Mapping Regions Within Cosmopolitan Inversion In(3R)Payne Associated With Natural Variation in Body Size in Drosophila melanogaster

Abstract

Associations between genotypes for inversions and quantitative traits have been reported in several organisms, but little has been done to localize regions within inversions controlling variation in these traits. Here, we use an association mapping technique to identify genomic regions controlling variation in wing size within the cosmopolitan inversion In(3R)Payne in Drosophila melanogaster. Previous studies have shown that this inversion strongly influences variation in wing size, a trait highly correlated with body size. We found three alleles from two separate regions within In(3R)Payne with significant additive effects on wing size after the additional effect of the inversion itself had been taken into account. There were also several alleles with significant genotype-by-inversion interaction effects on wing size. None of the alleles tested had a significant additive effect on development time, suggesting different genes control these traits and that clinal patterns in them have therefore arisen independently. The presence of multiple regions within In(3R)Payne controlling size is consistent with the idea that inversions persist in populations because they contain multiple sets of locally adapted alleles, but more work needs to be done to test if they are indeed coadapted.

ASSOCIATIONS between genotypes for inversions and quantitative traits have been reported in many organisms. This is especially the case in Drosophila, where inversions have been linked with traits such as body size (Fanara et al. 1997; Orengo and Prevosti 2002; Yadav and Singh 2003), heat and cold tolerance (Anderson et al. 2003), longevity (Rodriguez et al. 1999), development time (Betrán et al. 1998; Fernandez Iriarte and Hasson 2000), larva to adult viability (Fernandez Iriarte and Hasson 2000), female fecundity, and male mating success (Brockett et al. 1996). Associations are presumably due to genes controlling variation for these traits that are located within or near the inverted region (Hoffmann et al. 2004).

Because crossing over within inversion loops in heterokaryotypes gives rise to nonfunctional or nonviable meiotic products, thereby maintaining strong nonrandom associations, finer scale genetic mapping of traits associated with inversions has not been attempted. The prevailing view is that the lack of functional recombinant gametes would make mapping of inversion-associated traits impractical. However, molecular studies now suggest that linkage disequilibrium (LD) within inversions is not complete, especially toward the middle of the inversion, where less restricted homologous pairing can occur and gene exchange can result from multiple cross-over events and gene conversion (Hasson and Eanes 1996; Andolfatto et al. 2001; Schaeffer et al. 2003). Consequently, despite the occurrence of inviable meiotic products, genetic mapping within inversions may nonetheless be possible.

Aside from localizing genomic regions controlling variation in ecologically important traits, genetic mapping within inversions is of interest, because it may shed light on the reason why inversion polymorphisms persist in natural populations. If, as widely believed, inversions are maintained in populations because they hold together combinations of alleles that have high fitness (Dobzhansky 1970; Krimbas and Powell 1992), then we might expect there to be multiple regions within the inverted region controlling variation in fitness-related traits. More recently, Kirkpatrick and Barton (2006) have proposed that locally adapted alleles and migration can cause a new inversion to spread to high frequency. They show that neither drift nor coadaptation between alleles is needed for an inversion to become established, but it must contain at least two sets of locally adapted alleles. One way to evaluate the importance of these different models would be to test whether there are epistatic interactions between genes within inversions influencing fitness. The presence of gene interactions would support the coadaptation hypothesis, whereas their absence is consistent with the model proposed by Kirkpatrick and Barton (2006). However, before tests such as these can be carried out, it is first necessary to establish whether or not there are multiple regions within an inversion impacting components of fitness.

The cosmopolitan inversion In(3R)Payne in Drosophila melanogaster has been shown to have strong associations with body size in natural populations in eastern Australia (Weeks et al. 2002; Rako et al. 2006). Furthermore, this relationship is supported by indirect evidence, as QTL mapping indicates, that the region where the inversion is located controls a large amount of variation in body size in Australian and South American populations (Gockel et al. 2002; Calboli et al. 2003). Moreover, body size and In(3R)Payne show similar clinal patterns on several continents (Knibb 1982; Coyne and Beecham 1987; James et al. 1995).

