Cline coupling and uncoupling in a stickleback hybrid zone

Strong ecological selection on a genetic locus can maintain allele frequency differences between populations in different environments, even in the face of hybridization. When alleles at divergent loci come into tight linkage disequilibrium, selection acts on them as a unit and can significantly reduce gene flow. For populations interbreeding across a hybrid zone, linkage disequilibria between loci can force clines to share the same slopes and centers. However, strong ecological selection on a locus can also pull its cline away from the others, reducing linkage disequilibrium and weakening the barrier to gene flow. We looked for this “cline uncoupling” effect in a hybrid zone between stream resident and anadromous sticklebacks at two genes known to be under divergent natural selection (Eda and ATP1a1) and five morphological traits that repeatedly evolve in freshwater stickleback. These clines were all steep and located together at the top of the estuary, such that we found no evidence for cline uncoupling. However, we did not observe the stepped shape normally associated with steep concordant clines. It thus remains possible that these clines cluster together because their individual selection regimes are identical, but this would be very surprising given their diverse roles in osmoregulation, body armor, and swimming performance.     

GENETIC ANALYSIS OF A HYBRID ZONE BETWEEN THE FIRE-BELLIED TOADS,BOMBINA BOMBINA AND B. VARIEGATA,NEAR CRACOW IN SOUTHERN POLAND

The fire-bellied toads Bombina bombina and B. variegata differ extensively in biochemistry, morphology, and behavior. We use a survey of five diagnostic enzyme loci across the hybrid zone near Cracow in Southern Poland to estimate the dispersal rate, selection pressures, and numbers of loci which maintain this zone. The enzyme clines coincide closely with each other and with morphological and mitochondrial DNA clines. Although the zone lies on a broad transition between environments suitable for bombina and variegata, the close concordance of diverse characters, together with increased aberrations and mortality in hybrids, suggest that the zone is maintained largely by selection against hybrids. There are strong “linkage disequilibria” between each pair of (unlinked) enzyme loci (R? = 0.129 [2-unit support limits: 0.119–0.139]). These are probably caused by gene flow into the zone, and they give an estimate of dispersal (σ = 890 [790–940] m gen^?½). The clines are sharply stepped, with most of the change occurring within 6.15 (5.45–6.45) km, but with long tails of introgression on either side. This implies that the effective selection pressure on each enzyme marker (due largely to disequilibrium with other loci) is s* = 0.17 (0.159–0.181) at the center but that the selection acting directly on the enzyme loci is weak or zero (s_e < 0.0038). The stepped pattern implies a barrier to gene flow of 220 (48–415) km. This would substantially delay neutral introgression but would have little effect on advantageous alleles; the two taxa need not evolve independently. Strong selection is needed to maintain such a barrier: hybrid populations must have their mean fitness reduced by a factor of 0.65 (0.60–0.77). This selection must be spread over a large number of loci to account for the concordant patterns and the observed cline widths (N = 300 [80–2,000]).     

Inferences of selection and migration in the Danish house mouse hybrid zone

We analysed the patterns of allele frequency change for ten diagnostic autosomal allozyme loci in the hybrid zone between the house mouse subspecies Mus musculus domesticus and M. m. musculus in central Jutland. After determining the general orientation of the clines of allele frequencies, we analysed the cline shapes along the direction of maximum gradient. Eight of the ten clines are best described by steep central steps with coincident positions and an average width of 8.9 km (support limits 7.6–12.4) flanked by tails of introgression, indicating the existence of a barrier to gene flow and only weak selection on the loci studied. We derived estimates of migration from linkage disequilibrium in the centre of the zone, and by applying isolation by distance methods to microsatellite data from some of these populations. These give concordant estimates of σ =  0.5–0.8 km generation     . The barrier to gene flow is of the order of 20 km (support limits 14–28), and could be explained by selection of a few per cent at 43–120 underdominant loci that reduces the mean fitness in the central populations to 0.45. Some of the clines appear symmetrical, whereas others are strongly asymmetrical, and two loci appear to have escaped the central barrier to gene flow, reflecting the differential action of selection on different parts of the genome. Asymmetry is always in the direction of more introgression into musculus , indicating either a general progression of domesticus into the musculus territory, possibly mediated by differential behaviour, or past movement of the hybrid zone in the opposite direction, impeded by potential geographical barriers to migration in domesticus territory.  © 2005 The Linnean Society of London, Biological Journal of the Linnean Society , 2005, 84 , 593–616.     

