number of loci involved in epistatic interactions

Abstract We investigated the role of the number of loci coding for a neutral trait on the release of additive variance for this trait after population bottlenecks. Different bottleneck sizes and durations were tested for various matrices of genotypic values, with initial conditions covering the allele frequency space. We used three different types of matrices. First, we extended Cheverud and Routman's model by defining matrices of "pure" epistasis for three and four independent loci; second, we used genotypic values drawn randomly from uniform, normal, and exponential distributions; and third we used two models of simple metabolic pathways leading to physiological epistasis. For all these matrices of genotypic values except the dominant metabolic pathway, we find that, as the number of loci increases from two to three and four, an increase in the release of additive variance is occurring. The amount of additive variance released for a given set of genotypic values is a function of the inbreeding coefficient, independently of the size and duration of the bottleneck. The level of inbreeding necessary to achieve maximum release in additive variance increases with the number of loci. We find that additive-by-additive epistasis is the type of epistasis most easily converted into additive variance. For a wide range of models, our results show that epistasis, rather than dominance, plays a significant role in the increase of additive variance following bottlenecks.     

WILL POPULATION BOTTLENECKS AND MULTILOCUS EPISTASIS INCREASE ADDITIVE GENETIC VARIANCE?

We apply new analytical methods to understand the consequences of population bottlenecks for expected additive genetic variance. We analyze essentially all models for multilocus epistasis that have been numerically simulated to demonstrate increased additive variance. We conclude that for biologically plausible models, large increases in expected additive variance--attributable to epistasis rather than dominance--are unlikely. Naciri-Graven and Goudet (2003) found that as the number of epistatically interacting loci increases, additive variance tends to be inflated more after a bottleneck. We argue that this result reflects biologically unrealistic aspects of their models. Specifically, as the number of loci increases, higher-order epistatic interactions become increasingly important in these models, with an increasing fraction of the genetic variance becoming nonadditive, contrary to empirical observations. As shown by Barton and Turelli (2004), without dominance, conversion of nonadditive to additive variance depends only on the variance components and not on the number of loci per se. Numerical results indicating that more inbreeding is needed to produce maximal release of additive variance with more loci follow directly from our analytical results, which show that high levels of inbreeding (F > 0.5) are needed for significant conversion of higher-order components. We discuss alternative approaches to modeling multilocus epistasis and understanding its consequences.     

Epistasis and the temporal change in the additive variance-covariance matrix induced by drift

The effect of population bottlenecks on the components of the genetic covariance generated by two neutral independent epistatic loci has been studied theoretically (additive, covA; dominance, covD; additive-by-additive, covAA; additive-by-dominance, covAD; and dominance-by-dominance, covDD). The additive-by-additive model and a more general model covering all possible types of marginal gene action at the single-locus level (additive/dominance epistatic model) were considered. The covariance components in an infinitely large panmictic population (ancestral components) were compared with their expected values at equilibrium over replicates randomly derived from the base population, after t consecutive bottlenecks of equal size N (derived components). Formulae were obtained in terms of the allele frequencies and effects at each locus, the corresponding epistatic effects and the inbreeding coefficient Ft. These expressions show that the contribution of nonadditive loci to the derived additive covariance (covAt) does not linearly decrease with inbreeding, as in the pure additive case, and may initially increase or even change sign in specific situations. Numerical examples were also analyzed, restricted for simplicity to the case of all covariance components being positive. For additive-by-additive epistasis, the condition covAt > covA only holds for high frequencies of the allele decreasing the metric traits at each locus (negative allele) if epistasis is weak, or for intermediate allele frequencies if it is strong. For the additive/dominance epistatic model, however, covAt > covA applies for low frequencies of the negative alleles at one or both loci and mild epistasis, but this result can be progressively extended to intermediate frequencies as epistasis becomes stronger. Without epistasis the same qualitative results were found, indicating that marginal dominance induced by epistasis can be considered as the primary cause of an increase of the additive covariance after bottlenecks. For all models, the magnitude of the ratio covAt/covA was inversely related to N and t.     

Effect on linkage disequilibrium of selection for a quantitative character with epistasis

Summary Selection for a character controlled by additive genes induces linkage disequilibrium which reduces the additive genetic variance usable for further selective gains. Additive x additive epistasis contributes to selection response through development of linkage disequilibrium between interacting loci. To investigate the relative importance of the two effects of linkage disequilibrium, formulae are presented and results are reported of simulations using models involving additive, additive x additive and dominance components. The results suggest that so long as epistatic effects are not large relative to additive effects, and the proportion of pairs of loci which show epistasis is not very high, the predominant effect of linkage disequilibrium will be to reduce the rate of selection response.     

