A quantitative genetic model for analyzing species differences in outcrossing species

A genetic model based on a two-level intra- and interspecific mating design is proposed to estimate the genetic architecture of species differences and heterosis for outcrossing species. The underlying genetic analyses make use of classical quantitative genetic theories and recent results from molecular genetic studies. Gene effects across different quantitative trait loci (QTL) can be approximated by a geometric series. Under natural selection, gene effects are often associated with allele frequencies in a particular way, which can be approximated by the gamma distribution. By incorporating these approximations into family structural analyses in the mating design, we are able to estimate a number of genetic parameters that contribute to quantitative genetic variation based on a nonlinear optimization approach. These parameters include the number of QTL, their gene effects, and their allele frequencies in the parental populations. We perform simulation studies and illustrate an example to demonstrate the statistical property and procedure of the method.     

The relationship between parental genetic or phenotypic divergence and progeny variation in the maize nested association mapping population

Appropriate selection of parents for the development of mapping populations is pivotal to maximizing the power of quantitative trait loci detection. Trait genotypic variation within a family is indicative of the family's informativeness for genetic studies. Accurate prediction of the most useful parental combinations within a species would help guide quantitative genetics studies. We tested the reliability of genotypic and phenotypic distance estimators between pairs of maize inbred lines to predict genotypic variation for quantitative traits within families derived from biparental crosses. We developed 25 families composed of ~200 random recombinant inbred lines each from crosses between a common reference parent inbred, B73, and 25 diverse maize inbreds. Parents and families were evaluated for 19 quantitative traits across up to 11 environments. Genetic distances (GDs) among parents were estimated with 44 simple sequence repeat and 2303 single-nucleotide polymorphism markers. GDs among parents had no predictive value for progeny variation, which is most likely due to the choice of neutral markers. In contrast, we observed for about half of the traits measured a positive correlation between phenotypic parental distances and within-family genetic variance estimates. Consequently, the choice of promising segregating populations can be based on selecting phenotypically diverse parents. These results are congruent with models of genetic architecture that posit numerous genes affecting quantitative traits, each segregating for allelic series, with dispersal of allelic effects across diverse genetic material. This architecture, common to many quantitative traits in maize, limits the predictive value of parental genotypic or phenotypic values on progeny variance.     

MATING SYSTEM AND ASYMMETRIC HYBRIDIZATION IN A MIXED STAND OF EUROPEAN OAKS

The sessile (Quercus petraea [Matt.] Liebl.) and pedunculate (Quercus robur L.) oaks are two closely related species having a wide sympatric distribution over Europe. Under natural conditions, they frequently form mixed forests, where hybridization is suspected to occur. In this paper, two different approaches have been applied to the study of the mating system and the interspecific gene flow in a mixed stand formed by the two species. The mating systems of both species have been studied separately by means of the mixed-mating model. The relative contribution of the parental species to the progenies have been estimated with two different methods. The first uses the admixture model. The second is an extension of the mixed-mating model and subdivides the outcrossing rate into intra- and interspecific components. The two species were almost completely outcrossing. This high level of outcrossing and interspecific gene flow could play an important role in the maintenance of the genetic diversity in these long-lived forest tree species. The contribution of the sessile oak to the pedunculate oak progenies varied from 17% to 48%. In contrast, ovules of sessile oak trees appear to be preferentially fertilized by other extreme sessile genotypes. We suggest that interspecific and directional gene flow was responsible for such patterns. Pedunculate oak is considered as a pioneer species and is progressively replaced by sessile oak. Our present findings add a further genetic component to this succession scheme, suggesting that unidirectional gene flow reinforces succession between the two species.     

