Effects of Spatially Varying Selection on Nucleotide Diversity and Linkage Disequilibrium: Insights From Deer Mouse Globin Genes
Jay F. Storz, John K. Kelly

Abstract

An important goal of population genetics is to elucidate the effects of natural selection on patterns of DNA sequence variation. Here we report results of a study to assess the joint effects of selection, recombination, and gene flow in shaping patterns of nucleotide variation at genes involved in local adaptation. We first describe a new summary statistic, Zg, that measures the between-sample component of linkage disequilibrium (LD). We then report results of a multilocus survey of nucleotide diversity and LD between high- and low-altitude populations of deer mice, Peromyscus maniculatus. The multilocus survey included two closely linked α-globin genes, HBA-T1 and HBA-T2, that underlie adaptation to different elevational zones. The primary goals were to assess whether the α-globin genes exhibit the hallmarks of spatially varying selection that are predicted by theory (i.e., sharply defined peaks in the between-population components of nucleotide diversity and LD) and to assess whether peaks in diversity and LD may be useful for identifying specific sites that distinguish selectively maintained alleles. Consistent with theoretical expectations, HBA-T1 and HBA-T2 were characterized by highly elevated levels of diversity between populations and between allele classes. Simulation and empirical results indicate that sliding-window analyses of Zg between allele classes may provide an effective means of pinpointing causal substitutions.

NATURAL populations of most species are characterized by some degree of geographically defined genetic subdivision. In cases where spatially separated subpopulations are adapted to local environmental conditions, the gene pool may also be subdivided into different genetic backgrounds at loci that contribute to fitness variation. These genetic backgrounds are defined by alternative allelic states at each “selected locus,” which in this context could be a single-nucleotide site or a linked set of multiple sites. The partitioning of neutral DNA variation within and between allele classes is determined by the interplay between mutation, recombination, drift, and selection (Charlesworth et al. 1997, 2003; Nordborg 1997; Navarro and Barton 2002; Nordborg and Innan 2003; Charlesworth 2006).

Charlesworth et al. (1997) derived analytical approximations for the expected coalescence times of neutral sites that are linked to a locus subject to spatially varying selection. In the case of an island model with symmetrical migration among n subpopulations of equal effective size Ne, the mean coalescence time of two alleles sampled randomly from the same subpopulation is TS = 2nNe, and the mean coalescence time of two alleles sampled randomly from the total population isMath(1)where m is the migration rate. The effects of spatially varying selection on the coalescence times at linked neutral sites can be understood in terms of the effective migration rate, m′, between locally adapted subpopulations. In the case of a two-deme island model with strong divergent selection, the effective migration rate at a neutral site is m′ = mr/(s + r), where m is the migration rate, r is the recombination rate between the neutral and selected loci, and s is the selection coefficient against the locally maladaptive allele (Charlesworth et al. 1997). As a result of the reduced effective migration rate at sites closely linked to the divergently selected locus, TT will be increased while TS will remain unchanged. The consequence is that sites closely linked to the selected locus will exhibit an elevated level of divergence relative to the genomewide average.

This is most transparent under the infinite-sites mutation model where equilibrium levels of nucleotide diversity are proportional to mean coalescence times: the level of nucleotide diversity in the total population (πT) is proportional to TT and the mean nucleotide diversity within subpopulations (πS) is proportional to TS (Hudson 1990; Hudson et al. 1992; Charlesworth et al. 2003). The difference between these two diversity components, πT − πS (hereafter denoted δST; Nei and Kumar 2000, Equation 12.74), provides an absolute measure of nucleotide divergence and is proportional to the difference in mean coalescence times between a pair of alleles sampled randomly from the total population and a pair of alleles sampled randomly from a single subpopulation (Charlesworth et al. 1997, 2003; Charlesworth 1998). As a result of spatially varying selection, πT will be increased and πS will remain unchanged. This effect on πT will dissipate at a rate proportional to the recombinational distance from the selected locus. Thus, in comparisons between subpopulations and in comparisons between alternative allele classes, spatially varying selection is expected to produce a pronounced peak in nucleotide divergence that is centered on the selected locus. Each allele class should also accumulate a distinct set of mutations at linked sites, resulting in excess linkage disequilibrium (LD) among neutral polymorphisms in and around the selected locus (Strobeck 1983; Charlesworth et al. 1997; Kelly 1997). Thus, any type of selection that maintains polymorphism is expected to increase the component of LD between allele classes as well as the component of nucleotide diversity between allele classes.

Theory suggests that the detection of peaks in nucleotide diversity or LD may be useful for the purpose of identifying loci that are subject to spatially varying selection or other modes of diversity-enhancing selection (Hudson and Kaplan 1988; Charlesworth et al. 1997, 2003; Kelly and Wade 2000; Schierup et al. 2000; Nordborg and Innan 2003; Storz 2005; Charlesworth 2006). If rates of intralocus recombination are sufficiently high, it may also be possible to use such peaks to pinpoint causal substitutions that distinguish the alternative alleles maintained by selection. However, the inherent stochasticity of the coalescent process suggests that sharply defined peaks of nucleotide diversity and LD may often be difficult to detect in practice (Nordborg and Innan 2003). Moreover, spatially varying selection may often be too ephemeral or episodic to promote stable genetic subdivision between alternative haplotype backgrounds, or the turnover rate of alternative alleles may be too high to promote differentiation between the alternative backgrounds (Wiuf et al. 2004; Charlesworth 2006; Hedrick 2006; Kelly 2006).

