Migration-selection Balance Research Articles

GENE FLOW FROM DOMESTICATED SPECIES TO WILD RELATIVES: MIGRATION LOAD IN A MODEL OF MULTIVARIATE SELECTION

Domesticated species frequently spread their genes into populations of wild relatives through interbreeding. The domestication process often involves artificial selection for economically desirable traits. This can lead to an indirect response in unknown correlated traits and a reduction in fitness of domesticated individuals in the wild. Previous models for the effect of gene flow from domesticated species to wild relatives have assumed that evolution occurs in one dimension. Here, I develop a quantitative genetic model for the balance between migration and multivariate stabilizing selection. Different forms of correlational selection consistent with a given observed ratio between average fitness of domesticated and wild individuals offsets the phenotypic means at migration-selection balance away from predictions based on simpler one-dimensional models. For almost all parameter values, correlational selection leads to a reduction in the migration load. For ridge selection, this reduction arises because the distance the immigrants deviates from the local optimum in effect is reduced. For realistic parameter values, however, the effect of correlational selection on the load is small, suggesting that simpler one-dimensional models may still be adequate in terms of predicting mean population fitness and viability.

PREDICTING ADAPTATION UNDER MIGRATION LOAD: THE ROLE OF GENETIC SKEW

Quantitative genetics models have been used to predict the constraints on local adaptation caused by gene flow between populations under migration-selection balance. One key assumption of this approach is that genetic values within a population are normally distributed. Gene flow, however, may generate distributions that are skewed toward the immigrant's mean value. If the response to selection from a skewed distribution is different from that expected under the assumption of normality, models may result in inaccurate predictions. We use individual-based computer simulations to explore this problem, comparing our results to a recent model developed by Hendry et al. (2001). We show that this model underestimates the equilibrium divergence between populations at migration-selection balance. The extent of this underestimation is correlated with the amount of genetic skew generated by migration and is partly explained by the fact that the analytical model ignores direct selection against hybrid phenotypes. We also show that all else being equal, response to selection in a population with a skewed distribution of genotypes is greater than in a population with normally distributed genotypes. The production of skew under migration-selection balance, however, is itself dependent upon the genetic architecture, with greater deviations from normality produced when alleles contributing to population differentiation have very different effect sizes. We find that both the skew and discrepancies between the models are greatest at intermediate migration rates and moderate to strong selection, which is exactly the region of parameter space that is most empirically relevant.

PHENOTYPE-DEPENDENT NATIVE HABITAT PREFERENCE FACILITATES DIVERGENCE BETWEEN PARAPATRIC LAKE AND STREAM STICKLEBACK

Adaptive divergence between adjoining populations reflects a balance between the diversifying effect of divergent selection and the potentially homogenizing effect of gene flow. In most models of migration-selection balance, gene flow is assumed to reflect individuals' inherent capacity to disperse, without regard to the match between individuals' phenotypes and the available habitats. However, habitat preferences can reduce dispersal between contrasting habitats, thereby alleviating migration load and facilitating adaptive divergence. We tested whether habitat preferences contribute to adaptive divergence in a classic example of migration-selection balance: parapatric lake and stream populations of three-spine stickleback (Gasterosteus aculeatus). Using a mark-transplant-recapture experiment on morphologically divergent parapatric populations, we showed that 90% of lake and stream stickleback returned to their native habitat, reducing migration between habitats by 76%. Furthermore, we found that dispersal into a nonnative habitat was phenotype dependent. Stream fish moving into the lake were morphologically more lake-like than those returning to the stream (and the converse for lake fish entering the stream). The strong native habitat preference documented here increases the extent of adaptive divergence between populations two- to fivefold relative to expectations with random movement. These results illustrate the potential importance of adaptive habitat choice in driving parapatric divergence.

Multilocus selection in subdivided populations II. Maintenance of polymorphism under weak or strong migration

The potential of maintaining multilocus polymorphism by migration-selection balance is studied. A large population of diploid individuals is distributed over finitely many demes connected by migration. Generations are discrete and nonoverlapping, selection may vary across demes, and loci are multiallelic. It is shown that if migration and recombination are strong relative to selection, then with weak or no epistasis and intermediate dominance at every locus and in every deme, arbitrarily many alleles can be maintained at arbitrarily many loci at a stable equilibrium. If migration is weak relative to selection and recombination, then with weak or no epistasis and intermediate dominance at every locus and in every deme, as many alleles as there are demes can be maintained at arbitrarily many loci at equilibrium. In both cases open sets of such parameter combinations are constructed, thus the results are robust with respect to small, but arbitrary, perturbations in the parameters. For weak migration, the number of demes is, in fact, a generic upper bound to the number of alleles that can be maintained at any locus. Thus, several scenarios are identified under which multilocus polymorphism can be maintained by migration-selection balance when this is impossible in a panmictic population.

