Population estimators or progeny tests: what is the best method to assess null allele frequencies at SSR loci?

Nuclear SSRs are notorious for having relatively high frequencies of null alleles, i.e. alleles that fail to amplify and are thus recessive and undetected in heterozygotes. In this paper, we compare two kinds of approaches for estimating null allele frequencies at seven nuclear microsatellite markers in three French Fagus sylvatica populations: (1) maximum likelihood methods that compare observed and expected homozygote frequencies in the population under the assumption of Hardy-Weinberg equilibrium and (2) direct null allele frequency estimates from progeny where parent genotypes are known. We show that null allele frequencies are high in F. sylvatica (7.0% on average with the population method, 5.1% with the progeny method), and that estimates are consistent between the two approaches, especially when the number of sampled maternal half-sib progeny arrays is large. With null allele frequencies ranging between 5% and 8% on average across loci, population genetic parameters such as genetic differentiation (F _ST) may be mostly unbiased. However, using markers with such average prevalence of null alleles (up to 15% for some loci) can be seriously misleading in fine scale population studies and parentage analysis.     

MAXIMUM-LIKELIHOOD ESTIMATION OF POPULATION DIVERGENCE TIMES AND POPULATION PHYLOGENY IN MODELS WITHOUT MUTATION

In this paper we present a method for estimating population divergence times by maximum likelihood in models without mutation. The maximum-likelihood estimator is compared to a commonly applied estimator based on Wright's F_ST statistic. Simulations suggest that the maximum-likelihood estimator is less biased and has a lower variance than the F_ST-based estimator. The maximum-likelihood estimator provides a statistical framework for the analysis of population history given genetic data. We demonstrate how maximum-likelihood estimates of the branching pattern of divergence of multiple populations may be obtained. We also describe how the method may be applied to test hypotheses such as whether populations have maintained equal population sizes. We illustrate the method by applying it to two previously published sets of human restriction fragment length polymorphism (RFLP) data.     

Moderately and Highly Polymorphic Microsatellites Provide Discordant Estimates of Population Divergence in Sockeye Salmon, Oncorhynchus nerka

Mutation rate can vary widely among microsatellite loci. This variation may cause discordant single-locus and multi-locus estimates of F_ST, the commonly used measure of population divergence. We use 16 microsatellite and five allozyme loci from 14 sockeye salmon populations to address two questions about the affect of mutation rate on estimates of F_ST: (1) does mutation rate influence F_ST estimates from all microsatellites to a similar degree relative to allozymes?; (2) does the influence of mutation rate on F_ST estimates from microsatellites vary with geographic scale in spatially structured populations? For question one we find that discordant estimates of F_ST among microsatellites as well as between the two marker classes are correlated with mean within-population heterozygosity (H_S) and thus are likely due to differences in mutation rate. Highly polymorphic microsatellites (H_S > 0.84) provide significantly lower estimates of F_ST than moderately polymorphic microsatellites and allozymes (H_S < 0.60). Estimates of F_ST from binned allele frequency data and R_ST provide more accurate measures of population divergence for highly polymorphic but not for moderately polymorphic microsatellites. We conclude it is more important to pool loci of like H_S rather than marker class when estimating F_ST. For question two we find the F_ST values for moderately and highly polymorphic loci, while significantly different, are positively correlated for geographically proximate but not geographically distant population pairs. These results are consistent with expectations from the equilibrium approximation of Wright's infinite island model and confirm that the influence of mutation on estimates of F_ST can vary in spatially structured populations presumably because the rate of migration varies inversely with geographic scale.     

Estimation and adjustment of microsatellite null alleles in nonequilibrium populations

Nonamplified (null) alleles are a common feature of microsatellite genotyping and can bias estimates of allele and genotype frequencies, thereby hindering population genetic analyses. The frequency of microsatellite null alleles in diploid populations can be estimated for populations that are in Hardy–Weinberg equilibrium. However, many microsatellite data sets are from nonequilibrium populations, often with known inbreeding coefficients (F) or fixation indices (F_IS or F_ST). Here, we propose a novel null allele estimator that can be used to estimate the null allele frequency and adjust visible allele frequencies in populations for which independent estimates of F, F_IS or F_ST are available. The algorithm is currently available as an Excel macro that can be downloaded at no cost from http://www.microchecker.hull.ac.uk/ and will be incorporated into the software micro ‐checker .     