An empirical evaluation of theoretical predictions requires a system in which it is possible to identify specific loci that are subject to spatially varying selection, ideally where the identity of causal nucleotide changes is known a priori. In addition to testing for the presence of sharply defined peaks of nucleotide diversity and LD in and around the selected locus, surveys of polymorphism in flanking regions make it possible to test predictions about the genomic scale at which selection at one site influences patterns of variation at linked neutral sites along a recombining chromosome. Unfortunately, there are few cases where it has been possible to establish causal links between molecular variation and fitness-related trait variation under natural conditions. One of the rare cases in which adaptive significance can be ascribed to specific mutations involves a complex hemoglobin polymorphism in the deer mouse, Peromyscus maniculatus (Storz 2007; Storz et al. 2007). This polymorphism plays a well-documented role in physiological adaptation to high-altitude hypoxia (Snyder 1981; Chappell and Snyder 1984; Chappell et al. 1988; Snyder et al. 1988).

Deer mice possess triplicated copies of the adult α-globin gene and each of the three copies segregates functionally distinct alleles that exhibit pronounced allele-frequency differences between high- and low-altitude populations (Snyder et al. 1988; Storz 2007; Storz et al. 2007, 2008). Allelic variation at two of the three α-globin genes, HBA-T1 and HBA-T2, contributes to fitness-related variation in aerobic capacity and thermogenic capacity under hypoxic conditions, and these effects on whole-animal physiological performance stem directly from effects on hemoglobin–oxygen affinity (Chappell and Snyder 1984; Chappell et al. 1988). Experiments by Chappell and Snyder (1984) and Chappell et al. (1988) revealed that the high-affinity α-globin genotype is associated with superior aerobic performance under hypoxic conditions at high altitude, but is associated with poor performance (relative to the alternative low-affinity genotype) under normoxic conditions at sea level. This can be explained by physiological trade-offs in the efficiency of blood–oxygen transport at different partial pressures of oxygen (Storz 2007). In summary, the physiological effects of α-globin polymorphism in deer mice clearly contribute to fitness variation in natural populations (Hayes and O'Connor 1999), and the abrupt altitudinal shifts in allele frequencies across western North America appear to be attributable to spatially varying selection that favors different hemoglobin–oxygen affinities in different elevational zones (Snyder 1981; Chappell and Snyder 1984; Chappell et al. 1988; Snyder et al. 1988; Storz 2007; Storz et al. 2007).

The purpose of this study is to use the deer mouse α-globin polymorphism as a model system to investigate the joint effects of spatially varying selection, recombination, and gene flow in shaping patterns of DNA sequence variation. The primary goals are (1) to assess whether the α-globin genes exhibit the hallmarks of spatially varying selection that are predicted by population genetic theory (i.e., sharply defined peaks of nucleotide divergence and LD in comparisons between populations and between allele classes), (2) to assess whether peaks in diversity and LD may be useful for pinpointing specific sites that represent the target of divergent selection, and (3) to assess whether analyses based on the between-population components of nucleotide diversity and LD are more illuminating than conventional neutrality tests that are exclusively based on patterns of within-population variation.

We first describe a new summary statistic, Zg, that measures the between-population (or between-allele class) component of LD. We then perform a simulation analysis to evaluate the utility of δST and Zg as summary statistics for detecting the effects of spatially varying selection. Next, we report the results of a multilocus survey of DNA sequence variation in a pair of high- and low-altitude populations of deer mice. Specifically, we compare levels of diversity and LD at a total of 11 loci: the two divergently selected genes (HBA-T1 and HBA-T2), three additional α-like globin genes that are closely linked to the selected genes (HBZ, HBQ, and HBA-T3), and six unlinked nuclear genes that are presumably neutral and therefore provide a baseline expectation for levels and patterns of nucleotide variation across the genome. Finally, we present sliding-window analyses of nucleotide diversity and LD to detect the signature of selection in specific gene regions and also to gain insights into the nature of selection maintaining the α-globin polymorphism in natural populations of deer mice.

MATERIALS AND METHODS

Samples:

We sampled a total of 34 P. maniculatus from a pair of high- and low-altitude localities in eastern Colorado. The high-altitude sample (n = 17 mice) was collected from the summit of Mt. Evans, Clear Creek County, Colorado, 4347 m above sea level, and the low-altitude sample (n = 17 mice) was collected from a prairie grassland site in Yuma County, Colorado, 1158 m above sea level. The two sampling localities are separated by a linear distance of 285 km and 3189 m of vertical relief. All deer mouse specimens used in this study are cataloged in the zoological collection of the University of Nebraska State Museum, as described in Storz et al. (2007).

Here we report polymorphism data for 11 nuclear genes in deer mice including the triplicated α-globin genes: HBA-T1, HBA-T2, and HBA-T3. The analysis combines new sequence data for 5 genes (HBA-T1, HBA-T2, HBZ, HBQ, and rhodopsin) and previously published data for six genes (HBA-T3, β-fibrinogen, LCAT, RAG1, AP5, and vimentin; Storz et al. 2007). Although polymorphism data for HBA-T2 were reported in the previous study by Storz et al. (2007), the sequenced fragment did not extend beyond the initiation and termination codons so it was not possible to investigate levels and patterns of nucleotide variation in the flanking chromosomal regions. Here we report new resequencing data for both HBA-T1 and HBA-T2 that include the entire coding region as well as upstream and downstream flanking sequence.

Genomic structure of the α-globin gene cluster:

The α-globin gene cluster of P. maniculatus consists of five paralogous genes arranged in the following linkage order: 5′-HBZ, HBA-T1, HBA-T2, HBA-T3, HBQ-3′. From the 5′ end of HBZ to the 3′ end of HBQ, the gene cluster spans ∼30 kb on chromosome 8 (Storz et al. 2008). The HBA-T1 and HBA-T2 paralogs are separated by 5 kb of noncoding DNA. The gene at the 5′ end of the cluster, HBZ (ζ-globin), encodes the α-chain subunit of embryonic hemoglobin. The three α-globin paralogs, HBA-T1, HBA-T2, and HBA-T3, encode the α-chain subunit of fetal and adult hemoglobin. The gene at the 3′ end of the cluster, HBQ (θ-globin), does not encode a subunit chain of hemoglobin in deer mice or in other mammals and its function remains a mystery.

