Biomedical subjects
Publications and source records attributed to N H Barton.
A recent analysis has shown that divergence between human and chimpanzee varies greatly across the genome. Although this is consistent with "hybridisation" between the diverging human and chimp lineages, such observations can be explained more simply by the null model of allopatric speciation.
We apply new analytical methods to understand the consequences of population bottlenecks for expected additive genetic variance. We analyze essentially all models for multilocus epistasis that have been numerically simulated to demonstrate increased additive variance. We conclude that for biologically plausible models, large increases in expected additive variance--attributable to epistasis rather than dominance--are unlikely. Naciri-Graven and Goudet (2003) found that as the number of epistatically interacting loci increases, additive variance tends to be inflated more after a bottleneck. We argue that this result reflects biologically unrealistic aspects of their models. Specifically, as the number of loci increases, higher-order epistatic interactions become increasingly important in these models, with an increasing fraction of the genetic variance becoming nonadditive, contrary to empirical observations. As shown by Barton and Turelli (2004), without dominance, conversion of nonadditive to additive variance depends only on the variance components and not on the number of loci per se. Numerical results indicating that more inbreeding is needed to produce maximal release of additive variance with more loci follow directly from our analytical results, which show that high levels of inbreeding (F > 0.5) are needed for significant conversion of higher-order components. We discuss alternative approaches to modeling multilocus epistasis and understanding its consequences.
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.
We present two novel methods to infer mating patterns from genetic data. They differ from existing statistical methods of parentage inference in that they apply to populations that deviate from Hardy-Weinberg and linkage equilibrium, and so are suited for the study of assortative mating in hybrid zones. The core data set consists of genotypes at several loci for a number of full-sib clutches of unknown parentage. Our inference is based throughout on estimates of allelic associations within and across loci, such as heterozygote deficit and pairwise linkage disequilibrium. In the first method, the most likely parents of a given clutch are determined from the genotypic distribution of the associated adult population, given an explicit model of nonrandom mating. This leads to estimates of the strength of assortment. The second approach is based solely on the offspring genotypes and relies on the fact that a linear relation exists between associations among the offspring and those in the population of breeding pairs. We apply both methods to a sample from the hybrid zone between the fire-bellied toads Bombina bombina and B. variegata (Anura: Disco glossidae) in Croatia. Consistently, both approaches provide no evidence for a departure from random mating, despite adequate statistical power. Instead, B. variegata-like individuals among the adults contributed disproportionately to the offspring cohort, consistent with their preference for the type of breeding habitat in which this study was conducted.
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We investigate three alternative selection-based scenarios proposed to maintain polygenic variation: pleiotropic balancing selection, G x E interactions (with spatial or temporal variation in allelic effects), and sex-dependent allelic effects. Each analysis assumes an additive polygenic trait with n diallelic loci under stabilizing selection. We allow loci to have different effects and consider equilibria at which the population mean departs from the stabilizing-selection optimum. Under weak selection, each model produces essentially identical, approximate allele-frequency dynamics. Variation is maintained under pleiotropic balancing selection only at loci for which the strength of balancing selection exceeds the effective strength of stabilizing selection. In addition, for all models, polymorphism requires that the population mean be close enough to the optimum that directional selection does not overwhelm balancing selection. This balance allows many simultaneously stable equilibria, and we explore their properties numerically. Both spatial and temporal G x E can maintain variation at loci for which the coefficient of variation (across environments) of the effect of a substitution exceeds a critical value greater than one. The critical value depends on the correlation between substitution effects at different loci. For large positive correlations (e.g., rho(ij)2>3/4), even extreme fluctuations in allelic effects cannot maintain variation. Surprisingly, this constraint on correlations implies that sex-dependent allelic effects cannot maintain polygenic variation. We present numerical results that support our analytical approximations and discuss our results in connection to relevant data and alternative variance-maintaining mechanisms.
