Evolution of the segregation ratio: modification of gene conversion and meiotic drive

We compare the evolutionary pressures that direct the modification of gene conversion and meiotic drive at loci subject to purifying and overdominant viability selection. Gene conversion differs from meiotic drive in that modifers do not affect their own segregation ratios, even when linked to the viability locus. Segregation distortion generates gametic level disequilibria between alleles at the viability locus and modifiers of gene conversion and meiotic drive: enhancers of segregation distortion become positively associated with driven alleles. Suppression of gene conversion evolves if the driven allele is marginally disadvantageous (overdominant viability selection), and higher rates evolve if the driven alleles are relatively advantageous (purifying viability selection). Gametic disequilibria permit enhancers of meiotic drive that are linked to the driven locus to promote their own segregation. We attribute the failure of genetic modifiers of gene conversion and meiotic drive to maximinize mean fitness to the generation of such associations.     

Rates of decay of linkage disequilibrium under two-locus models of selection

The effect of selection and linkage on the decay of linkage disequilibrium, D, is investigated for a hierarchy of two-locus models. The method of analysis rests upon a qualitative classification of the dynamic of D under selection relative to the neutral dynamic. To eliminate the confounding effects of gene frequency change, the behavior of D is first studied with gene frequencies fixed at their invariant values. Second, the results are extended to certain special situations where gene frequencies are changing simultaneously.A wide variety of selection regimes can cause an acceleration of the rate of decay of D relative to the neutral rate. Specifically, the asymptotic rate of decay is always faster than the neutral rate in the neighborhood of a stable equilibrium point, when viabilities are additive or only one locus is selected. This is not necessarily the case for models in which there is nonzero additive epistasis. With multiplicative viabilities, decay is always accelerated near a stable boundary equilibrium, but decay is only faster near the stable central equilibrium (with = 0) if linkage is sufficiently loose. In the symmetric viability model, decay may even be retarded near a stable boundary equilibrium. Decay is only accelerated near a stable corner equilibrium when the double homozygote is more fit than the double heterozygotes. Decay near a stable edge equilibrium may be retarded if there is loose linkage. With symmetric viabilities there is usually an acceleration of the decay process for gene frequencies near 1/2 when the central equilibrium (with = 0) is stable. This is always the case when the sign of the epistasis is negative or zero.Conversely, the decay ofD is retarded in the neighborhood of a stable equilibrium in the multiplicative and symmetric viability models if any of the conditions above are violated. Near an unstable equilibrium of any of the models considered,D may either increase or decay at a rate slower than, equal to, or faster than the neutral rate. These analytic results are supplemented by numerical studies of the symmetric viability model.     

On the evolution of genetic incompatibility systems. V. Origin of sporophytic self-incompatibility in response to overdominance in viability

Conditions for the origin of partial sporophytic self-incompatibility (SSI) are obtained from two quantitative models, which differ with respect to the determination of offspring viability. Offspring viability depends solely on the source (self or nonself) of the fertilizing pollen in the first model, which describes changes only at a primitive S-locus itself. Two loci evolve in the second model: overdominant viability selection maintains an arbitrary number of alleles at one locus, with SSI under the control of a separate locus. In both cases, the origin of SSI requires that the relative change in the numbers of offspring derived by the two reproductive modes compensate for the twofold cost of outcrossing. In the first model studied, the viability of inbred offspring fully determines the relative change in the numbers of inbred and outbred offspring produced. In the second model, the relative change in offspring numbers depends in addition on associations between the S-locus and the viability locus. Because these two-locus associations are comparable in magnitude to the differences between the viabilities of inbred and outbred offspring, SSI can arise under less restrictive conditions than expected from the one-locus model. Greater allelic multiplicity at the viability locus facilitates the origin of SSI by reducing the relative viability of inbred offspring. Tight linkage between the S-locus and the viability locus and high rates of receipt of self-pollen promote the generation and maintenance of associations between the S-locus and the viability locus. In populations in which more than two viability alleles are maintained, the active S-allele can invade even in the absence of linkage with the viability locus. The present study establishes that incompatibility systems can arise in response to identity disequilibrium between a modifier of incompatibility and a locus subject to overdominant viability selection; in particular, compensation for the twofold cost of outcrossing does not require preexisting gametic level disequilibria.     

