A SIMULATION OF WRIGHT'S SHIFTING-BALANCE PROCESS: MIGRATION AND THE THREE PHASES

Wright partitioned the shifting-balance process into three phases. Phase one is the shift of a deme within a population to the domain of a higher adaptive peak from that of the historical peak. Phase two is mass selection within a deme towards that higher peak. Phase three is the conversion of additional demes to the higher peak. The migration rate between demes is critical for the existence of phases one and three. Phase one requires small effective population sizes, hence low migration rates. Phase three is optimal under high migration rates that spread the most-fit genotype from deme to deme. Thus, a population-wide peak shift requires intermediate levels of migration. By altering the rates of phases one and three, migration affects the predominant direction of mass selection within a population. This study examines the degree to which migration, through its effects on phases one and three, determines the probability of a simulated population arriving at its genotypic optimum after 12,000 generations. These simulations reveal that there is a range of migration rates for which an entire population might be expected to shift to a higher peak. Below m = 0.001 peak shifts occur frequently (phases I and II) but are not successfully exported out of subpopulations (phase III), and above 0.01 peak shifts within demes (phase I and II), required to initiate phase III, become increasingly uncommon. Because it is unlikely that real populations will have uniform migration rates from generation to generation, the probable effects of varying migration rates on broadening the range of conditions producing peak shifts are discussed.     

THE EFFECTS OF GENE FLOW ON REINFORCEMENT

We explore the possibility that differences in the pattern of gene flow between populations may affect the evolution of reinforcement by comparing pairs of populations undergoing one-way migration versus symmetric migration. The case of symmetric migration is modeled by a two-island model, where the two populations exchange equal proportions of migrants each generation. One-way migration is modeled by a continent-island model, where migration is in one direction from a large continental population with a fixed genotype to an island population whose genotype frequencies can vary. Hybrid inviability is assumed to be caused by epistatic interactions between background loci. We examine the spread of an introduced preference allele for a previously unpreferred male trait that characterizes one of the populations. Computer simulations indicate that with a weak introduced preference, reinforcement is possible under a wide range of parameter values in a symmetric migration model but cannot occur in a one-way migration model. Reinforcement with one-way migration can occur only with a very strong introduced preference and very strong selection against hybrids. Our results suggest that the speciation of a peripheral isolate, which undergoes essentially one-way migration, may be difficult to complete if secondary contact occurs before reproductive isolation is fully developed.     

Detecting selection along environmental gradients: analysis of eight methods and their effectiveness for outbreeding and selfing populations

Thanks to genome‐scale diversity data, present‐day studies can provide a detailed view of how natural and cultivated species adapt to their environment and particularly to environmental gradients. However, due to their sensitivity, up‐to‐date studies might be more sensitive to undocumented demographic effects such as the pattern of migration and the reproduction regime. In this study, we provide guidelines for the use of popular or recently developed statistical methods to detect footprints of selection. We simulated 100 populations along a selective gradient and explored different migration models, sampling schemes and rates of self‐fertilization. We investigated the power and robustness of eight methods to detect loci potentially under selection: three designed to detect genotype–environment correlations and five designed to detect adaptive differentiation (based on F_ST or similar measures). We show that genotype–environment correlation methods have substantially more power to detect selection than differentiation‐based methods but that they generally suffer from high rates of false positives. This effect is exacerbated whenever allele frequencies are correlated, either between populations or within populations. Our results suggest that, when the underlying genetic structure of the data is unknown, a number of robust methods are preferable. Moreover, in the simulated scenario we used, sampling many populations led to better results than sampling many individuals per population. Finally, care should be taken when using methods to identify genotype–environment correlations without correcting for allele frequency autocorrelation because of the risk of spurious signals due to allele frequency correlations between populations.     

Estimation of migration from a perturbation experiment in natural populations of Drosophila buzzatii Patterson & Wheeler

In order to estimate migration and gene flow, allele frequencies in populations at two sites separated by 120 m were differentially perturbed by the continuous release over 413 days of flies homozygous at particular allozyme loci. The effects of perturbation were determined by genotype assay at two collections prior to, thirteen during and nine after the perturbation period. Maximum likelihood methods were developed to estimate migration into the two populations from the homozygous releases, and migration between the two populations. The successful perturbation of allele frequencies in a natural population is demonstrated. A plateau in allele frequencies during perturbation and a return to original frequencies following cessation of perturbation was most likely due to selection during development against recessive alleles concurrently introduced into the populations by the released flies. There is unequivocal evidence for short distance gene flow between the two populations. The migration rates estimated at ten times over a nine month period were extremely variable, but with higher population density at one site positively related with migration from that site to the other.     