Here, we examine associations between genetic markers within and near In(3R)Payne and wing size in a population located centrally in the eastern Australian cline. In a previous study (Kennington et al. 2006), we found that LD between markers located within the genomic region covered by In(3R)Payne and In(3R)Payne was not complete. Multi-allelic estimates of Lewontin D' ranged from 0.18 to 0.85. We identified three regions where markers were in strong LD with In(3R)Payne, near each of the breakpoints and toward the middle of the inversion where the potential for gene exchange between chromosome arrangements is higher. Outside these regions, LD with In(3R)Payne was significantly lower. In this study, our aim was to map regions controlling variation in wing size within In(3R)Payne. If multiple regions within the inversion are found, we can then test for interaction effects between these regions to see which model explaining the spread of inversions is best supported. We also examined associations between the genetic markers and development time, a trait that exhibits weak clinal variation in Australia (James and Partridge 1995) and might contribute to natural variation in body size.

MATERIALS AND METHODS

Fly collections:

Four hundred female flies were collected from a population at Coffs Harbour, New South Wales (30.27°S, 153.49°E), located approximately midway along the body size cline on the east coat of Australia (James et al. 1995; Gockel et al. 2001). Progeny from individual wild-caught females were reared at a controlled density by collecting 20 eggs per female from spoons with medium and placing them in vials containing 20 ml of a sucrose-dead yeast-agar laboratory medium. Vials were held at 19° 12:12-hr light:dark cycle until eclosion, when the egg to adult development time was recorded.

Virgin female and male offspring were collected from each vial, and females and males originating from different field mothers (no more than two males or females per mother) were set up in pairs for the parental generation. In total, 500 pairs were set up. Eggs were obtained from each pair (2 vials each with 20 eggs per pair) and reared at 19° 12:12-hr light:dark cycle. This process was repeated over 3 days to obtain 2 × 4 sets of vials for each pair. Following egg collection, wings were removed from these parental pairs and the flies were preserved in 100% ethanol for DNA analysis.

Measurement of phenotypic traits:

Development time of the parental and offspring generations was scored by collecting emerging adults at 12-hr intervals. Following emergence, adult offspring were frozen at −80° for analysis of wing size. Wing size in the offspring generation was obtained by removing a wing from 1–2 females per line, attaching the wing to a slide with double-sided sticky tape, and obtaining an image with a video camera following Weeks et al. (2002). This experimental design, involving genotyping of the parental generation and phenotyping the offspring generation, is potentially a powerful way of detecting marker-phenotype associations, but only when five or more offspring are scored per family (Rako et al. 2007) and we therefore expected marker associations for offspring traits to be weaker than those for the parents. The coordinates of five landmarks around the external margins of each wing were recorded [described in Hoffmann and Shirriffs (2002) and determined using tpsDig version 1.2 written by F. James Rohlf], from which the centroid size (the square root of the squared distances between each landmark) was calculated and used as the measure of wing size.

Genotyping:

DNA extraction from individual flies, PCR protocols, and allele scoring followed methods outlined in Gockel et al. (2001). Each individual was genotyped for 24 microsatellite loci and the 8-bp insertion/deletion polymorphism at the 5′ end of the Hsr-omega gene (Mckechnie et al. 1998). The genetic and cytological positions of these markers are shown in Table 1. All were located on the right arm of chromosome 3, with most close to or within the breakpoints of In(3R)Payne. The chromosomal arrangement of each fly was determined by genotyping an SNP polymorphism shown to be in complete LD with In(3R)Payne in Australia (Anderson et al. 2005) using the BI-PASA method described in Liu et al. (1997).

TABLE 1.

Details and variability of the markers used

Marker	Cytological position	H	Alleles observed	Alleles tested
DROPROSA	86E4	0.75	9	3
DMTRXIII2	88B1	0.49	3	2
DROTROPI2	88E13	0.59	6	2
AC006414	89A2	0.14	4	1
AC007647	89B14	0.49	8	2
DROABDB	89E4	0.58	8	2
3R1302339ga	90A1	0.66	8	3
DMEHAB	90B1	0.04	3	1
DMCP017G	90D1	0.65	6	3
AC009394	90F10	0.68	9	3
DRONANOS	91F4	0.85	18	6
3R15743903gt	92C1	0.79	11	3
3R16177365gt	92E8	0.44	4	2
AC009347	93A3	0.20	8	1
Hsr-omega	93D4	0.50	2	1
DROHOXNK4	93D9	0.08	4	1
DMU25686	93F14	0.67	13	3
AC008193	94D2	0.83	9	6
DMU1951	95C5	0.80	12	3
DMTF125	95C9	0.62	9	3
3R19639736ta	95C10	0.63	10	2
3R20604755a	96B2	0.67	8	3
DROROUGH	97D5	0.29	4	2
3R23156893gt	97F11	0.76	10	4
DROLMALK	98A14	0.76	7	4

