The generalized multiplicative model for viability selection at multiple loci

Selection due to differential viability is studied in an n-locus two-allele model using a set indexation that allows the simplicity of the one-locus two-allele model to be carried to multi-locus models. The existence condition is analyzed for polymorphic equilibria with linkage equilibrium: Robbins' equilibria. The local stability condition is given for the Robbins' equilibria on the boundaries in the generalized non-epistatic selection regimes of Karlin and Liberman (1979). These generalized non-epistatic regimes include the additive selection model, the multiplicative selection model and the multiplicative interaction model, and their symmetric versions cover all the symmetric viability models.Research supported by grant no. 11-7805 from the Danish Natural Science Research Council, by NIH grant GM 28016, by a fellowship from the Research Foundation of Aarhus University, and by a visiting fellowship from the University of New England, N.S.W.     

Global convergence properties in multilocus viability selection models: the additive model and the Hardy-Weinberg law

A natural coordinate system is introduced for the analysis of the global stability of the Hardy-Weinberg (HW) polymorphism under the general multilocus additive viability model. A global convergence criterion is developed and used to prove that the HW polymorphism is globally stable when each of the loci is diallelic, provided the loci are overdominant and the multilocus recombination is positive. As a corollary the multilocus Hardy-Weinberg law for neutral selection is derived.Research supported in part by NIH grants GM 39907-01, GM 10452-26 and NSF Grant DMS 86-06244Research supported in part by a US-Israel Binational Science Foundation grant 85-00021 and NIH grant GM 28016     

上位性及其在遗传育种研究中的应用

上位性引入遗传学已有一个多世纪,直到近些年才受到广泛关注,成为复杂性状遗传研究体系的一个重要组成部分。上位性可分为统计上位性和功能上位性两类,前者具有群体特性,后者属于基因型现象。分子标记技术是研究上位性的一个有力工具,理论与实验研究证实上位性在动植物数量性状的表现中具有重要作用。上位性在作物育种中的应用因作物的繁殖方式,育种方法等不同而异,上位性是杂种优势形成的重要遗传基础。     

A symmetric two locus model with viability and fertility selection

A two locus deterministic population genetic model is analysed. One locus is under viability selection, the other under fertility selection with both forms of selection completely symmetric. It is shown that linkage equilibrium may occur at two different equilibrium points. For a two-locus polymorphism to be stable, it is necessary that the viability locus be overdominant but not necessary that the fertility locus, considered separately, be able to support a stable polymorphism. The overlaps in stability are not as complex as under two locus symmetric fertilities, but considerably more complex than with symmetric viabilities. Extensions of the analysis for the central linkage equilibrium point with multiple viability and fertility loci are indicated.Research supported in part by NIH grants GM 28106 and GM 10452     

Epistasis Creates Invariant Sites and Modulates the Rate of Molecular Evolution

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

Modeling Epistasis in Genomic Selection

Modeling epistasis in genomic selection is impeded by a high computational load. The extended genomic best linear unbiased prediction (EG-BLUP) with an epistatic relationship matrix and the reproducing kernel Hilbert space regression (RKHS) are two attractive approaches that reduce the computational load. In this study, we proved the equivalence of EG-BLUP and genomic selection approaches, explicitly modeling epistatic effects. Moreover, we have shown why the RKHS model based on a Gaussian kernel captures epistatic effects among markers. Using experimental data sets in wheat and maize, we compared different genomic selection approaches and concluded that prediction accuracy can be improved by modeling epistasis for selfing species but may not for outcrossing species.     

Epistasis can accelerate adaptive diversification in haploid asexual populations

A fundamental goal of the biological sciences is to determine processes that facilitate the evolution of diversity. These processes can be separated into ecological, physiological, developmental and genetic. An ecological process that facilitates diversification is frequency-dependent selection caused by competition. Models of frequency-dependent adaptive diversification have generally assumed a genetic basis of phenotype that is non-epistatic. Here, we present a model that indicates diversification is accelerated by an epistatic basis of phenotype in combination with a competition model that invokes frequency-dependent selection. Our model makes use of a genealogical model of epistasis and insights into the effects of balancing selection on the genealogical structure of a population to understand how epistasis can facilitate diversification. The finding that epistasis facilitates diversification may be informative with respect to empirical results that indicate an epistatic basis of phenotype in experimental bacterial populations that experienced adaptive diversification.     

A general approach for the study of a population of testcross progenies and consequences for recurrent selection

Summary A model to study genetic effects at the level of a population of testcross progenies is presented. As there is no dominance for the testcross value, with the restriction of epistasis to pairs of loci, only additive x additive epistasis can contribute to the variance among progenies. To estimate the variance among progenies due to epistasis, it is necessary to have the population structured in families of full sibs, half sibs or S₁, with only a few plants per family tested in combination with the tester. Using a two-way mating design to produce the families, it is possible to estimate the variance due to additive x additive epistasis. The consequence of the presence of epistasis is studied at the level of recurrent selection for combining ability with the tester. It seems that epistasis itself does not change the efficiency of the breeding methods considered. However, when the population from intercrossing is structured in families, it could be efficient to use a combined selection when the heritability is very low. In this case it would be efficient to produce full-sib families (by single-pair matings) at the level of intercrossing. The best procedure is to produce such families at the same time as crossing with the tester. In comparison to the classical scheme of selection for combining ability with a tester, such a modification increases the efficiency of selection 41.1% if an off-season generation can be used.     

