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Unusual Haplotype Structure at the Proximal Breakpoint of In(2L)t in a Natural Population of Drosophila melanogaster
Peter Andolfattoa, Jeffrey D. Wallb, and Martin Kreitmana,ba Committee on Genetics, University of Chicago, Chicago, Illinois 60637
b Department of Ecology and Evolution, University of Chicago, Chicago, Illinois 60637
Corresponding author: Peter Andolfatto, Department of Ecology and Evolution, 1101 E. 57th St., University of Chicago, Chicago, Illinois 60637., pandolfa{at}midway.uchicago.edu (E-mail)
Communicating editor: G. A. CHURCHILL
| ABSTRACT |
|---|
The existence of temporally stable frequency clines for In(2L)t in natural populations of Drosophila melanogaster suggests a role for selection in the maintenance of this polymorphism. We have collected nucleotide polymorphism data from the proximal breakpoint junction regions of In(2L)t to infer its evolutionary history. The finding of a novel LINE-like element near the In(2L)t breakpoint junction in sampled inverted chromosomes supports a transposable element-mediated origin for this inversion. An analysis of nucleotide variation in a Costa Rican population sample of standard and inverted chromosomes indicates a unique and relatively recent origin for In(2L)t. Additional In(2L)t alleles from three geographically diverse populations reveal no detectable geographic differentiation. Low levels of In(2L)t nucleotide polymorphism suggest a recent increase in the inversion's frequency in tropical populations. An unusual feature of our sample of standard alleles is a marked heterogeneity in levels of linkage disequilibrium among polymorphic sites across the breakpoint region. We introduce a test of neutral equilibrium haplotype structure that corrects both for multiple tests and for an arbitrarily chosen window size. It reveals that an ~1.4-kb region immediately spanning the breakpoint has fewer haplotypes than expected under the neutral model, given the expected level of recombination in this genomic region. Certain features of our data suggest that the unusual pattern in standard chromosomes is the product of selection rather than demography.
INVERSION polymorphisms in the genus Drosophila are widely believed to be among the best examples of balanced polymorphisms. They have been used extensively as model systems for the study of the adaptive processes involved in the maintenance of genetic variation (reviewed in ![]()
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Population genetic models suggest that a possible advantage of inversions lies in their ability to suppress recombination in karyotypic heterozygotes and thus maintain favorable epistatic interactions between alleles at linked loci (![]()
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In Drosophila, the linkage disequilibrium between selected sites and linked neutral variants predicted by epistatic or balancing selection models decays rapidly in the presence of gene conversion (![]()
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An alternative is to investigate the distribution of molecular variation within and between chromosomal arrangements at loci closely linked to the inversion breakpoints (![]()
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We have investigated nucleotide variation in a 5-kb region surrounding the proximal breakpoint of In(2L)t. Our a priori prediction is that the long-term maintenance of the inversion by selection will have led to the accumulation of a large number of fixed differences between karyotypic classes. ![]()
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An unexpected feature of our sample of standard alleles is an unusually strong association among segregating sites close to the breakpoint. The presence of selection and recombination in a region can lead to considerable heterogeneity in levels of linkage disequilibrium (![]()
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| MATERIALS AND METHODS |
|---|
Localizing the 34A breakpoint:
The In(2L)t proximal breakpoint (34A8-9) was first localized by in situ hybridization on polytene chromosomes (modified from ![]()
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Population samples:
Field collections were made from a single, large population of D. melanogaster in San Jose, Costa Rica. This tropical population was chosen because it was likely to have an appreciable frequency of In(2L)t. Wild-caught females were used to start isofemale lines. After several days of egg laying, genomic DNA was prepared from each original wild-caught female and PCR genotyped for In(2L)t. The use of specific primer pairs allowed the recovery of standard or In(2L)t alleles from inversion heterozygotes identified in the above screen. For the sampling of standard alleles, a 5-kb region spanning the proximal breakpoint (C/D in Figure 1) was PCR amplified from In(2L)t heterozygotes (primer C, GCCACGCCCCCATTCACTTAC; primer D, AATGCTTGGTGGCTTTGGAATGGT). These PCR-generated templates were sequenced directly with a set of forward and reverse primers. Similarly, for In(2L)t alleles, the two breakpoint junction regions (A/C and B/D in Figure 1) were amplified separately and sequenced from seven individuals (primer InA412, TTCGATCCACCGACAATCTGAAC; primer InB124, GTACTTTCACTGTTTGCTGACGACGC). Inversion frequencies were also determined by PCR for three other populations (Florida City, FL; Yeppoon, Australia; and Zimbabwe, Africa) for comparison to previously published estimates. Australian and African isofemale lines were kindly provided by C.-I Wu. Primers used for karyotyping individual flies for In(2L)t are as follows: StC545, GACTCATTCTGCTTCGATCACTAAG; StD18, CTGTTCCCACCGCACAGAGTTGCCTGTC; InA151, TATTTTGGTGGCCTGTTTCAG. Expected PCR products are ~500 bp for primer pair StC545/StD18 and ~250 bp for primer pair StC545/InA151.
