The effect of variable environments on polymorphism at loci with several alleles II. Submultiplicative viabilities

Circumstances assuring a unique stable equilibrium are investigated for a subdivided population with several alleles segregating at a single locus. For a broad class of selection regimes entailing heterozygote viabilities greater than the geometric mean of the corresponding homozygote viabilities, a stable fixation state precludes any other stable equilibria if either total-panmixia or temporal variation is operating. This extends known results for two alleles at a single locus and partially delimits when some of the bizarre behaviour engendered by multiple alleles may occur.Supported in part by National Science Foundation (USA) grant MCS-8002227     

GEOGRAPHIC VARIATION, FREQUENCY-DEPENDENT SELECTION, AND THE MAINTENANCE OF A FEMALE-LIMITED POLYMORPHISM

A central problem in evolutionary biology is to understand how spatial and temporal variation in selection maintain genetic variation within and among populations. Brown anole lizards ( Anolis sagrei ) exhibit a dorsal pattern polymorphism that is expressed only in females, which occur in "diamond,""bar," and intermediate "diamond-bar" morphs. To understand the inheritance of this polymorphism, we conducted a captive breeding study that refuted several single-locus models and supported a two-locus mode of inheritance. To describe geographic variation in morph frequencies, we surveyed 13 populations from two major islands in The Bahamas. Morph frequencies differed substantially between major islands but were highly congruent within each island. Finally, we measured viability selection on each island to test two hypotheses regarding the maintenance of the polymorphism: (1) that spatial variation in selection maintains variation in morph frequencies between islands, and (2) that temporal variation in selection across years maintains variation within islands. Although bar females had relatively lower survival where they were rare, our data do not otherwise suggest that selection varies spatially between islands. However, diamond-bar females were subject to positive frequency-dependent selection across years, and the relative fitness of bar and diamond females alternated across years. We propose that this polymorphism is maintained by temporal variation in selection coupled with the sheltering of alleles via a two-locus inheritance pattern and sex-limited expression.     

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.      

Nucleotide polymorphism and natural selection at the pantophysin (Pan I) locus in the Atlantic cod, Gadus morhua (L.)

Molecular studies of nucleotide sequence variation have rarely attempted to test hypotheses related to geographically varying patterns of natural selection. The present study tested the role of spatially varying selection in producing significant linkage disequilibrium and large differences in the frequencies of two common alleles at the pantophysin (Pan I) locus among five populations of the Atlantic cod, Gadus morhua. Nucleotide sequences of 124 Pan I alleles showed strong evidence for an unusual mix of balancing and directional selection but no evidence of stable geographically varying selection. The alleles were highly divergent at both the nucleotide level (differing on average by 19 mutations) and at amino acid level (each having experienced three amino acid substitutions since diverging from a common ancestral allele). All six amino acid substitutions occurred in a 56-residue intravesicular loop (IV1 domain) of the vesicle protein and each involved a radical change. An analysis of molecular variation revealed significant heterogeneity in the frequencies of recently derived mutations segregating within both allelic classes, suggesting that two selective sweeps may be presently occurring among populations. The dynamic nature of the Pan I polymorphism in G. morhua and clear departure from equilibrium conditions invalidate a simple model of spatially varying selection.     

Diversifying selection underlies the origin of allozyme polymorphism at the phosphoglucose isomerase locus in Tigriopus californicus