Batesian Mimicry: Can a Leopard Change Its Spots — and Get Them Back?

Can undefended mimics survive outside the range of their noxious models? Two recent studies on Batesian mimicry suggest they can, but alternative survival strategies and morphologies are then favoured.

Evidence for asymmetric migration load in a pair of ecologically divergent stickleback populations

Gene flow between ecologically divergent populations can prevent local adaptation, resulting in lower mean fitness and directional selection within a population. Such maladaptation should tend to be stronger in populations receiving a relatively larger fraction of immigrants. We test this expectation by comparing the strength of selection in a pair of three-spine stickleback populations in adjoining but unequal-sized lake basins in British Columbia. A larger deeper basin is connected to a smaller shallower basin by a short channel that allows extensive migration between populations. The two basins contain distinct habitats and prey communities, and stickleback stomach contents and isotope ratios differ accordingly. Trophic morphology is correlated with diet, so we would expect these ecological differences to be accompanied by morphological divergence. However, high gene flow appears to constrain adaptive divergence: microsatellites indicate that the two basins represent a single panmictic gene pool, and phenotypic divergence is very subtle. As a result, fish in the smaller lake basin are subject to persistent directional selection towards a more benthic phenotype, whereas the larger population exhibits no significant selection. The results illustrate the potentially asymmetrical effect of migration-selection balance, and its effect on fitness within populations.

Localization of Candidate Regions Maintaining a Common Polymorphic Inversion (2La) in Anopheles gambiae

Chromosomal inversion polymorphisms are thought to play a role in adaptive divergence, but the genes conferring adaptive benefits remain elusive. Here we study 2La, a common polymorphic inversion in the African malaria vector Anopheles gambiae. The frequency of 2La varies clinally and seasonally in a pattern suggesting response to selection for aridity tolerance. By hybridizing genomic DNA from individual mosquitoes to oligonucleotide microarrays, we obtained a complete map of differentiation across the A. gambiae genome. Comparing mosquitoes homozygous for the 2La gene arrangement or its alternative (2L+a), divergence was highest at loci within the rearranged region. In the 22 Mb included within alternative arrangements, two ∼1.5 Mb regions near but not adjacent to the breakpoints were identified as being significantly diverged, a conclusion validated by targeted sequencing. The persistent association of both regions with the 2La arrangement is highly unlikely given known recombination rates across the inversion in 2La heterozygotes, thus implicating selection on genes underlying these regions as factors responsible for the maintenance of 2La. Polymorphism and divergence data are consistent with a model in which the inversion is maintained by migration-selection balance between multiple alleles inside these regions, but further experiments will be needed to fully distinguish between the epistasis (coadaptation) and local adaptation models for the maintenance of 2La.

Building of an Experimental Cline With Arabidopsis thaliana to Estimate Herbicide Fitness Cost

Various management strategies aim at maintaining pesticide resistance frequency under a threshold value by taking advantage of the benefit of the fitness penalty (the cost) expressed by the resistance allele outside the treated area or during the pesticide selection "off years." One method to estimate a fitness cost is to analyze the resistance allele frequency along transects across treated and untreated areas. On the basis of the shape of the cline, this method gives the relative contributions of both gene flow and the fitness difference between genotypes in the treated and untreated areas. Taking advantage of the properties of such migration-selection balance, an artificial cline was built up to optimize the conditions where the fitness cost of two herbicide-resistant mutants (acetolactate synthase and auxin-induced target genes) in the model species Arabidopsis thaliana could be more accurately measured. The analysis of the microevolutionary dynamics in these experimental populations indicated mean fitness costs of approximately 15 and 92% for the csr1-1 and axr2-1 resistances, respectively. In addition, negative frequency dependence for the fitness cost was also detected for the axr2-1 resistance. The advantages and disadvantages of the cline approach are discussed in regard to other methods of cost estimation. This comparison highlights the powerful ability of an experimental cline to measure low fitness costs and detect sensibility to frequency-dependent variations.