Recombination can evolve in large finite populations given selection on sufficient loci

It is well known that an allele causing increased recombination is expected to proliferate as a result of genetic drift in a finite population undergoing selection, without requiring other mechanisms. This is supported by recent simulations apparently demonstrating that, in small populations, drift is more important than epistasis in increasing recombination, with this effect disappearing in larger finite populations. However, recent experimental evidence finds a greater advantage for recombination in larger populations. These results are reconciled by demonstrating through simulation without epistasis that for m loci recombination has an appreciable selective advantage over a range of population sizes (am, bm). bm increases steadily with m while am remains fairly static. Thus, however large the finite population, if selection acts on sufficiently many loci, an allele that increases recombination is selected for. We show that as selection acts on our finite population, recombination increases the variance in expected log fitness, causing indirect selection on a recombination-modifying locus. This effect is enhanced in those populations with more loci because the variance in phenotypic fitnesses in relation to the possible range will be smaller. Thus fixation of a particular haplotype is less likely to occur, increasing the advantage of recombination.     

Inference of Unexpected Genetic Relatedness among Individuals in HapMap Phase III

The International Haplotype Map Project (HapMap) has provided an essential database for studies of human population genetics and genome-wide association. Phases I and II of the HapMap project generated genotype data across ∼3 million SNP loci in 270 individuals representing four populations. Phase III provides dense genotype data on ∼1.5 million SNPs, generated by Illumina and Affymetrix platforms in a larger set of individuals. Release 3 of phase III of the HapMap contains 1397 individuals from 11 populations, including 250 of the original 270 phase I and phase II individuals and 1147 additional individuals. Although some known relationships among the phase III individuals have been described in the data release, the genotype data that are currently available provide an opportunity to empirically ascertain previously unknown relationships. We performed a systematic analysis of genetic relatedness and were able not only to confirm the reported relationships, but also to detect numerous additional, previously unidentified pairs of close relatives in the HapMap sample. The inferred relative pairs make it possible to propose standardized subsets of unrelated individuals for use in future studies in which relatedness needs to be clearly defined.     

Migration rates, frequency-dependent selection and the self-incompatibility locus in Leavenworthia (brassicaceae)

Loci subject to negative frequency-dependent selection are expected to exhibit higher effective migration rates compared to reference loci. Although the number of gene copies transferred between populations by migration is the same for all genes, those subject to negative frequency-dependent selection are more likely to be retained in the immigrant population because rare alleles are selectively favored. So far, evidence for this prediction has been indirect, based on summary statistics rather than on migration rate estimates. Here, we introduce an approximate Bayesian procedure to jointly estimate migration rates at two predefined sets of loci between two populations. We applied the procedure to compare migration rate estimates at the self-incompatibility locus (S-locus) with that at 10 reference loci in two plant species, Leavenworthia alabamica and L. crassa (Brassicaceae). The maximum likelihood estimate for the proportion of migrants (m) was four times higher at the S-locus than at reference loci, but the difference was not statistically significant. Lack of significance might be due to insufficient data, but perhaps also to the recent divergence of the two species (311 ka), because we also show using simulations that the effective migration rate at the S-locus is expected to increase with increasing divergence time. These findings aid in understanding the evolutionary dynamics of negative frequency-dependent selection and they suggest that divergence time should be accounted for when employing migration rates to help detect negative frequency-dependent selection.     

Esterase genes in parallel composite cross barley populations

The California population of Composite Cross V of barley was used as the source of three subpopulations that were started from generations 10, 20 and 30, respectively, and were grown in parallel environmental conditions in Cambridge for eight generations. Outcrossing rates (0.2%) were even lower than in the California material, and heterozygotes were correspondingly rare, so that the populations were essentially mixtures of homozygous lines. Four esterase loci that were polymorphic in the base Composite Cross V remained so in all the derived populations, but showed considerable changes in allelic frequency over time, particularly at two of the genes. Multilocus analysis showed that strong directional changes occurred in all three populations, but they were not consistent. One particular genotype became predominant in the population derived from generation 10, whereas in the other two populations it was a genotype with different alleles at the Est1 and Est3 loci that rose to frequencies of more than 50%. Strong directional selection undoubtedly occurred in these populations, but did not cause parallel changes in esterase gene frequencies. These data do not facilitate a discrimination between the alternative explanations of hitchhiking or multilocus selection at these loci.     