Genetics of postzygotic isolation in Eucalyptus: whole-genome analysis of barriers to introgression in a wide interspecific cross of Eucalyptus grandis and E. globulus

The genetic architecture of hybrid fitness characters can provide valuable insights into the nature and evolution of postzygotic reproductive barriers in diverged species. We determined the genome-wide distribution of barriers to introgression in an F(1) hybrid of two Eucalyptus tree species, Eucalyptus grandis (W. Hill ex Maiden.) and E. globulus (Labill.). Two interspecific backcross families (N = 186) were used to construct comparative, single-tree, genetic linkage maps of an F(1) hybrid individual and two backcross parents. A total of 1354 testcross AFLP marker loci were evaluated in the three parental maps and a substantial proportion (27.7% average) exhibited transmission ratio distortion (alpha = 0.05). The distorted markers were located in distinct regions of the parental maps and marker alleles within each region were all biased toward either of the two parental species. We used a Bayesian approach to estimate the position and effect of transmission ratio distorting loci (TRDLs) in the distorted regions of each parental linkage map. The relative viability of TRDL alleles ranged from 0.20 to 0.72. Contrary to expectation, heterospecific (donor) alleles of TRDLs were favored as often as recurrent alleles in both backcrosses, suggesting that positive and negative heterospecific interactions affect introgression rates in this wide interspecific pedigree.     

Variable patterns of introgression in two sculpin hybrid zones suggest that genomic isolation differs among populations

Theory predicts that reproductive isolation may be due to intrinsic genetic incompatibilities or extrinsic ecological factors. Therefore, an understanding of the genetic basis of isolation may require analyses of evolutionary processes in situ to include environmental factors. Here we study genetic isolation between populations of sculpins ( Cottus ) at 168 microsatellites. Genomic clines were fit using 480 individuals sampled across independent natural hybrid zones that have formed between one invading species and two separate populations of a resident species. Our analysis tests for deviations from neutral patterns of introgression at individual loci based on expectations given genome-wide admixture. Roughly 51% of the loci analysed displayed significant deviations. An overall deficit of interspecific heterozygotes in 26% and 21% of the loci suggests that widespread underdominance drives genomic isolation. At the same time, selection promotes introgression of almost 30% of the markers, which implies that hybridization may increase the fitness of admixed individuals. Cases of overdominance or epistatic interactions were relatively rare. Despite the similarity of the two hybrid zones in their overall genomic composition, patterns observed at individual loci show little correlation between zones and many fit different genotypic models of fitness. At this point, it remains difficult to determine whether these results are due to differences in external selection pressures or cryptic genetic differentiation of distinct parental populations. In the future, data from mapped genetic markers and on variation of ecological factors will provide additional insights into the contribution of these factors to variation in the evolutionary consequences of hybridization.     

Coevolution of self-fertilization and inbreeding depression. I. Mutation-selection balance at one and two loci

Simple theories for the evolution of breeding systems suggest that the fate of an allele that modifies the rate of self-fertilization hinges only on the degree to which selfing reduces opportunities for outcrossing ("pollen discounting") and the extent of inbreeding depression. These theories predict that outcrossing evolves whenever deleterious mutations have a more severe effect in combination than expected from their individual effects. We study the evolutionary dynamics of a modifier of the rate of self-fertilization in populations subject to complete pollen discounting and recurrent mutations which impair viability at a single locus in diploids and at two loci in haploids. Our analysis indicates that genetic associations arising immediately upon the introduction of a rare modifier allele generate substantial quantitative and qualitative departures from expectation. Higher rates of segregation under selfing in our one-locus diploid model generate positive associations between enhancers of selfing and wild-type viability alleles, which in turn favor the evolution of selfing under a wider range of conditions than expected. Greater opportunities for recombination under outcrossing in our two-locus haploid model generate positive associations between enhancers of outcrossing and wild-type viability alleles. These associations favor the evolution of outcrossing under a wider range of conditions, and introduce the possibility of stable mixed mating systems involving both selfing and outcrossing. Our explicit analysis of genetic associations between loci affecting viability and the rate of self-fertilization indicates that modifiers that enhance the production of offspring with very high (and very low) viability by promoting segregation or recombination develop positive associations with high viability. This advantage of producing extremes can compensate for an initial disadvantage in offspring number.     