PCR, cloning, and sequencing:

Genomic DNA was extracted from frozen liver of each mouse using DNeasy kits (QIAGEN, Valencia, CA). The HBZ, HBA-T3, and HBQ genes were PCR amplified using Ampli-Taq Gold chemistry (Applied Biosystems, Foster City, CA) under the following cycling parameters: 94° (120 sec) initial denaturing; 94° (30 sec), 58° (30 sec), 72° (60 sec) 30 times; and a final extension at 72° (120 sec). The HBA-T1 and HBA-T2 genes were PCR amplified using High-Fidelity PCR master mix (Roche Molecular Diagnostics, Basel, Switzerland) using the above protocol, and the products were gel purified prior to subcloning. The same PCR primers were also used for sequencing reactions, although the annealing temperature was increased to 60°. M13 primers were used to amplify cloned products (55° annealing temperature) and internal T7/T3 primers were used for sequencing. All sequencing reactions and samples were run on an ABI 3730 capillary sequencer using Dye Terminator chemistry (Applied Biosystems).

To resolve haplotype phase of the five α-like globin genes, we adopted an experimental protocol that involved cloning both alleles of diploid PCR products in all individuals. After cloning diploid PCR products into pCR4-TOPO vector (Invitrogen, Carlsbad, CA), we sequenced the complete coding region and intervening introns of multiple cloned alleles per locus (eight or more clones per locus for HBA-T1, HBA-T2, and HBA-T3 and four or more clones per locus for HBZ and HBQ). Thus, for each of the five α-like globin genes, the exact haplotype phase of all heterozygous sites was determined experimentally. Moreover, in the case of the HBA-T1 and HBA-T2 genes, we recovered diploid genotypes for each mouse. For each mouse in our sample, we were able to confirm that we had successfully cloned both alleles from each HBA paralog by matching our sequence data with results of a thin-layer isoelectrofocusing analysis of allelic variation at the protein level (see Storz et al. 2007).

For the purpose of making comparisons with the linked set of α-like globin genes, we surveyed variation at six unlinked autosomal loci: β-fibrinogen (619 bp), LCAT (456 bp), RAG1 (1182 bp), AP5 (385 bp), vimentin (785 bp), and rhodopsin (1319 bp). Each of these six loci was PCR amplified as described above and was then sequenced on the ABI 3730. After first obtaining direct sequence data for each of the nuclear loci, we then cloned both alleles from >75% of individuals that were heterozygous at multiple sites. We then used the program PHASE (version 2; Stephens et al. 2001; Stephens and Donnelly 2003) to infer haplotype phase for the remaining individuals. All new sequences have been deposited in GenBank (accession nos. EF369525EF369576, EF369772EF369807, and EU544948EU545129).

Genetic data analysis:

DNA sequences were aligned and contigs assembled using Clustal X (Thompson et al. 1997) and the Sequencher program (Gene Codes, Ann Arbor, MI). All sequences were verified by visual inspection of chromatograms. Summary statistics of nucleotide polymorphism and LD were computed with the programs SITES (Hey and Wakeley 1997) and DnaSP v4.10 (Rozas et al. 2003) and with custom programs written in C (available upon request). To detect intragenic recombination within each of the nuclear loci, we used the four-gamete test of Hudson and Kaplan (1985) to estimate RM, the minimum number of recombination events in the history of the sample. We used two different measures of DNA sequence variation: nucleotide diversity, π (the average number of pairwise differences between sequences), and Watterson's (1975) estimator of θ (= 4Nu for diploid autosomal loci) that is based on the number of segregating sites. We used variation at coding and noncoding sites to compute two different estimators of the per-nucleotide recombination rate, ρ (Hudson 1987) and γ (Hey and Wakeley 1997), as well as the ratio c/u, the estimated number of recombination events per mutation (based on the ratio γ/θW, where θW is estimated from coding and noncoding sites). We used the method of Betran et al. (1997) to detect gene conversion tracts in HBA-T1 and HBA-T2 that were derived from the divergent HBA-T3 paralog.

For each of the 11 loci, we calculated δST as a measure of nucleotide divergence between high- and low-altitude population samples (Mt. Evans, CO, and Yuma County, CO, respectively). For sliding-window analyses, we used the statistic Dxy with Jukes–Cantor correction (Nei and Kumar 2000, Equation 12.65) to measure the average number of nucleotide substitutions per site between population samples or between allele classes. We calculated two different neutrality test statistics for silent sites at each locus: Tajima's (1989) D, which provides a measure of the site-frequency distribution, and Kelly's (1997) ZnS, which provides a measure of intralocus LD. Specifically, ZnS is the average squared correlation in allele frequencies across all pairwise comparisons of polymorphic sites.

The original theory for ZnS was developed for a sample of alleles from a single panmictic population. Here we note that a more detailed characterization of LD is possible in the case of a subdivided population. Specifically, we can partition LD into within- and between-population components (Ohta 1982). Let Dij denote the LD between sites i and j in a sample of n sequences:Math(2)Here, k indexes populations, nk is the number of sequences sampled from population k, qi,k is the allele frequency at site i in population sample k, and qi is the frequency in the total sample. qj,k and qj define the analogous quantities for site j. Finally, Dij,k measures LD within the sample for population k. The first term is the within-population component of LD while the second term is the between-population component. The between-population component of ZnS, hereafter denoted Zg, can be defined asMath(3)where S is the number of polymorphic sites in the sample. This equation assumes that there are two bases segregating at each polymorphic site.