The coalescent process can describe the effects of selection at linked loci only if selection is so strong that genotype frequencies evolve deterministically. Here, we develop methods proposed by Kaplan, Darden, and Hudson to find the effects of weak selection. We show that the overall effect is given by an extension to Price's equation: the change in properties such as moments of coalescence times is equal to the covariance between those properties and the fitness of the sample of genes. The distribution of coalescence times differs substantially between allelic classes, even in the absence of selection. However, the average coalescence time between randomly chosen genes is insensitive to the current allele frequency and is affected significantly by purifying selection only if deleterious mutations are common and selection is strong (i.e., the product of population size and selection coefficient, Ns>3). Balancing selection increases mean coalescence times, but the effect becomes large only when mutation rates between allelic classes are low and when selection is extremely strong. Our analysis supports previous simulations that show that selection has surprisingly little effect on genealogies. Moreover, small fluctuations in allele frequency due to random drift can greatly reduce any such effects. This will make it difficult to detect the action of selection from neutral variation alone.
We analyze the changes in the mean and variance components of a quantitative trait caused by changes in allele frequencies, concentrating on the effects of genetic drift. We use a general representation of epistasis and dominance that allows an arbitrary relation between genotype and phenotype for any number of diallelic loci. We assume initial and final Hardy-Weinberg and linkage equilibrium in our analyses of drift-induced changes. Random drift generates transient linkage disequilibria that cause correlations between allele frequency fluctuations at different loci. However, we show that these have negligible effects, at least for interactions among small numbers of loci. Our analyses are based on diffusion approximations that summarize the effects of drift in terms of F, the inbreeding coefficient, interpreted as the expected proportional decrease in heterozygosity at each locus. For haploids, the variance of the trait mean after a population bottleneck is var(delta(z)) = sigma(n)k=1 FkV(A(k)), where n is the number of loci contributing to the trait variance, V(A(1)) = V(A) is the additive genetic variance, and V(A(k)) is the kth-order additive epistatic variance. The expected additive genetic variance after the bottleneck, denoted (V*(A)), is closely related to var(delta(z)); (V*(A)) = (1 - F) sigma(n)k=1 kFk-1V(A(k)). Thus, epistasis inflates the expected additive variance above V(A)(1 - F), the expectation under additivity. For haploids (and diploids without dominance), the expected value of every variance component is inflated by the existence of higher order interactions (e.g., third-order epistasis inflates (V*(AA. This is not true in general with diploidy, because dominance alone can reduce (V*(A)) below V(A)(1 - F) (e.g., when dominant alleles are rare). Without dominance, diploidy produces simple expressions: var(delta(z)) = sigma(n)k=1 (2F)kV(A(k)) and (V(A)) = (1 - F) sigma(n)k=1 k(2F)k-1V(A(k)). With dominance (and even without epistasis), var(delta(z)) and (V*(A)) no longer depend solely on the variance components in the base population. For small F, the expected additive variance simplifies to (V*(A)) approximately equal to (1 - F)V(A) + 4FV(AA) + 2FV(D) + 2FC(AD), where C(AD) is a sum of two terms describing covariances between additive effects and dominance and additive X dominance interactions. Whether population bottlenecks lead to expected increases in additive variance depends primarily on the ratio of nonadditive to additive genetic variance in the base population, but dominance precludes simple predictions based solely on variance components. We illustrate these results using a model in which genotypic values are drawn at random, allowing extreme and erratic epistatic interactions. Although our analyses clarify the conditions under which drift is expected to increase V(A), we question the evolutionary importance of such increases.
What is the chance that some part of a stretch of genome will survive? In a population of constant size, and with no selection, the probability of survival of some part of a stretch of map length y < 1 approaches y/log(yt/2) for log(yt) > or = 1. Thus, the whole genome is certain to be lost, but the rate of loss is extremely slow. This solution extends to give the whole distribution of surviving block sizes as a function of time. We show that the expected number of blocks at time t is 1+yt and give expressions for the moments of the number of blocks and the total amount of genome that survives for a given time. The solution is based on a branching process and assumes complete interference between crossovers, so that each descendant carries only a single block of ancestral material. We consider cases where most individuals carry multiple blocks, either because there are multiple crossovers in a long genetic map, or because enough time has passed that most individuals in the population are related to each other. For species such as ours, which have a long genetic map, the genome of any individual which leaves descendants (approximately 80% of the population for a Poisson offspring number with mean two) is likely to persist for an extremely long time, in the form of a few short blocks of genome.