Markers underlined are located within In(3R)Payne. H, expected heterozygosity.

Data analysis:

Expected heterozygosity was calculated for each marker using the GDA software package (Lewis and Zaykin 2001). All other analyses were performed using available functions or custom scripts written in the R statistical language (http://www.R-project.org).

Associations between alleles at molecular markers and traits were tested using the approach followed by Macdonald et al. (2006). Briefly, this method involved carrying out single-marker tests of association using ANOVA models. These models assume that the effects of each allele tested are independent of alleles at other markers, i.e., the effects are additive over loci. An important difference between the ANOVA models used here and those used by Macdonald et al. (2006) was that we included inversion karyotype as a factor in our analyses to determine whether each allele had any explanatory power beyond that attributable to LD with In(3R)Payne.

For each trait in the parental generation, a factorial genotype-by-sex-by-inversion ANOVA model was applied. The model is Y_ijkl = μ + G_i + S_j + I_k + (G × S)_ij + (G × I)_ik + (S × I)_jk + (G × S × I)_ijk + ε_ijkl, where Y_ijkl is the wing size or development time of the lth individual, μ is the grand mean, G_j is the fixed effect of genotype (–1, 0, +1), S_i is the fixed effect of sex, I_j is the fixed effect of the inversion karyotype (–1, 0, +1), (G × S)_ij is the genotype-by-sex interaction, (G × I)_ik is the genotype-by-inversion interaction, (S × I)_jk is the sex-by-inversion interaction, (G × S × I)_ijk is the genotype-by-sex-by-inversion interaction, and ε_ijkl is the error. This model corresponds to a multiple regression with the phenotypic data as the dependent variable and the number of marker alleles present in each individual, sex, the number of inverted chromosomes present in each individual, and their interactions as the explanatory variables. It should be noted that the effect of genotype in the model is effectively the effect of an allele against all others at the marker locus and the number of models used per marker was equal to the number of common alleles (frequency greater than 0.1).

The same model was used for analyzing each trait in the offspring generation, with the exception that the effect of sex and interactions involving sex were left out of the model, because only females were measured in this generation. The fixed effect of genotype in the offspring data (0, 0.25, 0.5, 0.75, 1) was based on the allele frequency in each family calculated from parental genotypes assuming equal viability of genotypes and Mendelian segregation. Following Macdonald et al. (2006), type II sum of squares were used for the factorial ANOVA models and were applied using the “car” R package (http://cran-r-project.org). For each single-marker test, we ensured that each genotypic class was represented by at least 10 individuals. In some cases, this was achieved by comparing only the two most common genotypic classes.

To control for multiple testing and to ensure that the type I error rate over all tests was ≤0.05, we performed a permutation test (Churchill and Doerge 1994) to each of the ANOVA models applied to the data. For each model, this was achieved by generating 1000 permuted data sets where the phenotypic data were randomly shuffled with respect to the multilocus genotype of the individuals. For the parental data, phenotypes were shuffled within each sex and each inversion karyotypic class. For the offspring data, where only one sex was analyzed, phenotypes were shuffled within each inversion karyotypic class. After testing all marker alleles, the smallest P-value was extracted from each permutated data set. The P-value of the real nonpermuted data was considered significant at P < 0.05 if it was lower than the 5% percentile of the distribution of 1000 permuted values.