Genetic coadaptation in the chromosomal polymorphism of Drosophila subobscura II. Changes of gametic disequilibrium in experimental populations

Experimental populations were examined for temporal changes of gametic disequilibria between allozyme loci (Lap and Pept-1) and gene arrangements of the O chromosome of Drosophila subobscura (O _st and O ₃₊₄₊₇) under several environmental conditions. In the foundation of the experimental populations a genetic perturbation was carried out in order to test the relevance of the current hypotheses used to explain the allozyme-inversion associations observed in natural populations. Differential changes of gametic disequilibria were detected over generations under the different environmental conditions. Mere mechanical or stochastic factors cannot explain the results and natural selection is probably the major agent generating the detected gametic associations. The observations are interpreted as a proof of coadaptation of D. subobscura inversions.     

Evolution du polymorphisme enzymatique dans des populations expérimentales de Drosophila melanogaster III. Déséquilibre de linkage entre les locus Adh et α-Gpdh

Evolution of enzyme polymorphism in experimental populations of Drosophila melanogaster III. Linkage disequilibrium between alleles of the Adh and -Gpdh loci — The evolution of gametic frequencies and linkage disequilibria between alleles of the Adh and -Gpdh-loci was followed in two experimental populations of Drosophila melanogaster maintained at different temperatures. The results observed were compared with those expected on the basis of theoretical models of gametic selection. Gametic fitness values were estimated from the analysis of the productivity of the different homozygous genotypes.Our experimental results indicate that the selection favours an association between the alleles Adh-F and -Gpdh-S, but it is impossible to generate and/or maintain a stable linkage disequilibrium between the two alleles.     

Inference from Clines Stabilized by Frequency-Dependent Selection

Frequency-dependent selection against rare forms can maintain clines. For weak selection, s, in simple linear models of frequency-dependence, single locus clines are stabilized with a maximum slope of between square root of s/square root of 8 sigma and square root of s/square root of 12 delta, where sigma is the dispersal distance. These clines are similar to those maintained by heterozygote disadvantage. Using computer simulations, the weak-selection analytical results are extended to higher selection pressures with up to three unlinked genes. Graphs are used to display the effect of selection, migration, dominance, and number of loci on cline widths, speeds of cline movements, two-way gametic correlations ("linkage disequilibria"), and heterozygote deficits. The effects of changing the order of reproduction, migration, and selection, are also briefly explored. Epistasis can also maintain tension zones. We show that epistatic selection is similar in its effects to frequency-dependent selection, except that the disequilibria produced in the zone will be higher for a given level of selection. If selection consists of a mixture of frequency-dependence and epistasis, as is likely in nature, the error made in estimating selection is usually less than twofold. From the graphs, selection and migration can be estimated using knowledge of the dominance and number of genes, of gene frequencies and of gametic correlations from a hybrid zone.     

Further analysis of complex allozyme polymorphisms in a barley population

New theory has recently been developed for two-locus models. In the light of this theory, an earlier analysis of esterase allozyme data from an experimental barley population has been modified to take proper account of initial gametic phase (linkage) disequilibria. The results show that the directions in which two-locus genotypic frequencies deviated from products of one-locus frequencies in this population followed those predicted by neutral descent theory. The observed departures were, however, much larger in size than predicted by the new descent measure theory, indicating that selection is operating in the population.     

The Genetical Response to Natural Selection by Varied Environments. IV. Gametic Disequilibrium in Spatially Varied Environments

Gametic disequilibria between allozyme loci were related to spatial variation of the environment in caged populations of Drosophila melanogaster . Two experiments, one with flies collected at "Chateau Tahbilk," South Australia, and the other with flies from "Groningen," The Netherlands, were sampled at generations 16 and 32. Spatial variation of the environment was stimulated using three food media. Eight polymorphic allozyme loci were used to estimate gametic disequilibria from digenic combinations of allotypes. All populations were duplicated within an environment and maintained at about 2500 adults. Standardized gametic disequilibria were compared by a weighted least squares analysis of the z-transformed statistical correlation of allele frequencies. Gametic disequilibria were strongly dependent upon food niche and food-niche interactions. The effects also varied with sampling time and were similar in duplicate populations. Gametic disequilibria were most often detected in the "Groningen"-derived populations and their strength was not strongly associated with recombination fraction. Many of the disequilibria concerned unlinked loci. The strength of selection was probably considerable and populations were evolving genetic architectures which reflected niche selection by the different foods without marked genetic isolation between foods; gene frequencies did not vary between niches within a population cage.     