Gene Flow and Selection in a Two-Locus System

A model of gene flow and selection in two linked loci is analyzed. The problems considered are the effects of linkage on the clines in frequencies at the two loci and the role of gene flow in producing linkage disequilibrium between the loci. Also, the possible significance of linkage as a mechanism for permitting a population of "track" spatial changes in the environment is considered. The results are that when the recombination fraction between the loci is of the same order of magnitude as the selection coefficients or smaller, then linkage is important in determining the gene frequencies and a substantial amount of linkage disequilibrium is present in the cline. Depending on the spatial pattern of selection on the two loci, linkage can either decrease or increase a population's response to local selection.     

Adaptation to a steep environmental gradient and an associated barrier to gene exchange in Littorina saxatilis

Steep environmental gradients offer important opportunities to study the interaction between natural selection and gene flow. Allele frequency clines are expected to form at loci under selection, but unlinked neutral alleles may pass easily across these clines unless a generalized barrier evolves. Here we consider the distribution of forms of the intertidal gastropod Littorina saxatilis, analyzing shell shape and amplified fragment length polymorphism (AFLP) loci on two rocky shores in Britain. On the basis of previous work, the AFLP loci were divided into differentiated and undifferentiated groups. On both shores, we have shown a sharp cline in allele frequencies between the two morphs for differentiated AFLP loci. This is coincident with a habitat transition on the shore where the two habitats (cliff and boulder field) are immediately contiguous. The allele frequency clines coincide with a cline in shell morphology. In the middle of the cline, linkage disequilibrium for the differentiated loci rises in accordance with expectation. The clines are extremely narrow relative to dispersal, probably as a result of both strong selection and habitat choice. An increase in F(ST) for undifferentiated AFLPs between morphs, relative to within-morph comparisons, is consistent with there being a general barrier to gene flow across the contact zone. These features are consistent either with an episode of allopatric divergence followed by secondary contact or with primary, nonallopatric divergence. Further data will be needed to distinguish between these alternatives.     

The Genetic Content of Chromosomal Inversions across a Wide Latitudinal Gradient

There is increasing evidence regarding the role of chromosomal inversions in relevant biological processes such as local adaptation and speciation. A classic example of the adaptive role of chromosomal polymorphisms is given by the clines of inversion frequencies in Drosophila subobscura, repeatable across continents. Nevertheless, not much is known about the molecular variation associated with these polymorphisms. We characterized the genetic content of ca. 600 individuals from nine European populations following a latitudinal gradient by analysing 19 microsatellite loci from two autosomes (J and U) and the sex chromosome (A), taking into account their chromosomal inversions. Our results clearly demonstrate the molecular genetic uniformity within a given chromosomal inversion across a large latitudinal gradient, particularly from Groningen (Netherlands) in the north to Málaga (Spain) in the south, experiencing highly diverse environmental conditions. This low genetic differentiation within the same gene arrangement across the nine European populations is consistent with the local adaptation hypothesis for th evolutionof chromosomal polymorphisms. We also show the effective role of chromosomal inversions in maintaining different genetic pools within these inverted genomic regions even in the presence of high gene flow. Inversions represent thus an important barrier to gene flux and can help maintain specific allelic combinations with positive effects on fitness. Consistent patterns of microsatellite allele-inversion linkage disequilibrium particularly in loci within inversions were also observed. Finally, we identified areas within inversions presenting clinal variation that might be under selection.     

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.     

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.     

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.     

