Nicholas H. Barton

A comparison of three indirect methods for estimating average levels of gene flow

Three methods for estimating the average level of gene flow in natural population are discussed and compared. The three methods are FST, rare alleles, and maximum likelihood. All three methods yield estimates of the combination of parameters (the number of migrants [Nm] in a demic model or the neighborhood size [4πDσ2] in a continuum model) that determines the relative importance of gene flow and genetic drift. We review the theory underlying these methods and derive new analytic results for the expectation of FST in stepping‐stone and continuum models when small sets of samples are taken. We also compare the effectiveness of the different methods using a variety of simulated data. We found that the FST and rare‐alleles methods yield comparable estimates under a wide variety of conditions when the population being sampled is demographically stable. They are roughly equally sensitive to selection and to variation in population structure, and they approach their equilibrium values at approximately the same rate. We found that two different maximum‐likelihood methods tend to yield biased estimates when relatively small numbers of locations are sampled but more accurate estimates when larger numbers are sampled. Our conclusion is that, although FST and rare‐alleles methods are expected to be equally effective in analyzing ideal data, practical problems in estimating the frequencies of rare alleles in electrophoretic studies suggest that FST is likely to be more useful under realistic conditions.

The role of hybridization in evolution

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.

Theory and speciation

The study of speciation has become one of the most active areas of evolutionary biology, and substantial progress has been made in documenting and understanding phenomena ranging from sympatric speciation and reinforcement to the evolutionary genetics of postzygotic isolation. This progress has been driven largely by empirical results, and most useful theoretical work has concentrated on making sense of empirical patterns. Given the complexity of speciation, mathematical theory is subordinate to verbal theory and generalizations about data. Nevertheless, mathematical theory can provide a useful classification of verbal theories; can help determine the biological plausibility of verbal theories; can determine whether alternative mechanisms of speciation are consistent with empirical patterns; and can occasionally provide predictions that go beyond empirical generalizations. We discuss recent examples of progress in each of these areas.

Chromosome Inversions, Local Adaptation and Speciation

We study the evolution of inversions that capture locally adapted alleles when two populations are exchanging migrants or hybridizing. By suppressing recombination between the loci, a new inversion can spread. Neither drift nor coadaptation between the alleles (epistasis) is needed, so this local adaptation mechanism may apply to a broader range of genetic and demographic situations than alternative hypotheses that have been widely discussed. The mechanism can explain many features observed in inversion systems. It will drive an inversion to high frequency if there is no countervailing force, which could explain fixed differences observed between populations and species. An inversion can be stabilized at an intermediate frequency if it also happens to capture one or more deleterious recessive mutations, which could explain polymorphisms that are common in some species. This polymorphism can cycle in frequency with the changing selective advantage of the locally favored alleles. The mechanism can establish underdominant inversions that decrease heterokaryotype fitness by several percent if the cause of fitness loss is structural, while if the cause is genic there is no limit to the strength of underdominance that can result. The mechanism is expected to cause loci responsible for adaptive species-specific differences to map to inversions, as seen in recent QTL studies. We discuss data that support the hypothesis, review other mechanisms for inversion evolution, and suggest possible tests.

Understanding quantitative genetic variation.

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.

The barrier to genetic exchange between hybridising populations.

Suppose that selection acts at one or more loci to maintain genetic differences between hybridising populations. Then, the flow of alleles at a neutral marker locus which is linked to these selected loci will be impeded. We define and calculate measures of the barrier to gene flow between two distinct demes, and across a continuous habitat. In both cases, we find that in order for gene flow to be significantly reduced over much of the genome, hybrids must be substantially less fit, and the number of genes involved in building the barrier must be so large that the majority of other genes become closely linked to some locus which is under selection. This conclusion is not greatly affected by the pattern of epistasis, or the position of the marker locus along the chromosome.

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 (R̄ = 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 (se < 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]).

Understanding quantitative genetic variation

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.

The dynamics of hybrid zones

SummaryThis paper investigates the dynamic behaviour of hybrid zones which are maintained by a balance between dispersal and selection against hybrids. In the first section it is shown that a hybrid zone involving a single locus can move in response to a selective imbalance between the two homozygotes, and also to variation in population density and dispersal rate. It can be trapped by natural barriers, and so an allele which is selected against when rare cannot advance, even if it is advantageous when common. The continuous model used in deriving these results is shown to be a good approximation to the stepping-stone model, provided that the cline contains several demes.The effect of stochastic forces on multi-locus hybrid zones is then considered. An expression giving the shift in position after an arbitrary perturbation in gamete frequency is derived. Using this formula, it is found that sampling drift is negligible unless the zone includes few organisms and involves few loci. Random variations in population structure are the dominant force, and could allow considerable movement in an even environment. However, natural barriers can still trap hybrid zones, and so it is likely that they will remain roughly where they first formed.

PERSPECTIVE : A CRITIQUE OF SEWALL WRIGHT'S SHIFTING BALANCE THEORY OF EVOLUTION

We evaluate Sewall Wrights three‐phase “shifting balance” theory of evolution, examining both the theoretical issues and the relevant data from nature and the laboratory. We conclude that while phases I and II of Wrights theory (the movement of populations from one “adaptive peak” to another via drift and selection) can occur under some conditions, genetic drift is often unnecessary for movement between peaks. Phase III of the shifting balance, in which adaptations spread from particular populations to the entire species, faces two major theoretical obstacles: (1) unlike adaptations favored by simple directional selection, adaptations whose fixation requires some genetic drift are often prevented from spreading by barriers to gene flow; and (2) it is difficult to assemble complex adaptations whose constituent parts arise via peak shifts in different demes. Our review of the data from nature shows that although there is some evidence for individual phases of the shifting balance process, there are few empirical observations explained better by Wrights three‐phase mechanism than by simple mass selection. Similarly, artificial selection experiments fail to show that selection in subdivided populations produces greater response than does mass selection in large populations. The complexity of the shifting balance process and the difficulty of establishing that adaptive valleys have been crossed by genetic drift make it impossible to test Wrights claim that adaptations commonly originate by this process. In view of these problems, it seems unreasonable to consider the shifting balance process as an important explanation for the evolution of adaptations.