The marine copepod Tigriopus californicus lives in intertidal rock pools along the Pacific coast, where it exhibits strong, temporally stable population genetic structure. Previous allozyme surveys have found high frequency private alleles among neighboring subpopulations, indicating that there is limited genetic exchange between populations. Here we evaluate the factors responsible for the diversification and maintenance of alleles at the phosphoglucose isomerase (Pgi) locus by evaluating patterns of nucleotide variation underlying previously identified allozyme polymorphism. Copepods were sampled from eleven sites throughout California and Baja California, revealing deep genetic structure among populations as well as genetic variability within populations. Evidence of recombination is limited to the sample from Pescadero and there is no support for linkage disequilibrium across the Pgi locus. Neutrality tests and codon-based models of substitution suggest the action of natural selection due to elevated non-synonymous substitutions at a small number of sites in Pgi. Two sites are identified as the charge-changing residues underlying allozyme polymorphisms in T. californicus. A reanalysis of allozyme variation at several focal populations, spanning a period of 26 years and over 200 generations, shows that Pgi alleles are maintained without notable frequency changes. Our data suggest that diversifying selection accounted for the origin of Pgi allozymes, while McDonald-Kreitman tests and the temporal stability of private allozyme alleles suggests that balancing selection may be involved in the maintenance of amino acid polymorphisms within populations.     

The multiple-locus symmetric fertility model

Selection due to variation in the fecundity among matings of genotypes with respect to many loci each with two alleles is studied. The fitness of a mating depends only on the genotypic distinction between homozygote and heterozygote at each locus in the two individuals, and differences among loci are allowed. This symmetric fertility model is therefore a generalization of the multiple-locus symmetric viability model. The phenomena seen in the two-locus symmetric fertility model generalize—e.g., the possibility of joint stability of equilibria with linkage equilibrium and with linkage disequilibrium, and the existence of different types of totally polymorphic equilibria with the gametic proportions in linkage equilibrium. The central equilibrium with genotypic frequencies in Hardy-Weinberg proportions and gametic frequencies in Robbins proportions exists for all symmetric fertility models. For some symmetric fertility regimes additional equilibria exist with gametic frequencies in linkage equilibrium and with genotypic frequencies in Hardy-Weinberg proportions at all except one locus. These equilibria may exist in the dioecious symmetric viability model, and then they will be locally stable. For free recombination the stable equilibria show linkage equilibrium, but several of these with different numbers of polymorphic loci may be stable simultaneously.     

Spatial variation in coevolutionary dynamics

Summary Computer simulations of coevolutionary dynamics between two hosts and two parasites show that extensive spatial variation in polymorphism can be maintained among environmentally identical patches. Spatial variation can be maintained under frequent migration when the dynamics within patches are locally unstable, and the cycles in host and parasite abundances remain out of phase among patches. Additionally, spatial variation can be maintained when host-parasite interactions cause local extinctions, and migration subsequently allows for recolonization. The temporal dynamics that cause spatial variation are difficult to study directly because of the long time scale over which they occur. The simulations suggest that sampling over space at one or a few points in time may provide much information about temporal dynamics.     

Polymorphism in the two-locus Levene model with nonepistatic directional selection

For the Levene model with soft selection in two demes, the maintenance of polymorphism at two diallelic loci is studied. Selection is nonepistatic and dominance is intermediate. Thus, there is directional selection in every deme and at every locus. We assume that selection is in opposite directions in the two demes because otherwise no polymorphism is possible. If at one locus there is no dominance, then a complete analysis of the dynamical and equilibrium properties is performed. In particular, a simple necessary and sufficient condition for the existence of an internal equilibrium and sufficient conditions for global asymptotic stability are obtained. These results are extended to deme-independent degree of dominance at one locus. A perturbation analysis establishes structural stability within the full parameter space. In the absence of genotype-environment interaction, which requires deme-independent dominance at both loci, nongeneric equilibrium behavior occurs, and the introduction of arbitrarily small genotype-environment interaction changes the equilibrium structure and may destroy stable polymorphism. The volume of the parameter space for which a (stable) two-locus polymorphism is maintained is computed numerically. It is investigated how this volume depends on the strength of selection and on the dominance relations. If the favorable allele is (partially) dominant in its deme, more than 20% of all parameter combinations lead to a globally asymptotically stable, fully polymorphic equilibrium.     