The consequences of using inadequate testers in the simplified triple test-cross.

The genetical consequences of common alleles in the L1 and L2 testers of a simplified version of the triple test-cross which is applicable to populations of inbred lines are examined. The test for epistasis under these circumstances becomes ambiguous and can spuriously detect non-allelic interactions when they may not exist although it still provides a test for epistasis and the adequacy of the testers simultaneously. The tests of significance and the estimates of additive variation are biased to an extent related to the dominance and dominance x additive effects of the common loci while the significance and estimates of dominance variation are deflated because they reflect the dominance effects at the non-common loci only. The covariance of sums and differences is also underestimated for the same reasons. These expectations are illustrated by analysing the 190 simplified triple test-crosses that could be extracted from a 20 x 20 diallel set of crosses between pure-breeding lines of Nicotiana rustica.     

Inheritance of female mating preference in a sympatric sibling species pair of Lake Victoria cichlids: implications for speciation

Female mate choice has often been proposed to play an important role in cases of rapid speciation, in particular in the explosively evolved haplochromine cichlid species flocks of the Great Lakes of East Africa. Little, if anything, is known in cichlid radiations about the heritability of female mating preferences. Entirely sympatric distribution, large ecological overlap and conspicuous differences in male nuptial coloration, and female preferences for these, make the sister species Pundamilia pundamilia and P. nyererei from Lake Victoria an ideally suited species pair to test assumptions on the genetics of mating preferences made in models of sympatric speciation. Female mate choice is necessary and sufficient to maintain reproductive isolation between these species, and it is perhaps not unlikely therefore, that female mate choice has been important during speciation. A prerequisite for this, which had remained untested in African cichlid fish, is that variation in female mating preferences is heritable. We investigated mating preferences of females of these sister species and their hybrids to test this assumption of most sympatric speciation models, and to further test the assumption of some models of sympatric speciation by sexual selection that female preference is a single-gene trait. We find that the differences in female mating preferences between the sister species are heritable, possibly with quite high heritabilities, and that few but probably more than one genetic loci contribute to this behavioural speciation trait with no apparent dominance. We discuss these results in the light of speciation models and the debate about the explosive radiation of cichlid fishes in Lake Victoria.     

Self-fertilization and the evolution of recombination

In this article, we study the effect of self-fertilization on the evolution of a modifier allele that alters the recombination rate between two selected loci. We consider two different life cycles: under gametophytic selfing, a given proportion of fertilizations involves gametes produced by the same haploid individual, while under sporophytic selfing, a proportion of fertilizations involves gametes produced by the same diploid individual. Under both life cycles, we derive approximations for the change in frequency of the recombination modifier when selection is weak relative to recombination, so that the population reaches a state of quasi-linkage equilibrium. We find that gametophytic selfing increases the range of epistasis under which increased recombination is favored; however, this effect is substantial only for high selfing rates. Moreover, gametophytic selfing affects the relative influence of different components of epistasis (additive x additive, additive x dominance, dominance x dominance) on the evolution of the modifier. Sporophytic selfing has much stronger effects: even a small selfing rate greatly increases the parameter range under which recombination is favored, when there is negative dominance x dominance epistasis. This effect is due to the fact that selfing generates a correlation in homozygosity at linked loci, which is reduced by recombination.     

A complete classification of epistatic two-locus models

Background

The study of epistasis is of great importance in statistical genetics in fields such as linkage and association analysis and QTL mapping. In an effort to classify the types of epistasis in the case of two biallelic loci Li and Reich listed and described all models in the simplest case of 0/1 penetrance values. However, they left open the problem of finding a classification of two-locus models with continuous penetrance values.

Results

We provide a complete classification of biallelic two-locus models. In addition to solving the classification problem for dichotomous trait disease models, our results apply to any instance where real numbers are assigned to genotypes, and provide a complete framework for studying epistasis in QTL data. Our approach is geometric and we show that there are 387 distinct types of two-locus models, which can be reduced to 69 when symmetry between loci and alleles is accounted for. The model types are defined by 86 circuits, which are linear combinations of genotype values, each of which measures a fundamental unit of interaction.