Allelic diversity at the Mhc-DQA locus of woodmouse populations (Apodemus sylvaticus) present in the islands and mainland of the northern Mediterranean

Aim Polymorphism at neutral markers and at MHC loci in rodent populations living on islands is generally low. The main genetic factors that may contribute to a reduced level of genetic variability are genetic drift, reduced gene flow and founder events. We investigated the pattern of polymorphism at the second exon of the Mhc‐DQA gene in island populations of Apodemus sylvaticus and in their mainland counterparts to investigate the pattern of MHC polymorphism in a phylogeographical context and to assess the impact of insularity on diversity at this locus. Location Eight north Mediterranean populations of Apodemus sylvaticus were studied, including five island populations (Majorca, Minorca, Porquerolles, Port‐Cros and Sicily) and three mainland populations. Methods cDNA sequencing and nucleotide sequences analyses. Synonymous and non‐synonymous substitutions were examined at the PBR and non‐PBR sites. The DQA allelic distribution in populations was compared with the woodmouse phylogeography. Results This study presents novel DQA alleles. High polymorphism of the DQA locus is recorded in natural populations of A. sylvaticus with 13 alleles being widely distributed irrespective of the geographical origin and palaeoclimatic history of populations. The DQA locus does not show the expected pattern for non‐synonymous substitutions at the PBR sites. However, island populations show a weak loss of polymorphism in comparison with their mainland counterparts. Main conclusions The DQA locus in the woodmouse seems to be subject to weak selection and does not allow resolution of phylogeographical relationships among European woodmouse populations. The presence of at least three alleles in island populations and the maintenance of five alleles between the two European lineages over 1.5 Myr suggest that balancing selection may act within populations, and more precisely within island populations, to maintain genetic variability. This study shows that phylogeographical studies are a prerequisite for any genetic investigation of selected genes in natural populations.     

Epistasis affecting litter size in mice

Litter size is an important reproductive trait as it makes a major contribution to fitness. Generally, traits closely related to fitness show low heritability perhaps because of the corrosive effects of directional natural selection on the additive genetic variance. Nonetheless, low heritability does not imply, necessarily, a complete absence of genetic variation because genetic interactions (epistasis and dominance) contribute to variation in traits displaying strong heterosis in crosses, such as litter size. In our study, we investigated the genetic architecture of litter size in 166 females from an F2 intercross of the SM/J and LG/J inbred mouse strains. Litter size had a low heritability (h2 = 12%) and a low repeatability (r = 33%). Using interval-mapping methods, we located two quantitative trait loci (QTL) affecting litter size at locations D7Mit21 + 0 cM and D12Mit6 + 8 cM, on chromosomes 7 and 12 respectively. These QTL accounted for 12.6% of the variance in litter size. In a two-way genome-wide epistasis scan we found eight QTL interacting epistatically involving chromosomes 2, 4, 5, 11, 14, 15 and 18. Taken together, the QTL and their interactions explain nearly 49% (39.5% adjusted multiple r2) of the phenotypic variation for litter size in this cross, an increase of 36% over the direct effects of the QTL. This indicates the importance of epistasis as a component of the genetic architecture of litter size and fitness in our intercross population.     

Relevance of Higher-Order Epistasis in Drug Resistance

We studied five chemically distinct but related 1,3,5-triazine antifolates with regard to their effects on growth of a set of mutants in dihydrofolate reductase. The mutants comprise a combinatorially complete data set of all 16 possible combinations of four amino acid replacements associated with resistance to pyrimethamine in the malaria parasite Plasmodium falciparum. Pyrimethamine was a mainstay medication for malaria for many years, and it is still in use in intermittent treatment during pregnancy or as a partner drug in artemisinin combination therapy. Our goal was to investigate the extent to which the alleles yield similar adaptive topographies and patterns of epistasis across chemically related drugs. We find that the adaptive topographies are indeed similar with the same or closely related alleles being fixed in computer simulations of stepwise evolution. For all but one of the drugs the topography features at least one suboptimal fitness peak. Our data are consistent with earlier results indicating that third order and higher epistatic interactions appear to contribute only modestly to the overall adaptive topography, and they are largely conserved. In regard to drug development, our data suggest that higher-order interactions are likely to be of little value as an advisory tool in the choice of lead compounds.     