Polymorphism analyses:
Tests of the neutral equilibrium model that compare polymorphism and divergence (e.g., ![]()
= 4Nu, where N is the effective population size of the species and u is the neutral mutation rate, was estimated from both
, the average pairwise difference per base pair (![]()
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Tree construction, In(2L)t historical frequency, and age:
Bootstrapped parsimony phylograms were constructed using PAUP3.1.1 (![]()
If we assume the former model and that the inversion is at equilibrium, then
and f can be estimated from the sample sizes of inverted and standard chromosomes (ni and ns, respectively) and the observed number of segregating sites within the inverted and standard chromosomes (Si and Ss, respectively; ![]()
k-1j=1 j-1. Then, E[Si] =
fani and E[Ss] =
(1 - f)ans. To estimate
and f, the expectations are replaced by their observed values. This yields
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(1) |
and
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(2) |
It is then straightforward to estimate the time to the most recent common ancestor of the inverted chromosomes by substituting (1) into
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(3) |
This yields an estimate of the minimum age of the inversion. An expected age of the inversion is also calculated based on the average net number of differences between arrangements scaled to the expected divergence time between D. melanogaster and D. simulans. It should be noted that these estimates have very large variances.
We investigate by simulation whether levels of In(2L)t variation are compatible with assumed historical inversion frequencies under a neutral equilibrium model. We run 100,000 coalescent simulations with sample size ni and population mutation parameter
f. Here
is estimated from (2), and we determine for which values of f the observation of Si segregating sites is within the middle 95% of the simulated distribution of Si.
Test of neutral equilibrium haplotype structure:
We constructed a test to determine whether any subsets of consecutive segregating sites in our data contain fewer distinct haplotypes than would be expected under a neutral equilibrium model. Suppose we have a data set with n chromosomes and S segregating sites. Define Sk to be the largest number of consecutive segregating sites that contain only k different haplotypes (1 < k < n). An empirical distribution of Sk is determined from 100,000 simulations using an infinite-sites, panmictic coalescent model conditional on n and S (![]()
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A concern is the violation of the "infinitely many sites" assumption of our null model. In particular, mutations can sometimes overlap in actual data, especially in the presence of deletions. It is not clear whether "infinite-sites" simulations are conservative when the actual data has overlapping mutations. On one hand, more windows are considered in the simulations than in the actual data, which is conservative. On the other, missing information for those chromosomes with deletions might lead to fewer haplotypes than expected under the infinite-sites assumption. We believe that both effects are rather minor, but a higher degree of caution should be exercised when interpreting the relevant significance levels.
Two different versions of the In(2L)t data are considered. In-dels are likely to be governed by a different mutational process than single nucleotide polymorphisms (hereafter SNPs); however, they are included in simulations that condition on S since nothing is assumed about the underlying mutation rate,
(![]()
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All parameters used in simulations, including n, S, and C are listed in Table 1. In reality, the effective rate of recombination depends on the arrangement class. Our assumptions of panmixia and the same recombination rate for all individuals are unrealistic in this regard. Nevertheless, we consider it to be a reasonable simplifying assumption. In fact, an explicit demographic model of equilibrium-balancing selection based on estimates of the inversion's age and historic frequency yielded more significant P values (results not shown). Since individuals were not sampled randomly, both versions used a random sample based on the observed frequency (20.8%) of In(2L)t chromosomes in the San Jose population. This sample included all 11 standard chromosomes as well as cr40i, cr44i, and cr46i (see Figure 2). Since In(2L)t varies in frequency among geographic locations, and the inferred historical frequency was estimated to be between 4 and 23% (see RESULTS), we also considered representative samples with zero to four inverted alleles.
