Evolution and polymorphism in the multilocus Levene model with no or weak epistasis

Evolution and the maintenance of polymorphism under the multilocus Levene model with soft selection are studied. The number of loci and alleles, the number of demes, the linkage map, and the degree of dominance are arbitrary, but epistasis is absent or weak. We prove that, without epistasis and under mild, generic conditions, every trajectory converges to a stationary point in linkage equilibrium. Consequently, the equilibrium and stability structure can be determined by investigating the much simpler gene-frequency dynamics on the linkage-equilibrium manifold. For a haploid species an analogous result is shown. For weak epistasis, global convergence to quasi-linkage equilibrium is established. As an application, the maintenance of multilocus polymorphism is explored if the degree of dominance is intermediate at every locus and epistasis is absent or weak. If there are at least two demes, then arbitrarily many multiallelic loci can be maintained polymorphic at a globally asymptotically stable equilibrium. Because this holds for an open set of parameters, such equilibria are structurally stable. If the degree of dominance is not only intermediate but also deme independent, and loci are diallelic, an open set of parameters yielding an internal equilibrium exists only if the number of loci is strictly less than the number of demes. Otherwise, a fully polymorphic equilibrium exists only nongenerically, and if it exists, it consists of a manifold of equilibria. Its dimension is determined. In the absence of genotype-by-environment interaction, however, a manifold of equilibria occurs for an open set of parameters. In this case, the equilibrium structure is not robust to small deviations from no genotype-by-environment interaction. In a quantitative-genetic setting, the assumptions of no epistasis and intermediate dominance are equivalent to assuming that in every deme directional selection acts on a trait that is determined additively, i.e., by nonepistatic loci with dominance. Some of our results are exemplified in this quantitative-genetic context.     

Mitochondrial iso-citrate dehydrogenase variation in the Australian bush-rat, Rattus fuscipes greyii

Four reproductively isolated populations of the Australian bush-rat, Rattus fuscipes greyii , are polymorphic for electrophoretic variants of the mitochondrial enzyme, NADP-dependent iso-citrate dehydrogenase (M-Idh). The electrophoretic patterns of M-Idh and a small amount of breeding data are in agreement with the hypothesis that the variation is controlled by two alleles at an autosomal locus, Idh-2. In three relatively large populations, the proportion of heterozygotes at the Idh-2 locus ranges from 0.07 to 0.23, while on a small off-shore island it is 0.60. In this latter population there is an excess of heterozygotes which is on the borderline of statistical significance, suggesting that heterotic selection may be maintaining the polymorphism. Populations on eight other small islands are monomorphic for the allele which is the most frequent in the large populations. In most species M-Idh is less variable than most other enzymic proteins and the results presented here constitute one of the few published examples of an extensive M-Idh polymorphism.     

Gene interactions from maternal effects

Theoretical analyses have demonstrated a potential role for epistasis in many of the most important processes in evolution. These analyses generally assume that an individual's genes map directly to its phenotype and epistasis results from interactions among loci that contribute to the same biochemical or developmental pathways (termed physiological, or within-genotype, epistasis). For many characters, particularly those expressed early in life, an individual's phenotype may also be affected by genes expressed by its parents. The presence of these parental effects allows for interactions between the genes present in the parental and offspring genomes. When the phenotypic effect of a locus in the offspring depends on the alleles possessed by its parents, genotype-by-genotype, or among-genotype, epistasis occurs. The among-genotype epistasis resulting from parental effects may contribute to ruggedness of adaptive landscapes because early mortality often accounts for much of the variance in fitness in populations. To demonstrate how parent-offspring interactions can result in among-genotype epistasis, I use a two-locus model, with one maternal effect locus and one direct effect locus, each with two alleles. Dynamical equations are presented for the two-locus model and are directly contrasted with the dynamical equations derived for a model for physiological epistasis. The relationship between the evolutionary dynamics resulting from these two forms of epistasis is discussed. Three scenarios are presented to illustrate systems in which maternal-offspring, genotype-by-genotype epistasis may occur. The implications of maternal-offspring epistasis for quantitative-trait-loci studies are also discussed.     