PATTERNS OF MATING IN WILD SUNFLOWER HYBRID ZONES

Theory predicts that homoploid hybrid speciation will be facilitated by selfing, yet most well-documented hybrid species are outcrossers. One possible explanation for this puzzle is that conditions in hybrid populations may favor selfing, even in otherwise outcrossing species. For example, in self-incompatible plants, mixtures of self and interspecific pollen often induce selfing. Here, we examine patterns of mating in three hybrid zones and four “pure” populations of Helianthus annuus and H. petiolaris, wild, self-incompatible sunflower species that are thought to have parented three homoploid hybrid species. Fourteen to 16 maternal families from each pure population and 44–46 maternal families from each hybrid zone were analyzed for seven polymorphic isozyme loci. Maximum-likelihood (ML) methods were used to estimate multilocus outcrossing rates (T_m) and hybridization frequencies for each maternal family, each phenotypic group within each hybrid zone (annuus-like, hybrid, and petiolaris-like), and each population. As predicted for self-incompatible species, all four parental populations have outcrossing rate ML estimates of 1.0. Within the hybrid zones, outcrossing rates were lowest in the H. annuus–like fraction of the population (0.73, 0.72, and 0.74 in the three hybrid zones, respectively), largely intermediate in the H. petiolaris–like group (0.94, 0.90, and 0.94), and highest in the hybrid group (0.97, 0.93, and 0.97). Although outcrossing rates are lower in hybrid zones than in pure populations, it is unlikely that the observed decrease facilitates hybrid speciation because outcrossing rates in the critical hybrid fraction of the population do not differ significantly from 1.0. Dividing the outcrossed pollen pool into intraspecific and interspecific components revealed that maternal plants are largely fertilized by conspecific pollen, confirming an important role for pollen competition as a reproductive barrier. Highly sterile hybrid plants do not appear to discriminate between parental species pollen, but hybrids with higher fertility tend to be fertilized by pollen from the parental group they resemble genetically. Thus, gametic selection leads to substantial assortative mating in these hybrid zones.     

Unexpected ancestry of Populus seedlings from a hybrid zone implies a large role for postzygotic selection in the maintenance of species

In the context of potential interspecific gene flow, the integrity of species will be maintained by reproductive barriers that reduce genetic exchange, including traits associated with prezygotic isolation or poor performance of hybrids. Hybrid zones can be used to study the importance of different reproductive barriers, particularly when both parental species and hybrids occur in close spatial proximity. We investigated the importance of barriers to gene flow that act early vs. late in the life cycle of European Populus by quantifying the prevalence of homospecific and hybrid matings within a mosaic hybrid zone. We obtained genotypic data for 11 976 loci from progeny and their maternal parents and constructed a Bayesian model to estimate individual admixture proportions and hybrid classes for sampled trees and for the unsampled pollen parent. Matings that included one or two hybrid parents were common, resulting in admixture proportions of progeny that spanned the whole range of potential ancestries between the two parental species. This result contrasts strongly with the distribution of admixture proportions in adult trees, where intermediate hybrids and each of the parental species are separated into three discrete ancestry clusters. The existence of the full range of hybrids in seedlings is consistent with weak reproductive isolation early in the life cycle of Populus. Instead, a considerable amount of selection must take place between the seedling stage and maturity to remove many hybrid seedlings. Our results highlight that high hybridization rates and appreciable hybrid fitness do not necessarily conflict with the maintenance of species integrity.     

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.     