The Zg statistic measures the covariance of allele frequencies at different polymorphic sites over populations. Unlike ZnS, it depends only on allele frequencies and not on gamete (haplotype) frequencies. As explained below, we performed a simulation analysis to evaluate the utility of Zg as a neutrality test statistic and also to evaluate whether localized peaks of Zg can be used to identify causal substitutions that distinguish alternative fitness-determining alleles. Unless 4Nm is very low, Zg should be small (close to zero) in a neutrally evolving sequence. In contrast, spatially varying selection can potentially maintain covariances of allele frequencies at linked sites in the face of migration and genetic drift. We used Zg to measure the between-population component of LD for each of the 11 loci, and in the case of HBA-T1 and HBA-T2, we used the same statistic to measure LD between allele classes. For the calculation of LD, we excluded HBA-T1 and HBA-T2 alleles that contained gene conversion tracts derived from the divergent HBA-T3 paralog. After excluding these partially converted alleles, the total sample size for the HBA-T1 gene was reduced from 68 to 63 sequences, and the sample size for the HBA-T2 gene was reduced from 68 to 64 sequences.

For individual amino acid polymorphisms in the HBA-T1 and HBA-T2 genes, we tested for differentiation between high- and low-altitude samples by using an exact test of genotype frequencies based on the log-likelihood G-statistic (Goudet et al. 1996). We also tested for site-specific deviations from Hardy–Weinberg equilibrium (HWE) by using a randomization test based on Weir and Cockerham's (1984) estimators, f (= FIS) and F (= FIT). To test for HWE within samples, a null distribution of f values was generated by permuting alleles among individuals within each sample. To test for HWE in the total population, a null distribution of F values was generated by permuting alleles among individuals from the pooled sample. To measure the partitioning of site-specific variation within and between populations, we used Nei's (1987) diversity measures, where HS is the average gene diversity in the high- and low-altitude samples, HT is the gene diversity in the total population sample, and DST (= HTHS) is an absolute measure of divergence between the high- and low-altitude samples. The site-specific HS, HT, and DST statistics are directly analogous to the sequence-based πS, πT, and δST statistics, respectively.

Simulation study:

We built a forward-time simulation model that tracks evolution within a population composed of 1000 diploid individuals. This population was subdivided into two subpopulations of equal size that exchanged migrants at rate m. Molecular evolution was modeled within the flanking regions of two unlinked loci. The first locus was selectively neutral and the second locus was subject to spatially varying selection. The two alleles at the selected locus, A0 and A1, underwent reversible mutation at rate μ, and each was favored in one of the two subpopulations. In subpopulation 0, the fitnesses of A0A0, A0A1, and A1A1 were 1, 1 − s/2, and 1 − s, respectively, while the opposite selection regime obtained in subpopulation 1. Mating was random within subpopulations and migration was gametic.

We monitored molecular evolution within a 50- to 200-bp window bracketing each locus. Each site within this window was subject to reversible mutation between two alternative alleles and recombination occurred with equal probability between each pair of adjacent sites in the sequence. Each simulation run was initiated with all individuals heterozygous (A0/A1) at the selected locus and homozygous at linked neutral sites. We allowed the population to evolve for 10N (= 10,000) generations before sampling sequences. This “burn-in” allowed mutation, selection, migration, and genetic drift to reach statistical equilibrium. Subsequent to the burn-in, we sampled 32 sequences from each subpopulation (mimicking the empirical sampling design). The neutral sequence at each locus was recorded, as was the allelic identity at the selected locus (A0 or A1). For each locus in the total population sample, we calculated S, π, Tajima's D, and ZnS. For each locus in the comparison between subpopulations, we calculated δST and Zg. In the case of the selected locus, we also calculated δST and Zg with the sample subdivided according to the A0/A1 allele classes. Tajima's D, ZnS, and Zg were not calculated in samples with an insufficient number of polymorphic sites (S < 2). To provide a meaningful statistical comparison for the allele-based statistics at the selected locus, we also partitioned samples for the neutral locus. We randomly selected a neutral mutation with minor allele frequency >0.1, and we then partitioned the entire sample into alternative allele classes defined by this site to calculate δST and Zg. These statistics were calculated only when there was at least one intermediate-frequency polymorphism in the neutral sample. Random sampling was repeated at intervals of N (= 1000) generations and each simulation run lasted 1,000,000 generations. We aggregated samples from 10 independent runs to produce estimates for each parameter combination.

To parameterize the simulation model, we used empirical results from the survey of six unlinked nuclear loci (the “background” loci) in the high- and low-altitude samples of deer mice. Two key nuisance parameters are the scaled neutral mutation rate (4Nu) and the scaled recombination rate (4Nr). Here, N is the effective size of the total diploid population and u is the neutral mutation rate. On the basis of empirical parameter estimates from the set of background loci (see results), we set 4Nu = 0.02/bp and considered a set of different values for 4Nr ranging from 0 to 0.1/bp. For 4Nm and s, we considered combinations of values that were roughly consistent with the globin gene data. With weak selection (s = 0.01), polymorphism could be maintained with low to moderate levels of gene flow (4Nm = 1–10). With stronger selection (s = 0.1), polymorphism could be maintained with higher levels of gene flow (4Nm = 100).

RESULTS

We first present simulation results to provide expectations for patterns of nucleotide diversity and LD at neutral sites linked to a locus that is subject to spatially varying selection. We then present empirical results of our multilocus survey of DNA sequence variation between high- and low-altitude populations of deer mice, and we compare observed and expected patterns of nucleotide diversity and LD across all loci.