Fixation probability in spatially changing environments.

The fixation probability of a mutant in a subdivided population with spatially varying environments is investigated using a finite island model. This probability is different from that in a panmictic population if selection is intermediate to strong and migration is weak. An approximation is used to compute the fixation probability when migration among subpopulations is very weak. By numerically solving the two-dimensional partial differential equation for the fixation probability in the two subpopulation case, the approximation was shown to give fairly accurate values. With this approximation, we show in the case of two subpopulations that the fixation probability in subdivided populations is greater than that in panmictic populations mostly. The increase is most pronounced when the mutant is selected for in one subpopulation and is selected against in the other subpopulation. Also it is shown that when there are two types of environments, further subdivision of subpopulations does not cause much change of the fixation probability in the no dominance case unless the product of the selection coefficient and the local population size is less than one. With dominance, the effect of subdivision becomes more complex.     

The diffusion model for migration and selection in a dioecious population

The diffusion approximation is derived for migration and selection at a multiallelic locus in a dioecious population subdivided into a lattice of panmictic colonies. Generations are discrete and nonoverlapping; autosomal and X-linked loci are analyzed. The relation between juvenile and adult subpopulation numbers is very general and includes both soft and hard selection; the zygotic sex ratio is the same in every colony. All the results hold for both adult and juvenile migration. If ploidy-weighted average selection, drift, and diffusion coefficients are used, then the ploidy-weighted average allelic frequencies satisfy the corresponding partial differential equation for a monoecious population. The boundary conditions and the unidimensional transition conditions for coincident discontinuities in the carrying capacity and migration rate extend identically. The previous unidimensional formulation and analysis of symmetric, nearest-neighbor migration of a monoecious population across a geographical barrier is generalized to symmetric migration of arbitrary finite range, and the transition conditions are shown to hold for a dioecious population. Thus, the entire theory of clines and of the wave of advance of favorable alleles is applicable to dioecious populations.This work was supported by National Science Foundation grant BSR-9006285     

Spatial heterogeneity in the strength of selection against deleterious alleles and the mutation load

According to current estimates of genomic deleterious mutation rates (which are often of the order 0.1-1) the mutation load (defined as a reduction in the average fitness of a population due to the presence of deleterious alleles) may be important in many populations. In this paper, I use multilocus simulations to explore the effect of spatial heterogeneity in the strength of selection against deleterious alleles on the mutation load (for example, it has been suggested that stressful environments may increase the strength of selection). These simulations show contrasted results: in some situations, spatial heterogeneity may greatly reduce the mutation load, due to the fact that migrants coming from demes under stronger selection carry relatively few deleterious alleles, and benefit from a strong advantage within demes under weaker selection (where individuals carry many more deleterious alleles); in other situations, however, deleterious alleles accumulate within demes under stronger selection, due to migration pressure from demes under weaker selection, leading to fitness erosion within those demes. This second situation is more frequent when the productivity of the different demes is proportional to their mean fitness. The effect of spatial heterogeneity is greatly reduced, however, when the response to environmental differences is inconsistent across loci.     

Ecologically and evolutionarily important SNPs identified in natural populations

Evolution by natural selection acts on natural populations amidst migration, gene-by-environmental interactions, constraints, and tradeoffs, which affect the rate and frequency of adaptive change. We asked how many and how rapidly loci change in populations subject to severe, recent environmental changes. To address these questions, we used genomic approaches to identify randomly selected single nucleotide polymorphisms (SNPs) with evolutionarily significant patterns in three natural populations of Fundulus heteroclitus that inhabit and have adapted to highly polluted Superfund sites. Three statistical tests identified 1.4-2.5% of SNPs that were significantly different from the neutral model in each polluted population. These nonneutral patterns in populations adapted to highly polluted environments suggest that these loci or closely linked loci are evolving by natural selection. One SNP identified in all polluted populations using all tests is in the gene for the xenobiotic metabolizing enzyme, cytochrome P4501A (CYP1A), which has been identified previously as being refractory to induction in the three highly polluted populations. Extrapolating across the genome, these data suggest that rapid evolutionary change in natural populations can involve hundreds of loci, a few of which will be shared in independent events.     