Epistasis in natural populations of a predominantly selfing plant

Populations of predominantly selfing plant species often show spatial genetic structure but little is known whether epistatic gene interactions are spatially structured. To detect a possible epistatic effect and a spatial scale at which it operates, we created artificial crosses between plants spanning a range of fixed distances from 1 to 400 m in three populations of wild barley. The self-pollinated and crossed progeny (F₁) and two generations of segregated progeny (F₂ and F₃) were tested in experimentally simulated population environments for relative performance (RP). The measured fitness traits included number of seeds, total seed weight and seed germination. For any of these traits, there was no association between RP of F₁, F₂ and F₃ plants and either pairwise kinship coefficients or crossing distance. In contrast, in all three populations, we found lower seed viability of outcrossed as compared with self-pollinated genotypes in the first generation of segregation. However, in the F₃ generation this outbreeding effect disappeared in the two populations and greatly decreased in the third population. For seed production, heterosis in F₁ and outbreeding depression in F₂ were observed only in the population with unusually high number of heterozygotes. Our findings support the view that in selfing species a spatial mosaic of various locally abundant genotypes represents not randomly fixed combinations of alleles but the co-adapted gene complexes that were sieved by selection, while heterozygotes are characteristic for the transient phase of this process, when segregation and purging of maladaptive genotypes have not yet occurred.     

Epistasis buffers the fitness effects of rifampicin- resistance mutations in Pseudomonas aeruginosa

Epistatic interactions between resistance mutations in antibiotic-free environments potentially play a crucial role in the spread of resistance in pathogen populations by determining the fitness cost associated with resistance. We used an experimental evolution approach to test for epistatic interactions between 14 different pairs of rifampicin mutations in the pathogenic bacterium Pseudomonas aeruginosa in 42 different rifampicin-free environments. First, we show that epistasis between rifampicin-resistance mutations tends to be antagonistic: the fitness effect of having two mutations is generally smaller than that predicted from the effects of individual mutations on the wild-type. Second, we show that sign epistasis between resistance mutations is both common and strong; most notably, pairs of deleterious resistance mutations often partially or completely compensate for each others' costs, revealing a novel mechanism for compensatory adaptation. These results suggest that antagonistic epistasis between intragenic resistance mutations may be a key determinant of the cost of antibiotic resistance and compensatory adaptation in pathogen populations.     

Epistasis, phenotypic disequilibrium and contrasting associations with climate in the land snail Theba pisana

Hotter conditions favour effectively unbanded (EUB) shells in the snail Theba pisana. T. pisana is also polymorphic for colour of the shell's apex, determined by a pair of alleles at a locus linked to the banding locus. Apex colour is epistatic to shell banding, such that banded snails with a dark apex have darker bands. Annual censuses over 22 years across an ecotone between a sheltered Acacia thicket and open dune vegetation showed a persistent association of both EUB shells and pale apex with the Open habitat. The parallel variation was due partly to strong phenotypic disequilibrium, as the combination of EUB with dark apex was rare. Nevertheless, in fully banded shells the frequency of pale apex was also higher in the Open habitat, confirming independent, parallel associations of the two contributors to paleness. Within the Acacia habitat, temporal variation of the frequencies of banding morphs was much greater than for apex colour, and EUB shells were associated with hotter summers. Consistent with its primary effect only on the very small snails, apex colour did not vary with summer conditions, but instead, higher frequencies of pale apices were associated with sunnier winters. The intensity of selection was lower on apex colour than shell banding, due partly to the constraint of phenotypic disequilibrium. The shell traits in T. pisana are an example of complex responses to climatic variation, in which phenotypic disequilibrium constrains evolution of apex colour, but separate mechanisms of selection are evident.     

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.     

Developmental rate and viability of rainbow trout with a null allele at a lactate dehydrogenase locus

We show that a previously described isozyme polymorphism in rainbow trout(Salmo gairdneri) is the result of an enzymatically inactive (i.e., null) allele(n). Ldh3 null homozygotes(n/n) and heterozygotes(100/n) have reductions of about 20 and 12% in total lactate dehydrogenase (LDH) activity at hatching, respectively. As juveniles,(100/n) fish have reductions in LDH activity of 15, 37, and 21% in brain, heart, and white muscle, respectively. Embryos with differntLdh3 phenotypes from 11 families do not differ significantly in either survival or hatching time. However, a second measure of developmental rate, the amount of malate dehydrogenase (MDH) and phosphoglucomutase (PGM) activity in 33-day-old embryos, suggests that(100/n) embryos develop more slowly than(100/100) embryos. In three of four families examined,(100/n) embryos have significantly lower amounts of total MDH activity (8–10%). In one of these,(100/n) embryos also have significantly lower total PGM activity (15%). These data suggest that the reduction in total LDH activity is associated with small but detectable delays in developmental rate but nondetectable differences in survival to hatching.This research was supported by NSF Grant BSR-8300039 to F. W. Allendorf and a postgraduate scholarship from the NSERC (Canada) to M. M. Ferguson.     

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

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