To test the effect of interactions among significantly associated marker alleles on the phenotypic data, a factorial genotype A-by-genotype B-by-sex-by-inversion ANOVA model was applied. This model was identical to the factorial genotype-by-sex-by-inversion ANOVA model outlined above except that the effect of genotype B and its interactions were added to the model. The same ANOVA model was used for the offspring data except that the effect of sex and interactions involving sex were left out of the model. Lastly, to test whether the effects of significantly associated alleles were independent of each other, a stepwise model fitting procedure was used. With this procedure, significantly associated alleles were individually added to an ANOVA model that included the best fitting (most significantly associated allele) to see if there was support for adding extra alleles to the model.

LD between each significantly associated marker allele and In(3R)Payne was measured using the scaled estimate of LD, D′, and the correlation coefficient, r. The significance of marker independence was tested using a chi-square test. Estimates of D′, r, and the chi-square tests were all calculated out using the “genetics” R package (http://cran-r-project.org). This package gets around the problem of distinguishing between the two types of double heterozygotes in the genotype data by calculating gametic frequencies using maximum likelihood and using these estimates in all computations.

RESULTS

Marker variation:

Markers differed in variability; expected heterozygosities ranged from 0.20 to 0.83 (Table 1) and the number of alleles for microsatellite loci ranged from 3 to 18. For each marker, the number of alleles tested for an association with a trait ranged from one to six.

Heritabilities:

Parent offspring regression indicated heritable variation for wing size. The regression of dam onto offspring was significant (F_[1,366] = 13.06, P < 0.001) with a regression coefficient of 0.102 ± 0.028, while the equivalent regression for the sires was also significant (F_[1,355] = 25.34, P < 0.001) with a coefficient of 0.161 ± 0.032. Taking into account the different variances in males and females (Falconer and Mackay 1996), these regressions suggest heritabilities for wing size in the range of 20–25%. This estimate is within the range of heritabilities reported for wing traits in Drosophila (see Hoffmann 2000) but is lower than the median or mean heritability reported for wing length in D. melanogaster (0.36 – 0.42; Houle 1992; Hoffmann 2000). For development time, the regressions of dam onto offspring females and dam onto offspring males were significant (females: F_[1,425] = 15.48, P < 0.001; males: F_[1,423] = 20.87, P < 0.001) with regression coefficients of 0.110 ± 0.028 and 0.134 ± 0.029, respectively. However, the regressions of sires onto female and male offspring were not significant (P > 0.05 in both cases), suggesting that the heritable variation for development time was due largely to maternal effects.

Correlations between traits and In(3RP)Payne:

Table 2 shows the correlations between traits and the frequency of In(3R)Payne in each sex/generation measured. Wing size was negatively correlated with development time in the female parents, but there was no significant correlation between these traits in the male parents or (female) offspring generation. As expected, wing size was negatively correlated with the frequency of In(3R)Payne in both male and female parents and the offspring generation. However, development time was not significantly correlated with In(3R)Payne frequency in any of the sex/generation combinations examined.

TABLE 2.

Correlations between traits and between traits and In(3R)Payne

Trait 1	Trait 2	N	rs	P
Parental generation: females
Wing size	Development time	423	−0.178	0.0002
Wing size	In(3R)Payne	423	−0.220	4.92 × 10−6
Development time	In(3R)Payne	423	0.011	0.8261
Parental generation: males
Wing size	Development time	413	−0.045	0.3594
Wing size	In(3R)Payne	413	−0.174	0.0004
Development time	In(3R)Payne	413	0.025	0.6162
Offspring generation: females
Wing size	Development time	371	0.056	0.2788
Wing size	In(3R)Payne	325	−0.230	2.94 × 10−5
Development time	In(3R)Payne	361	−0.067	0.2061

N, sample size used in the correlation tests; r_s, Spearman's rank correlation; P, corresponding P-value.

Marker-trait associations:

Alleles at three markers had a significant genotype (additive) effect on wing size in the parental data (Figure 1). These markers were located in two distinct regions within In(3R)Payne: at cytological positions 89E (allele 274 at marker DROABDB) and 95C (allele 193 at marker DMU1951 and allele 286 at marker DMTF125). The effects of each of these alleles on wing size were variable. Allele 274 at marker DROABDB and allele 286 at marker DMTF125 had a negative effect on wing size, whereas allele 193 at marker DMU1951 had a positive effect on wing size.