Conclusion

The circuits provide information on epistasis beyond that contained in the additive × additive, additive × dominance, and dominance × dominance interaction terms. We discuss the connection between our classification and standard epistatic models and demonstrate its utility by analyzing a previously published dataset.     

The effect of non-additive genetic interactions on selection in multi-locus genetic models

Additive genetic variance might usually be expected to decrease in a finite population because of genetic drift. However, both theoretical and empirical studies have shown that the additive genetic variance of a population could, in some cases, actually increase owing to the action of genetic drift in presence of non-additive effects. We used Monte-Carlo simulations to address a less-well-studied issue: the effects of directional truncation selection on a trait affected by non-additive genetic variation. We investigated the effects on genetic variance and the response to selection. We compared two different genetic models, representing various numbers of loci. We found that the additive genetic variance could also increase in the case of truncation selection, when dominance and epistasis was present. Additive-by-additive epistatic effects generally gave a higher increase in additive variance compared to dominance. However, the magnitude of the increase differed depending on the particular model and on the number of loci.     

EPISTASIS MODIFIES THE DOMINANCE OF LOCI CAUSING HYBRID MALE STERILITY IN THE DROSOPHILA PSEUDOOBSCURA SPECIES GROUP

Speciation, the evolution of reproductive isolation between populations, serves as the driving force for generating biodiversity. Postzygotic barriers to gene flow, such as F ₁ hybrid sterility and inviability, play important roles in the establishment and maintenance of biological species. F ₁ hybrid incompatibilities in taxa that obey Haldane's rule, the observation that the heterogametic sex suffers greater hybrid fitness problems than the homogametic sex, are thought to often result from interactions between recessive-acting X-linked loci and dominant-acting autosomal loci. Because they play such prominent roles in producing hybrid incompatibilities, we examine the dominance and nature of epistasis between alleles derived from Drosophila persimilis that confer hybrid male sterility in the genetic background of its sister species, D. pseudoobscura bogotana . We show that epistasis elevates the apparent dominance of individually recessive-acting QTL such that they can contribute to F ₁ hybrid sterility. These results have important implications for assumptions underlying theoretical models of hybrid incompatibilities and may offer a possible explanation for why, to date, identification of dominant-acting autosomal "speciation genes" has been challenging.     

Recent speciation between sympatric Tanganyikan cichlid colour morphs

Lake Tanganyika, Africa's oldest lake, harbours an impressive diversity of cichlid fishes. Although diversification in its radiating groups is thought to have been initially rapid, cichlids from Lake Tanganyika show little evidence for ongoing speciation. In contrast, examples of recent divergence among sympatric colour morphs are well known in haplochromine cichlids from Lakes Malawi and Victoria. Here, we report genetic evidence for recent divergence between two sympatric Tanganyikan cichlid colour morphs. These Petrochromis morphs share mitochondrial haplotypes, yet microsatellite loci reveal that their sympatric populations form distinct genetic groups. Nuclear divergence between the two morphs is equivalent to that which arises geographically within one of the morphs over short distances and is substantially smaller than that among other sympatric species in this genus. These patterns suggest that these morphs diverged only recently, yet that barriers to gene flow exist which prevent extensive admixture despite their sympatric distribution. The morphs studied here provide an unusual example of active diversification in Lake Tanganyika's generally ancient cichlid fauna and enable comparisons of speciation processes between Lake Tanganyika and other African lakes.     

The effect of epistasis on the excess of the additive and nonadditive variances after population bottlenecks

The effect of population bottlenecks on the components of the genetic variance generated by two neutral independent epistatic loci has been studied theoretically (VA, additive; VD, dominant; VAA, additive x additive; VAD, additive x dominant; VDD; dominant x dominant components of variance). Nonoverdominance and overdominance models were considered, covering all possible types of marginal gene action at the single locus level. The variance components in an infinitely large panmictic population (ancestral components) were compared with their expected values at equilibrium, after t consecutive bottlenecks of equal size N (derived components). Formulae were obtained in terms of allele frequencies and effects at each locus and the corresponding epistatic value. An excess of VA after bottlenecks can be assigned to two sources: (1) the spatiotemporal changes in the marginal average effects of gene substitution alpha(i), which are equal to zero only for additive gene action within and between loci; and (2) the covariance between alpha2(i) and the heterozygosity at the loci involved, which is generated by dominance, with or without epistasis. Numerical examples were analyzed, indicating that an increase in VA after bottlenecks will only occur if its ancestral value is minimal or very small. For the nonoverdominance model with weak reinforcing epistasis, that increase has been detected only for extreme frequencies of the negative allele at one or both loci. With strong epistasis, however, this result can be extended to a broad range of intermediate frequencies. With no epistasis, the same qualitative results were found, indicating that dominance can be considered as the primary cause of an increase in VA following bottlenecks. In parallel, the derived total nonadditive variance exceeded its ancestral value (V(NA) = V(D) + V(AA) + V(AD) + V(DD)) for a range of combinations of allele frequencies covering those for an excess of VA and for very large frequencies of the negative allele at both loci. For the overdominance model, an increase in V(A) and V(NA) was respectively observed for equilibrium (intermediate) frequencies at one or both loci or for extreme frequencies at both loci. For all models, the magnitude of the change of V(A) and V(NA) was inversely related to N and t. At low levels of inbreeding, the between-line variance was not affected by the type of gene action. For the models considered, the results indicate that it is unlikely that the rate of evolution may be accelerated after population bottlenecks, in spite of occasional increments of the derived V(A) over its ancestral value.     