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Recombination:
The implications of recombination on the predictions of population genetic models are poorly understood. Perhaps as a result, investigators often conduct statistical tests with the assumption of no recombination. However, since there is evidence for recombination in our (and other) data, it is more realistic to assume C > 0 in simulations. In addition, ignoring the effect of recombination does not always lead to a conservative test (![]()
The use of estimators of the population recombination rate, C = 4Nr, on the basis of nucleotide polymorphism data (e.g., ![]()
![]()
, where
is the per base pair, per generation rate of recombination obtained from laboratory measurements of the exchange of flanking markers (cf. ![]()
![]()
/4µ, where
is estimated from the average nucleotide diversity at silent sites and noncoding DNA of loci in regions of intermediate recombination (![]()
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The presence of an inversion in our sample makes the parameter C difficult to interpret. We expect that reduced exchange in inversion heterozygotes (i.e., genetic isolation) will affect the overall levels of exchange. When calculating Clab for use in simulations, we account for lack of recombination in D. melanogaster males and assume an absence of recombination in inversion heterozygotes. Thus, Clab = (1 - 2q(1 - q)) 2N
, where q is the assumed inversion frequency. Note that the maximum effect of an inversion on the recombination rate among standard chromosomes is a factor of two (assuming an inversion at 50% frequency and no recombination in inversion heterozygotes).
Analysis of other data sets:
To demonstrate the effect that an arbitrarily chosen window size can have on the likelihood of a data set, we assess the significance of nonneutral haplotype structure reported in additional studies of D. melanogaster populations: the white locus data of ![]()
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for each locus (![]()
| RESULTS |
|---|
Polymorphism summary:
Figure 2 summarizes 176 polymorphic sites found in the sampled 5-kb of region C/D (see Figure 1). The data set contains 131 biallelic single nucleotide polymorphisms (SNPs). In addition, there are 27 biallelic insertion-deletion polymorphisms, denoted by i, d, or M. Complex polymorphisms are denoted by M; they are either multiple insertions (or deletions) that are very close to each other, or one or more nucleotide mutations associated with an insertion or deletion. The spatial distribution of insertion-deletion variation does not appear to be different from that for SNPs and does not significantly affect Tajima's D statistic (results not shown). The In(2L)t breakpoint occurs between positions 2826 and 2919, where all sampled inverted chromosomes (n = 18) contain a 94-bp deletion.
Inversion frequencies and uniqueness of origin:
Estimates of In(2L)t frequencies assessed by PCR assay in Yeppoon and Florida City samples were 22.9% (n = 43) nd 25.0% (n = 100), respectively. These estimates are similar to those based on the cytology of geographically proximate populations (![]()
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Recombination within and between chromosomal arrangements:
For the chromosomal band 34A8-9, the laboratory estimate of the crossover rate is 2.9 x 10-8 per site per generation in females (![]()
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Despite the large number of informative polymorphisms, there is almost no evidence for genetic exchange between arrangements in our data. A possible exception is site 174 (Figure 2), which may be a multiple hit. This observation is consistent with the finding of suppressed exchange between standard and inverted classes at the breakpoint of the inversion (![]()
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History of In(2L)t:
A bootstrapped parsimony phylogram for 2.3 kb of sequence (positions 1491 to 3822) immediately spanning the inversion breakpoint is shown in Figure 3. All mutations in this segment are consistent with a single genealogical tree (i.e., there are no inferred recombination events in the segment). From the tree, we can infer that the inversion is relatively recently derived from one of two distinct haplotype classes of standard chromosomes. Trees based on three other recombination-free segments (positions 189492, 6391020, and 39464354) all produce similar topologies: In(2L)t alleles form a distinct cluster that is closely related to one or more standard haplotypes.
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In total, 12 biallelic segregating polymorphisms were found in the 7 sampled In(2L)t alleles. Of these, 9 are SNPs (see Figure 2). Estimates of
and
for the In(2L)t alleles are 11 and 7%, respectively, of those for standard alleles (Table 1). Assuming the population is at equilibrium, this level of diversity is consistent with a low (i.e., ~10%) average historical frequency.
