The role of deleterious mutations in allopatric speciation

Allopatric speciation is often assumed to occur as a consequence of adaptive divergence between two isolated populations. However, there are some scenarios in which reproductive isolation can be favored due to accumulated unconditionally deleterious mutations. If deleterious mutations have synergistic epistatic effects, it is shown here that the average fitness of recombinants between two parental lines with a given number of fixed mutations is lower than that of the parents in both the F1 and F2 generations. If individual mutations are only slightly deleterious, then they will tend to fixation at a high enough rate to cause lower hybrid fitness. If the fitness effects of mutation give rise to antagonistic epistasis, the hybrids tend to have a higher average fitness than the parental lines, suggesting a possible scenario for the origin of hybrid vigor. The other model of deleterious mutations investigated is the accumulation of knockout mutants in a duplicated gene family. While neutral in the parental lines, upon contact the F1 and later generations have a significant probability of carrying double knockouts. Under this scenario, selection may also favor reproductive isolation between the two lines. Even when the selection coefficients generated are too low to drive speciation, epistatic interactions between deleterious mutations offer a possible explanation for both outbreeding depression and hybrid vigor.     

THE PROBABILITY OF PEAK SHIFTS IN A FOUNDER POPULATION. II. AN ADDITIVE POLYGENIC TRAIT

Stochastic shifts between two alternative stable equilibria in an additive polygenic system are modelled. The effect of selection on the character is represented by a double-peaked function relating individual fitness to phenotypic value. The mean of a large population will equilibrate near one of the two peaks, although with weak selection there may be a substantial displacement from the closest peak, due to the attraction exerted by the other peak. It is assumed that a small population is founded as a random sample from a large population at equilibrium under selection, and that genetic drift and selection interact to determine the evolution of the mean and variance of the polygenic character during the phase of exponential population growth that follows the foundation of the population. The effects on the frequencies of peak shifts of selectively induced linkage disequilibrium, randomly induced linkage disequilibrium, and random deviations from Hardy-Weinberg equilibrium are investigated by computer simulation. The results are compared with the probabilities of shifts calculated by an approximate analytic method. It is found that the approximations are reasonably accurate when the heights of the peaks in fitness are similar, but the approximations fail when one of the peaks is much higher than the other. The probability of a peak shift is shown to be a decreasing function of the strength of selection on the character. Although substantial changes in phenotypic mean can be induced by a founder event, the probability of a peak shift that induces a significant degree of reproductive isolation is low. The significance of these findings in relation to theories of speciation is discussed.     

EPISTASIS AND THE EFFECT OF FOUNDER EVENTS ON THE ADDITIVE GENETIC VARIANCE

Models of founder events have focused on the reduction in the genetic variation following a founder event. However, recent work (Bryant et al., 1986; Goodnight, 1987) suggests that when there is epistatic genetic variance in a population, the total genetic variance within demes may actually increase following a founder event. Since the additive genetic variance is a statistical property of a population and can change with the level of inbreeding, some of the epistatic genetic variance may be converted to additive genetic variance during a founder event. The model presented here demonstrates that some of the additive-by-additive epistatic genetic variance is converted to additive genetic variance following a founder event. Furthermore, the amount of epistasis converted to additive genetic variance is a function of the recombination rate and the propagule size. For a single founder event of two individuals, as much as 75% of the epistatic variance in the ancestral population may become additive genetic variance following the founder event. For founder events involving two individuals with free recombination, the relative contribution of epistasis to the additive genetic variance following a founder event is equal to its proportion of the total genetic variance prior to the founder event. Traits closely related to fitness are expected to have relatively little additive genetic variance but may have substantial nonadditive genetic variance. Founder events may be important in the evolution of fitness traits, not because they lead to a reduction in the genetic variance, but rather because they lead to an increase in the additive genetic variance.     