Figure 1.—

Single-marker tests for association between wing size and marker alleles in the region of In(3R)Payne in D. melanogaster. (A–D) Each point represents a P-value (–log₁₀ transformed) for the genotype term (A), the genotype-by-inversion term (B), the genotype-by-sex term (C), and the genotype-by-sex-by-inversion term (D) of a single-marker ANOVA test on the parental generation. (E and F) Each point is the P-value for the genotype term (E) and the genotype-by-inversion term (F) from a single-marker ANOVA test on the offspring generation. The dashed line represents the experiment-wise significance threshold calculated using a permutation test developed by Churchill and Doerge (1994). The crosses on the x-axis depict the locations of the In(3R)Payne breakpoints.

Stepwise model fitting revealed that a significant improvement of fit could be gained by adding one of the significantly associated alleles (allele 193 at marker DMU1951) to a factorial genotype-by-sex-by-inversion ANOVA model that included the allele with the most significant effect on wing size (allele 274 at marker DROABDB) as the genotype term (F_736,753 = 13.30, P < 0.001). By contrast, the addition of the other significantly associated allele (allele 286 at marker DMTF125) to the model did not result in a significant improvement of fit (F_736,753 = 0.40, P = 0.840). This suggests that two of the associated alleles (from a different region within the inversion) had effects on wing size that are independent of the other.

Only one allele had a significant genotype effect on wing size in the offspring data (Table 3). The allele (allele 274 at marker DROABDB) was one of the three significantly associated alleles identified in the parental generation. It had a negative effect on wing size, the same direction as the effect in the parental generation.

TABLE 3.

Significant single-marker associations

				Genotype term			Genotype-by-inversion term
Marker (allele)	Location	Trait	Na	Fa	Pa	a (SE)b	Fa	Pa	a × inv (SE)c
Parents
DROABDB (274)	89E4	Wing size	803	22.35	2.69 × 10−6	–9.35 (2.41)	2.39	0.1222	−2.68 (1.78)
DROABDB (282)	89E4	Wing size	803	9.93	0.0017	5.46 (1.53)	11.42	0.0008	5.46 (1.61)
DMU1951 (193)	95C4	Wing size	798	22.94	1.99 × 10−6	8.31 (1.73)	0.14	0.7113	0.76 (2.04)
DMTF125 (286)	95C9	Wing size	810	16.32	5.87 × 10−5	−7.46 (2.32)	1.62	0.2037	−2.21 (1.79)
DMTF125 (301)	95C9	Wing size	810	3.47	0.0628	4.31 (1.66)	16.44	5.52 × 10−5	7.42 (1.83)
AC006414 (195)	89A1	Development time	804	2.21	0.1377	−8.26 (2.58)	15.73	7.98 × 10−5	12.33 (3.16)
Offspring
DROABDB (274)	89E4	Wing size	302	20.94	6.96 × 10−6	–33.49 (9.10)	0.78	0.3774	8.49 (9.61)
DROLMALK (173)	98A14	Wing size	302	1.20	0.2750	−27.26 (7.70)	11.48	0.0008	39.96 (11.80)

^aThe sample size (N) used in the ANOVA and the resulting F-statistic (F) and P-value (P). Values underlined are the significant terms. Statistical significance was determined using the permutation procedure developed by Churchill and Doerge (1994).

^bThe genotype effect of an allele (a) and its SE.

^cThe genotype-by-inversion effect of an allele (a × inv) and its SE.

No significant genotype-by-sex or genotype-by-sex-by-inversion interaction effects on wing size were evident in any of the generations measured (Figure 1). However, significant genotype-by-inversion effects on size were evident at two alleles in the parents (allele 282 at marker DROABDB and allele 301 at marker DMTF125) and one allele in the offspring generation (allele 173 at marker DROLMALK). These markers are situated at cytological positions 89E, 95C, and 98A, respectively. All alleles with a significant genotype-by-inversion effect had a nonsignificant positive genotype (additive) effect on wing size and a positive genotype-by-inversion effect (Table 3).