Evidence for Linkage Disequilibrium Maintained by Selection in Two Natural Populations of DROSOPHILA SUBOBSCURA

One island and one mainland population of Drosophila subobscura were found polymorphic at the XDH (xanthine dehydrogenase) and the AO (aldehyde oxidase) loci. It was observed that one allele at the XDH locus, which has a low frequency in both populations, is nonrandomly associated with the alleles at the AO locus. Two lines of evidence support the thesis that this linkage disequilibrium is due to epistasis rather than random drift: (1) D or r, measures of the disequilibrium, have the same sign and magnitude in both populations. (2) The linkage disequilibrium is not due to inversions. Inversions segregating on the chromosome carrying XDH and AO have been separated into two classes, between which exchange of alleles at the two loci is suppressed. Linkage disequilibrium for XDH and AO was observed within each class. In the absence of any exchange of alleles, these disequilibria must have arisen and been maintained independently. The suggestion is made that the epistatic disequilibrium results from the close structural and physiological relationship which exists between the two enzymes.     

Inheritance of parthenocarpy in summer squash (Cucurbita pepo L.)

The inheritance of the tendency to set parthenocarpic fruit in the summer squash (Cucurbita pepo L.) line Whitaker was studied. Two parental lines, Whitaker (parthenocarpic) and Caserta (non-parthenocarpic), and the F1 and F2 generations and backcrosses to both parents were tested. The parthenocarpic tendency of individual plants was scored on a scale from 1 (non-parthenocarpic fruit) to 5 (parthenocarpic fruit). The Whitaker line produced parthenocarpic fruit and had a mean score of 4.2, whereas Caserta did not set parthenocarpic fruit and had a score of 1.55. The heritability estimates indicated that genetic gains from selection were feasible. The additive-dominant model showed a good fit, with epistasis being negligible or nonexistent. The hypothesis of monogenic inheritance with incomplete dominance was not rejected within the degree of dominance range from 0.2 to 0.5. These results indicate that parthenocarpy is controlled by a single locus, with incomplete dominance in the direction of parthenocarpic expression.     

Evolution of dominance in polymorphic Batesian mimicry

Models of two simple genetic systems of two alleles segregating at two loci are used to study the evolution of dominance of a Batesian mimic maintained in a population by frequency-dependent selection. The alleles at one locus determine the mimetic patterns, and their dominance is modified by the alleles at the other locus. In the model, the modifiers of dominance may themselves be either fully dominant or have additive effects on the dominance of the mimics. When the modifier is fully dominant in its effect on the dominance of a new mimic, the mimic will evolve dominance irrespective of the initial frequency of the modifier. When the modifiers act additively on the dominance of the mimics, a new mimic will evolve either dominance or recessiveness depending on the initial frequency of the modifiers. Unless the modifier is initially at quite a high frequency dominance will not evolve. And dominance will not evolve fully unless the modifiers are more or less selectively neutral in their effects on all other characters except the mimicry. The significance of these results is discussed with reference to the different dominance relations of the mimics in different races of the butterfly Papilio dardanus.     

Molecular mechanisms of dominance evolution in Müllerian mimicry

Natural selection acting on dominance between adaptive alleles at polymorphic loci can be sufficiently strong for dominance to evolve. However, the molecular mechanisms underlying such evolution are generally unknown. Here, using Müllerian mimicry as a case‐study for adaptive morphological variation, we present a theoretical analysis of the invasion of dominance modifiers altering gene expression through different molecular mechanisms. Toxic species involved in Müllerian mimicry exhibit warning coloration, and converge morphologically with other toxic species of the local community, due to positive frequency‐dependent selection acting on these colorations. Polymorphism in warning coloration may be maintained by migration–selection balance with fine scale spatial heterogeneity. We modeled a dominance modifier locus altering the expression of the warning coloration locus, targeting one or several alleles, acting in cis or trans, and either enhancing or repressing expression. We confirmed that dominance could evolve when balanced polymorphism was maintained at the color locus. Dominance evolution could result from modifiers enhancing one allele specifically, irrespective of their linkage with the targeted locus. Nonspecific enhancers could also persist in populations, at frequencies tightly depending on their linkage with the targeted locus. Altogether, our results identify which mechanisms of expression alteration could lead to dominance evolution in polymorphic mimicry.     