LANDSCAPE GENOMICS OF POPULUS TRICHOCARPA: THE ROLE OF HYBRIDIZATION,LIMITED GENE FLOW,AND NATURAL SELECTION IN SHAPING PATTERNS OF POPULATION STRUCTURE

Populus trichocarpa is an ecologically important tree across western North America. We used a large population sample of 498 accessions over a wide geographical area genotyped with a 34K Populus SNP array to quantify geographical patterns of genetic variation in this species (landscape genomics). We present evidence that three processes contribute to the observed patterns: (1) introgression from the sister species P. balsamifera, (2) isolation by distance (IBD), and (3) natural selection. Introgression was detected only at the margins of the species’ distribution. IBD was significant across the sampled area as a whole, but no evidence of restricted gene flow was detected in a core of drainages from southern British Columbia (BC). We identified a large number of F_ST outliers. Gene Ontology analyses revealed that F_ST outliers are overrepresented in genes involved in circadian rhythm and response to red/far‐red light when the entire dataset is considered, whereas in southern BC heat response genes are overrepresented. We also identified strong correlations between geoclimate variables and allele frequencies at F_ST outlier loci that provide clues regarding the selective pressures acting at these loci.     

A MULTISPECIES APPROACH TO THE ANALYSIS OF GENE FLOW IN MARINE SHORE FISHES

Ten species of marine shore fishes with a wide range of life-history strategies were collected from four areas in southern California, U.S.A., and Baja California, Mexico, and examined for patterns of genetic differentiation. Multilocus D and F_ST values (based on 32–42 presumptive gene loci in each species) were both negatively correlated with estimated dispersal capability. These results were robust to variations in the number and type of loci used in the analysis and are compatible with the hypothesis that levels of genetic differentiation in these shore fishes are determined primarily by gene flow and genetic drift. There is no a priori reason to expect the observed correlation to result from natural selection or historical factors. The findings thus suggest that populations of these shore fishes are in at least a quasi-equilibrium with respect to migration, mutation, and genetic drift. Present data were also used to compare estimates of mN_e obtained by three different methods. Estimates based on F_ST values calculated by the methods of Nei and Chesser (F_ST(N)) and Weir and Cockerham (F_ST(W)) were highly correlated, but F_ST(N) ≤ F_ST(W) for every species, leading to generally higher mN_e estimates for Nei and Chesser's method. Estimates of mN_e based on the frequency of private alleles (Slatkin, 1985a) were not as strongly correlated with dispersal capability as were F_ST and D values. A low incidence of private alleles in many species may be responsible for this relatively weak correlation and may limit the general usefulness of Slatkin's method. In spite of their sensitivity to natural selection, F_ST and D may be better indicators of relative gene flow levels for high gene flow species.     

Development of polymorphic microsatellite loci in the hermaphroditic freshwater snails Drepanotrema surinamense and Drepanotrema depressissimum

We characterized new variable microsatellites in two congeneric species of hermaphroditic freshwater snails (Drepanotrema depressissimum and D. surinamense), as well as conditions for multiplexing and simultaneously genotyping sets of loci. D. depressissimum had high mean gene diversity (> 0.8) and large number of alleles (= 10.9) per population. Most loci and populations were at Hardy–Weinberg equilibrium. The F_ST estimates were low among lesser Antilles populations and larger with a Venezuelan population. Far less diversity was found in D. surinamense with mean number of alleles and gene diversity per population of 2.8 and 0.34, respectively. Very few heterozygous individuals were observed. The most likely explanation is a high selfing rate (> 0.825) in this species. Unsurprisingly, the F_ST estimates among populations were much higher than in D. depressissimum. Cross‐species amplification in three congeneric species was on the whole unsuccessful.     

Microgeographic structure of Anopheles gambiae in western Kenya based on mtDNA and microsatellite loci

The population genetic structure of the Anopheles gambiae in western Kenya was studied using length variation at five microsatellite loci and sequence variation in a 648-nt mtDNA fragment. Mosquitoes were collected from houses in villages spanning up to 50 km distance, The following questions were answered, (i) Are mosquitoes in a house more related genetically to each other than mosquitoes between houses? (ii) What degree of genetic differentiation occurs on these geographical scales? (iii) How consistent are the results obtained with both types of genetic markers? At the house level, no differentiation was detected by F_ST and R_ST, and the band sharing index test revealed no significant associations of alleles across loci. Likewise, indices of kinship based on mtDNA haplotypes in houses were even lower than in the pooled sample. Therefore, the hypothesis that mosquitoes in a house are more related genetically was rejected. At increasing geographical scales, microsatellite allele distributions were similar among all population samples and no subdivision of the gene pool was detected by F_ST or R_ST. Likewise, estimates of haplotype divergence of mtDNA between populations were not higher than the within population estimates, and mtDNA-based F_ST values were not significantly different from zero. That sequence variation in mtDNA provided matching results with microsatellite loci (while high genetic variation was observed in all loci), suggested that this pattern represents the whole genome. The minimum area associated with a deme of A. gambiae in western Kenya is therefore larger than 50 km in diameter.     