Comparative genetic linkage maps of <Emphasis Type="Italic">Eucalyptus grandis</Emphasis>, <Emphasis Type="Italic">Eucalyptus globulus</Emphasis> and their F<Subscript>1</Subscript> hybrid based on a double pseudo-backcross mapping approach

Comparative genetic mapping in interspecific pedigrees presents a powerful approach to study genetic differentiation, genome evolution and reproductive isolation in diverging species. We used this approach for genetic analysis of an F₁ hybrid of two Eucalyptus tree species, Eucalyptus grandis (W. Hill ex Maiden.) and Eucalyptus globulus (Labill.). This wide interspecific cross is characterized by hybrid inviability and hybrid abnormality. Approximately 20% of loci in the genome of the F₁ hybrid are expected to be hemizygous due to a difference in genome size between E. grandis (640 Mbp) and E. globulus (530 Mbp). We investigated the extent of colinearity between the two genomes and the distribution of hemizygous loci in the F₁ hybrid using high-throughput, semi-automated AFLP marker analysis. Two pseudo-backcross families (backcrosses of an F₁ individual to non-parental individuals of the parental species) were each genotyped with more than 800 AFLP markers. This allowed construction of de novo comparative genetic linkage maps of the F₁ hybrid and the two backcross parents. All shared AFLP marker loci in the three single-tree parental maps were found to be colinear and little evidence was found for gross chromosomal rearrangements. Our results suggest that hemizygous AFLP loci are dispersed throughout the E. grandis chromosomes of the F₁ hybrid.Communicated by O. Savolainen     

Detecting epistatic genetic variance with a clonally replicated design: models for lowvs high-order nonallelic interaction

A quantitative genetic model, that uses known family structure with clonal replicates to separate genetic variance into its additive, dominance and epistatic components, is available in the current literature. Making use of offspring testing, this model is based on the theory that components of variance from the linear model of an experimental design may be expressed in terms of expected covariances among relatives. However, if interactions between a pair of quantitative trait loci (QTLs) explain a large proportion of the total epistasis, it will seriously overestimate the additive and dominance variances but underestimate the epistatic variance. In the present paper, a new model is developed to manipulate this problem by combining parental and offspring material into the same test. Under the condition described above, the new model can provide an accurate estimate for additive x additive variances. Also, its accuracy in estimating dominance and total epistatic variances is much greater than the accuracy of the previous model. However, if there is obvious evidence showing the major contribution of high-order interactions, especially among 4QTLs, to the total epistasis, the previous model is more appropriate to partition the genetic variance for a quantitative trait. The re-analysis of an example from a factorial mating design in poplar shows large differences in estimating variance components between the new and previous models when two different assumptions (lowvs high-order epistatic interactions) are used. The new model will be an alternative to estimating the mode of quantitative inheritance for species, especially for longlived, predominantly outcrossing forest trees, that can be clonally replicated.     

HETEROGENEITY IN POLLEN ALLELE FREQUENCIES AMONG CONES,WHORLS, AND TREES OF TABLE MOUNTAIN PINE (PINUS PUNGENS)

Pinus pungens Lambert (Table Mountain pine) is characterized by serotinous cones that are borne several (two to five) per whorl. Sporophytic and gametophytic tissues from whorls collected in different canopy zones of eight trees were electrophoresed and surveyed for six allozyme loci. Pollen allele frequencies received by individual trees, whorls on trees, and cones in whorls were estimated and used to estimate outcrossing rates and the distribution of genetic diversity within and among each level. Significant differences in pollen allele frequencies were detected at all levels, indicating that the genetic composition of the pollen pool available to different female strobili is heterogeneous. The fine-scale genetic structure in the seed pool is a record of past reproductive events and is the precursor to genetic structure in the next generation.     

The stationary distribution of allele frequencies when selection acts at unlinked loci

We consider population genetics models where selection acts at a set of unlinked loci. It is known that if the fitness of an individual is multiplicative across loci, then these loci are independent. We consider general selection models, but assume parent-independent mutation at each locus. For such a model, the joint stationary distribution of allele frequencies is proportional to the stationary distribution under neutrality multiplied by a known function of the mean fitness of the population. We further show how knowledge of this stationary distribution enables direct simulation of the genealogy of a sample at a single-locus. For a specific selection model appropriate for complex disease genes, we use simulation to determine what features of the genealogy differ between our general selection model and a multiplicative model.     

