One of the earliest unexpected results to emerge from early long-term selection experiments on

*Drosophila* abdominal bristle number was that phenotypic variance in the high and low selection lines dramatically increased relative to the unselected controls, although response to selection for mean bristle number reached a limit (

Clayton & Robertson 1957). A similar phenomenon was observed in a spontaneous mutation accumulation line selected for low abdominal bristle number (

Mackay *et al*. 1994).

Hill & Zhang (2004) have shown that these results could be explained if the environmental variance among loci that affect the trait is not constant, as usually assumed, but is rather heterogenous. In this case, strong directional selection (i.e. a low proportion selected and high selection intensity) can readily cause substantial increases in environmental (and hence total phenotypic) variance. This is because genotypes with higher (or lower) means have a higher probability of selection if they also confer high variability.

What is the magnitude of genetic variance of residual environmental variance, i.e. genetic variance in environmental plasticity? An analysis of

Brotherstone & Hill (1986), which documented variation among herds of dairy cattle in the within-herd phenotypic variance of milk yield, hints that this could be large.

Sorensen & Waagepetersen (2003) also detected variation among genotypes in residual variation for litter size in pigs. Here, we show that there is substantial naturally segregating variance for environmental plasticity of abdominal and sternopleural bristle number.

(a) Variation in bristle number

We derived isofemale lines from the Raleigh, NC population, and used these to construct over 300 chromosome 2 and 3 substitution lines. Each of these lines contained an independent isogenic second or third chromosome, in the background of the homozygous Samarkand (

Lyman *et al*. 1996) inbred strain. We scored bristle number for five males and females in each of two replicate vials for each of these lines, and partitioned variance in bristle number using the two-way mixed model analysis of variance (ANOVA) model

, where

*μ* is the overall mean,

*S* and

*L* denote the cross-classified main effects of sex (fixed) and line (random), respectively,

*R* is replicate vial (random) and

*E* is the environmental variance within vials. As expected, there was considerable segregating variation for both traits on both autosomes (). The effect of line was significant at

*p*<0.0001 in all four analyses, and the effect of the line by sex interaction was significant at

*p*<0.0001 in all analyses except for sternopleural bristles on chromosome 2, for which the line by sex interaction was less pronounced (

*p*=0.02; data not shown).

We estimated the variance components (

*σ*^{2}) for all random effects in the models, and computed the proportion of the total variance attributable to the total genotypic variance among lines as

; where

*σ*_{L}^{2},

and

*σ*_{T}^{2} are the among-line, sex by line and total variance components, respectively (

Falconer & Mackay 1996). For sternopleural bristle number, these estimates were 0.34 for chromosome 2 and 0.53 for chromosome 3. For abdominal bristle number, the estimates were 0.45 for chromosome 2 and 0.41 for chromosome 3. We did not compute the heritabilities of bristle number, since this requires the assumption of strict additivity for completely inbred lines (

Falconer & Mackay 1996), which we will show is not true for these data.

We also crossed each of the isogenic chromosome substitution lines to the inbred Samarkand strain, and scored bristle numbers on the heterozygous progeny, using the same experimental design described above. The regressions (

*b*±s.e.) of mean heterozygous bristle score on mean homozygous bristle score for chromosomes 2 and 3, respectively, were

*b*=0.35±0.027 and

*b*=0.35±0.021 for sternopleural bristle number and

*b*=0.30±0.021 and

*b*=0.22±0.023 for abdominal bristle number. All estimates were significantly different from 0 and 0.5 (

*p*<0.0001). We estimated the average degree of dominance,

*k*, from the regressions as

*k*=2(

*b*−0.5;

Mackay 1987).

*k* thus ranges from

*k*=−1 (homozygous chromosomes recessive) through

*k*=0 (additivity) to

*k*=1 (homozygous chromosomes dominant). The effects QTLs that affect bristle number in this population are, on average, partially recessive. Estimates of

*k* for sternopleural bristle number were

*k*=−0.30 (both chromosomes). Estimates of

*k* for abdominal bristle number were

*k*=−0.4 (chromosome 2) and

*k*=−0.56 (chromosome 3).