Simulation results:

Simulation results from the neutral locus provide the “null distribution” for each sample statistic: D and ZnS for the total population sample and δST and Zg in comparisons between subpopulations and in comparisons between allele classes. The upper 95th percentiles of the distributions for ZnS, δST, and Zg represent the critical values for these statistics, while the 2.5th and 97.5th percentiles bound the acceptance region for D (it provides a two-sided test). For comparisons between allele classes, the critical values for δST and Zg were based on the 95th percentiles of these statistics calculated after randomly partitioning samples from the neutral locus as described in materials and methods. We enumerated values for each statistic from the simulated sequences flanking the selected locus. For each statistic, we calculated the fraction of samples that were significant (i.e., the fraction that exceeded the critical value determined from the neutral locus). This calculation provides a measure of statistical power for detecting spatially varying selection. Results for six distinct neutrality tests that were based on various measures of within- and between-population variation are provided in supplemental Table 1.

For comparisons between subpopulations, median values of δST and Zg from sequences flanking the selected locus greatly exceeded the critical value when 4Nm < 100 (Figure 1). For each statistic, the between-population values for the selected locus converged on the critical value when levels of gene flow were extremely high. This indicates that the diversifying effects of selection were partially counteracted by the homogenizing effects of gene flow. Under such conditions, local adaptation is constrained and populations suffer an appreciable migration load (i.e., a reduction in mean fitness due to the fact that maladapted genotypes are continually being introduced into the “wrong” environment). δST and Zg values for the selected locus were always higher for comparisons between allele classes than for comparisons between subpopulations (Figure 1). This simply reflects the fact that, in the presence of gene flow, the subpopulation samples will always include a mixture of the two alternative allele classes. At low levels of gene flow (4Nm = 1), values of δST between allele classes converge on values of δST between subpopulations. This reflects the fact that, when the migration rate is low, alternative alleles are nearly fixed in each subpopulation. With complete fixation, the comparison between subpopulations becomes identical to the comparison between allele classes.

Figure 1.—

Statistical power of δST (A) and Zg (B) for detecting the locus-specific effects of spatially varying selection between two subpopulations. For each test statistic, median values from simulations of a divergently selected locus are plotted as a function of gene flow between the two subpopulations. For both test statistics, the critical value is the 95th percentile of the simulation-based distribution for an unlinked neutral locus. For both δST and Zg, separate plots are shown for comparisons between subpopulations and for comparisons between allele classes. The simulations were based on a window size of 50 bp, with 4Nu = 0.02, 4Nr = 0.02, and s = 0.1 for the selected locus (see text for details).

The relative power of statistics based on comparisons between subpopulations vs. those based on comparisons between allele classes varied according to the parameter combinations used in the simulations and was also highly dependent on the window size under consideration (supplemental Table 1). The median values of δST and Zg at the selected locus were generally higher in comparisons between allele classes than in comparisons between subpopulations, and the critical values also tended to be substantially higher in the allele-based comparisons (Figure 1). With weaker selection (s = 0.01), the population-based Zg statistic generally performed better, although the difference in power was typically small for 200-bp windows. In general, the results are encouraging: both classes of statistics had reasonably high power to detect the effects of selection over a broad range of parameter values. Having documented the utility of δST and Zg for detecting the effects of spatially varying selection over a broad range of biologically plausible parameter combinations, we can now use the simulation-based null distributions as a basis for comparison with empirical values.

Empirical results:

Comparing levels and patterns of nucleotide variation among loci:

In the comparison between high- and low-altitude population samples, the HBA-T1 and HBA-T2 genes were characterized by the highest levels of nucleotide divergence of all 11 loci (Table 1 and Figure 2). In contrast to the high levels of between-population divergence at the HBA-T1 and HBA-T2 genes, the other α-like globin genes at the 5′ and 3′ ends of the gene cluster exhibited δST values that fell within the range of the unlinked loci (Figure 2).

Figure 2.—

Interlocus variation in nucleotide divergence between high- and low-altitude deer mice. The upper and lower ranges of values for the unlinked background loci are denoted by dashed lines and the mean is denoted by a dotted line.

View this table:
TABLE 1

Locus-specific measures of nucleotide divergence and LD between high- and low-altitude populations of deer mice

In comparison with the other linked and unlinked loci, the HBA-T1 and HBA-T2 genes also exhibited uniformly higher levels of silent-site diversity as measured by π in the total population sample (Mt. Evans and Yuma County) and in the individual samples (Table 2). Estimates of θW for the HBA-T1 and HBA-T2 genes were exceeded by those for only two loci in the total population sample (vimentin and rhodopsin) and one locus in the low-altitude sample (vimentin; Table 2). The elevated diversity levels at HBA-T1 and HBA-T2 were largely attributable to the fact that both genes were segregating two highly divergent protein alleles. Interestingly, the same two allele classes were segregating at both genes. This shared polymorphism is attributable to a history of interparalog gene conversion (Storz et al. 2008). At both HBA-T1 and HBA-T2, the two alternative alleles were distinguished from one another by five closely linked amino acid substitutions that span the highly conserved E-helix domain of the α-globin polypeptide: 50His/Pro, 57Gly/Ala, 60Ala/Gly, 64Asp/Gly, and 71Gly/Ser (Storz et al. 2007; Storz and Moriyama 2008). The products of the two alternative alleles correspond to the protein electromorphs that were functionally characterized by Chappell and Snyder (1984) and Chappell et al. (1988). The alternative protein alleles that are defined by these five amino acid changes exhibit pronounced frequency differences between high- and low-altitude populations: the five-site protein haplotype “50Pro/57Gly/60Ala/64Gly/71Ser” predominates at high altitude and is characterized by a high oxygen-binding affinity, whereas the alternative five-site protein haplotype “50His/57Asp/60Gly/64Asp/71Gly” predominates at low altitude and is characterized by a relatively low oxygen-binding affinity (Storz et al. 2007). Of the five polymorphisms that define the two allele classes, the charge-changing 64Asp/Gly polymorphism appears to be primarily responsible for the allelic differences in oxygen-binding affinity (Storz et al. 2007; Storz and Moriyama 2008) as well as the allelic differences in electrophoretic mobility that were assayed in previous studies (Chappell and Snyder 1984; Chappell et al. 1988; Snyder et al. 1988). We therefore used the allelic state at this site to classify alternative allele classes for our comparison of nucleotide diversity and LD: the derived 64Asp variant defines the “high-affinity” allele class, and the ancestral 64Gly variant defines the “low-affinity” allele class.