No alleles had a significant genotype (additive) effect on development time in the parental or offspring generation (Figure 2). There were also no significant genotype-by-sex or genotype-by-sex-by-inversion interaction effects on development time in any of the generations measured, although one allele in the parent data did have a significant genotype-by-inversion effect (Figure 2). This allele was at a marker (AC007647) located just outside the proximal breakpoint of In(3R)Payne at 89E. It had a nonsignificant negative genotype (additive) effect on development time and the genotype-by-inversion effect was positive (Table 3).

Figure 2.—

Single-marker tests for association between development time and marker alleles in the region of In(3R)Payne in D. melanogaster. (A–D) Each point represents a P-value (–log₁₀ transformed) for the genotype term (A), the genotype-by-inversion term (B), the genotype-by-sex term (C), and the genotype-by-sex-by-inversion term (D) of a single-marker ANOVA test on the parental generation. (E and F) Each point is the P-value for the genotype term (E) and the genotype-by-inversion term (F) from a single-marker ANOVA test on the offspring generation. The dashed line represents the experiment-wise significance threshold calculated using a permutation test developed by Churchill and Doerge (1994). The crosses on the x-axis depict the locations of the In(3R)Payne breakpoints.

Interaction effects among significantly associated alleles:

Genotype-by-genotype interaction effects were tested in only the parental data and only for wing size, because this was the only generation/trait combination where more than one significantly associated allele was found. No significant genotype-by-genotype interaction effects were found among any of the significantly associated alleles in the parental generation (Table 4). It should be noted, however, that recombinant genotypes among these markers were relatively scarce, with pairwise estimates of D′ among these markers ranging from 0.549 to 0.990. The power to detect genotype-by-genotype interaction effects was therefore likely to be low.

TABLE 4.

Two way interaction effects on wing size between significantly associated alleles

Allele 1	Allele 2	Na	Fa	Pa
DROABDB_274	DMU1951_193	765	0.01	0.922
DROABDB_274	DMTF125_286	782	0.83	0.362
DMU1951_193	DMTF125_286	772	0.01	0.931

^aThe sample size (N) used in the ANOVA, and the resulting F-statistic (F) and P-value (P).

Linkage disequlibrium between significantly associated alleles and In(3R)Payne:

All alleles with significant genotype (additive) effects on wing size were in strong LD with In(3R)Payne (Table 5). The associations between the alleles and In(3R)Payne were such that they were in the opposite direction of the effects on wing size. Alleles with a negative effect on wing size (allele 274 at marker DROABDB and allele 286 at marker DMTF125) were positively associated with In(3R)Payne and the allele with a positive effect on wing size (allele 193 at marker DMU1951) was negatively associated with In(3R)Payne. The direction of effects of these alleles, and their association with In(3R)Payne, is consistent with the correlation between In(3R)Payne and wing size.

TABLE 5.

Pairwise LD between significantly associated alleles and In(3R)Payne

Marker (allele)	Location	N	D′	r	χ2
DROABDB (274)	89E4	803	0.908	0.834	1116.5***
DROABDB (282)a	89E4	803	−0.664	−0.541	470.7***
DMU1951 (193)	95C4	798	−0.314	−0.165	42.7***
DMTF125 (286)	95C9	810	0.911	0.812	1067.0***
DMTF125 (301)a	95C9	810	−0.703	−0.494	394.8***
DROLMALK (173)a	98A14	808	0.104	0.053	4.4*

D′ is the scaled estimate of LD, r is the correlation coefficient, and χ² is the chi square statistic for LD.

* Significant at P < 0.05; *** significant at P < 0.001. N, sample size used in tests for LD.

^aSignificant association with wing size due to a genotype-by-inversion (a × inv) effect.

Alleles with genotype-by-inversion interaction effects on wing size tended to be negatively associated with In(3R)Payne (allele 282 at marker DROABDB and allele 301 at marker DMTF125) or were not significantly associated after correction for multiple comparisons (e.g., allele 173 at marker DROLMALK).

DISCUSSION

This study shows that association mapping can be used to map regions within inversions controlling variation in quantitative traits. In the parental generation, we found three alleles from two separate regions within In(3R)Payne with a significant additive effect on wing size after the background effect of the inversion was taken into account. Further, we were able to show that two of the significantly associated alleles, one from each of the two regions, had effects on size that were independent of the other. None of the alleles located outside In(3R)Payne were significantly associated with wing size. The two associated genomic regions were located near the proximal breakpoint at 89E and toward the distal side of the inversion at 95C. The distances between the nearest nonassociated markers either side of the two regions were 883 and 1029 kb, respectively. These distances represent ∼0.49 and 0.57% of the total genome and each contain between 181 and 219 genes according to FlyBase (Grumbling et al. 2006).