Regional heterogeneity and gene flow maintain variance in a quantitative trait within populations of lodgepole pine

Genetic variation is of fundamental importance to biological evolution, yet we still know very little about how it is maintained in nature. Because many species inhabit heterogeneous environments and have pronounced local adaptations, gene flow between differently adapted populations may be a persistent source of genetic variation within populations. If this migration-selection balance is biologically important then there should be strong correlations between genetic variance within populations and the amount of heterogeneity in the environment surrounding them. Here, we use data from a long-term study of 142 populations of lodgepole pine (Pinus contorta) to compare levels of genetic variation in growth response with measures of climatic heterogeneity in the surrounding region. We find that regional heterogeneity explains at least 20% of the variation in genetic variance, suggesting that gene flow and heterogeneous selection may play an important role in maintaining the high levels of genetic variation found within natural populations.

The genetic basis of adaptation: lessons from concealing coloration in pocket mice

Recent studies on the genetics of adaptive coat-color variation in pocket mice (Chaetodipus intermedius) are reviewed in the context of several on-going debates about the genetics of adaptation. Association mapping with candidate genes was used to identify mutations responsible for melanism in four different populations of C. intermedius. Here, I review four main results (i) a single gene, the melanocortin-1-receptor (Mc1r), appears to be responsible for most of the phenotypic variation in color in one population, the Pinacate site; (ii) four or fewer nucleotide changes at Mc1r appear to be responsible for the difference in receptor function; (iii) studies of migration-selection balance suggest that the selection coefficient associated with the dark Mc1r allele at the Pinacate site is large; and (iv) different (unknown) genes underlie the evolution of melanism on three other lava flows. These findings are discussed in light of the evolution of convergent phenotypes, the average size of phenotypic effects underlying adaptation, the evolution of dominance, and the distinction between adaptations caused by changes in gene dosage versus gene structure.

ECOLOGICAL GENETICS OF ADAPTIVE COLOR POLYMORPHISM IN POCKET MICE: GEOGRAPHIC VARIATION IN SELECTED AND NEUTRAL GENES

Patterns of geographic variation in phenotype or genotype may provide evidence for natural selection. Here, we compare phenotypic variation in color, allele frequencies of a pigmentation gene (the melanocortin-1 receptor, Mc1r), and patterns of neutral mitochondrial DNA (mtDNA) variation in rock pocket mice (Chaetodipus intermedius) across a habitat gradient in southern Arizona. Pocket mice inhabiting volcanic lava have dark coats with unbanded, uniformly melanic hairs, whereas mice from nearby light-colored granitic rocks have light coats with banded hairs. This color polymorphism is a presumed adaptation to avoid predation. Previous work has demonstrated that two Mc1r alleles, D and d, differ by four amino acids, and are responsible for the color polymorphism: DD and Dd genotypes are melanic whereas dd genotypes are light colored. To determine the frequency of the two Mc1r allelic classes across the dark-colored lava and neighboring light-colored granite, we sequenced the Mc1r gene in 175 individuals from a 35-km transect in the Pinacate lava region. We also sequenced two neutral mtDNA genes, COIII and ND3, in the same individuals. We found a strong correlation between Mc1r allele frequency and habitat color and no correlation between mtDNA markers and habitat color. Using estimates of migration from mtDNA haplotypes between dark- and light-colored sampling sites and Mc1r allele frequencies at each site, we estimated selection coefficients against mismatched Mc1r alleles, assuming a simple model of migration-selection balance. Habitat-dependent selection appears strong but asymmetric: selection is stronger against light mice on dark rock than against melanic mice on light rock. Together these results suggest that natural selection acts to match pocket mouse coat color to substrate color, despite high levels of gene flow between light and melanic populations.

The evolution of recombination in a heterogeneous environment.

Most models describing the evolution of recombination have focused on the case of a single population, implicitly assuming that all individuals are equally likely to mate and that spatial heterogeneity in selection is absent. In these models, the evolution of recombination is driven by linkage disequilibria generated either by epistatic selection or drift. Models based on epistatic selection show that recombination can be favored if epistasis is negative and weak compared to directional selection and if the recombination modifier locus is tightly linked to the selected loci. In this article, we examine the joint effects of spatial heterogeneity in selection and epistasis on the evolution of recombination. In a model with two patches, each subject to different selection regimes, we consider the cases of mutation-selection and migration-selection balance as well as the spread of beneficial alleles. We find that including spatial heterogeneity extends the range of epistasis over which recombination can be favored. Indeed, recombination can be favored without epistasis, with negative and even with positive epistasis depending on environmental circumstances. The selection pressure acting on recombination-modifier loci is often much stronger with spatial heterogeneity, and even loosely linked modifiers and free linkage may evolve. In each case, predicting whether recombination is favored requires knowledge of both the type of environmental heterogeneity and epistasis, as none of these factors alone is sufficient to predict the outcome.