Environmental heterogeneity and balancing selection in the acorn barnacle Semibalanus balanoides

The northern acorn barnacle Semibalans banlanoides occupies several intertidal microhabitats which vary greatly in their degree of physical stress. This environmental heterogeneity creates distinct selection regimes which can maintain genetic variation in natural populations. Despite considerable attention placed on the link between spatial variation in fitness and balancing selection at specific loci, experimental manipulations and fitness estimates for molecular polymorphisms have rarely been conducted in the wild. The aim of this transplant experiment was to manipulate the level of physical stress experienced by a cohort of barnacles in the field and then investigate the spatial variation in fitness for genotypes at three loci: two candidate allozymes and the mitochondrial DNA control region. The viability of mannose-6-phosphate isomerase (Mpi) genotypes was dependent on the level of physical stress experienced in the various treatments; alternative homozygotes were favoured in alternative high stress-low stress environments. In contrast, the fitness of genotypes at other loci was equivalent among treatments and unaffected by the manipulation. Evaluated in the light of balancing selection models, these data indicate that the presence of multiple environmental niches is sufficient to promote a stable Mpi polymorphism in barnacle populations and that allelic variation at this locus reflects the process of adaptation to the heterogeneous intertidal landscape.     

A symmetric two locus model with viability and fertility selection

A two locus deterministic population genetic model is analysed. One locus is under viability selection, the other under fertility selection with both forms of selection completely symmetric. It is shown that linkage equilibrium may occur at two different equilibrium points. For a two-locus polymorphism to be stable, it is necessary that the viability locus be overdominant but not necessary that the fertility locus, considered separately, be able to support a stable polymorphism. The overlaps in stability are not as complex as under two locus symmetric fertilities, but considerably more complex than with symmetric viabilities. Extensions of the analysis for the central linkage equilibrium point with multiple viability and fertility loci are indicated.Research supported in part by NIH grants GM 28106 and GM 10452     

Contrasting patterns of variation in MHC loci in the Alpine newt

Major histocompatibility complex (MHC) genes are essential in pathogen recognition and triggering an adaptive immune response. Although they are the most polymorphic genes in vertebrates, very little information on MHC variation and patterns of evolution are available for amphibians, a group known to be declining rapidly worldwide. As infectious diseases are invoked in the declines, information on MHC variation should contribute to devising appropriate conservation strategies. In this study, we examined MHC variation in 149 Alpine newts ( Mesotriton alpestris ) from three allopatric population groups in Poland at the northeastern margin of the distribution of this species. The genetic distinctiveness of the population groups has previously been shown by studies of skin graft rejection, allozymes and microsatellites. Two putative expressed MHC II loci with contrasting levels of variation and clear evidence of gene conversion/recombination between them were detected. The Meal-DAB locus is highly polymorphic (37 alleles), and shows evidence of historical positive selection for amino acid replacements and substantial geographical differentiation in allelic richness. On the contrary, the Meal-DBB locus exhibits low polymorphism (three alleles differing by up to two synonymous substitutions) and a uniform distribution of three alleles among geographical regions. The uniform frequencies of the presumptively neutral Meal-DBB alleles may be explained by linkage to Meal-DAB . We found differences in allelic richness in Meal-DAB between regions, consistent with the hypothesis that genetic drift prevails with increasing distance from glacial refugia. Pseudogene loci appear to have evolved neutrally. The level of DAB variation correlated with variation in microsatellite loci, implying that selection and drift interplayed to produce the pattern of MHC variation observed in marginal populations of the Alpine newt.     