Overdominant lethals as part of the conifer embryo lethal system

In pines, self-pollination rates can be as high as 34% yet only 5% of viable seed is a product of self-fertilization. This decline in selfed seed viability is the consequence of post-fertilization exclusion mechanisms operating via the embryo lethal system. Recent molecular marker dissection studies suggest that the embryo lethal system is composed of semilethal factors dispersed across the genome, but it is not clear whether overdominant lethal factors are rare or representative. The study objective was to determine if overdominance was rare for the embryo lethal system in conifers. Three cohorts of selfed offspring from a single Pinus taeda parent were genotyped for nuclear microsatellites. Maximum likelihood tests based on distorted segregation ratios for single markers and for interval mapping were used to infer the degree of dominance. Four hypotheses about overdominance lethal factors were tested: (1) overdominant lethal factors rarely occur within the embryo lethal system, (2) overdominant lethal factors are rarely detected because they are transient and display stage-specific expression, (3) overdominant lethal factors are rarely detected due to tight linkage with rare marker alleles and (4) dominance estimation is unbiased by gametic selection. Four out of the seven chromosomal segments were linked to an overdominant lethal factor. One of these four segments had symmetric overdominance, an effect which persisted from embryo maturity through germination. Four overdominant lethal factors were linked to common and rare marker alleles. Gametic selection was not a source of bias in dominance estimation. Overdominant or pseudo-overdominant lethal factors are a common component of the conifer embryo lethal system.     

Evolution of recombination due to random drift

In finite populations subject to selection, genetic drift generates negative linkage disequilibrium, on average, even if selection acts independently (i.e., multiplicatively) upon all loci. Negative disequilibrium reduces the variance in fitness and hence, by Fisher's (1930) fundamental theorem, slows the rate of increase in mean fitness. Modifiers that increase recombination eliminate the negative disequilibria that impede selection and consequently increase in frequency by "hitchhiking." Thus, stochastic fluctuations in linkage disequilibrium in finite populations favor the evolution of increased rates of recombination, even in the absence of epistatic interactions among loci and even when disequilibrium is initially absent. The method developed within this article allows us to quantify the strength of selection acting on a modifier allele that increases recombination in a finite population. The analysis indicates that stochastically generated linkage disequilibria do select for increased recombination, a result that is confirmed by Monte Carlo simulations. Selection for a modifier that increases recombination is highest when linkage among loci is tight, when beneficial alleles rise from low to high frequency, and when the population size is small.     

Estimates of Selection and Gene Flow from Measures of Cline Width and Linkage Disequilibrium in Heliconius Hybrid Zones

Hybrid zones can yield estimates of natural selection and gene flow. The width of a cline in gene frequency is approximately proportional to gene flow (sigma) divided by the square root of per-locus selection (square root of s). Gene flow also causes gametic correlations (linkage disequilibria) between genes that differ across hybrid zones. Correlations are stronger when the hybrid zone is narrow, and rise to a maximum roughly equal to s. Thus cline width and gametic correlations combine to give estimates of gene flow and selection. These indirect measures of sigma and s are especially useful because they can be made from collections, and require no field experiments. The method was applied to hybrid zones between color pattern races in a pair of Peruvian Heliconius butterfly species. The species are Müllerian mimics of one another, and both show the same changes in warning color pattern across their respective hybrid zones. The expectations of cline width and gametic correlation were generated using simulations of clines stabilized by strong frequency-dependent selection. In the hybrid zone in Heliconius erato, clines at three major color pattern loci were between 8.5 and 10.2 km wide, and the pairwise gametic correlations peaked at R approximately 0.35. These measures suggest that s approximately 0.23 per locus, and that sigma approximately 2.6 km. In erato, the shapes of the clines agreed with that expected on the basis of dominance. Heliconius melpomene has a nearly coincident hybrid zone. In this species, cline widths at four major color pattern loci varied between 11.7 and 13.4 km. Pairwise gametic correlations peaked near R approximately 1.00 for tightly linked genes, and at R approximately 0.40 for unlinked genes, giving s approximately 0.25 per locus and sigma approximately 3.7 km. In melpomene, cline shapes did not perfectly fit theoretical shapes based on dominance; this deviation might be explained by long-distance migration and/or strong epistasis. Compared with erato, sample sizes in melpomene are lower and the genetics of its color patterns are less well understood. In spite of these problems, selection and gene flow are clearly of the same order of magnitude in the two species. The relatively high per locus selection coefficients agree with "major gene" theories for the evolution of Müllerian mimicry, but the genetic architecture of the color patterns does not. These results show that the genetics and evolution of mimicry are still only sketchily understood.     