View this table:
TABLE 2

Summary of nucleotide polymorphism and LD at nuclear loci

Despite the high levels of between-population divergence at the HBA-T1 and HBA-T2 genes, both loci exhibited negative Tajima's D values in the total population sample and within both high- and low-altitude samples. This excess of low-frequency variants was not unique to the HBA-T1 and HBA-T2 genes, as most of the other nuclear loci also exhibited negative Tajima's D values (Table 2).

Site-specific patterns of amino acid polymorphism:

In the case of both HBA-T1 and HBA-T2, each of the five closely linked amino acid polymorphisms exhibited highly significant allele-frequency differences between the high- and low-altitude samples (Table 3). However, none of the sites exhibited statistically significant departures from HWE within samples or within the total population sample.

View this table:
TABLE 3

Inbreeding coefficients and gene diversity components for five amino acid polymorphisms in the HBA-T1 and HBA-T2 genes that exhibit significant allele frequency differences between high- and low-altitude samples

Comparing levels and patterns of LD among loci:

With regard to the between-population component of LD, the observed Zg for HBA-T2 fell in the upper range of values for the other linked and unlinked loci, but the observed Zg for HBA-T1 fell just below the mean value for the background loci (Table 1). In neither case did the observed Zg values exceed the simulation-based neutral expectations (supplemental Table 1). In comparison with the other linked and unlinked loci, the HBA-T1 and HBA-T2 genes exhibited uniformly higher levels of intragenic LD as measured by ZnS in the total population sample (Mt. Evans and Yuma County) and in the low-altitude sample (Table 2). In the high-altitude sample, the HBZ and HBA-T3 genes were characterized by ZnS values that were equal to or greater than those observed at HBA-T1 and HBA-T2.

Sliding-window analyses of nucleotide diversity and LD:

In sliding-window plots of silent-site diversity within and between population samples, the HBA-T1 and HBA-T2 genes both exhibited several pronounced peaks of nucleotide divergence (Figure 3). The critical value of Dxy between subpopulations was 0.0024 (based on simulations with 4Nu = 0.02, 4Nr = 0.05, and 4Nm = 20). As shown in Figure 3, levels of nucleotide divergence across the coding regions of both genes exceeded the simulation-based critical value. In both genes, one of the peaks of between-population nucleotide divergence was centered on the central region of exon 2 that harbors the five amino acid polymorphisms at residue positions 50, 57, 60, 64, and 71. In both cases, the region spanning exon 2 was characterized by an elevated level of divergence relative to the level of nucleotide diversity within the high-altitude sample. A similar pattern was seen at the 3′ end of the sequenced fragment that contained HBA-T1 (Figure 3A) and, to a lesser extent, in the corresponding region downstream of HBA-T2 (Figure 3B). In the case of both HBA-T1 and HBA-T2, the peak in nucleotide divergence that spanned exon 2 was especially pronounced in the comparison between high- and low-affinity allele classes (Figure 4). In both genes, the level of divergence was elevated relative to the level of diversity within the high-affinity allele class. As with the comparison between population samples, a peak in divergence relative to within-class diversity was also seen in the downstream flanking regions of both genes.

Figure 3.—

Sliding-window plot of silent-site diversity within and between populations. Results for the HBA-T1 and HBA-T2 genes are shown in A and B, respectively. The region of exon 2 that encodes the E-helix domain is shown in gray, and the five closely linked amino acid polymorphisms that distinguish the functionally defined allele classes are indicated by arrows.

Figure 4.—

Sliding-window plot of silent-site diversity within and between functionally defined allele classes. Results for the HBA-T1 and HBA-T2 genes are shown in A and B, respectively. The dashed horizontal lines denote critical values for Dxy. The critical values were derived from simulations based on a window size of 50 bp, with 4Nu = 0.02, 4Nr = 0.05, and 4Nm = 20. See Figure 3 legend for additional details.

In sliding-window plots of Zg between the high- and low-altitude samples, HBA-T1 exhibited a pronounced peak in intron 2, whereas HBA-T2 exhibited a similar-sized peak that was directly centered on the set of five amino acid polymorphisms in exon 2 (Figure 5A). In comparisons between the HBA-T2 allele classes, this peak in LD was even more pronounced (Figure 5B). By contrast, no such peaks were evident in the case of HBA-T1. In sliding-window plots of LD in the total population sample, both HBA-T1 and HBA-T2 were characterized by several pronounced peaks of ZnS (supplemental Figure 1). In HBA-T2, one of the peaks was centered on exon 2, but in both genes there were additional peaks of equal or greater magnitude in the downstream flanking regions.

Figure 5.—

Sliding-window plot of the HBA-T1 and HBA-T2 genes showing variation in Zg values in comparisons between populations (A) and between functionally defined allele classes (B). See Figure 3 legend for additional details. The dotted horizontal lines denote critical values for Zg. The critical values were derived from simulations based on a window size of 50 bp, with 4Nu = 0.02, 4Nr = 0.05, and 4Nm = 20.

