DISCUSSION

This survey brings two new aspects to the study of the reduction in DNA sequence polymorphism in regions of reduced crossing over per physical length in natural populations of D. melanogaster. First, two additional populations (African and European) are surveyed for su(s) and su(w^a), providing a more complete view of the pattern of DNA sequence polymorphism at su(w^a) and su(s) in D. melanogaster throughout its distribution. Second, the increased overall levels of DNA sequence polymorphism in the African population provide more accurate estimates and more powerful statistical inferences than were available in previous surveys of regions of low crossing over. Africa is thought to be the ancestral home of D. melanogaster (David and Capy 1988). It is not known when this species spread out of Africa to become the cosmopolitan species it is now. It may well have accompanied human ancestors as they migrated out of Africa. In any case, much like their human commensals (Cavalli-Sforzaet al. 1994), African D. melanogaster harbors most of the DNA sequence polymorphism found throughout the rest of the world and is significantly more heterozygous than populations on other continents (Begun and Aquadro 1993). It seems probable that African populations have been prehistorically larger and ecologically more stable than populations on other continents that were recently established. African populations are likely to be closer to the idealized populations assumed in theoretical analyses, while non-African populations may still be undergoing more intense adaptive selection to the non-African environments. For these statistical and biogeographical reasons the African sample affords the most straightforward interpretation.

The su(s) and su(w^a) region exhibits reduced crossing over per physical length. The map distance to y of genes near this X telomere is the most appropriate available measure of the crossing over per physical length for two reasons. First, it is the most direct and reliable quantitative observation. Second, and more important, is the asymmetry in the pattern of crossing over per physical length in this genomic region. That portion of the genome that is tightly linked to su(s) and su(w^a) is toward yellow and extends out to the X telomere. Crossing over between centromere proximal markers and y continues to decline distally throughout cytological section 1. Crossing over between y (cytological position 1B1; map position 0.0) and su(w^a) (1E1-4) is reported to be somewhat <10^-3 (M. Green, personal communication). R. Voelker and J. Mason (personal communication) report that rare recombinants between y and recessive lethals adjacent to su(s) (1B13) occur with a frequency somewhat <10^-4. And since meiotic crossing over near y and beyond is absent, this terminal region forms a “block” of loci, all at the same (crossing over) distance from su(s) or su(w^a). Crossing over is increasing so rapidly in the centromere-proximal direction that the impact of linked selected variation must be much less. For example, the white locus (3C2) crosses over with y ∼3% of the time.

su(s) and su(w^a) are thus tightly linked to ∼1% of the genome (cytological section 1) that undergoes little crossing over. This large reduction in crossing over per physical length can be compared to the reductions in polymorphism at the loci in this region. The average number of pairwise differences per site (and θ^ = 3Nμ) of loci in X chromosome regions of normal crossing over (white, vermilion, and G-6-pdh) is 0.007 (0.01) for Africa and 0.004 (0.004) for North America (Miyashita and Langley 1988; Begun and Aquadro 1993). The estimates π^∗ for su(w^a) are half, while those at su(s) are about one-fourth (see Table 5), consistent both with the linkage to y and with average levels of variation across populations. π^ for the y-ASC is reported to be 0.001 in both African and non-African populations (Aguadéet al. 1989; Martín-Camposet al. 1992; Begun and Aquadro 1993), which fits well into this pattern. Such simple comparisons of the levels of polymorphism will not discriminate among the proposed linked-selected-perturbation models. Any quantitative interpretation of a two- or fourfold reduction in expected heterozygosity depends on independent knowledge of several additional parameters (beyond crossing over per physical length) in all the proposed models. For directional hitchhiking the overall reduction depends on both the selection coefficient(s) and on the rate per centimorgan per generation at which rare favored alleles fix (Kaplanet al. 1989). Similarly the background selection model can predict such a reduction in the expected heterozygosity under a wide range of selection coefficients and deleterious mutation rates (Hudson and Kaplan 1995; Charlesworth 1996). In the random-environment-hitchhiking models that Gillespie (1997) analyzed the parameters are also difficult to independently ascertain. To discriminate among these models other properties of the polymorphism offer better prospects.