In(2L)t appears to be recently derived relative to standard lineages and the D. melanogaster-D. simulans divergence time. We estimate the E[TMRCA] of our sample of In(2L)t alleles to be ~0.3 Ne generations. This roughly corresponds to ~100,000 years, assuming an Ne ~3 x 106 (![]()
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A second estimate of the age can be obtained from the number of fixed differences between In(2L)t and standard lineages: the number (9) is small compared to the average pairwise divergence between standard chromosomes (48.5). This again suggests that In(2L)t is recently derived relative to standard lineages. We estimate the expected age of the inversion (~160,000 years) to be ~4% of the net divergence time for D. melanogaster and D. simulans.
In(2L)t nucleotide diversity and frequencies in natural populations:
Several features of the data suggest that In(2L)t is not at equilibrium. First, Tajima's D for the inverted class is negative (though the frequency spectrum is not significantly skewed). This finding is interesting given that Tajima's D is significantly positive for the random sample. Second, In(2L)t chromosomes show no segregating variation in a region of elevated
(positions 2637 to 3020, Figure 2). These observations suggest a recent origin and rapid increase in the inversion's frequency.
Evidence that In(2L)t has recently increased in frequency can be inferred from the geographic distribution of In(2L)t variation and the relative levels of diversity for standard and inverted chromosomes. We sequenced an ~0.8-kb region spanning the C/A breakpoint junction of 11 additional In(2L)t chromosomes (positions 2001 to 2819, Figure 2). Table 3 summarizes polymorphic variation found in this subregion for 18 In(2L)t alleles from four geographically diverse populations. Permutation tests (![]()
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Heterogeneity in nucleotide polymorphism:
Sliding-window profiles of nucleotide diversity (Figure 4) reveal considerable heterogeneity in levels of polymorphism across region C/D. For example, the large mutation-free stretch centered at ~1600 in Figure 4B (found between positions 1491 and 2019 in Figure 2) is highly unusual (P < 0.004 for all C) assuming a uniform mutation rate. Nonuniformity of mutations could arise from heterogeneity in selective constraint across the region. A comparatively large peak of intraspecific polymorphism is observed at the inversion breakpoint (approximately position 2600 in Figure 4A). Interestingly, most of this variation is distributed between two major haplotypic classes and not within them (Figure 4B), reflecting the strong linkage disequilibrium observed between sites close to the breakpoint (see Figure 2). The average pairwise divergence between haplotypic classes is ~10% at its highest point. This pattern is reminiscent of that observed between Fast and Slow allozyme classes at the Adh locus (![]()
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There seem to be fewer haplotypes at the breakpoint than expected under a neutral equilibrium model (given the sample size, the number of mutations, and the expected recombination rate). Unfortunately, Figure 4A and Figure 4B are tricky to interpret: for one, the division of standard chromosomes into two "haplotypic classes," as done in Figure 4B, is post hoc. In addition, the chosen window size is arbitrary. Given evidence for heterogeneity in constraint in the region, Figure 4 could be misleading since each window may not contain an equivalent number of "neutral" polymorphisms. In general, it is unclear how to test whether an arbitrarily defined window is unusual after having examined the data. To address this difficulty, the test described below corrects for a post hoc choice of window size.
Test of neutral equilibrium haplotype structure:
While there is evidence for recombination in our data (i.e., 10 minimum inferred recombination events), there are also strong associations among sites over a considerable distance spanning the In(2L)t breakpoint (see positions 14914109 in Figure 2). Although this observation seems unlikely under the null model, closely linked sites do have correlated histories in neutral genealogies with intermediate recombination (![]()
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Final P values that correct for a post hoc choice of window size are shown in Table 4. Each of these values reflect median P values for all possible random samples with three In(2L)t alleles (reflecting the sampled In(2L)t frequency of 20.8%). Since In(2L)t nucleotide diversity levels are consistent with frequencies of between ~4 and 23%, we conducted additional tests on random samples corresponding to In(2L)t frequencies of between 0 and 27%. Most of the tests on Version I of the data were not significant when C = Ccon. Version II of the data, which includes polymorphisms that overlap with the 94-bp deletion of In(2L)t alleles, is significant when C = Ccon for samples that included between zero and three In(2L)t alleles.
Figure 5 shows P vs. C for Version I of the data. Note that C = 0 is not conservative and that P decreases (almost) monotonically for C > Ccon. The pattern in Figure 5 (an initial increase in P for low values of C followed by a steady decrease as C increases) is a general feature of our test (results not shown). When running simulations with our a priori estimate of the recombination rate (Clab, corrected for the inversion's effect), all tests were highly significant (P < 0.001) for both versions of the data, including samples with zero to four In(2L)t alleles.