Variations de la malate déshydrogénase dans quatre espèces de Jaera albifrons: Etude génétique et variation géographique

Malate dehydrogenase has been detected in four species of the super-species Jaera albifrons. Two polymorphic enzymatic systems occur showing a one banded pattern for homozygotes and a three banded pattern for heterozygotes. Two independant autosomal loci control the variation as is shown by intra- and interspecific crosses. In European populations of the three species studied, MDH-1 is polymorphic and MDH-2 is monomorphic. In the American species, J. posthirsuta, the locus MDH-2 is polymorphic and MDH-1 is monomorphic.     

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.     

A sero-biochemical genetic study of Jalari and Brahmin caste populations of Andhra Pradesh, India

Blood specimens from Jalari and Brahmin caste populations of Andhra Pradesh, India, were examined for blood groups, red cell enzymes, and serum proteins. Of 33 genetic loci studied, 16 were observed to be invariant among both the castes, while common polymorphism or rare variants were observed in one or both populations for the other loci. Three rare heterozygotes at the phosphoglucoisomerase locus, two different peptidase A variants occurring once each and single cases of rare 6-phosphogluconate dehydrogenase and transferrin variants were recorded. Also a few cases of hemoglobin AS and anhaptoglobinemia were observed. The difference in rare variants between the two castes is conspicuous but large differences in their gene frequencies at the polymorphic loci were not observed. It is pointed out that the frequency of rare variants in the tribal and caste populations of Southern India appears to be higher than observed in temperate-dwelling civilized populations.     

Dominance Is the Major Genetic Basis of Heterosis in Rice as Revealed by Qtl Analysis Using Molecular Markers

A set of 194 F(7) lines derived from a subspecific rice cross showing strong F(1) heterosis was backcrossed to the two parents. The materials (388 BC(1)F(7) lines, 194 F(8) lines, two parents, F(1)) were phenotyped for 12 quantitative traits. A total of 37 significant QTLs (LOD >/= 2.0) was detected through 141 RFLP markers in the BC(1)F(7) populations. Twenty-seven (73%) quantitative trait loci (QTLs) were detected in only one of the BC(1)F(7) populations. In 82% of these cases, the heterozygotes were superior to the respective homozygotes. The remaining 10 (27%) QTLs were detected in both BC(1)F(7) populations, and the heterozygote had a phenotype falling between those of the two homozygotes and in no instances were the heterozygotes found to be superior to both homozygotes. These results suggest that dominance complementation is the major genetic basis of heterosis in rice. This conclusion was strengthened by the finding that there was no correlation between most traits and overall genome heterozygosity and that there were some recombinant inbred lines in the F(8) population having phenotypic values superior to the F(1) for all of the traits evaluated--a result not expected if overdominance was a major contributor to heterosis. Digenic epistasis was not evident.     

Restriction Fragment Length Polymorphism Mapping of Quantitative Trait Loci for Malaria Parasite Susceptibility in the Mosquito Aedes Aegypti

Susceptibility of the mosquito Aedes aegypti to the malarial parasite Plasmodium gallinaceum was investigated as a quantitative trait using restriction fragment length polymorphisms (RFLP). Two F(2) populations of mosquitoes were independently prepared from pairwise matings between a highly susceptible and a refractory strain of A. aegypti. RFLP were tested for association with oocyst development on the mosquito midgut. Two putative quantitative trait loci (QTL) were identified that significantly affect susceptibility. One QTL, pgs[2,LF98], is located on chromosome 2 and accounted for 65 and 49% of the observed phenotypic variance in the two populations, respectively. A second QTL, pgs[3,MalI], is located on chromosome 3 and accounted for 14 and 10% of the observed phenotypic variance in the two populations, respectively. Both QTL exhibit a partial dominance effect on susceptibility, wherein the dominance effect is derived from the refractory parent. No indication of epistasis between these QTL was detected. Evidence suggests that either a tightly linked cluster of independent genes or a single locus affecting susceptibility to various mosquito-borne parasites and pathogens has evolved near the LF98 locus; in addition to P. gallinaceum susceptibility, this general genome region has previously been implicated in susceptibility to the filarial nematode Brugia malayi and the yellow fever virus.     