The genetic control of seven isozymic loci in Vicia faba L. Identification of lines and estimates of outcrossing rates between plants pollinated by bumble bees

A simplified and non-destructive method using starch gel electrophoresis has been developed on seeds to identify inbred lines of Vicia faba and assess outcrossing rates and gene dispersal in pollination experiments. Six enzyme systems (Alcohol dehydrogenase, Aspartate aminotransferase, Glucose-6-phosphate isomerase, Isocitrate dehydrogenase, Phosphogluconate dehydrogenase and Shikimate dehydrogenase) were analysed from parental lines, crosses performed between lines bearing dissimilar isozyme patterns in pollination cages with Bombus and F₂ progenies obtained from manual selfing of F₁ hybrids. The allozymes at each of the seven studied loci segregated in the expected Mendelian fashion and behaved in a co-dominant manner except for the Adh-2 locus where the only variant was a null allele. No evidence of genetic linkage was observed between at least 13 of the 15 pairs of the studied loci. Percentage of cross fertilisation by Bombus between seven pairs of inbred lines ranged between 1.7% and 28.3%. Pollen transfer between a donor line and a recipient line by two species of Bombus did not lead to differences in outcrossing rates (both about 8%). The new PGD marker with two loci at three alleles each is particularly discriminating and valuable in pollination studies and breeding of V. faba.     

Maintaining their genetic distance: Little evidence for introgression between widely hybridizing species of Geum with contrasting mating systems

Within the plant kingdom, many genera contain sister lineages with contrasting outcrossing and inbreeding mating systems that are known to hybridize. The evolutionary fate of these sister lineages is likely to be influenced by the extent to which they exchange genes. We measured gene flow between outcrossing Geum rivale and selfing Geum urbanum, sister species that hybridize in contemporary populations. We generated and used a draft genome of G. urbanum to develop dd‐RAD data scorable in both species. Coalescent analysis of RAD data from allopatric populations indicated that the species diverged 2–3 Mya, and that historical gene flow between them was extremely low (1 migrant every 25 generations). Comparison of genetic divergence between species in sympatry and allopatry, together with an analysis of allele frequencies in potential parental and hybrid populations, provided no evidence of contemporary introgression in sympatric populations. Cluster‐ and species‐specific marker analyses revealed that, apart from four early‐generation hybrids, individuals in sympatric populations fell into two genetically distinct groups that corresponded exactly to their morphological species classification with maximum individual admixture estimates of only 1–3%. However, we did observe joint segregation of four putatively introgressed SNPs across two scaffolds in the G. urbanum population that was associated with significant morphological variation, interpreted as tentative evidence for rare, recent interspecific gene flow. Overall, our results indicate that despite the presence of hybrids in contemporary populations, genetic exchange between G. rivale and G. urbanum has been extremely limited throughout their evolutionary history.     

Mating Systems of Three Tropical Dry Forest Tree Species1

Polymorphic allozyme loci were used to estimate outcrossing rates for three tree species from a disturbed dry forest in southern Costa Rica. Estimates of the multilocus outcrossing rates of Cedrela odorata and Jacaranda copaia were 0.969 and 0.982, respectively, and suggest that these species may be self-incompatible. The subcanopy tree Stemmadenia donnell-smithii also demonstrated little self-fertilization based on an estimated outcrossing rate of 0.896. Significant heterogeneity in pollen allele frequencies among maternal trees was detected for at least two enzyme loci for each species. A test of correlated mating between progeny of S. donnell-smithii revealed that all seeds within a fruit were singly sired. In addition, the low estimates of biparental inbreeding and significant differences in pollen and ovule allele frequencies for this species suggest that gene flow into the sampled forest fragment may occur. The implications of deforestation on the mating systems of these tropical tree taxa are discussed.     