Stable hybrid zones in which ecologically divergent taxa give rise to a range of recombinants are natural laboratories in which the genetic basis of adaptation and reproductive isolation can be unraveled. One such hybrid zone is formed by the fire-bellied toads Bombina bombina and B. variegata (Anura: Discoglossidae). Adaptations to permanent and ephemeral breeding habitats, respectively, have shaped numerous phenotypic differences between the taxa. All of these are, in principle, candidates for a genetic dissection via QTL mapping. We present here a linkage map of 28 codominant and 10 dominant markers in the Bombina genome. In an F2 cross, markers that were mainly microsatellites, SSCPs or allozymes were mapped to 20 linkage groups. Among the 40 isolated CA microsatellites, we noted a preponderance of compound and frequently interleaved CA-TA repeats as well as a striking polarity at the 5' end of the repeats.
Mosaic hybrid zones arise when ecologically differentiated taxa hybridize across a network of habitat patches. Frequent interbreeding across a small-scale patchwork can erode species differences that might have been preserved in a clinal hybrid zone. In particular, the rapid breakdown of neutral divergence sets an upper limit to the time for which differences at marker loci can persist. We present here a case study of a mosaic hybrid zone between the fire-bellied toads Bombina bombina and B. variegata (Anura: Discoglossidae) near Apahida in Romania. In our 20 x 20 km study area, we detected no evidence of a clinal transition but found a strong association between aquatic habitat and mean allele frequencies at four molecular markers. In particular, pure populations of B. bombina in ponds appear to cause massive introgression into the surrounding B. variegata gene pool found in temporary aquatic sites. Nevertheless, the genetic structure of these hybrid populations was remarkably similar to those of a previously studied transect near Pescenica (Croatia), which had both clinal and mosaic features: estimates of heterozygote deficit and linkage disequilibrium in each country are similar. In Apahida, the observed strong linkage disequilibria should stem from an imperfect habitat preference that guides most (but not all) adults into the habitats to which they are adapted. In the absence of a clinal structure, the inferred migration rate between habitats implies that associations between selected loci and neutral markers should break down rapidly. Although plausible selection strengths can maintain differentiation at those loci adapting the toads to either permanent or temporary breeding sites, the divergence at neutral markers must be transient. The hybrid zone may be approaching a state in which the gene pools are homogenized at all but the selected loci, not dissimilar from an early stage of sympatric divergence.
Until recently, it was impracticable to identify the genes that are responsible for variation in continuous traits, or to directly observe the effects of their different alleles. Now, the abundance of genetic markers has made it possible to identify quantitative trait loci (QTL)--the regions of a chromosome or, ideally, individual sequence variants that are responsible for trait variation. What kind of QTL do we expect to find and what can our observations of QTL tell us about how organisms evolve? The key to understanding the evolutionary significance of QTL is to understand the nature of inherited variation, not in the immediate mechanistic sense of how genes influence phenotype, but, rather, to know what evolutionary forces maintain genetic variability.
Hybridization may influence evolution in a variety of ways. If hybrids are less fit, the geographical range of ecologically divergent populations may be limited, and prezygotic reproductive isolation may be reinforced. If some hybrid genotypes are fitter than one or both parents, at least in some environments, then hybridization could make a positive contribution. Single alleles that are at an advantage in the alternative environment and genetic background will introgress readily, although such introgression may be hard to detect. 'Hybrid speciation', in which fit combinations of alleles are established, is more problematic; its likelihood depends on how divergent populations meet, and on the structure of epistasis. These issues are illustrated using Fisher's model of stabilizing selection on multiple traits, under which reproductive isolation evolves as a side-effect of adaptation in allopatry. This confirms a priori arguments that while recombinant hybrids are less fit on average, some gene combinations may be fitter than the parents, even in the parental environment. Fisher's model does predict heterosis in diploid F1s, asymmetric incompatibility in reciprocal backcrosses, and (when dominance is included) Haldane's Rule. However, heterosis arises only when traits are additive, whereas the latter two patterns require dominance. Moreover, because adaptation is via substitutions of small effect, Fisher's model does not generate the strong effects of single chromosome regions often observed in species crosses.