Epistasis causes outbreeding depression in eucalypt hybrids

The genetic architecture underlying species differentiation is essential for understanding the mechanisms of speciation and post-zygotic reproductive barriers which exist between species. We undertook line-cross analysis of multiple hybrid (F₁, F₂ and backcrosses) and pure-species populations of two diploid eucalypt species from different subseries, Eucalyptus globulus and Eucalyptus nitens, to unravel the genetic architecture of their differentiation. The populations were replicated on two sites and monitored for growth and survival over a 14-year period. The hybrids exhibited severe outbreeding depression which increased with age. Of the composite additive, dominance and epistatic effects estimated, the additive × additive epistatic component was the most important in determining population divergence in both growth and survival. Significant dominance × dominance epistasis was also detected for survival at several ages. While favourable dominance and, in the case of survival, dominance × dominance epistasis could produce novel gene combinations which enhance hybrid fitness, at the population level, these effects were clearly overridden by adverse additive × additive epistasis which appears to be a major driver of overall outbreeding depression in the hybrid populations. The lack of model fit at older ages suggested that even high-order epistatic interactions may potentially have a significant contribution to outbreeding depression in survival. The estimated composite genetic parameters were generally stable across sites. Our results argue that the development of favourable epistasis is a key mechanism underlying the genetic divergence of eucalypt species, and epistasis is an important mechanism underlying the evolution of post-zygotic reproductive barriers.     

Sympatric speciation by sexual selection alone is unlikely

According to Darwin, sympatric speciation is driven by disruptive, frequency-dependent natural selection caused by competition for diverse resources. Recently, several authors have argued that disruptive sexual selection can also cause sympatric speciation. Here, we use hypergeometric phenotypic and individual-based genotypic models to explore sympatric speciation by sexual selection under a broad range of conditions. If variabilities of preference and display traits are each caused by more than one or two polymorphic loci, sympatric speciation requires rather strong sexual selection when females exert preferences for extreme male phenotypes. Under this kind of mate choice, speciation can occur only if initial distributions of preference and display are close to symmetric. Otherwise, the population rapidly loses variability. Thus, unless allele replacements at very few loci are enough for reproductive isolation, female preferences for extreme male displays are unlikely to drive sympatric speciation. By contrast, similarity-based female preferences that do not cause sexual selection are less destabilizing to the maintenance of genetic variability and may result in sympatric speciation across a broader range of initial conditions. Certain groups of African cichlids have served as the exclusive motivation for the hypothesis of sympatric speciation by sexual selection. Mate choice in these fishes appears to be driven by female preferences for extreme male phenotypes rather than similarity-based preferences, and the evolution of premating reproductive isolation commonly involves at least several genes. Therefore, differences in female preferences and male display in cichlids and other species of sympatric origin are more likely to have evolved as isolating mechanisms under disruptive natural selection.     

Genetic models to estimate additive and non-additive effects of marker-associated QTL using multiple regression techniques

Summary The development of molecular markers has recently raised expectations for their application in selection programs. However, some questions related to quantitative trait loci (QTL) identification are still unanswered. The objectives of this paper are (1) to develop statistical genetic models for detecting and locating on the genome multi-QTL with additive, dominance and epistatic effects using multiple linear regression analysis in the backcross and F_n generations from the cross of two inbred lines; and (2) to discuss the bias caused by linked and unlinked QTL on the genetic estimates. Non-linear models were developed for different backcross and F_n generations when both epistasis and no epistasis were assumed. Generation analysis of marked progenies is suggested as a way of increasing the number of observations for the estimates without additional cost for molecular scoring. Some groups of progenies can be created in different generations from the same scored individuals. The non-linear models were transformed into approximate multivariate linear models to which combined stepwise and standard regression analysis could be applied. Expressions for the biases of the marker classes from linked QTL were obtained when no epistasis was assumed. When epistasis was assumed, these expressions increased in complexity, and the biases were caused by both linked and unlinked QTL.     