Natural selection acts on Atlantic salmon major histocompatibility (MH) variability in the wild

Pathogen-driven balancing selection is thought to maintain polymorphism in major histocompatibility (MH) genes. However, there have been few empirical demonstrations of selection acting on MH loci in natural populations. To determine whether natural selection on MH genes has fitness consequences for wild Atlantic salmon in natural conditions, we compared observed genotype frequencies of Atlantic salmon (Salmo salar) surviving in a river six months after their introduction as eggs with frequencies expected from parental crosses. We found significant differences between expected and observed genotype frequencies at the MH class II alpha locus, but not at a MH class I-linked microsatellite or at seven non-MH-linked microsatellite loci. We therefore conclude that selection at the MH class II alpha locus was a result of disease-mediated natural selection, rather than any demographic event. We also show that survival was associated with additive allelic effects at the MH class II alpha locus. Our results have implications for both the conservation of wild salmon stocks and the management of disease in hatchery fish. We conclude that natural or hatchery populations have the best chance of dealing with episodic and variable disease challenges if MH genetic variation is preserved both within and among populations.     

Polymorphism in multilocus host parasite coevolutionary interactions

Numerous loci in host organisms are involved in parasite recognition, such as major histocompatibility complex (MHC) genes in vertebrates or genes involved in gene-for-gene (GFG) relationships in plants. Diversity is commonly observed at such loci and at corresponding loci encoding antigenic molecules in parasites. Multilocus theoretical models of host-parasite coevolution predict that polymorphism is more likely than in single-locus interactions because recurrent coevolutionary cycles are sustained by indirect frequency-dependent selection as rare genotypes have a selective advantage. These cycles are stabilized by direct frequency-dependent selection, resulting from repeated reinfection of the same host by a parasite, a feature of most diseases. Here, it is shown that for realistically small costs of resistance and virulence, polycyclic disease and high autoinfection rates, stable polymorphism of all possible genotypes is obtained in parasite populations. Two types of epistatic interactions between loci tend to increase the parameter space in which stable polymorphism can occur with all possible host and parasite genotypes. In the parasite, the marginal cost of each additional virulence allele should increase, while in the host, the marginal cost of each additional resistance allele should decrease. It is therefore predicted that GFG polymorphism will be stable (and hence detectable) when there is partial complementation of avirulence genes in the parasite and of resistance genes in the host.     

Coexistence of cytoplasmic incompatibility and male-killing-inducing endosymbionts, and their impact on host gene flow

Male-killing (MK) and cytoplasmic incompatibility (CI) inducing bacteria are among the most common endosymbionts of arthropods. Previous theoretical research has demonstrated that these two types of endosymbionts cannot stably coexist within a single unstructured host population if no doubly infected host individuals occur. Here, we analyse a model of two host subpopulations connected by migration. We demonstrate that coexistence of MK- and CI-inducing endosymbionts is possible if migration rates are sufficiently low. In particular, our results suggest that for coexistence to be possible, migration rates into the subpopulation infected predominantly with MK-inducing endosymbionts must be considerably low, while migration rates from the MK- to the CI-infected subpopulation can be very high. We also analyse how the presence of MK- and CI-inducing endosymbionts affects host gene flow between the two subpopulations. Employing the concept of the 'effective migration rate', we demonstrate that compared with an uninfected subdivided population, gene flow is increased towards the MK-infected island, but decreased towards the CI-infected island. We discuss our results with respect to the butterfly Hypolimnas bolina, in which infection polymorphism of CI- and MK-inducing Wolbachia has been reported across South-Pacific island populations.     

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.     