DISCUSSION

An important goal of population genetics is to elucidate the effects of natural selection on patterns of DNA sequence variation. A powerful means of accomplishing this goal involves the analysis of nucleotide diversity and LD in genes that are known to contribute to adaptive trait variation in natural populations. The detailed study of sequence variation in such genes provides a rare opportunity to characterize the signature of selection and can provide insights into the particular features of polymorphism data that may be useful for detecting different types of selection. This was the motivation for our analysis of nucleotide diversity and LD at two closely linked α-globin genes, HBA-T1 and HBA-T2, that are known to be subject to divergent selection between populations of deer mice that inhabit different elevational zones. These two genes segregate the same pair of functionally distinct protein alleles due to a history of interparalog gene conversion. In each case, it was possible to focus our attention on a set of five closely linked amino acid substitutions that distinguish the high- and low-affinity allele classes at both genes.

Levels and patterns of nucleotide variation:

As expected, HBA-T1 and HBA-T2 were characterized by generally higher levels of silent-site diversity than the other nuclear loci (Table 2). The overall levels of variation and the partitioning of the variation within and between population samples (and within and between allele classes) are consistent with the idea that the polymorphism is being maintained by spatially varying selection (Snyder 1981, 1985; Snyder et al. 1982, 1988). When two or more alleles are maintained as a balanced polymorphism, it is commonly the case that “variation begets variation” because recombination between differentiated genetic backgrounds results in the continued production of novel sequence haplotypes. In the case of the HBA-T1 and HBA-T2 genes, spatially varying selection appears to be responsible for maintaining two alternative allele classes, and the elevated level of silent-site diversity at the two genes is further augmented by recombination between differentiated alleles as well as recombination between nonallelic genetic backgrounds (interparalog gene conversion).

In addition to the high levels of silent-site diversity, our survey revealed that the HBA-T1 and HBA-T2 genes were also characterized by higher levels of altitudinal differentiation relative to the other linked and unlinked nuclear loci (Figure 2). At these two genes, the observed levels of nucleotide divergence exceeded neutral expectations over a broad range of parameter combinations for scaled rates of migration and recombination. In both HBA-T1 and HBA-T2, a pronounced peak of between-population divergence was directly centered on exon 2 (Figure 3). Although this peak was one of several equal-sized peaks in the coding region and in the downstream flanking region, the peak of between-population divergence in exon 2 was associated with a reduced level of diversity within the high-altitude sample. In the case of both genes, the peak of between-population divergence in exon 2 was somewhat more pronounced in the comparison between allele classes, and in this case the divergence was associated with a reduced level of diversity within the high-affinity allele class (Figure 4). In the absence of a priori knowledge about the causal substitutions that distinguish alternative allele classes, it appears that sliding-window plots of diversity levels alone would not provide a clear means of identifying such sites.

Contrary to theoretical expectations of a standard balancing selection model, neither HBA-T1 nor HBA-T2 were characterized by an excess of intermediate-frequency variants in the total population sample (Table 2). In fact, both genes yielded strongly negative Tajima's D values like the other unlinked nuclear loci. There are a number of possible explanations for this pattern. Recent theory suggests that selection on standing variation will typically produce an extremely large variance in the frequency distribution of polymorphic sites (Hermisson and Pennings 2005; Przeworski et al. 2005). Thus, the distribution of allele frequencies at selected loci may often be indistinguishable from neutral-equilibrium expectations, especially if copies of the selected allele occur on multiple-haplotype backgrounds due to recurrent mutation or migration (Hermisson and Pennings 2005; Pennings and Hermisson 2006). Alternatively, the effects of selection may be partially masked by the effects of demographic history. For the majority of nuclear loci, values for Tajima's D were negative in the individual samples and in the total sample (Table 1), and the same pattern was observed in a survey of mitochondrial DNA variation (E. J. Gering, J. C. Opazo and J. F. Storz, unpublished data). This excess of rare variants at multiple unlinked loci suggests that the demographic history of deer mice from the Great Plains/Rocky Mountains region may have involved a population bottleneck and subsequent expansion. Such a history seems plausible given that this region of North America was probably recolonized sometime since the last glacial maximum. If the demographic history of deer mice in the Great Plains/Rocky Mountain region has resulted in a genomewide excess of rare variants (as reflected by negative Tajima's D values across multiple unlinked loci), then this departure from equilibrium conditions would at least partially offset the effects of spatially varying selection at HBA-T1 and HBA-T2, which might otherwise be expected to produce positive D values in the total population sample.

Levels and patterns of LD:

In contrast to the interlocus variation in δST values (Figure 2), the HBA-T1 and HBA-T2 genes did not exhibit Zg values that exceeded the simulation-based neutral expectations. This may be partly attributable to the fact that Zg is characterized by a higher sampling variance than δST. Within the coding regions of HBA-T1 and HBA-T2, the most striking pattern was seen in the analysis of LD between allele classes. Exon 2 of HBA-T2 exhibited a sharply defined peak in LD between silent-site polymorphisms that were shared between the high- and low-affinity allele classes (Figure 5B). This region of exon 2 harbored the set of five amino acid substitutions that distinguish the two functionally distinct allele classes. In conjunction with our simulation-based power analysis, the striking pattern shown in Figure 5B suggests that, with sufficiently high rates of intragenic recombination, sliding-window plots of Zg values may provide a means of pinpointing causal substitutions that distinguish alternative alleles that are maintained as a balanced polymorphism.

Detecting the signature of balancing selection:

In principle, peaks of nucleotide diversity or LD could be generated by balancing selection that is uniform across subpopulations or by spatially varying selection that favors different alleles in different subpopulations (Charlesworth et al. 1997, 2003). The latter is a form of balancing selection at the level of the total population but not at the level of individual subpopulations. Both types of selection are expected to increase nucleotide diversity and LD between allele classes. However, under spatially varying selection, the alternative allele classes will be present at different frequencies in different subpopulations. Consequently, only spatially varying selection is expected to increase the component of diversity and LD between subpopulations relative to the within-subpopulation component. To distinguish between spatially uniform selection and spatially varying selection it is important to use an appropriate geographic sampling scheme. Obviously, spatially varying selection can be detected only if the sample under consideration includes representatives of two or more divergently selected subpopulations. It is also important to survey variation at multiple unlinked loci to account for geographic population subdivision that may be superimposed on the subdivision between different genetic backgrounds at the selected locus.