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Multiple tests, recombination, and haplotype structure at other loci:
Correcting for multiple tests and an arbitrary window size can have an impact on the significance of the data. For example, the most unusual subset of the Acp70A data (![]()
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The assumed rate of recombination also has a large effect on our interpretation of the data (Table 5). For example, under conservative recombination the white locus (![]()
0.004). Interestingly, significant haplotype structure is not detected in the two African samples of vermilion, even when C = Clab (P = 0.817 and 0.270 for Kenya and Zimbabwe, respectively). Thus, these two samples are in accordance with the predictions of a neutral equilibrium model under expected levels of recombination (i.e., C = Clab).
Open reading frames:
A scan of 8.4 kb of the proximal breakpoint sequence (see Figure 1) with open reading frame (ORF) Finder (http://www.ncbi.nlm.nih.gov) revealed an ~200-amino-acid open reading frame between positions 7701 and 8343. A search of the protein databases revealed that this putative exon encodes a shaggy-like protein kinase. The position and direction of this exon is indicated in Figure 1. This putative exon was not included in our polymorphism study. GRAIL v. 1.3 software (http://compbio.ornl.gov) identified a second putative ORF (Figure 1) between positions 3078 and ~3227. This putative ORF is oriented in the same direction as the shaggy-like ORF and contains a helix-loop-helix dimerization motif. It is unknown whether or not these ORFs are contained in a single gene. The proximity of this putative coding region to the In(2L)t breakpoint raises the possibility that the inversion may affect patterns of gene expression. This finding would not be unprecedented in the literature (cf. ![]()
A scan for ORFs in the In(2L)t B/D junction region revealed a 93-amino-acid open reading frame oriented toward the breakpoint that encodes the 3'-end of a novel putative reverse transcriptase of the LINE family of retro-elements (![]()
| DISCUSSION |
|---|
Origin and age of In(2L)t:
A LINE-like retrotransposon is found immediately at one of the breakpoint junctions. This element is absent in standard chromosomes but fixed in In(2L)t chromosomes, suggesting a transposable element-mediated origin for the inversion. This finding supports other recent work indicating a role for transposable elements in the formation of naturally occurring chromosomal rearrangements (![]()
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Patterns of polymorphism and divergence between chromosomal arrangements in the San Jose population sample suggest that In(2L)t has a unique and relatively recent origin. Our estimate of In(2L)t's age, ~160,000 years old (or ~1.6 million generations), is similar to the age reported for In(3L)P (![]()
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An alternative to the "long-lived balanced polymorphism" scenario is that In(2L)t has very recently increased in frequency in some populations due to selection. If so, the inverted class should have either reduced levels of variation, as observed in one allelic class at the Sod locus of D. melanogaster (![]()
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In(2L)t is not at equilibrium in natural populations:
A recent increase in the frequency of In(2L)t can be inferred by considering relative levels of nucleotide diversity in standard and inverted arrangement classes (Table 1 and Table 2) as well as world-wide inversion frequency estimates (![]()
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Genetic exchange between arrangements is suppressed at inversion breakpoints:
Our data suggest that exchange between arrangements, including gene conversion, is significantly suppressed at breakpoint regions relative to other regions. This is manifested by the lack of shared polymorphism between arrangements (Table 2) and the low diversity of In(2L)t and In(3L)P alleles (relative to standard alleles) at the junction region. We find no evidence for genetic exchange between karyotypic classes despite the large number of informative sites in the region sequenced (with the possible exception of site 174, Figure 2). In contrast, patterns of variation at Adh and Fabp2 are consistent with considerable levels of between-karyotype exchange at these loci. Patterns of nucleotide polymorphism at multiple loci linked to In(3L)P lead to a similar conclusion (Table 3).
The distribution of polymorphism within and between arrangements at rp49 is significantly different from that observed at both In(2L)t and In(3L)P breakpoints (Table 2, two-tailed P < 0.01 and P < 0.04, respectively, by a Fisher's exact test). Est-5 of D. pseudoobscura (Table 2) shows a pattern more consistent with the patterns observed at In(2L)t and In(3L)P. The rp49 data may be unusual due to the complex nature of the associated inversion system in D. subobscura (![]()
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Unusual haplotype structure at the In(2L)t breakpoint:
An unexpected feature of our data is a marked heterogeneity in levels of linkage disequilibrium across the sequence (Figure 2) among standard chromosomes. Two deeply diverged standard arrangement haplotypes exhibit strong associations among sites close to the inversion breakpoint. Yet there is ample evidence for recombination in other regions of the data set.