The frequency spectra at loci demonstrating clear reductions in expected heterozygosity associated with reduced crossing over per physical length offer some hope. Braverman et al. (1995) showed that simple directional hitchhiking, which reduces heterozygosity by these observed amounts, should lead to a strong skew in the frequency spectra. This distortion from expectation under selective neutrality should be detectable in samples of the size reported here. Background selection is not expected to produce detectable skew (Charlesworth 1996). While Gillespie’s analyses of various random environment models do not provide sample properties nor any indication of statistical power, they do show a clear correlation between the reduction in average heterozygosity and the skew toward an excess of rare polymorphisms (Gillespie 1997). As Table 5 shows, the frequency spectra of nucleotide polymorphisms at both su(w^a) and su(s) in both the African and European samples are skewed toward rare sites unlike those observed previously in the North American sample (Aguadéet al. 1994). The European samples reach nominal statistical significance in the deviations of Tajima’s D from the predictions of the neutral model or background selection. The results from the survey of su(s) and su(w^a) from Europe and Africa favor a directional hitchhiking explanation over background selection. But how well do the observations fit the predictions of directional hitchhiking? Using the simulation approach in Braverman et al. (1995), the rates of directional hitchhiking (and selection coefficient) were set to yield the observed reductions in average number of pairwise differences per site from those expected in regions of normal crossing over, 0.007 in Africa and 0.004 in Europe and North America. Figure 3 shows above the probabilities of the observed Tajima’s D’s or less under the neutral or background selection models for the six locus samples. Depicted below the x-axis in Figure 3 are the proportions of directional hitchhiking simulations in which the Tajima’s D value exceeded that observed. The lack of linkage disequilibrium between these two loci suggests that the similarities are unlikely due to a single recent event.

It is evident in Figure 3 that the North American sample (especially the su(s) result) appears exceptional. Since the African, European, and North American populations cannot be considered strictly independent, it is prudent to take the African results as the most representative, since they are based on many more segregating sites and are from the putative ancestral region. While neither the background selection and neutral models nor the directional hitchhiking model can be rejected by Tajima’s D values from the African sample, these results favor some form of hitchhiking. And, indeed, the European results also support hitchhiking over background selection. The inconsistency of the North American results with this pattern might be attributed to transient hitchhiking associated with the more recent colonization of the Western Hemisphere (David and Capy 1988).

It has been suggested from empirical studies (Stephan and Langley 1989; Begun and Aquadro 1993) and from theoretical modeling (Nordborget al. 1996; Stephanet al. 1998) that geographic differentiation in DNA sequence polymorphism might be greater in those regions of the genome where crossing over per physical length is reduced. But the inherent paucity of variation and other considerations place considerable limitations on empirically based conclusions (Charlesworth 1998). The consideration of the genetic differentiation among populations of D. melanogaster has two broad aspects: the relatively greater overall level of polymorphism in Africa and the variance in site frequencies among populations. Figure 4, a-d, shows the distributions of F_ST of individual sites for su(s), Europe and Africa; su(s), North America and Africa; su(w^a), Europe and Africa; and su(w^a), North America and Africa, respectively. The patterns of these distributions are remarkably consistent in both their shape and the large contribution of polymorphism of the African sample. There is no evidence of “fixed differences” between populations. The mean F_ST values (Hudsonet al. 1992) for su(s) and su(w^a) between the African and European (and North American) samples are 0.153 (0.245) and 0.291 (0.343), respectively. Comparable values for loci in regions of normal crossing over have been reported (white, 0.28; vermilion, 0.32; G-6-pdh, 0.30; Pgd, 0.25), while greater differentiation was reported for three loci in regions of low crossing over per physical length [yellow, 0.56; achaete, 0.54; su(f), 0.60; Begun and Aquadro 1993]. This difference in the apparent level of geographic differentiation can be attributed to the small number of polymorphic sites surveyed at the three loci in that study.

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Figure 2.

—Polymorphism and linkage disequilibria in the European sample. The positions of polymorphic sites detected (ticks on the third level) in the survey of the 5′ portion of the su(w^a) (a) and of su(s) (b) in 51 alleles from a European population are indicated below a depiction of the gene structure (the open box is the 5′ untranslated portion, the solid boxes are coding portions of exons, and the thin lines are the introns). Only those polymorphisms at which the least common state occurred twice or more in the sample are shown. Directly below the gene structure are the positions and sizes of the PCR fragments surveyed by SSCP and DNA sequencing. The triangular matrix of squares represents the statistical significance determined by Fisher’s exact test (uncorrected for multiple tests); white, P > 0.05; light gray, P < 0.05; dark gray, P < 0.01; and black, P < 0.005. The dashed lines connect the polymorphic sites to their corresponding columns in the matrix. The shading of the circles at the top of each column increases with the expected heterozygosity of the polymorphic site. Along the left margin of the matrix are the positions in the published sequence of the corresponding polymorphic sites. Along the right margin are the inferred positions of the “minimum” number of recombination events in the history of the sample (Hudson and Kaplan 1985).

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Figure 3.