Complex genetic architecture of population differences in adult lifespan of a beetle: nonadditive inheritance, gender differences, body size and a large maternal effect

Evolutionary responses to selection can be complicated when there is substantial nonadditivity, which limits our ability to extrapolate from simple models of selection to population differentiation and speciation. Studies of Drosophila melanogaster indicate that lifespan and the rate of senescence are influenced by many genes that have environment- and sex-specific effects. These studies also demonstrate that interactions among alleles (dominance) and loci (epistasis) are common, with the degree of interaction differing between the sexes and among environments. However, little is known about the genetic architecture of lifespan or mortality rates for organisms other than D. melanogaster. We studied genetic architecture of differences in lifespan and shapes of mortality curves between two populations of the seed beetle, Callosobruchus maculatus (South India and Burkina Faso populations). These two populations differ in various traits (such as body size and adult lifespan) that have likely evolved via host-specific selection. We found that the genetic architecture of lifespan differences between populations differs substantially between males and females; there was a large maternal effect on male lifespan (but not on female lifespan), and substantial dominance of long-life alleles in females (but not males). The large maternal effect in males was genetically based (there was no significant cytoplasmic effect) likely due to population differences in maternal effects genes that influence lifespan of progeny. Rearing host did not affect the genetic architecture of lifespan, and there was no evidence that genes on the Y-chromosome influence the population differences in lifespan. Epistatic interactions among loci were detectable for the mortality rate of both males and females, but were detectable for lifespan only after controlling for body size variation among lines. The detection of epistasis, dominance, and sex-specific genetic effects on C. maculatus lifespan is consistent with results from line cross and quantitative trait locus studies of D. melanogaster.     

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.     

Isolation and characterization of nine microsatellite loci from the pike-perch, Sander lucioperca (Linnaeus, 1758)

In order to facilitate studies on the genetic structure of wild populations as well as to monitor genetic changes in cultured stocks, nine polymorphic microsatellite loci were isolated from pike-perch (Sander lucioperca). Single loci allele numbers varied between two (loci MSL-3 and MSL-7) and six (loci MSL-1 and MSL-2), and observed heterozygosities ranged from 0.36 (locus MSL-2) to 1.00 (locus MSL-9) in a test panel of 25 individuals. Only one pair of loci (MSL-5 and MSL-8) displayed significant linkage disequilibrium after sequential Bonferroni corrections. Hardy-Weinberg tests revealed significant excesses of heterozygotes at three loci (MSL-1, MSL-7, and MSL-9).     

Colour pattern specification in the Mocker swallowtail Papilio dardanus: the transcription factor invected is a candidate for the mimicry locus H

The swallowtail butterfly, Papilio dardanus, is an iconic example of a polymorphic Batesian mimic. The expression of various female-limited colour forms is thought to be controlled by a single autosomal locus, termed H, whose function in determining the wing pattern remains elusive. As a step towards the physical mapping of H, we established a set of 272 polymorphic amplified fragment length polymorphism (AFLP) markers (EcoRI-MseI). Segregation patterns in a 'female-informative' brood (exploiting the absence of crossing over in female Lepidoptera) mapped these AFLPs to 30 linkage groups (putative chromosomes). The difference between the hippocoon and cenea female forms segregating in this family resides on a single one of these linkage groups, defined by 14 AFLPs. In a 'male-informative' cross (markers segregating within a linkage group), a pair of AFLPs co-segregated closely with the two female forms, except in four recombinants out of 19 female offspring. Linkage with these AFLP markers using four further female-informative families demonstrated that the genetic factor determining other morphs (poultoni, lamborni and trimeni) also maps to this same linkage group. The candidate gene invected, obtained in a screen for co-segregation of developmental genes with the colour forms, resides in a 13.9 cM interval flanked by the two AFLP markers. In the male-informative family invected co-segregated perfectly with the hippocoon/cenea factor, despite the four crossovers with the AFLPs. These findings make invected, and possibly its closely linked paralogue engrailed, strong candidates for H. This is supported by their known role in eyespot specification in nymphalid butterfly wings.     