NATURAL SELECTION ON PLEIOTROPIC QUANTITATIVE TRAIT LOCI AFFECTING A LIFE-HISTORY TRADE-OFF IN AVENA BARBATA

We applied QTL mapping to fitness variation of Avena barbata under well-watered greenhouse conditions. One hundred eighty recombinant inbred lines were assayed for flowering time, total size, mass allocation, and fitness. Composite Interval Mapping identified two to five loci affecting these traits. These were well supported in more powerful Multiple and Bayesian interval mapping analyses that indicated that additional QTL, as well as epistatic interactions also affect the traits. The posterior distribution of the number of QTL peaked at five to eight additive loci and one to two interactions, but the specific locations of the additional loci could not be determined with certainty. In most cases in which loci for separate traits mapped to similar locations, explicit tests supported pleiotropy over close linkage of separate loci. Alleles that hastened first flowering generally reduced vegetative mass, increased reproductive mass, and were associated with high fitness. Because effects on mass allocation generally cancelled one another, few loci affected total plant size. Only one QTL affected vegetative mass independent of reproductive mass and this locus had little effect on fitness. Thus selection acts to shift the mass allocation toward greater reproductive allocation, because the correlated decrease in vegetative mass poses only a minor fitness cost.     

Rapid speciation via parallel, directional selection on regulatory genetic pathways

Regulatory genetic pathways are ubiquitous in organisms and play a central role in the realization of the phenotype during development. We explored the proposition that these pathways can provide a plausible source of the epistatic variation that has been implicated in the evolution of postzygotic reproductive isolation. We modeled gene regulation as a matching function between the product of one locus and the promoter site of the next locus in the pathway, with binding strength determining the amount of product. When the phenotype is subject to parallel selection in a pair of independent populations, we find that the fitnesses of F(1)and F(2)hybrids often drop to very low values as the populations respond in genetically different and incompatible ways. The simulations support the predictions of the analytical models. Hybrid fitness reduction occurs more often as the number of loci in the pathway increases, and as the binding site interactions become more complex. Less hybrid fitness reduction is seen when the populations start with imperfect binding in the pathway. In contrast, when we constructed the phenotype without gene regulation using multiplicative rules, isomorphic to the additive phenotype commonly assumed in evolutionary models, we found no appreciable F(1)fitness reduction and only slight F(2)fitness reduction. The interaction of genetic drift and mutation, even at very high rates, did not reduce hybrid fitness at all on the time-scales we considered. Clearly, the evolution of regulatory genetic pathways can play an important role in speciation, but much more empirical information is needed on the effect of allelic variability in regulatory site interactions before this role is fully understood.     

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 F₁ hybrids, reduced fitness evolved in a window of intermediate strengths of epistatic interactions, but F₂ 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.     

The mapping of epistatic effects onto a genealogical tree in haploid populations

In this paper we present a model that maps epistatic effects onto a genealogical tree for a haploid population. Prior work has demonstrated that genealogical structure causes the genotypic values of individuals to covary. Our results indicate that epistasis can reduce genotypic covariance that is caused by genealogical structure. Genotypic effects (both additive and epistatic) occur along the branches of a genealogical tree, from the base of the tree to its tips. Epistasis reduces genotypic covariance because there is a reweighting of the contribution of branches to the states of genotypes compared to the additive case. Branches near the tips of a genealogical tree contribute proportionally more genetic effects with epistasis than without epistasis. Epistatic effects are most numerous at basal positions in a genealogical tree when a population is constant in size and experiencing no selection, optimizing selection, diversifying selection or directional selection, indicating that epistatic effects are typically old. For a population that is growing in size, epistatic effects are most numerous at midpoints in a genealogical tree, indicating epistatic effects are of moderate age. Our results are important in that they suggest epistatic effects may typically explain deep (old) divergences and broad patterns of divergence that exist in populations, except in growing populations. In a growing population, epistatic effects may cause more within group divergence higher up in a tree and less between group divergence that is deep in a tree. The distribution of the number of epistatic effects and the expected variance and covariance in the number of epistatic effects is also provided assuming neutrality.     

