### Extraction of O chromosomes and fly handling

A large number of *D. subobscura* isochromosomal lines for the O chromosome in an otherwise homogeneous genetic background were derived from an outbred stock collected at Puerto Montt (Chile; 41° 28' S) in November 1999 as previously indicated [38]. Briefly, wild-type males were individually crossed to three or four virgin females from the highly homogeneous *ch-cu* marker strain, which is homozygous for the morphological recessive markers on the O chromosome *cherry* eyes (*ch*) and *curled* wings (*cu*) and fixed for the gene arrangement O_{3+4}. A single
/O_{+ cu + ch
}male from the offspring was backcrossed to *ch-cu* females, and its arrangement on the wild-type chromosome was identified after four generations of backcrosses. Followed by at least another backcross to *ch-cu* females, a single male from each line carrying the wild chromosome was crossed to two virgin females from the *Va/Ba* balanced marker stock. This strain was derived from the *ch-cu* stock and carries the dominant lethal genes *Varicose* (*Va*) and *Bare* (*Ba*) on the O chromosome. The isochromosomal lines were established from the final crosses ♀♀ O_{
Va ch + cu
}/
× ♂♂ O_{
Va ch + cu
}/
. All lines used here had a quasi-normal viability according to the recorded proportions of wild-type flies raised in the final crosses to obtain the isochromosomal lines [38]. The lines were kept at 18°C (12:12 light/dark cycle) in 130-mL bottles with low adult density to standardize the rearing conditions before egg collections.

As previously indicated the experimental flies were obtained from 54 crosses. Reciprocal crosses were made for all outbred combinations by mating one-week virgin females and males. After three days the males were discarded and equal numbers of females from each reciprocal cross were placed together in a plastic chamber with a spoon containing non-nutritive agar with a generous smear of live yeast for egg collections. To standardize the experimental conditions, eggs from the inbred (isogenic) crosses were also obtained in a similar way; namely, after mating the flies in bottles and transferring the females to plastic chambers. Eggs were placed in six 2 × 8 cm vials with 6 mL of food (26 eggs/vial); three vials were kept at 18°C (optimal temperature) and the other three at 23°C (sub-optimal temperature). Within each experimental temperature the vials were randomly placed on the same incubator shelf. As a result, the total experiment consisted of 324 vials (162 vials at each experimental temperature), and all eggs were sampled on the same day. Emerging flies (not less than 2 or 3 days old) were stored in Eppendorf tubes with a 3:1 mixture of alcohol and glycerol at 4°C before wing measurements.

All fly handling was done at room temperature using CO_{2} anesthesia on flies not less than 6 h after eclosion.

### Wing measurements

Two randomly sampled females and males emerged from each vial were used for morphometric analyses. Both wings were removed from each fly and fixed in DPX under coverslips on microscope slides. Bitmap images were captured with a video camera (Sony CCD-Iris, Tokyo, Japan) connected to a PC computer with MGI VideoWave software and mounted on a compound microscope (Zeiss Axioskop, Jena, Germany), using a 2.5 × objective. Calibration of the optical system was checked at each session. The images were stored on a Dell Workstation PWS350. To quantify and minimize measurement error all wings were digitized two times at different sessions as follows: images of both the left and right wings were captured during a given session and after an entire round on all individuals the same process was repeated again. A similar procedure was also used to record the *x* and *y* coordinates of 13 morphological landmarks (i.e., labeled geometric points located at the intersections of wing veins or at sites where veins reach the wing margin; Fig. 12) by using the Scion Image for Windows software [64]. Therefore, the process we used guaranteed that the observer was blind with respect to the results from previous measurements.

### Analysis of wing size and shape

Geometric morphometrics precisely separates morphological variation (i.e., variation in form) into size and shape components [21, 22]. Size is a one-dimensional trait and the measure most widely used in geometric morphometrics is centroid size (CS), computed here in a normalized form as the square root of the sum of squared Euclidian distances between each landmark to the centroid (center of gravity) of all landmarks divided by the square root of the number of landmarks. Individual size is therefore represented by four scalars, one for each side and session.