Relative performance of Bayesian clustering software for inferring population substructure and individual assignment at low levels of population differentiation

Traditional methods for characterizing genetic differentiation among populations rely on a priori grouping of individuals. Bayesian clustering methods avoid this limitation by using linkage and Hardy–Weinberg disequilibrium to decompose a sample of individuals into genetically distinct groups. There are several software programs available for Bayesian clustering analyses, all of which describe a decrease in the ability to detect distinct clusters as levels of genetic differentiation among populations decrease. However, no study has yet compared the performance of such methods at low levels of population differentiation, which may be common in species where populations have experienced recent separation or high levels of gene flow. We used simulated data to evaluate the performance of three Bayesian clustering software programs, PARTITION, STRUCTURE, and BAPS, at levels of population differentiation below F _ST=0.1. PARTITION was unable to correctly identify the number of subpopulations until levels of F _ST reached around 0.09. Both STRUCTURE and BAPS performed very well at low levels of population differentiation, and were able to correctly identify the number of subpopulations at F _ST around 0.03. The average proportion of an individual’s genome assigned to its true population of origin increased with increasing F _ST for both programs, reaching over 92% at an F _ST of 0.05. The average number of misassignments (assignments to the incorrect subpopulation) continued to decrease as F _ST increased, and when F _ST was 0.05, fewer than 3% of individuals were misassigned using either program. Both STRUCTURE and BAPS worked extremely well for inferring the number of clusters when clusters were not well-differentiated (F _ST=0.02–0.03), but our results suggest that F _ST must be at least 0.05 to reach an assignment accuracy of greater than 97%.     

ESTIMATION OF GENE FLOW FROM F-STATISTICS

We present theory clarifying the general behavior of F_ST-based and G_ST-based estimators of gene flow, and confirm these predictions with simulations. In particular, we use the correlation of genes within groups within populations to define an estimator. The theoretical value of the correlation doe not depend on the number of groups in a population, and properties of the estimated correlation do not depend on the number of groups sampled or the number of individuals sampled per group. This invariance is in contrast to properties of G_ST. For a complete census of a population, bias and variance considerations would suggest the use of the G_ST-based estimator of gene flow, but lack of knowledge of population size or group number in practice suggests preference be given to the correlation-based estimator. We acknowledge that these estimators require that several conditions of a population-genetic model be met, since they do not make use of direct observations on the flow of genes. Our results differ from some of those based on simulation in a series of recent papers by M. Slatkin.     

Comparing Pool‐seq,Rapture, and GBS genotyping for inferring weak population structure: The American lobster (Homarus americanus) as a case study

Unraveling genetic population structure is challenging in species potentially characterized by large population size and high dispersal rates, often resulting in weak genetic differentiation. Genotyping a large number of samples can improve the detection of subtle genetic structure, but this may substantially increase sequencing cost and downstream bioinformatics computational time. To overcome this challenge, alternative, cost‐effective sequencing approaches, namely Pool‐seq and Rapture, have been developed. We empirically measured the power of resolution and congruence of these two methods in documenting weak population structure in nonmodel species with high gene flow comparatively to a conventional genotyping‐by‐sequencing (GBS) approach. For this, we used the American lobster (Homarus americanus) as a case study. First, we found that GBS, Rapture, and Pool‐seq approaches gave similar allele frequency estimates (i.e., correlation coefficient over 0.90) and all three revealed the same weak pattern of population structure. Yet, Pool‐seq data showed F_ST estimates three to five times higher than GBS and Rapture, while the latter two methods returned similar F_ST estimates, indicating that individual‐based approaches provided more congruent results than Pool‐seq. We conclude that despite higher costs, GBS and Rapture are more convenient approaches to use in the case of species exhibiting very weak differentiation. While both GBS and Rapture approaches provided similar results with regard to estimates of population genetic parameters, GBS remains more cost‐effective in project involving a relatively small numbers of genotyped individuals (e.g., <1,000). Overall, this study illustrates the complexity of estimating genetic differentiation and other summary statistics in complex biological systems characterized by large population size and migration rates.     