Epistasis for fitness-related quantitative traits in Arabidopsis thaliana grown in the field and in the greenhouse

The extent to which epistasis contributes to adaptation, population differentiation, and speciation is a long-standing and important problem in evolutionary genetics. Using recombinant inbred (RI) lines of Arabidopsis thaliana grown under natural field conditions, we have examined the genetic architecture of fitness-correlated traits with respect to epistasis; we identified both single-locus additive and two-locus epistatic QTL for natural variation in fruit number, germination, and seed length and width. For fruit number, we found seven significant epistatic interactions, but only two additive QTL. For seed germination, length, and width, there were from two to four additive QTL and from five to eight epistatic interactions. The epistatic interactions were both positive and negative. In each case, the magnitude of the epistatic effects was roughly double that of the effects of the additive QTL, varying from -41% to +29% for fruit number and from -5% to +4% for seed germination, length, and width. A number of the QTL that we describe participate in more than one epistatic interaction, and some loci identified as additive also may participate in an epistatic interaction; the genetic architecture for fitness traits may be a network of additive and epistatic effects. We compared the map positions of the additive and epistatic QTL for germination, seed width, and seed length from plants grown in both the field and the greenhouse. While the total number of significant additive and epistatic QTL was similar under the two growth conditions, the map locations were largely different. We found a small number of significant epistatic QTL x environment effects when we tested directly for them. Our results support the idea that epistatic interactions are an important part of natural genetic variation and reinforce the need for caution in comparing results from greenhouse-grown and field-grown plants.     

Impact of epistasis and pleiotropy on evolutionary adaptation

Evolutionary adaptation is often likened to climbing a hill or peak. While this process is simple for fitness landscapes where mutations are independent, the interaction between mutations (epistasis) as well as mutations at loci that affect more than one trait (pleiotropy) are crucial in complex and realistic fitness landscapes. We investigate the impact of epistasis and pleiotropy on adaptive evolution by studying the evolution of a population of asexual haploid organisms (haplotypes) in a model of N interacting loci, where each locus interacts with K other loci. We use a quantitative measure of the magnitude of epistatic interactions between substitutions, and find that it is an increasing function of K. When haplotypes adapt at high mutation rates, more epistatic pairs of substitutions are observed on the line of descent than expected. The highest fitness is attained in landscapes with an intermediate amount of ruggedness that balance the higher fitness potential of interacting genes with their concomitant decreased evolvability. Our findings imply that the synergism between loci that interact epistatically is crucial for evolving genetic modules with high fitness, while too much ruggedness stalls the adaptive process.     

The evolution of evolvability in genetic linkage patterns

A number of factors have been proposed that may affect the capacity for an evolutionary system to generate adaptation. One that has received little recent attention among biologists is linkage patterns, or the ordering of genes on chromosomes. In this study, a simple model of genetic interactions, implemented in an evolutionary simulation, demonstrates that clustering of epistatically interacting genes increases the rate of adaptation. Moreover, long-term evolution with inversion can reorganize linkage patterns from random gene ordering into this more modular organization, thereby facilitating adaptation. These results are consistent with a large body of biological observations and some mathematical theory. Although linkage patterns are neutral with respect to individual fitness in this model, they are subject to lineage level selection for evolvability. At least two candidate mechanisms may contribute to improved evolvability under epistatic clustering: clustering may reduce interference between selection on different traits, and it may allow the simultaneous optimization of different recombination rates for gene pairs with additive and epistatic fitness effects.     

Very low levels of direct additive genetic variance in fitness and fitness components in a red squirrel population

A trait must genetically correlate with fitness in order to evolve in response to natural selection, but theory suggests that strong directional selection should erode additive genetic variance in fitness and limit future evolutionary potential. Balancing selection has been proposed as a mechanism that could maintain genetic variance if fitness components trade off with one another and has been invoked to account for empirical observations of higher levels of additive genetic variance in fitness components than would be expected from mutation–selection balance. Here, we used a long‐term study of an individually marked population of North American red squirrels (Tamiasciurus hudsonicus) to look for evidence of (1) additive genetic variance in lifetime reproductive success and (2) fitness trade‐offs between fitness components, such as male and female fitness or fitness in high‐ and low‐resource environments. “Animal model” analyses of a multigenerational pedigree revealed modest maternal effects on fitness, but very low levels of additive genetic variance in lifetime reproductive success overall as well as fitness measures within each sex and environment. It therefore appears that there are very low levels of direct genetic variance in fitness and fitness components in red squirrels to facilitate contemporary adaptation in this population.     