The shape of an original configuration of landmarks is the geometrical information that is invariant to uniform scaling (variation in size), translation (differences in position), and rotation (differences in orientation). In contrast to size, shape is an inherently multidimensional space and we used Procrustes superimposition to characterize shape variation. This method allows comparing configurations of landmarks by optimally superimposing (according to a least-squares criterion) homologous landmarks in two or more specimens to achieve an overall best fit [65].Because the data set included both left and right wings (i.e., we are dealing with "matching symmetry" [66, 67]) our analyses also removed differences due to reflection by changing the sign of the *x* coordinate of every landmark for configurations from the right side. The reflection, scaling, and superposition steps were performed for all wings within each cross and temperature simultaneously, which allows contrasting wing shapes between different lines or crosses. The final iteration to minimize the sum of the squared distances between the landmarks of all wings in the sample was done without additional scaling and, consequently, we performed a partial Procrustes fit according to Dryden and Mardia [22]. Given the small amounts of shape variation in this analysis rescaling the coordinates of each configuration by the scaling option 1/cos(*ρ*) [65] would have negligible effects on the results.

The landmark coordinates after Procrustes superimposition are amenable to standard multivariate analyses. However, it is important to remember that the removal of size, position (in two dimensions), and orientation reduces the dimensional space to 2 *p* – 4, where *p* is the number of landmarks [22]. Thus, for the present study of 13 landmarks, with 2 coordinates each, the shape dimension is 22. Sums of squares and cross-products (SSCP) matrices are therefore not full-ranked, and the degrees of freedom need to be adjusted. There are three alternative ways of avoiding these difficulties [22, 67]: (i) to omit, after Procrustes superimposition of the complete configurations, the coordinates of any two landmarks; (ii) to retain 22 PC scores from the covariance matrix of the data set; (iii) to slightly modify the multivariate statistics (see below) by using the Moore-Penrose generalized inverse of the SSCP matrices so they can tolerate singular matrices, and compute the product of nonzero eigenvalues instead of the determinant of SSCP matrices. We have used here the second scheme.

### Experimental design and asymmetry analysis

Quantitative genetic studies of directional and fluctuating asymmetry obviously require measures from individuals that can be grouped into families or independent lines. Our final data set was a fully balanced design, comprising 54 crosses × 3 vials per cross × 2 females per vial × 2 males per vial × 2 sides per fly × 2 measurements per wing × 2 temperatures = 5,184 wing landmark configurations in total. Within each sex and temperature, least-squares (ANOVA) estimates of variance components (i.e. CS) can be easily obtained from the linear model:

*Y*
_{
ijkl
}= *μ* + *κ*
_{
i
}+ *l*
_{
j (i)}+ *ν*
_{
k (ji)}+ *ε*
_{
l (kji)},

where *μ* is the overall grand mean, *κ*
_{
i
}is the effect of the *i* th karyotype, *l*
_{
j (i)}is the random effect of the *j* th cross within karyotype *i*, *ν*
_{
k (ji)}is the random effect of the *k* th vial within cross *j* and karyotype *i*, and *ε*
_{
l (kji)}is the residual error associated with the trait (i.e. the individual means computed from both sides and the two replicated measurements per side) of the *l* th individual within vial *k*, cross *j*, and karyotype *i*. Since there was no genetic variation within crosses, the residual error provides an estimate of the total special environmental effects variance (i.e.
). Variation among the three replicated vials was generally negligible (results not shown) and, therefore, we have conveniently reduced the previous model to a two-level nested ANOVA after grouping flies across vials.

To first partition the total phenotypic variation into interindividual, intraindividual and measurement error components, we used the conventional mixed model, two-way ANOVA (or its MANOVA generalization; see below) for the study of left-right asymmetries [39]. In this ANOVA the main random effect of individuals stands for phenotypic variation in the trait (i.e. CS), the main fixed effect of body side is for directional asymmetry (DA) and tests whether or no the signed differences between the left and right wings [designated as (
)] have a mean of zero, the interaction term is a measure of fluctuating asymmetry (the variation in left-right differences among individuals) provided that there is no genetic variation for DA [51], and the error term gives an estimate of the measurement error. The two-level nested ANOVA can be straightforwardly subsumed within the two-way ANOVA.

We now digress slightly to point out some inconsistencies in the literature on what is the appropriate error term to test for the "interindividual" effect in the mixed model, two-way ANOVA (either the individual × side interaction effect or the measurement error [13, 15, 68, 69]). Interindividual variation, even if of no general interest in most studies of asymmetry, comprises here genetic components ("karyotype" plus "crosses within karyotypes") and special environmental effects variance (
; there is no genetic variance within crosses). An estimated of the among-fly special environmental effects variance (i.e.
) is therefore obtained by subtracting the individual × side interaction effect (which includes
plus measurement error) as the appropriate error term. However, when genetic variation for DA is present the unbiased within-fly special environmental effects variance (i.e. FA) is estimated after partitioning the individual × side interaction effect into its causal components [51].