Dynamics of Correlated Genetic Systems. V. Rates of Decay of Linkage Disequilibria in Experimental Populations of DROSOPHILA MELANOGASTER

The dynamic behavior of four-locus gametic frequency distributions was studied in five replicate cage populations of Drosophila melanogaster for up to 50 generations. The joint frequency distributions were resolved into gene frequencies and various disequilibrium measures. In addition, F statistics for marginal single-locus genotypic frequency distributions were followed through time. The gene frequency, disequilibrium and F statistics were obtained for four chromosome 3 enzyme marker loci [isocitrate dehydrogenase (3–27.1), esterase-6 (3–36.8), phosphoglucomutase (3–43.4) and esterase-C (3–49.0)]. The initial structure of the experimental populations featured random mating proportions, and two complementary gametic types with respect to the marker loci, thus assuring complete pairwise linkage disequilibrium among the markers.——The experimental results indicate: (1) the between-replicate variance in gene frequency varied substantially among loci, with isocitrate dehydrogenase showing the greatest between-replicate variance, and esterase-C the least. (2) The F statistics initially were strongly negative but decayed to the neighborhood of zero for all marker loci except esterase-C. The rate at which the F statistics approached zero varied among the marker loci, indicating substantial differences in the distribution of selective effects along the chromosome. The centromeric region, marked by esterase-C, shows the strongest selective effects. (3) The rate of decay of linkage disequilibrium was much faster than expected for pairs of neutral loci, averaging 1.82 times the neutral rate over all replicates and pairs of loci. This acceleration, which was observed for all six pairwise combinations of loci, was interpreted as resulting from the interaction between selection and recombination. Our experimental results are consistent with many investigations of linkage disequilibrium in natural populations of Drosophila melanogaster that show little or no disequilibrium among enzyme loci. (4) A fortuitous contamination of two cages revealed an apparent regulatory interaction between the migrant and nonmigrant chromosomes at the esterase-C locus. The migrant chromosomes were very rapidly absorbed into the recipient populations, despite this interaction. This result suggests that the dynamics of migration in populations may be phenomenologically richer than anticipated by simple theory.     

A general multilocus two-allele model for epistatic selection

Observations show that evolutionary processes often relate to multilocus epistatic selection. Here we develop further the approach suggested earlier by Zhivotovsky and Gavrilets to admit arbitrary multilocus epistasis. The obtained dynamic equations for allelic frequencies and gametic disequilibria are represented in a simple form. If selection is weak, this result extends Wright’s evolutionary equation to the case of cis-trans effects and sex differences in both recombination rates and genotypic fitnesses. Additionally to Wright’s equations for allelic frequencies, we derive equations for the gametic disequilibrium terms. We also give a general expression for the gametic disequilibria in a quasi-linkage state.     

Gametic selection in anther culture of rice (Oryza sauva L.)

Summary The segregation and recombination of heterozygous isozyme markers have been monitored in anther culture derivatives (i.e., six nonmorphogenic microspore-derived callus [NMC] populations and two anther culture plant [ACP] populations) and F₂ plants generated from six F₁ hybrids of rice, including five japonica upland/improved indica tropical hybrids. The alleles in excess at some loci displaying skewed segregations in the F₂s were consistently overrepresented in the NMC populations. These alleles were also generally found to be overabundant in the two ACP populations except for certain loci that contrastingly segregated in a 11 ratio. Additional distortions were found to be specific to AC derivatives indicating the existence of in vitro gametic selection. Overall, however, the gametic selection in the ACP materials was neutral with regard to the indica and japonica differentiation. Estimates of linkages between markers borne by chromosome 6 using AC-derivative data were consistent with those noted in the F₂s and with current knowledge of the isozyme locus linkage map. Given the average neutrality of gametic selection and the consistency of linkage relationships in the ACPs, their further use as rice molecular mapping and gene tagging populations can be investigated with confidence.Joint contribution with Research Institute for Tropical Food Crops, Department of the International Centre of Agronomical Research for Development (IRAT-CIRAD), 45bis avenue de la Belle Gabrielle, F-94736 Nogent s/Marne Cédex, France and International Rice Research Institute (IRRI), P.O.Box 933, Manila, Philippines     