Cross prediction studies on spring barley

Summary The genetical and environmental control of three height characters, two maturity characters and neck length in five barley pair crosses was studied using both F₂ triple test cross and model fitting analysis.Significant additive and dominance effects were found for all six characters with some evidence of epistasis for each character. Generally, dominance was incomplete for the height characters but was significantly directional for increased height in those crosses where dwarfing genes were segregating. Variable dominance effects were found for both the maturity characters. Complete dominance was found in three cases, otherwise incomplete dominance was found. Significant directional dominance for earliness was found for both maturity characters in one cross but this was attributed to the presence of a daylength insensitivity factor in one of the parents. Most of the genetic variation for neck length was additive, though some evidence of dominance was found.Broad sense and narrow sense heritability estimates generally were found to be high for the height and maturity characters but low for neck length. It was concluded that early generation selection for height at ear emergence, for final height and for awn emergence was worthwhile. Early generation selection for neck length was not recommended from the results of this study.     

A two-locus mutation—Selection model and some of its evolutionary implications

The deterministic properties of a two-locus model with mutation and selection have been investigated. The mutation process is unidirectional, and the model is so constructed that the genetic variation at one locus is selectively neutral in the absence of a mutant allele at the other locus. All genotypes with three or four mutant alleles are deleterious, while the double heterozygotes may have the same fitness as the standard genotype. If one of the mutant alleles becomes fixed in the population, then the other locus will show a regular one-locus mutation-selection balance. Such a boundary equilibrium may be unstable or stable in the full two-locus setting. In the symmetric case, which is analyzed in details, the population will either go to one of the two boundary equilibria, or to a fully polymorphic equilibrium at which both the mutant alleles are rare. The origin of reproductive separation between two populations via the fixation of complementary deleterious mutants at different loci, and the fixation of nonfunctional alleles at duplicated loci, are two biological processes which both can be studied with the present model. In the last part of the paper we show how the results from the deterministic analysis can be used to predict how different factors will influence the rates of evolution in these systems.     

A single origin of Batesian mimicry among hybridizing populations of admiral butterflies (Limenitis arthemis) rejects an evolutionary reversion to the ancestral phenotype

Batesian mimicry is a fundamental example of adaptive phenotypic evolution driven by strong natural selection. Given the potentially dramatic impacts of selection on individual fitness, it is important to understand the conditions under which mimicry is maintained versus lost. Although much empirical and theoretical work has been devoted to the maintenance of Batesian mimicry, there are no conclusive examples of its loss in natural populations. Recently, it has been proposed that non-mimetic populations of the polytypic Limenitis arthemis species complex represent an evolutionary loss of Batesian mimicry, and a reversion to the ancestral phenotype. Here, we evaluate this conclusion using segregating amplified fragment length polymorphism markers to investigate the history and fate of mimicry among forms of the L. arthemis complex and closely related Nearctic Limenitis species. In contrast to the previous finding, our results support a single origin of mimicry within the L. arthemis complex and the retention of the ancestral white-banded form in non-mimetic populations. Our finding is based on a genome-wide sampling approach to phylogeny reconstruction that highlights the challenges associated with inferring the evolutionary relationships among recently diverged species or populations (i.e. incomplete lineage sorting, introgressive hybridization and/or selection).     

A multiplicative-epistatic model for analyzing interspecific differences in outcrossing species

Epistasis may play an important role in evolution and speciation. Under multiplicative interactions between different loci, an analytical model is proposed to estimate genetic parameters at the individual locus level that contribute to interspecific differences in outcrossing species. The multiplicative epistasis model, inferred from a number of animal and plant experiments, suggests that genotypes at a pair of loci have genotypic values equal to the product of genotypic values at the two different loci. By considering the genetic property of outcrossing species (i.e., high polymorphisms) in the multilevel family structure analysis for an intra- and interspecific factorial mating design, a method is developed to provide estimates for allele frequencies and additive and dominant effects at individual loci in each of the two parental populations, the genotypic values of newly formed heterozygotes through species combination each with one allele from a parental population and the second from the other parental population, and the numbers of genetic factors that lead to species differentiation. Use of clones offers a tremendous power to test the adequacy of the model. However, the utilization of the model with species that cannot be cloned is also discussed. An example with interspecific hybrids of two forest tree species is used to demonstrate the model.