Our simulation results indicate that both δST and Zg are useful sample statistics for detecting spatially varying selection. The fact that δST and Zg between allele classes retained high power under essentially panmictic conditions (e.g., when 4Nm = 100; Figure 1) suggests that these statistics may be useful for detecting any form of balancing selection as long as it is possible to identify alternative allele classes. To pinpoint causal substitutions, moderately high levels of both migration and recombination may be optimal because these conditions maximize the expected difference between Zg values that are based on comparisons between allele classes and those that are based on comparisons between subpopulations. As predicted by theory, the HBA-T1 and HBA-T2 genes of deer mice exhibited δST values between high- and low-altitude samples that exceeded the upper range of values for other linked and unlinked nuclear loci. However, neither of the two α-globin genes was clearly different from the other loci with regard to the frequency distribution of polymorphic sites. This suggests that tests that consider the between-population component of nucleotide variation are generally more useful for detecting the effects of spatially varying selection than conventional neutrality tests that are exclusively based on within-population variation. It seems clear that if the adaptive significance of the two-locus α-globin polymorphism were not already known, neutrality tests based on the frequency distribution of polymorphic sites would not provide any indication of selection.

How general are these results? Is it commonly the case that genes under balancing selection may exhibit patterns of nucleotide variation that are consistent with neutral-equilibrium expectations? We do not yet have a clear answer to this question due to the paucity of empirical case studies in which functional variation at the DNA sequence level can be related to a specific, fitness-related phenotype under natural conditions. At least in eukaryotic organisms, there are very few population-level studies of sequence variation in selected genes where adaptive significance can be ascribed to specific mutations. In addition to the α-globin polymorphism in deer mice, other cases in which the adaptive significance of specific mutations has been empirically verified involve human genes that contribute to resistance to falciparum and/or vivax malaria (Hamblin and Di Rienzo 2000; Modiano et al. 2001; Currat et al. 2002; Hamblin et al. 2002; Saunders et al. 2002, 2005; Verrelli et al. 2002; Ohashi et al. 2004). However, even in cases where independent lines of clinical and epidemioloigical evidence have implicated strong selection for resistance that could be ascribed to the effects of specific mutations, the expected signature of selection was not always clearly discernible in patterns of DNA sequence variation. Typically, the effects of selection could be detected in only some features of the polymorphism data, such as long-range LD within a single allele class (e.g., Sabeti et al. 2002; Saunders et al. 2002, 2005; Verrelli et al. 2002).

In general, balancing selection is expected to produce an excess of intermediate-frequency variants and an excess of LD only if the same alleles are maintained for time spans that far exceed neutral expectations. If mutation continually produces new alleles that are functionally equivalent to either of the preexisting alleles that are maintained as a balanced polymorphism, then the same functional types of alleles may be maintained for long periods of time even though the individual alleles are not especially long lived. This continuous turnover of alleles would generate a very different age distribution of mutations than would be the case if the same individual alleles were maintained for long periods of time, and elevated D and ZnS values would not necessarily be expected (Charlesworth 2006; Kelly 2006). This is one reason why loss-of-function alleles are unlikely to be maintained as part of an ancient balanced polymorphism (Nordborg and Innan 2003). Since there are many possible mutational changes that could produce a loss of function, the rate of origin of such mutations may be sufficiently high that preexisting alleles are continually replaced by newly arisen versions that have equivalent phenotypic effects.

Inferences about the mode of selection:

Our analysis of polymorphism data for the HBA-T1 and HBA-T2 genes provides proof-of-principle that δST and Zg can be used to detect the locus-specific effects of spatially varying selection. Have the results of these analyses also provided biological insights into the nature of selection that is responsible for maintaining the α-globin polymorphism in deer mice? First of all, the fact that there is no marked asymmetry in diversity levels between the high- and low-affinity allele classes suggests that the alleles may be roughly similar in age. If one of the alleles were recently driven up to high frequency by directional selection (a “partial sweep”), we would expect to see reduced diversity and elevated LD only within that particular allele class (Hudson et al. 1994) and we would not necessarily expect elevated divergence or LD between allele classes. Thus, at both HBA-T1 and HBA-T2, the observed partitioning of nucleotide diversity and LD within and between allele classes is consistent with long-term balancing selection. Finally, although we focused our attention on the five amino acid changes that were associated with measured differences in hemoglobin–oxygen affinity (Chappell and Snyder 1984; Chappell et al. 1988; Storz et al. 2007), peaks of between-population diversity and ZnS in downstream flanking regions of both genes suggest the possibility of selection on noncoding DNA. Although the peaks do not coincide with known cis-regulatory elements, the observed patterns suggest the possibility that the adaptive variation in hemoglobin function could be partly attributable to epistatic interactions between closely linked structural and regulatory polymorphisms.

Acknowledgments

We thank A. Di Rienzo and two anonymous reviewers for helpful comments, F. G. Hoffmann for help with sequence alignments, and J. Sukumaran and M. Holder for loading our simulation programs onto computer clusters at the University of Kansas. This work was supported by grants to J.F.S. from the National Science Foundation (DEB-0614342), the National Institutes of Health (R01 HL087216-01A2), and the Nebraska Research Council and by grants to J.K.K. from the National Science Foundation (DEB-0543052) and the National Institutes of Health (R01 GM073990-01A1).

Footnotes

  • Received March 1, 2008.
  • Accepted June 16, 2008.

References

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