A multilocus-multiallele analysis of frequency-dependent selection induced by intraspecific competition

The study of the mechanisms that maintain genetic variation has a long history in population genetics. We analyze a multilocus-multiallele model of frequency- and density-dependent selection in a large randomly mating population. The number of loci and the number of alleles per locus are arbitrary. The n loci are assumed to contribute additively to a quantitative character under stabilizing or directional selection as well as under frequency-dependent selection caused by intraspecific competition. We assume the strength of stabilizing selection to be weak, whereas the strength of frequency dependence may be arbitrary. Density-dependence is induced by population regulation. Our main result is a characterization of the equilibrium structure and its stability properties in terms of all parameters. It turns out that no equilibrium exists with more than two alleles segregating per locus. We give necessary and sufficient conditions on the strength of frequency dependence to ensure the maintenance of multilocus polymorphism. We also give explicit formulas on the number of polymorphic loci maintained at equilibrium. These results are based on the assumption that selection is sufficiently weak compared with recombination, so that linkage equilibrium can be assumed. If additionally the population size is assumed to be constant, we prove that the dynamics of the model form a generalized gradient system. For the model in its general form we are able to derive necessary and sufficient conditions for the stability of the monomorphic equilibria. Furthermore, we briefly analyze a special symmetric two-locus two-allele model for a constant population size but allowing for linkage disequilibrium. Finally, we analyze a single diallelic locus with dominance to illustrate the complications that can occur if the assumption of additivity is relaxed.     

Meiotic drive influences the outcome of sexually antagonistic selection at a linked locus

Most meiotic drivers, such as the t‐haplotype in Mus and the segregation distorter (SD) in Drosophila, act in a sex‐specific manner, gaining a transmission advantage through one sex although suffering only the fitness costs associated with the driver in the other. Their inheritance is thus more likely through one of the two sexes, a property they share with sexually antagonistic alleles. Previous theory has shown that pairs of linked loci segregating for sexually antagonistic alleles are more likely to remain polymorphic and that linkage disequilibrium accrues between them. I probe this similarity between drive and sexual antagonism and examine the evolution of chromosomes experiencing these selection pressures simultaneously. Reminiscent of previous theory, I find that: the opportunity for polymorphism increases for a sexually antagonistic locus that is physically linked to a driving locus; the opportunity for polymorphism at a driving locus also increases when linked to a sexually antagonistic locus; and stable linkage disequilibrium accompanies any polymorphic equilibrium. Additionally, I find that drive at a linked locus favours the fixation of sexually antagonistic alleles that benefit the sex in which drive occurs. Further, I show that under certain conditions reduced recombination between these two loci is selectively favoured. These theoretical results provide clear, testable predictions about the nature of sexually antagonistic variation on driving chromosomes and have implications for the evolution of genomic architecture.     

Evidence for Positive Selection in the Superoxide Dismutase (Sod) Region of Drosophila Melanogaster

DNA sequence variation in a 1410-bp region including the Cu,Zn Sod locus was examined in 41 homozygous lines of Drosophila melanogaster. Fourteen lines were from Barcelona, Spain, 25 were from California populations and the other two were from laboratory stocks. Two common electromorphs, SOD(S) and SOD(F), are segregating in the populations. Our sample of 41 lines included 19 Sod(S) and 22 Sod(F) alleles (henceforward referred to as Slow and Fast alleles). All 19 Slow alleles were identical in sequence. Of the 22 Fast alleles sequenced, nine were identical in sequence and are referred to as the Fast A haplotypes. The Slow allele sequence differed from the Fast A haplotype at a single nucleotide site, the site that accounts for the amino acid difference between SOD(S) and SOD(F). There were nine other haplotypes among the remaining 13 Fast alleles sequenced. The overall level of nucleotide diversity (π) in this sample is not greatly different than that found at other loci in D. melanogaster. It is concluded that the Slow/Fast polymorphism is a recently arisen polymorphism, not an old balanced polymorphism. The large group of nearly identical haplotypes suggests that a recent mutation, at the Sod locus or tightly linked to it, has increased rapidly in frequency to around 50%, both in California and Spain. The application of a new statistical test demonstrates that the occurrence of such large numbers of haplotypes with so little variation among them is very unlikely under the usual equilibrium neutral model. We suggest that the high frequency of some haplotypes is due to natural selection at the Sod locus or at a tightly linked locus.     