—The estimated relative probabilities of Tajima’s D values less than that observed under the neutral or background selection models, “N.T.,” or greater than that observed under the directional hitchhiking model, “H.H.” Neutral coalescent simulations (Hudson 1990) were conducted to generate 10,000 samples of size 50 for each locus in each population. Given the observed numbers of segregating sites the distribution of Tajima’s D was obtained. The proportion of simulations yielding a value less than that observed in the data (Table 3) is plotted above (gray bars for 3Nc = 0.0; hatched bars for 3Nc = 5.0). Simulations of recurrent, random directional hitchhiking (Bravermanet al. 1995) were conducted with the hitchhiking intensity sufficient to reduce the average number of pairwise differences per site to the observed values from a neutral expectation of 0.007 for Africa and to 0.004 for Europe and North America. The proportion of 10,000 such simulations yielding a Tajima’s D value greater than the observed is plotted below (open bars). The horizontal dashed lines indicate P > 0.05.

Figure 5 shows the distributions of the linkage disequilibria (measured as squared correlation coefficient, r²) between pairs of sites plotted against distances (base pairs) for su(w^a) and su(s), respectively, for the African sample (the sample with the most polymorphism and thus the most linkage disequilibrium information). Also, as argued above from a biogeographic perspective, the African population may be closer to equilibrium with respect to mutation, drift, selection, and recombination. Only sites where the rarer state occurred at least twice in the sample can be considered in the linkage disequilibrium analysis. Clearly most of the large linkage disequilibria (r² > 0.5) occur between sites separated by small distances, <200 bp. Also shown are the means over six contiguous intervals of distance [63 and 105 r² values averaged in each interval for su(s) and su(w^a), respectively]. As expected from previous surveys and theoretical predictions, the scatter is large for individual r² values. The distribution of the mean r² values reinforces the view that linkage disequilibrium tends to dissipate quickly and is near that expected from sampling, 0.02 for distances >500 bp.

To summarize the distributions of r² an empirical function was developed and fitted. Under the assumption of r = 0.0, the expected value of r² is the reciprocal of the sample size, 0.02 in this case. Under Wright-Fisher sampling the mean value of r² in the absence of any recombination can be estimated by simulation (Hudson 1990). Specifically an estimate of this “intercept” was derived from 1000 neutral, infinite site model coalescent simulations of samples of size 50 with 15 segregating sites and 4Nc = 20, where N is the diploid population size and c is the recombination per generation (Hudson 1990). As in our data analysis from the su(s) and su(w^a) loci, only sites where the rarer state occurred at least twice in the sample were considered. The value 0.337 was obtained by fitting a and λ in r² = 0.02 + a/(1 + λ ^* distance) to the 45,434 simulated r² values, where distance is in units of 4Nc (Hill and Weir 1994). The fitted λ for the simulated data was 0.354. The impact of recombination (proportional to distance) can be extended to include random gene conversion events with exponentially distributed tract lengths, r2=0.02+0.3371+c⋅distance+2gt(1−e−distance∕t), where g is the rate of gene conversion, t is the average gene conversion tract length, and c is the rate of crossing over (Andolfatto and Nordborg 1998). These parameters (all constrained ≥0.0) were fitted by least-squares to the su(s) and su(w^a) r² values separately and the predicted curves are also plotted in Figure 5. Remarkably, the fitted curves for the linkage disequilibria at the two loci are quite similar. The fitted estimates of rate of crossing over, c, are both 0.0. The estimated rates of gene conversion, g, are similar, 0.010 [su(s)] and 0.006 [su(w^a)]; these would be scaled in 4N under equilibrium Wright-Fisher sampling in the absence of selection. And the estimated tract lengths, 302 and 538 bp, respectively, are also not significantly different.

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Figure 4.

—Distributions of F_ST values for individual polymorphic sites at the su(s) and su(w^a) loci in comparisons of the African sample with the European (a and c) and the North American (b and d). The F_ST was calculated as 1 - (H_w/H_b), where H_w is the unweighted average expected heterozygosity and H_b is the expected heterozygosity of an unweighted pooled population. The solid portion of each bar reflects the number of sites polymorphic only in the African sample and exhibiting an F_ST value within the particular range. The open portion shows the number polymorphic only in the non-African sample, while the gray portion indicates the number of sites polymorphic in both samples.

Two aspects of these distributions of linkage disequilibria at su(s) and su(w^a) in the African sample are unexpected. First the scale of linkage disequilibrium is not different between these two loci, despite the fact that the density of crossing over per physical length is estimated to be as much as 10-fold less at su(s). Equally surprising is the fact that this pattern and scale of linkage disequilibrium is the same as that observed at the white locus (Miyashita and Langley 1988; Miyashitaet al. 1993). The white locus is in a genomic region of normal crossing over and exhibits much higher levels of polymorphism. It is clear that the rate of crossing over is not the determining parameter of linkage disequilibrium within these loci. Gene conversion is the obvious alternative recombination mechanism. The scale of strong linkage disequilibrium (r² > 0.3; <400 bp) is approximately that reported for both meiotic and mitotic gene conversion in Drosophila. While quantification of gene conversion rates in Drosophila is limited, the evidence indicates that half or more of all meiotic recombination events among intragenic sites are gene conversions (Finnerty 1976). Thus gene conversion should have at least the same impact on intragenic linkage disequilibrium as crossing over. Most meiotic and mitotic conversion tracts are small (<500), comparable to the estimates above. The reported mean P-element-associated conversion tract is ≈1400 bp (Preston and Engels 1996), while that for meiotic gene conversion tracts is estimated to be ≈400 bp (Hillikeret al. 1994).