THE ROLE OF DEME SIZE,REPRODUCTIVE PATTERNS,AND DISPERSAL IN THE DYNAMICS OF t-LETHAL HAPLOTYPES

The t-lethal haplotypes (t) found in house mouse (Mus musculus) populations are recessive lethals favored by gametic selection whereby male heterozygotes exhibit a non-Mendelian transmission ratio of about 95% t. The expected equilibrium frequency is 0.385; however, empirical values are lower, averaging close to 0.13. We examined the hypothesis that interdemic selection is the cause of the low empirical values by using a deme-structured simulation model that included overlapping generations, a realistic breeding system, differential deme productivity, and a large total population. We found that under some conditions interdemic selection could lower t frequency below 0.13 in the face of immigration rates up to 5%. Low frequencies were correlated with effective deme size (n_e), regardless of whether n_e was changed through changing deme size (n) or through changing the proportion of breeding adults. Earlier workers showed how the first two phases of interdemic selection (random genetic differentiation and mass selection) interacted to reduce the haplotype frequency, but here we show the importance of the third phase (differential productivity of demes) once demes are linked by dispersal. The effect of this phase is not due to the (negative) covariation between deme productivity and haplotype frequency, but occurs when differential deme productivity generates a difference in t frequency between the population of juveniles recruited into their natal deme and the population of juvenile dispersers. This difference was maximized when the average productivity of demes was low, either because few adult females bred at any one time and/or because fecundity was low. Contrary to an earlier prediction, male-biased dispersal also reduced haplotype frequency, and this probably stems from the relative excess of wild-type genotypes among dispersers compared to the deme residents. Another unexpected finding was that the randomly generated excess of heterozygotes (F_IS < 0) found in small demes favored t haplotypes; however, the effect was only seen when the more powerful influence of the third phase of interdemic selection was removed. Simulations of neutral polymorphisms showed that a deme structure giving F_ST ≤ 0.6 is inconsistent with a haplotype frequency below 0.13. Based on current empirical estimates of F_ST (about 0.2), we concluded that immigration rates in the field are too high for interdemic selection alone to cause the observed deficit of lethal haplotypes. One factor that could combine with population structure effects is the observation that the transmission ratio is lowered to around 0.6 in litters produced from postpartum estrus (PPE). Incorporating this factor, we showed that interdemic selection could be effective in lowering the frequency of t below 0.13 when F_ST was above 0.43 even when migration rates were up to 10%. These results suggest that if empirical haplotype and F_ST estimates are accurate, then additional factors such as a lowered fitness of heterozygotes may be involved.     

Estimating FST and kinship for arbitrary population structures

F_ST and kinship are key parameters often estimated in modern population genetics studies in order to quantitatively characterize structure and relatedness. Kinship matrices have also become a fundamental quantity used in genome-wide association studies and heritability estimation. The most frequently-used estimators of F_ST and kinship are method-of-moments estimators whose accuracies depend strongly on the existence of simple underlying forms of structure, such as the independent subpopulations model of non-overlapping, independently evolving subpopulations. However, modern data sets have revealed that these simple models of structure likely do not hold in many populations, including humans. In this work, we analyze the behavior of these estimators in the presence of arbitrarily-complex population structures, which results in an improved estimation framework specifically designed for arbitrary population structures. After generalizing the definition of F_ST to arbitrary population structures and establishing a framework for assessing bias and consistency of genome-wide estimators, we calculate the accuracy of existing F_ST and kinship estimators under arbitrary population structures, characterizing biases and estimation challenges unobserved under their originally-assumed models of structure. We then present our new approach, which consistently estimates kinship and F_ST when the minimum kinship value in the dataset is estimated consistently. We illustrate our results using simulated genotypes from an admixture model, constructing a one-dimensional geographic scenario that departs nontrivially from the independent subpopulations model. Our simulations reveal the potential for severe biases in estimates of existing approaches that are overcome by our new framework. This work may significantly improve future analyses that rely on accurate kinship and F_ST estimates.     