Adaptive maintenance of genetic polymorphism in an intertidal barnacle: habitat- and life-stage-specific survivorship of Mpi genotypes

In the northern acorn barnacle, Semibalanus balanoides, genotype frequencies of three genetic markers were tracked over time in four types of intertidal habitats. These habitats were selected to represent natural variation in several environmental parameters, specifically the degree of physical stress experienced by barnacles. Frequencies for one allozyme locus (Gpi) and a presumably neutral mtDNA marker were homogeneous among habitats in each temporal sample. Similarly, no temporal stratification in genotype frequencies was evident across the five sampling intervals: from planktonic larvae sampled in March to juveniles collected at the end of June. In contrast to the Gpi and mtDNA loci, Mpi genotypes significantly changed in frequency in two habitats in the high intertidal zone. On exposed substrate, the Mpi-FF homozygote increased in frequency, whereas the alternative homozygote, Mpi-SS, significantly decreased in frequency. Barnacles that were protected from environmental stress at high intertidal heights by the Ascophyllum nodosum algal canopy demonstrated the opposite pattern. In both habitats, the change in frequency of the heterozygote was intermediate to that of the homozygous genotypes. Furthermore, these patterns of genotype-by-environment association reflected a pulse of genotype-specific mortality that occurred over a two-week interval subsequent to metamorphosis from the larval to the adult form. These data indicate that each Mpi homozygote is the highest fitness genotype in some portion of the intertidal environment. Using the Levene (1953) model to evaluate the spatial variation in genotypic fitness, the stable maintenance of the Mpi polymorphism is predicted under certain subsets of conditions. Environmental heterogeneity in the intertidal zone translates to spatial variation in selection pressures, which may result in the active maintenance of the Mpi polymorphism in this species.     

Genetic drift vs. natural selection in a long-term small isolated population: major histocompatibility complex class II variation in the Gulf of California endemic porpoise (Phocoena sinus)

Although many studies confirm long-term small isolated populations (e.g. island endemics) commonly sustain low neutral genetic variation as a result of genetic drift, it is less clear how selection on adaptive or detrimental genes interplay with random forces. We investigated sequence variation at two major histocompatibility complex (Mhc) class II loci on a porpoise endemic to the upper Gulf of California, México (Phocoena sinus, or vaquita). Its unique declining population is estimated around 500 individuals. Single-strand conformation polymorphism analysis revealed one putative functional allele fixed at the locus DQB (n = 25). At the DRB locus, we found two presumed functional alleles (n = 29), differing by a single nonsynonymous nucleotide substitution that could increase the stability at the dimer interface of alphabeta-heterodimers on heterozygous individuals. Identical trans-specific DQB1 and DRB1 alleles were identified between P. sinus and its closest relative, the Burmeister's porpoise (Phocoena spinipinnis). Comparison with studies on four island endemic mammals suggests fixation of one allele, due to genetic drift, commonly occurs at the DQA or DQB loci (effectively neutral). Similarly, deleterious alleles of small effect are also effectively neutral and can become fixed; a high frequency of anatomical malformations on vaquita gave empirical support to this prediction. In contrast, retention of low but functional polymorphism at the DRB locus was consistent with higher selection intensity. These observations indicated natural selection could maintain (and likely also purge) some crucial alleles even in the face of strong and prolonged genetic drift and inbreeding, suggesting long-term small populations should display low inbreeding depression. Low levels of Mhc variation warn about a high susceptibility to novel pathogens and diseases in vaquita.     