(b) Genetic variance of environmental variance

We computed the environmental coefficient of variation (

, where

*σ*_{E} is the within-vial environmental standard deviation and

is the vial mean bristle score), separately for each sex and replicate vial, for each of the chromosome substitution lines. To assess whether or not there was genetic variation between the lines for environmental plasticity, we partitioned the variance in CV

_{E} using the ANOVA model

, where

*μ*,

*S* and

*L* are as defined above, and

*E* is the variance in CV

_{E} between replicate vials. The striking results are that there is highly significant genetic variance in residual variance for both bristle traits, on both chromosomes ( and ; ); i.e. there is a genetic component for sensitivity to environmental variation. The residual variance of abdominal bristle number for chromosome 2 is highly sex-specific; females are far more variable than males. The estimates of the proportion of the total variance in CV

_{E} attributable to the total genotypic variance in CV

_{E} among lines for sternopleural bristle number were 0.10 for chromosome 2 and 0.16 for chromosome 3. For abdominal bristle number, the estimates were 0.60 for chromosome 2 and 0.48 for chromosome 3.

| **Table 1**Analyses of genetic variance of environmental plasticity for homozygous chromosome 2 substitution lines. |

| **Table 2**Analyses of genetic variance of environmental plasticity for homozygous chromosome 3 substitution lines. |

We performed the same analyses on heterozygous progeny from crosses of the isogenic chromosome substitution lines to Samarkand. The results are given in and . The first observation to note is that the total residual variance among the heterozygous chromosomes is in all cases less than that of the homozygous chromosomes, but the reduction in variance is far more pronounced for abdominal than for sternopleural bristle number. The total variance in environmental plasticity of abdominal bristle number in second and third chromosome heterozygotes was only 17 and 24% that of the second and third chromosome homozygotes, respectively. For sternopleural bristle number, the reduction of total residual variance in heterozygous second and third chromosomes was 59 and 72% that of the respective homozygous chromosomes. This observation echoes earlier reports that homozygous lines are more sensitive to environmental variation than heterozygous lines, for abdominal bristle number (

Rasmuson 1952) and for other quantitative traits (

Reeve & Robertson 1953;

Robertson & Reeve 1955).

| **Table 3**Analyses of genetic variance of environmental plasticity for heterozygous chromosome 2 substitution lines. |

| **Table 4**Analyses of genetic variance of environmental plasticity for heterozygous chromosome 3 substitution lines. |

Inspection of the genotypic component of variance of environmental sensitivity for the heterozygous chromosomes reveals that genetic effects on environmental plasticity are largely recessive. For example, the among-line genotypic variance

in sensitivity for abdominal bristle number in second and third chromosome heterozygotes is 6.3 and 8.2% for that of the second and third chromosome homozygotes, respectively. The large sex by line effect for second chromosome homozygotes is recessive and disappears in chromosome 2 heterozygotes.

We quantified the average degree of dominance for CV_{E} from the regressions of heterozygous on homozygous metrics, as described above. The regressions (*b*±s.e.) of mean heterozygous CV_{E} on mean homozygous CV_{E} for sternopleural bristle number were *b*=0.04±0.04 and *b*=0.04±0.05 for chromosomes 2 and 3, respectively. Since these estimates are not significantly different from 0, the corresponding estimates of *k* are not significantly different from −1, which indicates completely recessive effects. The respective chromosome 2 and 3 regressions of mean heterozygous CV_{E} on mean homozygous CV_{E} for abdominal bristle number were *b*=0.12±0.01 and *b*=0.07±0.02 for chromosomes 2 and 3, respectively. These estimates are significantly different from both 0 and 0.5, and yield estimates of *k*=−0.76 (chromosome 2) and *k*=−0.86 (chromosome 3); i.e. largely recessive.

(c) Abnormal abdomen?

The correlation (*r*) between mean sternopleural bristle number and the average CV_{E} for sternopleural bristle number was not significantly different from zero for either the chromosome 2 (*r*=−0.04, *p*=0.45) or chromosome 3 (*r*=0.10, *p*=0.08) homozygous substitution lines (*e*,*f*). However, there were strong negative correlations between the mean and CV_{E} for abdominal bristle number of *r*=−0.84 (*p*<0.0001) and *r*=−0.76 (*p*<0.0001) for the homozygous chromosome 2 and chromosome 3 substitution lines, respectively (*e*,*f*).

The strong negative association between CV

_{E} and mean abdominal bristle number is partly attributable to 14 chromosome 2 lines (4.3%) and 15 chromosome 3 lines (4.6%) that exhibit striking developmental abnormalities. In these lines, the repeatability (

Falconer & Mackay 1996) of abdominal bristle number between adjacent abdominal sternites within individual flies is very low (data not shown). This indicates dysfunction in developmental homeostasis. Further analysis is necessary to determine the extent to which the observed environmental variation between individuals is associated with within-individual environmental variation in general. However, we note that various disruptions of the sternites and tergites are associated with this phenotype, including hemireduction of one or more sternites and tergites, one-sided lateral reductions of tergites and sternites, disrupted pigmentation, low viability and slow development time. These phenotypes are strikingly similar to the

*abnormal abdomen* syndrome described by

Sobels (1952) over 50 years ago, and which we have repeatedly observed to segregate in the Raleigh population. We now have the tools available to map the QTLs responsible for this odd phenotype, and elucidate the mechanisms responsible for its persistence at appreciable frequencies in natural populations.