Partitioning of population genetic variance under multiplicative-epistatic gene action

Determining the way in which different QTLs interact (epistasis) in their effects on the phenotype is crucial to many areas in population genetics and evolutionary biology. For example, in the founder event, a separated population readapts to a new environment through the release of cryptic gene-gene interactions. In hybrid zones, hybrid speciation must be subjected to natural selection for epistasis resulting from genomic recombinations between different species. However, there is a severe shortage of relevant methodologies to estimate epistatic genetic effects and variances. A statistical model has recently been proposed to estimate the number of QTLs, their genetic effects and allelic frequencies in segregating populations. This model is based on multiplicative gene action and derived from a two-level intra- and interspecific mating design. In this paper, we formulate a statistical procedure for partitioning the genetic variance into additive, dominant and various kinds of epistatic components in an intra- or mixed intra- and interspecific hybrid population. The procedure can be used to study the genetic architecture of fragmented populations and hybrid zones, thus allowing for a better recognition of the role of epistasis in evolution and hybrid speciation. A real example for two Populus species, P. tremuloides and P. tremula, is provided to illustrate the procedure. In this example, we found that considerable new genetic variation is formed through genomic recombination between two aspen species. Received: 1 May 1999 / Accepted: 27 July 1999     

Quantifying the genetic component of phenotypic variation in unpedigreed wild plants: tailoring genomic scan for within-population use

The study of adaptive genetic variation in natural populations is central to evolutionary biology. Quantitative genetics methods, however, are hardly applicable to long-lived organisms, and current knowledge on adaptive genetic variation in wild plants mostly refers to annuals and short-lived perennials. Studies on long-lived species are essential to explore possible life-history correlates of genetic variation, selection, and trait heritability. In this paper, we propose a method based on molecular markers to quantify the genetic basis of individual phenotypic differences in wild plants under natural conditions. Rather than focusing on inferring individual relatedness to estimate the heritability of phenotypic traits, we directly estimate the proportion of observed phenotypic variance that is statistically accounted for by genotypic differences between individuals. This is achieved by (i) identifying loci that are correlated across individuals with the phenotypic trait of interest by means of an amplified fragment length polymorphism (AFLP)-based explorative genomic scan, and (ii) fitting multiple regression and linear random effect models to estimate the effects of genotype, environment and genotype × environment on phenotypes. We apply this method to estimate genotypic and environmental effects on cumulative maternal fecundity in a wild population of the long-lived Viola cazorlensis monitored for 20 years. Results show that between 56–63% (depending on estimation method) of phenotypic variance in fecundity is accounted for by genotypic differences in 11 AFLP loci that are significantly related to fecundity. Genotype × environment effects accounted for 38% of fecundity variance, which may help to explain the unexpectedly high levels of genetic variance for fecundity found.     

Natural selection influences AFLP intraspecific genetic variability and introgression patterns in Atlantic eels

Investigating patterns of genetic variation in hybridizing species provides an opportunity to understand the impact of natural selection on intraspecific genetic variability and interspecific gene exchange. The Atlantic eels Anguilla rostrata and A. anguilla each occupy a large heterogeneous habitat upon which natural selection could differentially shape genetic variation. They also produce viable hybrids only found in Iceland. However, the possible footprint of natural selection on patterns of genetic variation within species and introgressive hybridization in Icelandic eels has never been assessed. We revisited amplified fragment length polymorphism data collected previously using population genomics and admixture analyses to test if (i) genetic variation could be influenced by non-neutral mechanisms at both the intra- and interspecific levels, and if (ii) selection could shape the spatio-temporal distribution of Icelandic hybrids. We first found candidate loci for directional selection within both species. Spatial distributions of allelic frequencies displayed by some of these loci were possibly related with the geographical patterns of life-history traits in A. rostrata , and could have been shaped by natural selection associated with an environmental gradient along European coasts in A. anguilla . Second, we identified outlier loci at the interspecific level. Non-neutral introgression was strongly suggested for some of these loci. We detected a locus at which typical A. rostrata allele hardly crossed the species genetic barrier, whereas three other loci showed accelerated patterns of introgression into A. anguilla in Iceland. Moreover, the level of introgression at these three loci increased from the glass eel to the yellow eel stage, supporting the hypothesis that differential survival of admixed genotypes partly explains the spatio-temporal pattern of hybrid abundance previously documented in Iceland.     

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.