As pointed out by Klingenberg et al. [67] it is fairly straightforward to extent the preceding ANOVA approach to a full two-factor MANOVA to analyze wing shape asymmetry since all effects are computed from averages or contrasts in the same shape space. Recall that the traces of the corresponding SSCP matrices are just the sum of squares in the Procrustes ANOVA as implemented by Klingenberg and McIntyre [13], but this ANOVA is based on an isotropic model (i.e., it assumes that there is an equal amount of non-directional variation at each landmark [70]) that is not generally correct for any real data. Covariance (VCV) matrices for each effect in the MANOVA were calculated as a simple multivariate extension of the two-way ANOVA. Thus, the SSCP matrices were divided by the appropriate degrees of freedom, and effects were separated according to the expected mean squares in the ANOVA by subtracting the interaction covariance (VCV) matrix from the interindividual VCV matrix, and the error VCV matrix from the interaction one. Therefore, for (e.g.) outbred crosses the interindividual covariance components were calculated as
and the covariance components of FA as
, were SSCP_{I} is the interindividual SSCP matrix, SSCP_{IS} is the interaction SSCP matrix, and SSCP_{ME} is the measurement error SSCP matrix.

The SSCP_{I} matrix was further partitioned into among-karyotype SSCP_{K} matrix, among-cross within karyotype SSCP_{C⊂K} matrix, and the residual SSCP_{
e
}matrix corresponding to the special environmental effects. As a result, genetic effects for overall wing shape were separated from special environmental effects according to the expected means squares in the two-level nested ANOVA. Therefore, for (e.g.) outbred crosses the karyotype covariance components were calculated as
(remind that the entries in the SSCP_{I} matrix are equal to those computed from individual means times twice the number of independent measurements per wing), the cross covariance components as
, and the among-fly special environmental effects covariance components as
.

Similarly, genetic effects for DA can be investigated after partitioning the SSCP_{IS} matrix into their causal components [51].

### Morphological patterns of variation

Within each sex and temperature, principal component analyses [41] of the VCV matrices were performed for each source of variation with the purpose of describing the landmark displacements corresponding to each emerging principal component (PC), and also to test for the congruence of these displacements between effects. This technique extracts new shape variables (PCs) which successively account for the maximal amount of shape variation and contain information on how the variables relate to each other. The PCs form an orthonormal set of vectors (i.e., the inner product
for i ≠ j,
for i = j; superscript 'denotes transposition) in an n-dimensional space.

Correlations between corresponding VCV matrices were computed from the upper triangular part (diagonal entries were included) since covariance matrices are symmetrical, and statistical significance was assessed using permutation tests designed to maintain the associations between pairs of *x* - and *y* -coordinates (i.e., by permuting pairs of rows and columns [13, 15]); otherwise the null hypothesis would imply the complete absence of all geometric structure. The permutation procedure was carried out 10,000 times. Correlative patterns of whole shape variation are difficult to interpret: a significant correlation would suggest a real congruence, but a weak congruence does not imply a significant correlation.

A second test examined the congruence of the landmark displacements corresponding to each emergent PC for the different effects within groups. Because the PCs correspond to directions in the multivariate shape space, correlations can be obtained by angular comparisons of component vectors. Statistical significance of these correlations was then assessed by comparing those observed values to a null distribution of absolute angles between 100,000 pairs of 22-dimensional random vectors [71]. The 0.1% and 0.001% quantiles of the resulting distribution were 50.3° and 41.6°, respectively.

### Antisymmetry and allometric effects

The occurrence of antisymmetry (AS: a bimodal distribution of signed (
) [39]) for centroid size was investigated within each sample using the Lilliefors (Kolmogorov-Smirnov) test for the composite hypothesis of normality [69]. The independence between size and size FA within each sample was assessed by a linear regression of unsigned (
) against mean centroid size
.

Scatter plots of left-right differences for each landmark after Procrustes superimposition were visually checked to see whether or not there was evidence for clustering of these vectors that would have argue for the occurrence of AS [13, 15]. No indication of AS was detected. Finally, to test for size effects on shape asymmetry within each sample we used multivariate regression of vectors of both signed and "unsigned" shape asymmetries onto mean centroid size [13]. Shape asymmetries were not related to size (*P* -values > 0.10) and, therefore, no size corrections were necessary.

### Computer software for statistical analysis

The computer programs used for statistical data analyses were MATLAB (V.6. [72]) together with the collection of tools supplied by the Statistics Toolbox (V.3. [73]). Some helpful functions in morphometrics from the MATLAB toolboxes Res5 and Res6 developed by R. E. Strauss [74] were also used. Results (e.g., derivation of SSCP matrices) were checked with the statistical software packages STATISTICA V.6 [75] and SPSS V.11 [76].