The Genetics of DROSOPHILA SUBOBSCURA Populations. IX. Studies on Linkage Disequilibrium in Four Natural Populations

Gametic frequencies were obtained in four natural populations of D. sub-obscura by extracting wild chromosomes and subsequently analyzing them for inversions and allozymes. The genes Lap and Pept-1, both located within the same inversions of chromosome O, were found in striking nonrandom associations with them of the same kind and degree in all populations studied. On the contrary, the gene Acph, also located within the previously mentioned inversions, was found in linkage disequilibrium with them only in two populations and of opposite directions. This is also the case for the genes Est-9 and Hk, both located within chromosome E inversions. While the gene Est-9 was in strong linkage disequilibrium with the inversions, of the same kind and degree in all populations studied, Hk was found to be in linkage equilibrium. Allele frequencies for the 29 genes studied do not show geographical variation except for the genes Lap, Pept-1 and Est-9, the ones found in linkage disequilibria with the geographically varying gene arrangements. Although mechanical or historical explanations for these equilibria cannot be ruled out, these data cannot be explained satisfactorily by the "middle gene explanation," which states that loci displaying such linkage disequilibria are the ones located near the break points of inversions, while the ones displaying linkage equilibria with them are located in the middle of them. There is no evidence for consistent linkage disequilibria between pairs of loci, except for the closely linked genes of the complex locus, Est-9. This would imply, if it is not a peculiarity of the Est-9 complex, that the linkage disequilibria are found only between very closely linked loci or that, for less closely linked genes, the associations are too weak to be detected by the usual samples sizes.     

Dynamics of Correlated Genetic Systems. IV. Multilocus Effects of Ethanol Stress Environments

Four replicate populations of Drosophila melanogaster, two reared on medium supplemented with ethanol and two reared on standard medium, were electrophoretically monitored for 28 generations. During the first 12 generations, allelic, genotypic and gametic frequencies were determined for eight polymorphic enzymes: GOT, alpha-GPDH, MDH, ADH, TO, E6, Ec and ODH. Samples from generation 18 and 28 were electrophoretically typed for ADH and alpha-GPDH. In addition, samples from generation 27 were analyzed for the presence of inversion heterozygotes. The experimental results showed rapid gene-frequency divergence between control and treatment populations at the Adh locus in a direction consistent with the activity hierarchy of Adh genotypes. Gene-frequency divergence between control and treatment populations also occurred at the alpha-Gpdh locus, although the agreement among replicates appeared to have broken down by generation 28. No differential gene-frequency change occurred at any of the six remaining marker loci. Furthermore, values of linkage disequilibria among all linked pairs of genes were initially small and remained small throughout the course of the experiment. Taking these facts into account, it is argued that the gene-frequency response observed at ADH is most probably caused by selection at the Adh locus. The gene frequency response at alpha-Gpdh can also be be accounted for in terms of the effect of ethanol on energy metabolism, although other explanations cannot be excluded.     

Definition and Properties of Disequilibrium Statistics for Associations between Nuclear and Cytoplasmic Genotypes

We define and establish the interrelationships of four components of statistical association between a diploid nuclear gene and a uniparentally transmitted, haploid cytoplasmic gene: an allelic (gametic) disequilibrium (D), which measures associations between alleles at the two loci; and three genotypic disequilibria (D1, D2, D3), which measure associations between two cytotypes and the three respective nuclear backgrounds. We also consider an alternative set of measures, including D and the residual disequilibrium (d). The dynamics of these disequilibria are then examined under three conventional models of the mating system: (1) random mating; (2a) assortative mating without dominance (the "mixed-mating model"); and (2b) assortative mating with dominance ("O'Donald's model"). The trajectories of gametic disequilibria are similar to those for pairs of unlinked nuclear loci. The dynamics of genotypic disequilibria exhibit a variety of behaviors depending on the model and the initial conditions. Procedures for statistical estimation of cytonuclear disequilibria are developed and applied to several real and hypothetical data sets. Special attention is paid to the biological interpretations of various categories of allelic and genotypic disequilibria in hybrid zones. Genetic systems for which these statistics might be appropriate include nuclear genotype frequencies in conjunction with those for mitochondrial DNA, chloroplast DNA, or cytoplasmically inherited microorganisms.