(d) A candidate gene

The

*abnormal abdomen* phenotype resembles adult visible phenotypes associated with mutations that affect catecholamine biosynthesis, which include incomplete formation of abdominal tergites and loss of bristles (

Stathakis *et al*. 1999). We had available data on 36 molecular polymorphisms at

*Dopa decarboxylase* (

*Ddc*) for 173 of the second chromosome substitution lines (

DeLuca *et al*. 2003).

*Ddc* encodes the enzyme that catalyses the final step in the synthesis of dopamine, a major

*Drosophila* catecholamine and neurotransmitter, as well as serotonin.

*Ddc* is required for the production of dopamine and serotonin in the central nervous system (

Livingstone & Tempel 1983), and is essential in the hypoderm for the sclerotization and melanization of the cuticle (

Lunan & Mitchell 1969).

We assessed associations of each of the molecular polymorphisms at

*Ddc* with variation in abdominal bristle number, and CV

_{E} for abdominal bristle number, using the ANOVA model

, where

*μ* and

*S* are as defined above,

*M* is marker genotype and

*E* is the variance between line means within marker genotypes. Two markers were associated with variation in sternopleural bristle number at

*p*<0.05 (

*a*), which is close to the 1.7 associations at this significance level expected by chance given 34 tests (two of the 36 polymorphic sites were in complete LD with neighbouring sites). Perhaps surprisingly, however, one of the markers, T644G, was associated with CV

_{E} for abdominal bristle number at

*p*=0.0004, which is lower than the conservative Bonferroni-corrected significance threshold of

*p*=0.0015 ( and

*a*). In addition, T644G is in strong LD with T440G (

*χ*_{1}^{2}=48.42,

*p*<0.0001) and with a 12

bp insertion/deletion polymorphism (12pbin,

*χ*_{1}^{2}=59.40,

*p*<0.0001). These markers are also strongly associated with variation in CV

_{E} for abdominal bristle number (,

*a*).

| **Table 5**Analysis of variance of molecular marker–abdominal bristle number CV_{E} associations. |

The difference in mean abdominal bristle number CV_{E} between homozygous genotypes for the significant markers ranged from 4.14 to 5.18, or 0.33 to 0.47 genetic standard deviation units (). We estimated the genetic variance attributable to each marker by treating the marker term as a random effect in the ANOVA. The significant markers individually accounted for 6.33–9.99% of the total genotypic variance in abdominal bristle number CV_{E}. Since the three markers are in strong global LD (*χ*_{4}^{2}=249.36, *p*<0.0001; *b*), we assessed the contribution of the seven observed haplotypes to abdominal bristle number CV_{E}. There was significant variation in mean abdominal bristle number CV_{E} among the haplotypes (*F*_{6,658}=2.74, *p*=0.0122; *c*), which accounted for 5.97% of the total genotypic variance in abdominal bristle number CV_{E} attributable to this sample of second chromosomes. The contribution of the haplotypes to the total genetic variance is somewhat less than the individual markers because the effects of the markers are conditional on the genotype of the other markers. For example, the insertion/deletion polymorphism has no effect in the background of T440, T644; and the 440 polymorphism has no effect in the background of 12bpin, G644 (*c*). That is, there is apparently diminishing epistasis between the markers associated with this trait.

| **Table 6**Effects of molecular polymorphisms at *Ddc* on abdominal bristle number CV_{E}. |

All three markers associated with variation in abdominal bristle number CV

_{E} are in the promoter region. Normal expression of

*Ddc* in the hypoderm requires

*cis*-acting elements located in the promoter region 208

bp 5′ of the transcription start site, but not beyond this region (

Lundell & Hirsh 1994). The T644G polymorphism, which has the strongest individual association with abdominal bristle number CV

_{E}, is in the region required for hypodermal expression, and is plausibly associated causally with variation in this trait. The usual caveats regarding LD mapping pertain to this observation: the associations could be due to LD with true causal polymorphisms that were not genotyped, and the observation needs to be replicated in an independent sample. Nonetheless, the hypothesis that the

*abnormal abdomen* phenotype is associated with catecholamine metabolism is testable by measuring dopamine levels in the affected strains, and performing similar tests for association of the phenotype with molecular polymorphisms at other key genes in this pathway.