Our statistical test reveals that an ~1.4-kb region immediately spanning the In(2L)t breakpoint (Figure 2) has too few haplotypes to be compatible with a neutral equilibrium model under the expected level of recombination (i.e., Clab; see Table 4). It also suggests that the haplotype structure observed at In(2L)t is more extreme than at two other loci (i.e., white and Acp70A, Table 5) where unusual haplotype structure had previously been reported (![]()
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Unfortunately, the true recombination rate is unknown. Simulations run with Ccon do not always show a significant deficiency in the number of haplotypes at the In(2L)t breakpoint. However, on the basis of comparisons of physical and genetic maps (![]()
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) is likely to be a considerable underestimate of the true rate of exchange because it ignores the added contribution of gene conversion to C. Over small physical distances (i.e., on the order of ~1 kb), gene conversion is expected to contribute as much to the recombination rate as
(![]()
It is difficult to imagine that recombination rates are different enough in natural populations (relative to lab strains) to account for the unusual haplotype structure observed at the breakpoint. A study of 2nd chromosome recombination rates in the F1 progeny of lab strains and wild-caught D. melanogaster lines suggests that genetic background does not have a large effect (![]()
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Population genetic models:
There are several alternatives to the panmictic neutral model that make it more likely to observe fewer-than-expected haplotypes in a sample. These include some forms of selection and population subdivision. Epistatic selection (![]()
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The findings of strong associations among polymorphic sites in standard chromosomes and the extreme divergence between the two major haplotype classes (Figure 4B) raise the possibility that some form of selection on standard alleles predated the appearance of In(2L)t, and that these standard haplotype classes are quite old. Since we do not have a reasonable estimate of the divergence between species across this region, a plausible alternative explanation for the high level of nucleotide polymorphism at the breakpoint is that either the mutation rate or the level of selective constraint varies across the sequenced region. The possibility of a "hotspot" for mutation at the breakpoint seems unlikely given that polymorphisms in the In(2L)t class of chromosomes do not cluster near the location of this elevated window of polymorphism in standard chromosomes. The finding of at least one putative exon in the sequenced region does suggest that the level of selective constraint is likely to vary. Note, however, that while heterogeneity in selective constraint may be a sufficient explanation for the peak of elevated polymorphism, it does not explain the deficiency in the number of haplotypes.
An alternative to selection models for the pattern at the In(2L)t breakpoint are demographic models (cf. ![]()
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The main difference between selective and demographic models is that the latter are expected to affect the whole genome with equal strength, while with selection, recombination will tend to uncouple the histories of neutral sites from that of the site under selection. Thus, depending on the rate of recombination, selection models can lead to considerable heterogeneity in linkage disequilibrium across a given region (![]()
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Implications for clines and linkage disequilibrium between Adh and In(2L)t:
The Fast/Slow allozyme polymorphism of the Adh locus in D. melanogaster is in complete linkage disequilibrium with In(2L)t in many populations (reviewed in ![]()
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1 insertion-deletion were in significant linkage disequilibrium with In(2L)t. Thus, while all In(2L)t chromosomes have the Adh-Slow allele, there is evidence for considerable between-arrangement exchange at Adh (i.e., shared polymorphisms; see Table 2). In fact, laboratory estimates of recombination between Adh and In(2L)t are very high (~10-3 to 10-4; ![]()
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Standard-Adh-Fast and In(2L)t-Adh-Slow alleles coexist at intermediate frequencies in many populations world-wide (![]()
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| ACKNOWLEDGMENTS |
|---|
We thank J. Comeron, R. Hudson, A. Llopart, and M. Przeworski for computer programs and helpful discussions. Comments from G. Churchill, A. Crawford, B. Charlesworth, D. Charlesworth, M. Jensen, J. Karubian, and especially M. Przeworski significantly improved this manuscript. S.-C. Tsaur kindly provided unpublished Adh data. We are grateful to J. Gladstone for expert technical assistance. This research was supported by National Science Foundation grant DEB-9408869 to M.K. P.A. holds a Postgraduate Scholarship from the National Science and Engineering Research Council of Canada.
Manuscript received September 23, 1998; Accepted for publication July 9, 1999.
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