THE EFFECTIVE SIZE OF A HIERARCHICALLY STRUCTURED POPULATION

A knowledge of the effective size of a population (N_e) is important in understanding its current and future evolutionary potential. Unfortunately, the effective size of a hierarchically structured population is not, in general, equal to the sum of its parts. In particular, the inbreeding structure has a major influence on N_e. Here I link N_e to Wright's hierarchical measures of inbreeding, F_IS and F_ST, for an island-structured population (or metapopulation) of size N_T. The influence of F_ST depends strongly on the degree to which island productivity is regulated. In the absence of local regulation (the interdemic model), interdemic genetic drift reduces N_e. When such drift is combined with local inbreeding under otherwise ideal conditions, the effects of F_IS and F_ST are identical: increasing inbreeding either within or between islands reduces N_e, with N_e = N_T/[(1 + F_IS)(1 + F_ST) ? 2F_ISF_ST]. However, if islands are all equally productive because of local density regulation (the traditional island model), then N_e = N_T/[(1 + F_IS)(1 –F_ST)] and the effect of F_ST is reversed. Under the interdemic model, random variation in the habitat quality (and hence productivity) of islands act to markedly decrease N_e. This variation has no effect under the island model because, by definition, all islands are equally productive. Even when no permanent island structure exists, spatial differences in habitat quality can significantly increase the overall variance in reproductive success of both males and females and hence lower N_e. Each of these basic results holds when other nonideal factors are added to the model. These factors, deviations from a 1:1 sex ratio, greater than Poisson variance in female reproductive success, and variation in male mating success due to polygynous mating systems, all act to lower N_e. The effects of male and female variance on N_e have important differences because only females affect island productivity. Finally, it is noted that to use these relationships, F_IS and F_ST must be estimated according to Wright's definition (and corrected to have a zero expectation under the null model). A commonly used partitioning (θ, θ_g) can be biased if either island size or the number of islands is small.     

CORRELATION OF PAIRWISE GENETIC AND GEOGRAPHIC DISTANCE MEASURES: INFERRING THE RELATIVE INFLUENCES OF GENE FLOW AND DRIFT ON THE DISTRIBUTION OF GENETIC VARIABILITY

Attempts to relate estimates of regional F_ST to gene flow and drift via Wright's (1931) equation F_ST ≈ 1/ (4Nm + 1) are often inappropriate because most natural sets of populations probably are not at equilibrium (McCauley 1993), as assumed by the island model upon which the equation is based, or ineffective because the influences of gene flow and drift are confounded in the product Nm. Evaluations of the association between genetic (F_ST) and geographic distances separating all pairwise populations combinations in a region allows one to test for regional equilibrium, to evaluate the relative influences of gene flow and drift on population structure both within and between regions, and to visualize the behavior of the association across all degrees of geographic separation. Tests of the model using microsatellite data from 51 populations of eastern collared lizards (Crotaphytus collaris collaris) collected from four distinct geographical regions gave results highly consistent with predicted patterns of association based on regional differences in various historical and ecological factors that affect the amount of drift and gene flow. The model provides a prerequisite for and an alternative to regional F_ST analyses, which often simply assume regional equilibrium, thus potentially leading to erroneous and misleading inferences regarding regional population structure.     

Evidence for interannual variation in genetic structure of Dungeness crab (Cancer magister) along the California Current System

Using a combination of population‐ and individual‐based analytical approaches, we provide a comprehensive examination of genetic connectivity of Dungeness crab (Cancer magister) along ~1,200 km of the California Current System (CCS). We sampled individuals at 33 sites in 2012 to establish a baseline of genetic diversity and hierarchal population genetic structure and then assessed interannual variability in our estimates by sampling again in 2014. Genetic diversity showed little variation among sites or across years. In 2012, we observed weak genetic differentiation among sites (F_ST range = ?0.005–0.014) following a pattern of isolation by distance (IBD) and significantly high relatedness among individuals within nine sampling sites. In 2014, pairwise F_ST estimates were lower (F_ST range = ?0.014–0.007), there was no spatial autocorrelation, and fewer sites had significant evidence of relatedness. Based on these findings, we propose that interannual variation in the physical oceanographic conditions of the CCS influences larval recruitment and thus gene flow, contributing to interannual variation in population genetic structure. Estimates of effective population size (N_e) were large in both 2012 and 2014. Together, our results suggest that Dungeness crab in the CCS may constitute a single evolutionary population, although geographically limited dispersal results in an ephemeral signal of IBD. Furthermore, our findings demonstrate that populations of marine organisms may be susceptible to temporal changes in population genetic structure over short time periods; thus, interannual variability in population genetic measures should be considered.     