Evolutionary consequences of selected locus-specific variations in epistasis and fitness contribution in Kauffman's NK model

Mathematical analysis and computer simulations are used to evaluate three modifications to Kauffman's NK model in an attempt to incorporate unexplored aspects of epistatic interaction between loci in genome evolution. Two modifications--one to the amount and the other to the distribution of epistatic interaction--further support Kauffman's conclusion that high levels of epistatic interaction lead to a decrease in overall fitness of the genome. The third model, however, provides a condition under which increased epistatic interaction at certain loci results in higher genome fitness.     

Bayesian estimation of genomic clines

We developed a Bayesian genomic cline model to study the genetic architecture of adaptive divergence and reproductive isolation between hybridizing lineages. This model quantifies locus‐specific patterns of introgression with two cline parameters that describe the probability of locus‐specific ancestry as a function of genome‐wide admixture. ‘Outlier’ loci with extreme patterns of introgression relative to most of the genome can be identified. These loci are potentially associated with adaptive divergence or reproductive isolation. We simulated genetic data for admixed populations that included neutral introgression, as well as loci that were subject to directional, epistatic or underdominant selection, and analysed these data using the Bayesian genomic cline model. Under many demographic conditions, underdominance or directional selection had detectable and predictable effects on cline parameters, and ‘outlier’ loci were greatly enriched for genetic regions affected by selection. We also analysed previously published genetic data from two transects through a hybrid zone between Mus domesticus and M. musculus. We found considerable variation in rates of introgression across the genome and particularly low rates of introgression for two X‐linked markers. There were similarities and differences in patterns of introgression between the two transects, which likely reflects a combination of stochastic variability because of genetic drift and geographic variation in the genetic architecture of reproductive isolation. By providing a robust framework to quantify and compare patterns of introgression among genetic regions and populations, the Bayesian genomic cline model will advance our understanding of the genetics of reproductive isolation and the speciation process.     

The evolution of hybrid infertility: perpetual coevolution between gender-specific and sexually antagonistic genes

A new hypothesis is proposed for the rapid evolution of postzygotic reproductive isolation via hybrid infertility. The hypothesis is motivated by two lines of experimental research from Drosophila melanogaster that demonstrate that sexually antagonistic fitness variation is abundant and that epistatic fitness variation on the Y chromosome is common. The hypothesis states that the expression of sexually antagonistic genes leads to a gender-load in each sex. In response, gender-limited reproductive genes are selected to ameliorate, through pleiotropy, the expression of sexually antagonistic genes. Chronic coevolution between gender-limited genes and gender-unlimited sexually antagonistic genes causes rapid divergence of reproductive proteins among allopatric populations, ultimately leading to hybrid infertility.     

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.     

Genetic improvement of production while maintaining fitness

Selection for production tends to decrease fitness, in particular, major components such as reproductive performance. Under an infinitesimal genetic model restricted index selection can maintain reproductive performance while improving production. However, reproductive traits are thought to be controlled by a finite number of recessive alleles at low frequency. Culling for low reproduction may weed out the negative homozygous genotypes for reproduction in any generation, thus controlling the frequencies of alleles negative for reproduction. Restricted index selection, culling for low reproduction and a new method called empirical restricted index selection were compared for their efficiency in improving production while maintaining reproduction. Empirical restricted index selection selects animals that have on average the highest estimated breeding values for production and on average the same estimated breeding values for reproduction as the base population. An infinitesimal genetic model and models with a finite number of loci for reproduction with rare deleterious recessive alleles, which have additive, dominant or no pleiotropic effects on production, were considered. When reproduction was controlled by a finite number of loci with rare recessive alleles, restricted index selection could not maintain reproduction. The culling of 20% of the animals on reproduction maintained reproduction with all genetic models, except for the model where loci for reproduction had additive effects on production. Empirical restricted selection maintained reproduction with all models and yielded higher production responses than culling on reproduction, except when there were dominant pleiotropic effects on production.     

