THE B-MATRIX HARBORS SIGNIFICANT AND SEX-SPECIFIC CONSTRAINTS ON THE EVOLUTION OF MULTICHARACTER SEXUAL DIMORPHISM

Authors


Abstract

The extent to which sexual dimorphism can evolve within a population depends on an interaction between sexually divergent selection and constraints imposed by a genetic architecture that is shared between males and females. The degree of constraint within a population is normally inferred from the intersexual genetic correlation, rmf. However, such bivariate correlations ignore the potential constraining effect of genetic covariances between other sexually coexpressed traits. Using the fruit fly Drosophila serrata, a species that exhibits mutual mate preference for blends of homologous contact pheromones, we tested the impact of between-sex between-trait genetic covariances using an extended version of the genetic variance–covariance matrix, G, that includes Lande's (1980) between-sex covariance matrix, B. We find that including B greatly reduces the degree to which male and female traits are predicted to diverge in the face of divergent phenotypic selection. However, the degree to which B alters the response to selection differs between the sexes. The overall rate of male trait evolution is predicted to decline, but its direction remains relatively unchanged, whereas the opposite is found for females. We emphasize the importance of considering the B-matrix in microevolutionary studies of constraint on the evolution of sexual dimorphism.

Sexual dimorphism is a widespread phenomenon that has been studied from an evolutionary perspective in many species (Hedrick and Temeles 1989; Shine 1989; Andersson 1994; Fairbairn 1997; Geber et al. 1999; Blanckenhorn 2005; Fairbairn et al. 2007). Sexual dimorphism can evolve through either a response to disruptive selection between the sexes or sex differences in genetic variance (Lande 1980, 1987; Cheverud et al. 1985; Meagher 1999; Steven et al. 2007). The most conspicuous examples of sexual dimorphism come from sexual display traits (see Andersson 1994) which are often over expressed in one sex (usually males), and thought to be the result of persistent directional selection through mate choice from the other (usually females) (Darwin 1871; Andersson 1994).

The extent to which sexual dimorphism will evolve within a population will, to a large degree, depend on the interaction between sexually divergent selection and constraints imposed by a shared genetic architecture (Lande 1980). When the sexes simultaneously express traits that experience contrasting patterns of selection, shared genetic variance may constrain one or both sexes from reaching their respective optima, slowing the potential for sexual dimorphism to evolve (Lande 1980, 1987; Rice 1984; Parker and Partridge 1998; Reeve and Fairbairn 2001; Bonduriansky and Chenoweth 2009; Cox and Calsbeek 2009).

Quantitative genetic theory has provided many of the tools needed to detect genetic constraints on the evolution of sexual dimorphism (Lynch and Walsh 1998). The parameter most commonly used to quantify constraints for a single trait is the intersexual genetic correlation, rmf (Lande 1980; Lynch and Walsh 1998). For empirical studies of phenotypic traits, rmf estimates are interpreted as constraints on the evolution of sexual dimorphism when directional selection on the trait of interest is shown to be sexually divergent and rmf > 0 (Bonduriansky and Chenoweth 2009). Although rmf has been useful for interpreting potential constraints on the evolution of dimorphism in single traits (Delph et al. 2004; Poissant et al. 2010), it nonetheless, likely provides an incomplete picture of the evolutionary potential of each sex. As selection commonly acts on multiple rather than single traits simultaneously (Lande and Arnold 1983), genetic covariances between traits are expected to bias evolutionary trajectories (Lande 1979; Schluter 1996; Blows et al. 2004; Hansen and Houle 2008; Walsh and Blows 2009). Consequently, bivariate genetic correlations may by themselves provide a misleading picture of constraints (Conner 2003; Blows and Hoffmann 2005; Hansen and Houle 2008; Agrawal and Stinchcombe 2009; Walsh and Blows 2009; McGuigan and Blows 2010). Therefore, simple bivariate estimates such as rmf are likely to be similarly misleading in what they tell us about the evolution of sexual dimorphism in multiple characters.

Much of our theoretical understanding of how genetic covariances affect multitrait responses to selection has come from the Lande equation, Δz= (Lande 1979; Blows and Walsh 2008; Hansen and Houle 2008; Walsh and Blows 2009) which allows examination of how the predicted response to selection in multiple traits, Δz, is scaled and rotated by the genetic variance–covariance matrix, G, away from the optimal direction of selection, given by the vector of directional selection gradients β. However, although the Lande equation provides a necessary tool to understand the constraints imposed by trait covariances within a sex, the sex-specific structure of G and differences in selection will complicate such comparisons between the sexes (Lande 1980). For the case of sexually homologous characters, these problems can be addressed by considering Lande's (1980) partitioning of the G matrix into four sub-matrices:

image(1)

where Gm and Gf are the within-sex variance–covariance matrices and B is the between-sex covariance matrix. Despite not actually being expressed in any subset of individuals, B is the ultimate determinant of indirect selection between the sexes. The diagonal elements of B are estimates of the between-sex covariances and are used as the numerators for the calculation of rmf, whereas the off-diagonal elements of B are the estimates of intersexual genetic covariances between different traits (Lande 1980). Partitioning of the G matrix in this way may permit a greater understanding of how intersexual trait covariances influence the evolution of sexual dimorphism (Meagher 1999; Steven et al. 2007; Lewis et al. 2011).