The reasons that sex and recombination are so widespread remain elusive. One popular hypothesis is that sex and recombination promote adaptation to a changing environment. The strongest evidence that increased recombination may evolve because recombination promotes adaptation comes from artificially selected populations. Recombination rates have been found to increase as a correlated response to selection on traits unrelated to recombination in several artificial selection experiments and in a comparison of domesticated and nondomesticated mammals. There are, however, several alternative explanations for the increase in recombination in such populations, including two different evolutionary explanations. The first is that the form of selection is epistatic, generating linkage disequilibria among selected loci, which can indirectly favor modifier alleles that increase recombination. The second is that random genetic drift in selected populations tends to generate disequilibria such that beneficial alleles are often found in different individuals; modifier alleles that increase recombination can bring together such favorable alleles and thus may be found in individuals with greater fitness. In this paper, we compare the evolutionary forces acting on recombination in finite populations subject to strong selection. To our surprise, we found that drift accounted for the majority of selection for increased recombination observed in simulations of small to moderately large populations, suggesting that, unless selected populations are large, epistasis plays a secondary role in the evolution of recombination.
Selection on one or more genes inevitably perturbs other genes, even when those genes have no direct effect on fitness. This article reviews the theory of such genetic hitchhiking, concentrating on effects on neutral loci. Maynard Smith and Haigh introduced the classical case where the perturbation is due to a single favourable mutation. This is contrasted with the apparently distinct effects of inherited variation in fitness due to loosely linked loci. A model of fluctuating selection is analysed which bridges these alternative treatments. When alleles sweep between extreme frequencies at a rate lambda, the rate of drift is increased by a factor (1 + E[1/pq]lambda/(2(2lambda + r))), where the recombination rate r is much smaller than the strength of selection. In spatially structured populations, the effects of any one substitution are weaker, and only cause a local increase in the frequency of a neutral allele. This increase depends primarily on the rate of recombination relative to selection (r/s), and more weakly, on the neighbourhood size, Nb = 4(pi rho sigma)2. Spatial subdivision may allow local selective sweeps to occur more frequently than is indicated by the overall rate of molecular evolution. However, it seems unlikely that such sweeps can be sufficiently frequent to increase significantly the drift of neutral alleles.
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Analysis of multilocus evolution is usually intractable for more than n approximately 10 genes, because the frequencies of very large numbers of genotypes must be followed. An exact analysis of up to n approximately 100 loci is feasible for a symmetrical model, in which a set of unlinked loci segregate for two alleles (labeled "0" and "1") with interchangeable effects on fitness. All haploid genotypes with the same number of 1 alleles can then remain equally frequent. However, such a symmetrical solution may be unstable: for example, under stabilizing selection, populations tend to fix any one genotype which approaches the optimum. Here, we show how the 2(n)x2(n) stability matrix can be decomposed into a set of matrices, each no larger than nxn. This allows the stability of symmetrical solutions to be determined. We apply the method to stabilizing and disruptive selection in a single deme and to selection against heterozygotes in a linear cline.
Within hybrid zones that are maintained by a balance between selection and dispersal, linkage disequilibrium is generated by the mixing of divergent populations. This linkage disequilibrium causes selection on each locus to act on all other loci, thereby steepening clines, and generating a barrier to gene flow. Diffusion models predict simple relations between the strength of linkage disequilibrium and the dispersal rate, sigma, and between the barrier to gene flow, B, and the reduction in mean fitness, W. The aim of this paper is to test the accuracy of these predictions by comparison with an exact deterministic model of unlinked loci (r = 0.5). Disruptive selection acts on the proportion of alleles from the parental populations (p,q): W = exp[-S(4pq)beta], such that the least fit genotype has fitness e-s. Where beta << 1, fitness is reduced for a wide range of intermediate genotypes; where beta >> 1, fitness is only reduced for those genotypes close to p = 0.5. Even with strong epistasis, linkage disequilibria are close to sigma 2p'ip'j/rij, where p'i, p'j are the gradients in allele frequency at loci i, j. The barrier to gene flow, which is reflected in the steepening of neutral clines, is given by [formula: see text] where r, the harmonic mean recombination rate between the neural and selected loci, is here 0.5. This is a close approximation for weak selection, but underestimates B for strong selection. The barrier is stronger for small beta, because hybrid fitness is then reduced over a wider range of p. The widths of the selected clines are harder to predict: though simple approximations are accurate for beta = 1, they become inaccurate for extreme beta because, then, fitness changes sharply with p. Estimates of gene number, made from neutral clines on the assumption that selection acts against heterozygotes, are accurate for weak selection when beta = 1; however, for strong selection, gene number is overestimated. For beta > 1, gene number is systematically overestimated and, conversely, when beta < 1, it is underestimated.