A clever solution to a vexing problem

F_ST (as well as related measures such as G_ST) has long been used both as a measure of the relative amount of genetic variation between populations and as an indicator of the amount of gene flow among populations. Unfortunately, F_ST and its clones are also sensitive to mutation, particularly when the mutation rate per locus is greater than the migration rate among populations. Relatively high mutation rates cause estimates of F_ST and G_ST to be much lower than researchers sometimes expect, when migration rates are low in the studied species. Several recent suggestions for dealing with this problem have been unsatisfactory for one reason or another, and no general solution exists (if we are not to abandon these otherwise useful measures of differentiation). In an important article in this issue, Jinliang Wang (2015) shows that it is possible to identify whether the genetic markers in a given study are likely to give estimates of F_ST that are strongly affected by mutation. The proposed test is simple and elegant, and with it, molecular ecologists can determine whether the F_ST from their makers can be depended on for further inference about their species’ genome and the demographic forces which shaped its patterns.     

Population genetic structure and conservation of marbled murrelets (<Emphasis Type="Italic">Brachyramphus marmoratus</Emphasis>)

Marbled murrelets (Brachyramphus marmoratus) are coastal seabirds that nest from California to the Aleutian Islands. They are declining and considered threatened in several regions. We compared variation in the mitochondrial control region, four nuclear introns and three microsatellite loci among194 murrelets from throughout their range except Washington and Oregon. Significant population genetic structure was found: nine private control region haplotypes and three private intron alleles occurred at high frequency in the Aleutians and California; global estimates of F _ST or Φ_ST and most pairwise estimates involving the Aleutians and/or California were significant; and marked isolation-by-distance was found. Given the available samples, murrelets appear to comprise five genetic management units: (1) western Aleutian Islands, (2) central Aleutian Islands, (3) mainland Alaska and British Columbia, (4) northern California, and (5) central California.     

Size differentiation in Finnish house sparrows follows Bergmann's rule with evidence of local adaptation

Bergmann's rule predicts that individuals are larger in more poleward populations and that this size gradient has an adaptive basis. Hence, phenotypic divergence in size traits between populations (P_ST) is expected to exceed the level of divergence by drift alone (F_ST). We measured 16 skeletal traits, body mass and wing length in 409 male and 296 female house sparrows Passer domesticus sampled in 12 populations throughout Finland, where the species has its northernmost European distributional margin. Morphometric differentiation across populations (P_ST) was compared with differentiation in 13 microsatellites (F_ST). We find that twelve traits phenotypically diverged more than F_ST in both sexes, and an additional two traits diverged in males. The phenotypic divergence exceeded F_ST in several traits to such a degree that findings were robust also to strong between‐population environmental effects. Divergence was particularly strong in dimensions of the bill, making it a strong candidate for the study of adaptive molecular genetic divergence. Divergent traits increased in size in more northern populations. We conclude that house sparrows show evidence of an adaptive latitudinal size gradient consistent with Bergmann's rule on the modest spatial scale of ca. 600 km.     

Selection in a cycling population: differential response among skeletal traits

Abstract Population density cycles influence phenotypic evolution through both density‐dependent selection during periods of high density and through enhanced genetic drift during periods of low density. We investigated the response of different phenotypic traits to the same density cycles in a population of the yellow‐necked mouse, Apodemus flavicollis, from Bia?owieza National Park in Poland. We examined nonmetric skull traits, skull and mandible size, skull and mandible shape, and transferrin allele frequencies. We found that all of the traits changed significantly over the seven‐year study period. The greatest changes in nonmetric traits and mandible size occurred during periods of increasing density, and the magnitude of changes in skull and mandible shape was correlated with the magnitude of density changes. Frequencies of transferrin alleles changed the most when population density was in decline. Changes among the five phenotypic traits were generally uncorrelated with one another, except for skull and mandible shape. Nonmetric traits were selectively neutral when assessed with Q_ST/F_ST analysis, whereas mandible size, mandible shape, and skull shape showed evidence of fairly strong selection. Selection on skull size was weak or nonexistent. We discuss how different assumptions about the genetic components of variance affect Q_ST estimates when phenotypic variances are substituted for genetic ones. We also found that change in mandible size, mandible shape, skull size, and skull shape were greater than expected under a neutral model given reasonable assumptions about heritability and effective population size.