Statistical power for detecting epistasis QTL effects under the F-2 design

Epistasis refers to gene interaction effect involving two or more genes. Statistical methods for mapping quantitative trait loci (QTL) with epistasis effects have become available recently. However, little is known about the statistical power and sample size requirements for mapping epistatic QTL using genetic markers. In this study, we developed analytical formulae to calculate the statistical power and sample requirement for detecting each epistasis effect under the F-2 design based on crossing inbred lines. Assuming two unlinked interactive QTL and the same absolute value for all epistasis effects, the heritability of additive × additive (a × a) effect is twice as large as that of additive × dominance (a × d) or dominance × additive (d × a) effect, and is four times as large as that of dominance × dominance (d × d) effect. Consequently, among the four types of epistasis effects involving two loci, ''a × a'' effect is the easiest to detect whereas ''d × d'' effect is the most difficult to detect. The statistical power for detecting ''a × a'' effect is similar to that for detecting dominance effect of a single QTL. The sample size requirements for detecting ''a × d'', ''d × a'' and ''d × d'' are highly sensitive to increased distance between the markers and the interacting QTLs. Therefore, using dense marker coverage is critical to detecting those effects.     

Modeling quantitative trait Loci and interpretation of models

A quantitative genetic model relates the genotypic value of an individual to the alleles at the loci that contribute to the variation in a population in terms of additive, dominance, and epistatic effects. This partition of genetic effects is related to the partition of genetic variance. A number of models have been proposed to describe this relationship: some are based on the orthogonal partition of genetic variance in an equilibrium population. We compare a few representative models and discuss their utility and potential problems for analyzing quantitative trait loci (QTL) in a segregating population. An orthogonal model implies that estimates of the genetic effects are consistent in a full or reduced model in an equilibrium population and are directly related to the partition of the genetic variance in the population. Linkage disequilibrium does not affect the estimation of genetic effects in a full model, but would in a reduced model. Certainly linkage disequilibrium would complicate the detection of QTL and epistasis. Using different models does not influence the detection of QTL and epistasis. However, it does influence the estimation and interpretation of genetic effects.     

EPISTASIS AS A SOURCE OF INCREASED ADDITIVE GENETIC VARIANCE AT POPULATION BOTTLENECKS

The role of epistasis in evolution and speciation has remained controversial. We use a new parameterization of physiological epistasis to examine the effects of epistasis on levels of additive genetic variance during a population bottleneck. We found that all forms of epistasis increase average additive genetic variance in finite populations derived from initial populations with intermediate allele frequencies. Average additive variance continues to increase over many generations, especially at larger population sizes (N = 32 to 64). Additive-by-additive epistasis is the most potent source of additive genetic variance in this situation, whereas dominance-by-dominance epistasis contributes smaller amounts of additive genetic variance. With additive-by-dominance epistasis, additive genetic variance decreases at a relatively high rate immediately after a population bottleneck, rebounding to higher levels after several generations. Empirical examples of epistasis for murine adult body weight based on measured genotypes are provided illustrating the varying effects of epistasis on additive genetic variance during population bottlenecks.     

云南香型软米水稻资源农艺性状遗传效应研究

选取5份云南地方香型软米水稻种质资源和6份自育香型软米保持系按5×6不完全双列杂交设计(NCⅡ)配制成30个组合,采用加性-显性-上位性遗传模型,分析云南香型软米11个农艺性状的遗传效应。结果表明,云南香型软米多数农艺性状的遗传主要受加×加上位性效应、加性×环境效应、显性×环境效应的影响,还存在不同程度的加性效应和显性效应,单株产量受基因加性效应、显性效应、加×加上位性效应、加性×环境效应、显性×环境效应的影响;株高、有效穗的遗传率以普通狭义遗传率为主,其他性状的普通狭义遗传率和互作狭义遗传率均达极显著水平;产量构成性状之间存在不同类型和不同程度的遗传相关,多数性状之间以加×加上位性、加性×环境和显性×环境互作效应显著。