THE GENETIC STRUCTURE OF THE HYBRID ZONE BETWEEN THE FIRE-BELLIED TOADS BOMBINA BOMBINA AND B. VARIEGATA: COMPARISONS BETWEEN TRANSECTS AND BETWEEN LOCI

We compare the pattern of morphological and electrophoretic variation in the hybrid zone between Bombina bombina and B. variegata across two transects: one near Cracow and one 200 km away, near Przemy?l in southeastern Poland. Morphological variation across the Przemy?l transect had been surveyed more than 50 years ago; though we found a significant shift at one site, there is no evidence for gross movement over this period. Morphological and electrophoretic changes coincide, and the average shape of the clines is the same across both transects. At the center, most of the change in frequency of six diagnostic allozymes occurs within w = 6.05 km (2-unit support limits 5.56–6.54 km). These steep gradients are generated not by selection on the allozymes themselves, but by associations with other loci: though these markers are unlinked, they are in strong linkage disequilibrium with each other [R = D/√pquv = 0.22 (0.15–0.29) at the center]. Disequilibria are broken up as alleles diffuse away from the zone and flow into the new genetic background. The net barrier to the flow of genes from bombina into variegata, which is generated by these disequilibria, is B = 51 (22–81) km. The fitness of hybrids must be substantially reduced to produce such a barrier [W?_H/W?_P = 0.58 (0.54–0.68)], and this selection must be spread over many loci [N = 55 (26–88)]. Alleles introgress significantly less far than would be expected from the age of the zone and the estimated dispersal rate [σ = 0.99 (0.82–1.14) km gen.^1/2]: this implies selection of s_e = 0.37 (0.15–0.58)% on the enzymes themselves. There is weak but significant linkage disequilibrium well away from the center of the zone; this, together with the presence of parental and F₁ genotypes, suggests some long-range migration. However, such migration is not likely to cause significant introgression.     

Soft selective sweep near a gene that increases plant height in wheat

Strong selection within a given population locally reduces genetic variability not only in the selected gene itself but also in neighbouring loci. This so-called hitch-hiking effect is related to the initial linkage disequilibrium between markers and the selected gene, and depends mainly on the number of copies of the beneficial allele at the start of the selection phase. Contrary to the classical case, in which selection acts on a single, newly arisen beneficial mutation, we considered selection from standing variation (soft selective sweeps) on a gene ( Rht-B1 ) with a major effect on plant height, a selected trait in an experimental wheat population grown for 17 generations, and we documented the evolution of gene diversity and linkage disequilibrium near this gene. As expected, Rht-B1 was found to be under strong selection ( s  = 0.15) and its variation in frequency accounted for 15% of the total trait evolution. This led to a smaller genetic effective population size at Rht-B1 ( N_eg  = 18) compared to the whole genome estimation ( N_eg  = 167). When compared with expectations under genetic drift only, no significant decrease in gene diversity was found at the closest loci. We computed expected di-locus frequencies for any linked marker– Rht-B1 pair due to hitch-hiking effects. We found that hitch-hiking was expected to affect the two most closely linked loci, but expected reduction in gene diversity was not greater than that due to genetic drift, which was consistent with the observations. Such limited effect was attributed to the low level of linkage disequilibrium (0.16) estimated after parental intercrosses, together with a relatively high initial frequency of the gene. This situation is favourable to candidate gene approaches where small linkage disequilibrium around selected genes is expected.     

Meiosis and the evolution of recombination at low mutation rates

The classical understanding of recombination is that in large asexual populations with multiplicative fitness, linkage disequilibrium is negligible, and thus there is no selective agent driving an allele for recombination. This has led researchers to recognize the importance of synergistic epistatic selection in generating negative linkage disequilibrium that thereby renders an advantage to recombination. Yet data on such selection is equivocal, and various works have shown that synergistic epistasis per se, when left unquantified in its magnitude or operation, is not sufficient to drive the evolution of recombination. Here we show that neither it, nor any mechanism generating negative linkage disequilibrium among fitness-related loci, is necessary. We demonstrate that a neutral gene for recombination can increase in frequency in a large population under a low mutation rate and strict multiplicative fitness. We work in a parameter range where individuals have, on average, less than one mutation each, yet recombination can still evolve. We demonstrate this in two ways: first, by examining the consequences of recombination correlated with misrepaired DNA damage and, second, by increasing the probability of recombination with declining fitness. Interestingly, the allele spreads without repairing even a single DNA mutation.     