Reinforcement and divergence under assortative mating

Traits that cause assortative mating such as the flowering time in plants and body size in animals can produce reproductive isolation between hybridizing populations. Can selection against unfit hybrids cause two populations to diverge in their mean values for these kinds of traits? Here I present a haploid analytical model of one population that receives gene flow from another. The partial pre-zygotic isolation between the two populations is caused by assortative mating for a trait that is influenced by any number of genes with additive effects. The post-zygotic isolation is caused by selection against genetic incompatibilities that can involve any form of selection on individual genes and gene combinations (epistasis). The analysis assumes that the introgression rate and selection coefficients are small. The results show that the assortment trait mean will not diverge from the immigrants unless there is direct selection on the trait favouring it to do so or there are genes of very large effect. The amount of divergence at equilibrium is determined by a balance between direct selection on the assortment trait and introgression from the other population. Additional selection against hybrid genetic incompatibilities reduces the effective migration rate and allows greater divergence. The role of assortment in speciation is discussed in the light of these results.     

Short‐term insurance versus long‐term bet‐hedging strategies as adaptations to variable environments

Understanding how organisms adapt to environmental variation is a key challenge of biology. Central to this are bet‐hedging strategies that maximize geometric mean fitness across generations, either by being conservative or diversifying phenotypes. Theoretical models have identified environmental variation across generations with multiplicative fitness effects as driving the evolution of bet‐hedging. However, behavioral ecology has revealed adaptive responses to additive fitness effects of environmental variation within lifetimes, either through insurance or risk‐sensitive strategies. Here, we explore whether the effects of adaptive insurance interact with the evolution of bet‐hedging by varying the position and skew of both arithmetic and geometric mean fitness functions. We find that insurance causes the optimal phenotype to shift from the peak to down the less steeply decreasing side of the fitness function, and that conservative bet‐hedging produces an additional shift on top of this, which decreases as adaptive phenotypic variation from diversifying bet‐hedging increases. When diversifying bet‐hedging is not an option, environmental canalization to reduce phenotypic variation is almost always favored, except where the tails of the fitness function are steeply convex and produce a novel risk‐sensitive increase in phenotypic variance akin to diversifying bet‐hedging. Importantly, using skewed fitness functions, we provide the first model that explicitly addresses how conservative and diversifying bet‐hedging strategies might coexist.     

Genetics of postzygotic reproductive isolation in plants

Postzygotic reproductive isolation, based on negative interactions of genes, is a key aspect of divergent speciation in plants and animals. The effect of the interaction manifests as a drastic reduction in fitness of hybrids of the first of subsequent generations, which is expressed as hybrid lethality, weakness or sterility. Both simple genetic control of genetic incompatibility, which includes interallelic negative complementation or epistatic interactions of a limited number of genes, and more complex control, based on epistatic interactions of many genes, have been described in plants. It is thought that genes for reproductive isolation are nonuniformly distributed over the genome and are related to differential adaptation. The mosaic organization of the genomes in this respect provides restoration of their structural and functional integrity upon interspecies hybridization in natural conditions. Many cultured and wild plant species, in contrast to animals, were found to be polymorphic at genes controlling interspecies incompatibility. This fact facilitates genetic analysis of incompatibility and broadens perspectives in studying the structure, functions, and molecular evolution of the genes controlling postzygotic reproductive isolation, in view of the possible leading role of these genes in adaptive speciation.     

Life history affects the evolution of reproductive isolation among species of Coreopsis (Asteraceae)

The evolution of reproductive isolation within Coreopsis is investigated by integrating phylogenetic data with estimates of pollen viability of plants from inter- and intraspecific crosses. Three different models that predict F1 fitness are compared. The first uses ITS pairwise distances, the second is based on phylogenetic branch lengths derived from DNA sequences, and the third elaborates on the second model by dividing branch length according to reconstructions of the evolution of life history. This is the first study to use phylogenetic branch-length estimates for predicting levels of reproductive isolation. Estimated branch lengths (model 2) predict hybrid fitness more accurately than simply genetic distance (model 1) but only very slightly. This is probably because the two variables are strongly correlated in Coreopsis. Prediction is substantially improved by allowing evolutionary rates to differ between annual and perennial branches (model 3). A bootstrapping procedure indicates that the life-history effect is statistically significant. The more rapid evolution of reproductive isolation within annual species of Coreopsis may be due to differing mechanisms of reproductive isolation, that is, chromosomal rearrangements rather than genetic incompatibilities.