From both the distributions of r² in Figure 5 and the inferred minimum recombination event depicted in Figures 1 and 2, it is evident that these loci experienced a great deal of recombination in the history of these sampled alleles, despite their location in a region of greatly reduced crossing over and despite the drastic reduction in polymorphism (and thus time since the last common ancestor of the sampled alleles). No theoretical analysis of the impact of intragenic recombination (e.g., gene conversion) on the background selection effect or on the directional hitchhiking effect has been reported. If the impact of background selection on linkage disequilibrium is similar to its effect on polymorphism, it can be approximated by r² = 1/(1 + 4Nf₀c), where f₀ is the fraction of the deleterious-mutation-free chromosomes in the population, which can be estimated as the relative reduction in expected heterozygosity per nucleotide site (Charlesworthet al. 1993; Charlesworth 1994, 1996). The scale of linkage disequilibrium (in base pairs) should increase by 1/f₀, even if gene conversion is the dominant source of intragenic recombination and if the rates of gene conversion are similar in regions of low and normal crossing over per physical length. Similar arguments and preliminary computer simulations extending our previous approach (Bravermanet al. 1995) suggest that directional hitchhiking will also increase the scale of linkage disequilibrium, if gene conversion rates are uniform.

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Figure 5.

—Linkage disequilibria vs. genomic distance at su(s) and su(w^a) in the African sample. The squared correlation coefficient, r², for pairs of sites in su(s) (horizontal ticks) and in su(w^a) (vertical ticks) is plotted against the number of base pairs separating the sites. The mean r² over six contiguous intervals (k values) are also plotted: su(s), ▴, k = 63; and su(w^a), ▾, k = 105. Also plotted is a fit for each locus of the equation dashed line, su(s); and solid lines, su(w^a) (see text). The parameters, the rate of gene conversion, g (events per base pair per generation in the population), the mean length (base pairs) of a gene conversion tract, t, and the rate of crossing over per base pair, c (events per base pair per generation in the population), were estimated by nonlinear regression to the formula (see text): su(s), ĝ = 0.010, tˆ = 302, and ĉ = 0.0; su(w^a), ĝ = 0.006, tˆ = 538, and ĉ = 0.0. The mean r² for all the between-locus [su(s) - su(w^a)] pairs of polymorphic sites is plotted as a large circle at the far right.

The observation of extensive recombination (presumably gene conversion) in the obviously short histories of these alleles at loci in regions of low crossing over per physical length (and low polymorphism) demands a modification or extension of the proposed linked-selected-perturbation models if they are to survive as general explanations of the correlation between standing polymorphism and crossing over per physical length. The rate of gene conversion could go up as the crossing over rate goes down. While there is no evidence to support this idea, it may be that the suppression of crossing over (near centromeres and telomeres) is simply the shunting of incipient crossovers toward gene conversions. Another interesting potential explanation for the high level of recombination in the histories of these alleles is a heterozygosity-dependent rate of gene conversion (see Stephan and Langley 1992). If gene conversion occurs at a higher rate between alleles that differ by fewer sites, the rate of recombination would change dynamically with increasing heterozygosity. Thus as directional hitchhiking or background selection reduced standing polymorphism, the recombination rate would increase. At equilibrium, regions of low crossing over would contain less polymorphism and thus undergo more gene conversion. This hypothesis of a heterozygosity-dependent rate of gene conversion is supported by observations in many systems including Drosophila. Nassif and Engels (1993) concluded that 0.5% sequence heterozygosity reduces the rate of P-element-induced mitotic gene conversion to 25% of that without heterozygosity. Variations in levels of heterozygosity have little or no effect on the rates of crossing over (Rutherford and Carpenter 1988). This is attributed to the strong regulatory processes underlying interference and the interchromosomal effect in crossing over (Lucchesi and Suzuki 1968). It is not known if heterozygosity-dependent inhibitions occur for gene conversion arising during meiosis or by other mechanisms in mitotic cells in Drosophila, but it is well known in yeast (see Kirkpatricket al. 1998; Chen and Jinks-Robertson 1999). If this indication of population genetic consequences of the interaction between DNA sequence heterozygosity and rates of genetic exchange can be corroborated, our theories of the forces shaping genomic polymorphism and divergence will require interesting improvements.