THE SELECTION BARRIER BETWEEN POPULATIONS SUBJECT TO STABILIZING SELECTION

The introgression of genes carried by a small group of immigrants is studied. The recipient and the donor populations differ at several autosomal loci subject to weak selection, and two allelic forms of each gene are considered. Fitness variation is determined by additive allelic effects, by dominance effects, and by two-locus additive-by-additive epistatic interaction of the effects of the alleles. The fate of the group of immigrants is quantified by the selection barrier that describes the cumulative mean fitness of the hybrids and hybrid descendants relative to the fitness of the resident population. The monomorphic and the polymorphic loci of the recipient population contribute differently to the selection barrier. If the genetic difference between recipient and donor population is small, then the contribution of the monomorphic loci is dominated by a positive term dependent on the difference in gene frequencies. The contribution of the polymorphic loci depends only on the difference of the leading order in the pairwise linkage disequilibria between the two populations. This contribution may be positive or negative; and, thus, polymorphic loci may either contribute to the barrier or inflate the introgression.     

A Study of Linkage Disequilibrium in British Populations of DROSOPHILA SUBOBSCURA

Data have been obtained concerning the genetic content of samples of O chromosomes from three British populations, and J chromosomes from one population, of Drosophila subobscura. Some improvements to the genetic map of the O and J chromosomes have been made. Allele frequencies at the loci studied do not show much geographical variation, except where associations with geographically varying gene arrangements distort the picture. Striking nonrandom associations between alleles at three enzyme loci and closely linked O chromosome gene arrangements are present. Some historical explanation for these associations cannot at present be ruled out, but it is clear that a very high degree of genetic differentiation must exist between different gene arrangements in this species. There is no convincing direct evidence for linkage disequilibrium between pairs of enzyme loci, although there is a significant association between close linkage and a high value of the linkage disequilibrium measure. This suggests that there may be disequilibria between closely linked enzyme loci that are too small to be individually detectable. These results are in broad agreement with those reported by workers on other Drosophila species. At present there appears to be no evidence to support the concept that selection is sufficiently strong at individual enzyme loci to produce a high degree of nonrandom associations. (Franklin and Lewontin 1970).     

The Maintenance of Genetic Variability in Two-Locus Models of Stabilizing Selection

The maintenance of genetic variability at two diallelic loci under stabilizing selection is investigated. Generations are discrete and nonoverlapping; mating is random; mutation and random genetic drift are absent; selection operates only through viability differences. The determination of the genotypic values is purely additive. The fitness function has its optimum at the value of the double heterozygote and decreases monotonically and symmetrically from its optimum, but is otherwise arbitrary. The resulting fitness scheme is identical to the symmetric viability model. Linkage disequilibrium is neglected, but the results are otherwise exact. Explicit formulas are found for all the equilibria, and explicit conditions are derived fro their existence and stability. A complete classification of the six possible global convergence patterns is presented. In addition to the symmetric equilibrium (with gene frequency 1/2 at both loci), a pair of unsymmetric equilibria may exist; the latter are usually, but not always, unstable. If the ratio of the effect of the major locus to that of the minor one exceeds a critical value, both loci will be stably polymorphic. If selection is weak at the minor locus, the more rapidly the fitness function decreases near the optimum, the lower is this critical value; for rapidly decreasing fitness functions, the critical value is close to one. If the fitness function is smooth at the optimum, then a stable polymorphism exists at both loci only if selection is strong at the major locus.     

Linkage Disequilibrium in Subdivided Populations

The linkage disequilibrium in a subdivided populaton is shown to be equal to the sum of the average linkage disequilibrium for all subpopulations and the covariance between gene frequencies of the loci concerned. Thus, in a subdivided population the linkage disequilibrium may not be 0 even if the linkage disequilibrium in each subpopulation is 0. If a population is divided into two subpopulations between which migration occurs, the asymptotic rate of approach to linkage equilibrium is equal to either r or 2(m(1) + m(2)) - (m(1) + m(2))(2), whichever is smaller, where r is the recombination value and m(1) and m(2) are the proportions of immigrants in subpopulations 1 and 2, respectively. Thus, if migration rate is high compared with recombination value, the change of linkage disequilibrium in subdivided populations is similar to that of a single random mating population. On the other hand, if migration rate is low, the approach to lnkage equilibrium may be retarded in subdivided populations. If isolated populations begin to exchange genes by migration, linkage disequilibrium may increase temporarily even for neutral loci. If overdominant selection operates and the equilibrium gene frequencies are different in the two subpopulations, a permanent linkage disequilibrium may be produced without epistasis in each subpopulation.     