The evolution of dominance.

The evolution of dominance has been subject to intensive debate since Fisher first argued that modifiers would be selected for if they made wild-type alleles more dominant over mutant alleles. An alternative explanation, put forward by Wright, is that the commonly observed dominance of wild-type alleles is simply a physiological consequence of metabolic pathways. Wright's explanation has gained support over the years, largely ending the debate over the general recessivity of deleterious mutations. Nevertheless there is reason to believe that dominance relationships have been moulded by natural selection to some extent. First, the metabolic pathways are themselves products of evolutionary processes that may have led them to be more stable to perturbations, including mutations. Secondly, theoretical models and empirical experiments suggest that substantial selection for dominance modifiers exists during the spread of adaptive alleles or when a polymorphism is maintained either by overdominant selection or by migration-selection balance.

Balanced Polymorphisms and the Evolution of Dominance.

We explore the evolution of dominance at polymorphisms maintained either by overdominant selection or by migration-selection balance. At such balanced polymorphisms, heterozygotes remain at appreciable frequencies over long periods of time, allowing extensive modification of dominance to occur. The strength of selection favoring a modifier of dominance is roughly proportional to the probability that a modifier allele is found in a heterozygote at the locus subject to balancing selection times the heterozygote fitness increase caused by the modifier. Using a two-locus model, we elucidate the interesting ways in which recombination and migration cause departures from this rough expectation. For example, with overdominance, a genetic association with the rarest allele favors a modifier that increases heterozygote fitness because the modifier occurs more often in heterozygotes. With migration-selection balance, dominance evolves more readily in patches experiencing the strongest selection. We also find that, while there are more heterozygotes in sink populations (which have higher rates of immigration than emigration), selection for dominance in sink and source populations is nearly equal because sink populations make a lower genetic contribution to future generations. We conclude that the evolution of dominance is likely to occur whenever polymorphism is maintained by either overdominance or migration.

The Effects of Density Dependence and Immigration on Local Adaptation and Niche Evolution in a Black-Hole Sink Environment

We examine the effects of density dependence and immigration on local adaptation in a “black-hole sink” habitat, i.e., a habitat in which isolated populations of a species would tend to extinction but where a population is demographically maintained by recurrent one-way migration from a separate source habitat in which the species persists. Using a diploid, one-locus model of a discrete-generation sink population maintained by immigration from a fixed source population, we show that a locally favored allele will spread when rare in the sink if the absolute fitness (or, in some cases, the geometric-mean absolute fitness) of heterozygotes with the favored allele is above one in the sink habitat. With density dependence, the criterion for spread can depend on the rate of immigration, because immigration affects local densities and, hence, absolute fitness. Given the successful establishment of a locally favored allele, it will be maintained by a migration-selection balance and the resulting polymorphic population will be sustained deterministically with either stable or unstable dynamics. The densities of stable polymorphic populations tend to exceed densities that would be maintained in the absence of the favored allele. With strong density regulation, spread of the favored allele may destabilize population dynamics. Our analyses show that polymorphic populations which form subsequent to the establishment of favorable alleles have the capacity to persist deterministically without immigration. Finally, we examined the probabilistic rate at which new favored alleles arise and become established in a sink population. Our results suggest that favored alleles are established most readily at intermediate levels of immigration.

Migration versus mutation in the evolution of recombination under multilocus selection.

We use modifier theory to compare the evolution of recombination under mutation-selection and migration-selection balance models. Recombination between loosely linked loci subject to weak multilocus selection is controlled by the genotype at a selectively neutral modifier locus. We show that the success of a new modifier depends on the sign and amount of epistasis as well as on the linkage of the modifier locus to the loci under selection. With both migration and mutation, for recombination to increase requires negative (synergistic) epistasis. When epistasis is sufficiently weak, increased recombination is always favoured under mutation-selection balance and never under migration-selection balance. With stronger negative epistasis, there exists a critical recombination value. In this case, a recombination-increasing allele invades the population under mutation-selection balance if its recombination rate with the major loci is less than the critical recombination value, whereas with weak migration it must be above this value. These results are the same for haploid and diploid populations.