Multilocus Evolution in Fire Ants: Effects of Selection, Gene Flow and Recombination

The reproductive success of individual fire ant queens (Solenopsis invicta) previously has been shown to be strongly influenced by their genotype at a single enzyme-encoding gene, designated Pgm-3. This paper presents evidence that a second, tightly linked gene, designated Gp-9, is under similarly strong selection in these ants. Selection appears to act independently on the two genes and is detectable in only one of the two social forms of this species (the ``polygyne' social form, in which nests contain multiple fertile queens). Strong directional selection on Pgm-3 in this form involves worker destruction of all queens with genotype Pgm-3(AA) before they reproduce. Selection on Gp-9 is more complex, involving both lethality of all Gp-9(bb) females and a strong or even complete survival advantage to reproductive queens with the heterozygous genotype Gp-9(Bb). Pgm-3 and Gp-9 are tightly linked (r(f) = 0.0016) and exhibit strong gametic phase disequilibrium in introduced populations in the U.S. This disequilibrium seems not to have stemmed from the founder event associated with the introduction, because the same associations of alleles found in the U.S. apparently occur also in two native populations in Argentina. Rather, selection acting independently on Pgm-3 and Gp-9, in conjunction with gene flow from the alternate, ``monogyne' social form (in which nests contain a single fertile queen), may explain the origin of disequilibrium between the two loci in polygyne fire ants.     

Natural selection in populations subject to a migration load

Migration tends to oppose the effects of divergent natural selection among populations. Numerous theoretical and empirical studies have demonstrated that this migration-selection balance constrains genetic divergence among populations. In contrast, relatively few studies have examined immigration's effects on fitness and natural selection within recipient populations. By constraining local adaptation, migration can lead to reduced fitness, known as a "migration load," which in turn causes persistent natural selection. We develop a simple two-island model of migration-selection balance that, although very general, also reflects the natural history of Timema cristinae walking-stick insects that inhabit two host plant species that favor different cryptic color patterns. We derive theoretical predictions about how migration rates affect the level of maladaptation within populations (measured as the frequency of less-cryptic color-pattern morphs), which in turn determines the selection differential (the within-generation morph frequency change). Using data on color morph frequencies from 25 natural populations, we confirm previous results showing that maladaptation is higher in populations receiving more immigrants. We then present novel evidence that this increased maladaptation leads to larger selection differentials, consistent with our model. Our results provide comparative evidence that immigration elevates the variance in fitness, which in turn leads to larger selection differentials, consistent with Fisher's Theorem of Natural Selection. However, we also find evidence that recurrent adult migration between parapatric populations may tend to obscure the effects of selection.     

Selection on recombination in a multi-locus system

The model of Wills and Miller (1976) for selection on recombination rates in finite populations was studied by means of a computer model involving 80 selected loci and a linked or unlinked modifier gene affecting the map length occupied by the selected loci. The selected loci were subject to heterozygote advantage, and multiplicative fitness interactions between loci were assumed. In all cases studied, selection for reduction in recombination out-weighed any selection for increased recombination that may have been present.     

Genotypic selection in Daphnia populations consisting of inbred sibships

The genetic basis of fitness reduction associated with inbreeding is still poorly understood. Here we use associations between allozyme genotypes and fitness to investigate the genetic basis of inbreeding depression in experimental outdoor populations of the water flea, Daphnia magna. In Daphnia, a phase of clonal reproduction follows hatching from sexually produced resting eggs, and changes in genotype frequencies during the clonal phase can be used to estimate fitness. Our experiment resembles natural colonization of ponds in that single clones colonize an empty pool, expand asexually and produce sexual offspring by selfing (sisters mate with their clonal brothers). These offspring diapause and form populations consisting of selfed sibships in the following spring. In 12 of 13 experimental populations, genotypes of selfed hatchlings after diapause conformed to Mendelian expectations. During the subsequent ca. 10 asexual generations, however, genotype frequencies changed significantly at 19 of 27 single loci studied within populations, mostly in favour of heterozygotes, with heterozygosity at multiple loci affecting the change in genotype frequency multiplicatively. Because variance in heterozygosity among siblings at a given marker reflects only heterozygosity in the chromosomal region around this marker, our results suggest that selection at fitness-associated loci in the chromosomal regions near the markers were responsible for these changes. The genotype frequency changes were more consistent with selection acting on linked loci than on the allozymes themselves. Taken together, the evidence for abundant selection in the chromosomal regions of the markers and the fact that changes in genotype frequencies became apparent only after several generations of clonal selection, point to a genetic load consisting of many alleles of small or intermediate effects, which is consistent with the strong genetic differentiation and repeated genetic bottlenecks in the metapopulation from which the animals for this study were obtained.