The evolution of genetic canalization under fluctuating selection

Abstract.— If the direction of selection changes from generation to generation, the ability to respond to selection is maladaptive: the response to selection in one generation leads to reduced fitness in the next. Because the response is determined by the amount of genetic variance expressed at the phenotypic level, rapidly fluctuating selection should favor modifier genes that reduce the phenotypic effect of alleles segregating at structural loci underlying the trait. Such reduction in phenotypic expression of genetic variation has been named "genetic canalization." I support this argument with a series of two- and multilocus models with alternating linear selection and Gaussian selection with fluctuating optimum. A canalizing modifier gene affects the fitness of its carriers in three ways: (1) it reduces the phenotypic consequences of genetic response to previous selection; (2) it reduces the genetic response to selection, which is manifested as linkage disequilibrium between the modifier and structural loci; and (3) it reduces the phenotypic variance. The first two effects reduce fitness under directional selection sustained for several generations, but improve fitness when the direction of selection has just been reversed. The net effect tends to favor a canalizing modifier under rapidly fluctuating selection regimes (period of eight generations or less). The third effect improves fitness of the modifier allele if the fitness function is convex and reduces it if the function is concave. Under fluctuating Gaussian selection, the population is more likely to experience the concave portion of the fitness function when selection is stronger. Therefore, only weak to moderately strong fluctuating Gaussian selection favors genetic canalization. This paper considerably broadens the conditions that favor genetic canalization, which so far has only been postulated to evolve under long-term stabilizing selection.     

Interchromosomal Biased Gene Conversion, Mutation and Selection in a Multigene Family

A mathematical model of the effects of interchromosomal biased gene conversion, mutation and natural selection on a multigene family is developed and analyzed. The model assumes two allelic states at each of n loci. The effects of genetic drift are ignored. The model is developed under the assumption of no recombination, but the analysis shows that, at equilibrium, there is no linkage disequilibrium, which implies that the conclusions are valid for arbitrary recombination among loci. At equilibrium, the balance between mutation, gene conversion and selection depends on the ratio of the mutation rates to the quantity [s + g(2α - 1)/ n], where s is the increment or decrement in relative fitness with each additional copy of one of the alleles, g is the conversion rate, and α is a measure of the bias in favor of one of the alleles. When this quantity is large relative to the mutation rates, the allele that has the net advantage, combining the effects of selection and conversion, will be nearly fixed in the multigene family. A comparison of these results with those from a comparable model of intrachromosomal biased conversion shows that biased interchromosomal conversion leads to approximately the same equilibrium copy number as does intrachromosomal conversion of the same strength. Interchromosomal conversion is much more effective in causing the substitution of one allele by another. The relative frequencies of interchromosomal and intrachromosomal conversion is indicated by the extent of the linkage disequilibrium among the loci in a multigene family.     

Use of restriction fragment length polymorphisms for genetic counseling: Population genetic considerations

Two-locus population genetic models are analyzed to evaluate the utility of restriction fragment length polymorphisms for purposes of genetic counseling. It is shown that the linkage disequilibrium between a neutral marker and a tightly linked overdominant mutant will increase rapidly as the mutant moves to its polymorphic equilibrium. The linkage disequilibrium decays for deleterious recessive mutants. Two measures involving the linkage disequilibrium are investigated to determine how much information the transmission of the neutral marker provides about the transmission of the selected gene. In certain kinds of matings, where the parental two-locus genotypes and linkage phases are known, it is possible to determine whether or not a progeny is homozygous for the selected gene on the basis of the fetal genotype at the marker locus. A quantity of primary interest is the fraction of matings between individuals heterozygous for the selected gene in which exact diagnosis can be made in this way. The expected proportion of such matings, taken over all two-locus matings involving heterozygotes at the selected locus, is calculated as a function of the gene frequencies at the two loci and the linkage disequilibrium between them. This expected value is maximized when the linkage disequilibrium is at its maximum in absolute value. Fewer than half of all matings are informative if the linkage disequilibrium is small in magnitude or if the gene frequencies at the two loci are quite different. Consideration is also given to various conditional measures of association that may be useful when the parental two-locus genotypes are unknown. The results suggest that the utility of tightly linked neutral marker genes in predicting the transmission of a selected gene is generally less when selection acts against a recessive gene than for overdominant selection.