MAINTENANCE OF POLYGENIC VARIATION VIA A MIGRATION-SELECTION BALANCE UNDER UNIFORM SELECTION.

Population subdivision is often invoked to explain the large amount of heterozygosity found at single loci in natural populations (Felsenstein 1976; Hedrick et al., 1976; Karlin 1982; Hedrick 1986). Surprisingly, relatively few studies describe the effects of population structure on the maintenance of variance for polygenic (quantitative) traits. Felsenstein (1977) and Slatkin (1978) presented models in which additive variance can be maintained via migration along a cline (see also Barton and Turelli 1989). Goldstein and Holsinger (1992) used simulations to show that variance for quantitative traits could be maintained under uniform selection in a population subject to isolation by distance (see also Lande [1991]), and Slatkin and Lande (1994) demonstrated that the segregation variance generated by betweenpopulation crosses depends on how variance is generated within each population. Here I analyze the amount of variance that can be maintained deterministically via a migration-selection balance under uniform selection and conclude that a potentially large amount of variance can be generated in this way. This is true only when migration is very weak, so as not to overcome the influence of selection. When variance is maintained, it is maximal at the critical balance between migration and selection. The deterministic interaction between migration and selection has been the subject of a great deal of analysis in the context of Wright's shifting-balance theory (Crow et al. 1990; Barton 1992; Kondrashov 1992; Phillips 1993). These studies have shown that migration can be very effective at overcoming the effects of selection and driving populations to uniformity. For the shifting-balance process, this means that once a population has undergone a peak shift, it might be expected to drive peak shifts in neighboring populations, depending on the details of the system and population structure (Barton 1992; Phillips 1993). The purpose here is to explore regions of the parametric space in which this does not happen, but instead both populations remain polymorphic. Results from this deterministic approach will be contrasted with models that include stochastic effects and make somewhat different predictions (Lande 1991; Goldstein and Holsinger 1992; Barton and Rouhani 1993). Uniform stabilizing selection on an additive character generates disruptive selection at the level because various combinations of alleles can yield the same optimal phenotype, but the marginal fitness of any allele depends on the background in which it is found (Wright 1935). This is called genetic redundancy by Goldstein and Holsinger [1992]). Two populations can thus display the same phenotype but be fixed for different genotypes. If these populations were to exchange migrants, the mixing of the different genotypes would generate variance within each population. This would be a somewhat cryptic source of variation because there would be no obvious differentiation between the populations. Depending on the strength of migration, most of the variance generated by migration would then be quickly eliminated by selection, creating a migration-selection balance. This is the multilocus equivalent of a migration-selection polymorphism generated by underdominance at a single locus (Karlin and McGregor 1972). Because many characters are assumed to be under stabilizing selection, and because population structure is undoubtedly an important feature of natural populations, the interaction of migration and selection could obviously be an important influence on the maintenance of variance.

Evolution of dispersal in density regulated populations: A haploid model

The evolution of dispersal is explored in a density-dependent framework. Attention is restricted to haploid populations in which the genotypic fitnesses at a single diallelic locus are decreasing functions of the changing number of individuals in the population. It is shown that migration between two populations in which the genotypic response to density is reversed can maintain both alleles when the intermigration rates are constant or nondecreasing functions of the population densities. There is always a unique symmetric interior equilibrium with equal numbers but opposite gene frequencies in the two populations, provided the system is not degenerate. Numerical examples with exponential and hyperbolic fitnesses suggest that this is the only stable equilibrium state under constant positive migration rates ( m) less than 1 2 . Practically speaking, however, there is only convergence after a reasonable number of generations for relatively small migration rates ( m < 1 4 ). A migration-modifying mutant at a second, neutral locus, can successfully enter two populations at a stable migration-selection balance if and only if it reduces the intermigration rates of its carriers at the original equilibrium population size. Moreover, migration modification will always result in a higher equilibrium population size, provided the system approaches another symmetric interior equilibrium. The new equilibrium migration rate will be lower than that at the original equilibrium, even when the modified migration rate is a nondecreasing function of the population sizes. Therefore, as in constant viability models, evolution will lead to reduced dispersal.