Only one allele with a significant additive effect on wing size was found in the offspring generation. The allele (allele 274 at marker DROABDB) was located at 89E and was one of the three alleles found with a significant effect on wing size in the parental generation. The lower number of significantly associated alleles in the offspring generation may reflect lower statistical power in the offspring analyses and is consistent with our expectation that associations for offspring traits would be weaker than those for the parents given the relatively low number of offspring measured per family.

The significantly associated alleles that we found had both positive and negative effects on wing size. In addition, the direction of the effect on wing size tended to covary with the direction of LD between the allele and In(3R)Payne. For example, allele 274 at marker DROABDB and allele 286 at marker DMTF125 had negative effects on wing size and were positively associated with In(3R)Payne, while allele 193 at marker DMU1951 had a positive effect on wing size and was negatively associated with In(3R)Payne. These associations are consistent with the strong negative relationship between wing size and In(3R)Payne observed here and in previous studies (Weeks et al. 2002; Rako et al. 2006) and can be inferred from the opposite latitudinal patterns seen in Australia (Knibb et al. 1981; James et al. 1995; Anderson et al. 2005) and in North America (Mettler et al. 1977; Knibb 1982; Coyne and Beecham 1987). Genes located near these markers are therefore likely to be at least partly responsible for the link between In(3R)Payne and body size.

We found no evidence of genotype-by-genotype interactions among any of the alleles with significant additive effects on wing size. This result suggests there is no or very little epitasis among genes controlling wing size within In(3R)Payne and is consistent with the Kirkpatrick and Barton (2006) explanation for the selective advantage of inversions. However, an important caveat with our results is that genotype-by-genotype interactions were tested only among alleles with significant additive effects on wing size. It is possible that an alternative strategy where all pairwise comparisons were evaluated might have uncovered significant genotype-by-genotype interactions. In addition, the association between wing area and fitness itself may not be linear, leaving open the possibility of coadaptation in the absence of any epistatic interactions for wing area.

Despite there being no evidence of genotype-by-genotype interactions, several genotype-by-inversion effects on wing size were found. Epistatic interactions between QTL have been reported for several complex traits in D. melanogaster (see Mackay 2001), so it is unclear at this stage whether the interactions between marker alleles and In(3R)Payne we found indicate anything special about inversions or wing size.

Because of the generally high level of LD between the markers associated with body size, the tests for genotype-by-genotype interactions we carried out were likely to be of low statistical power. They are therefore unlikely to provide useful tests as to whether or not gene interactions are important for inversions to become established in populations and spread. A better way to test for genotype-by-genotype interactions may be to isolate lines with different combinations of alleles with significant additive effects and test whether their affects on size or fitness are nonadditive. Ultimately, the genes controlling variation in wing size should be identified, which will allow direct tests of the interaction effects that they have with other genes located within the same inversion (see Hoffmann et al. 2004).

Unlike wing size, none of the alleles tested in this study were significantly associated with development time. This might reflect measurement error, but the significant parent-offspring regression for development time and the correlation between wing size and development time in females suggests otherwise. Therefore, the lack of correspondence between additive effects of individual alleles on wing size and development time suggests that different genes are controlling variation in these traits. Latitudinal clines in wing size are therefore likely to have arisen independently of development time. Our result is also consistent with recent studies that suggest there is no association between development time and In(3R)Payne (Weeks et al. 2002; Rako et al. 2006).

Our study has shown that it is possible to localize regions within inversions controlling variation in complex traits using association mapping. Indeed, for wing size, we have been able to identify specific regions in which to start fine-scale genetic mapping. However, we were unable, with any confidence, to exclude epistatic interactions between genes within In(3R)Payne as an important component of the control of wing size. Our study provides some of the first evidence that inversions might harbor multiple sets of locally adapted alleles, which is an assumption common to several theoretical models explaining why inversions become established in populations and spread.