A two-locus mutation—Selection model and some of its evolutionary implications

The deterministic properties of a two-locus model with mutation and selection have been investigated. The mutation process is unidirectional, and the model is so constructed that the genetic variation at one locus is selectively neutral in the absence of a mutant allele at the other locus. All genotypes with three or four mutant alleles are deleterious, while the double heterozygotes may have the same fitness as the standard genotype. If one of the mutant alleles becomes fixed in the population, then the other locus will show a regular one-locus mutation-selection balance. Such a boundary equilibrium may be unstable or stable in the full two-locus setting. In the symmetric case, which is analyzed in details, the population will either go to one of the two boundary equilibria, or to a fully polymorphic equilibrium at which both the mutant alleles are rare. The origin of reproductive separation between two populations via the fixation of complementary deleterious mutants at different loci, and the fixation of nonfunctional alleles at duplicated loci, are two biological processes which both can be studied with the present model. In the last part of the paper we show how the results from the deterministic analysis can be used to predict how different factors will influence the rates of evolution in these systems.     

Extensive polymorphism and geographical variation at a positively selected MHC class II B gene of the lesser kestrel (Falco naumanni)

Understanding the selective forces that shape genetic variation in natural populations remains a high priority in evolutionary biology. Genes at the major histocompatibility complex (MHC) have become excellent models for the investigation of adaptive variation and natural selection because of their crucial role in fighting off pathogens. Here we present one of the first data sets examining patterns of MHC variation in wild populations of a bird of prey, the lesser kestrel, Falco naumanni . We report extensive polymorphism at the second exon of a putatively functional MHC class II gene, Fana- DAB*1. Overall, 103 alleles were isolated from 121 individuals sampled from Spain to Kazakhstan. Bayesian inference of diversifying selection suggests that several amino acid sites may have experienced strong positive selection (ω = 4.02 per codon). The analysis also suggests a prominent role of recombination in generating and maintaining MHC diversity (ρ = 4 Nc  = 0.389 per codon, θ = 0.017 per codon). Both the Fana -DAB*1 locus and a set of eight polymorphic microsatellite markers revealed an isolation-by-distance pattern across the Western Palaearctic ( r  = 0.67; P  = 0.01 and r  = 0.50; P  = 0.04, respectively). Nonetheless, geographical variation at the MHC contrasts with relatively uniform distributions in the frequencies of microsatellite alleles. In addition, we found lower fixation rates in the MHC than those predicted by genetic drift after controlling for neutral mitochondrial sequences. Our results therefore underscore the role of balancing selection as well as spatial variations in parasite-mediated selection regimes in shaping MHC diversity when gene flow is limited.     

Pleiotropy and Multilocus Polymorphisms

It is demonstrated that systems of two pleiotropically related characters controlled by additive diallelic loci can maintain under Gaussian stabilizing selection a stable polymorphism in more than two loci. It is also shown that such systems may have multiple stable polymorphic equilibria. Stabilizing selection generates negative linkage disequilibrium, as a result of which the equilibrium phenotypic variances are quite low, even though the level of allelic polymorphisms can be very high. Consequently, large amounts of additive genetic variation can be hidden in populations at equilibrium under stabilizing selection on pleiotropically related characters.     

The spatial patterns of directional phenotypic selection

Local adaptation, adaptive population divergence and speciation are often expected to result from populations evolving in response to spatial variation in selection. Yet, we lack a comprehensive understanding of the major features that characterise the spatial patterns of selection, namely the extent of variation among populations in the strength and direction of selection. Here, we analyse a data set of spatially replicated studies of directional phenotypic selection from natural populations. The data set includes 60 studies, consisting of 3937 estimates of selection across an average of five populations. We performed meta‐analyses to explore features characterising spatial variation in directional selection. We found that selection tends to vary mainly in strength and less in direction among populations. Although differences in the direction of selection occur among populations they do so where selection is often weakest, which may limit the potential for ongoing adaptive population divergence. Overall, we also found that spatial variation in selection appears comparable to temporal (annual) variation in selection within populations; however, several deficiencies in available data currently complicate this comparison. We discuss future research needs to further advance our understanding of spatial variation in selection.