Despite its theoretical appeal, and possibly due to the computational power needed to calculate such high dimensional matrices (estimation of Gmf requires almost four times as many parameters than separate Gm and Gf matrices), empirical work on the B-matrix has been limited (but see Meagher 1999; Steven et al. 2007; Barker et al. 2010; Lewis et al. 2011). Specifically, we know very little about how B may harbor constraints on the evolution of sexual dimorphism. In particular, examination of B may expose differences in the form of constraint in each sex that are not obvious from bivariate comparisons. Thus, incorporating the B matrix into microevolutionary predictions of trait evolution is a necessary first step in extending our understanding of how intersexual genetic covariances generate constraints on the evolution of sexual dimorphism.

In this article, we directly examine the potential for constraints on sexually homologous traits when including the B-matrix to predict responses to selection. We examine ways in which the B-matrix affects both the direction and magnitude of the response to selection in males and females, highlighting the potential for sexually asymmetric outcomes. We use the fruit fly Drosophila serrata, where between 5 and 50% of the phenotypic variance in male and female mating success can be attributed to mating preferences of the opposite sex for blends of contact pheromones, composed of cuticular hydrocarbons (CHCs; Rundle et al. 2005; Rundle and Chenoweth 2011). These effect sizes are typical of values reported for sexually selected traits across a range of species (10–30%; Whitlock and Agrawal 2009). The homologous expression of the CHC phenotypes found in the D. serrata system, combined with mutual mate choice and differences in the strength and direction of sexual selection, make it a useful model for the study of the evolution of sexual dimorphism (Chenoweth and Blows 2003, 2005; Chenoweth et al. 2008; Rundle and Chenoweth 2011). Using estimates of directional selection gradients in both sexes and genetic variance–covariance matrices for this set of sexually dimorphic contact pheromones of D. serrata, we demonstrate how incorporating B into estimates of the response to selection significantly alters predictions about the strength of genetic constraints and exposes previously unrecognized sex differences in the way that constraints are generated.

Materials and Methods

INBRED LINES AND EXPERIMENTAL SET UP

A panel of 45 inbred lines (IL) were created using inseminated females caught from a population in St Lucia, Brisbane, Australia. The lines were created directly from wild caught females using single-pair full-sib mating for a minimum of 15 generations, preventing large-scale adaptation to a laboratory environment and maintaining natural allelic variation representative of the Brisbane population from which they were founded. ILs offer an advantage over classic breeding designs such as paternal half-sibling analysis because X-linked genetic variance is included for both males and females. As males are heterogametic in D. serrata, and previous analyses suggested substantial X-linked genetic covariance between the sexes (Chenoweth et al. 2008), we favor this approach over more conventional designs. All of the ILs were density controlled one generation prior to the experiment. We conducted standard two-stimulus binomial mating trials on both sexes as outlined in Chenoweth and Blows (2005). In each trial a single focal fly from an IL was randomly paired with another individual of the same sex and a single individual of the opposite sex, which had both been randomly taken from the same set of 45 ILs. For each line we conducted 24 mating trials for each sex. The individuals designated as competitors from the stock had a small piece clipped from the end of their wings to allow for identification of the focal and competitor flies during the trials (Petfield et al. 2005; Chenoweth et al. 2007; McGuigan et al. 2008; Gosden and Chenoweth 2011). Once a mating was observed, the focal fly was removed, scored as either chosen or rejected, and their CHCs extracted using established techniques (Blows and Allan 1998). All flies were sexed as virgins and held for a minimum of six days; competitors/focal individual flies were held four per vial and flies making the choice held individually at 25°C with 12:12 h light:dark period. Trials were held over three days and all flies were the same age during the trials (six to eight days).

The CHC profiles for each focal male and female were analyzed by employing standard gas chromatography (GC) methods (Blows and Allan 1998). The areas under eight chromatograph peaks of interest (5,9-C24:2; 5,9-C25:2; 9-C25:1; Z-9-C26:1; 2-Me-C26, 5,9-C27:2; 2-Me-C28; 5,9-C29:2) were integrated and transformed into seven log-contrast values for subsequent statistical analyses following Aitchison (1986) and using 5,9-C24:2 as the common divisor:

image(2)

The methylalkane, 2-Me-C30, which has been included in many studies of D. serrata in the past, was unreliably scored in this dataset and so was excluded from this study. More detail on the statistical treatment of CHCs can be found in Blows and Allan (1998). For multivariate outlier detection and removal we employed the Mahalanobis distance technique described in Sall et al. (2005) and implemented in the multivariate package of JMP version 8 (SAS Institute, Cary, NC). After accounting for unsuccessful GC samples and multivariate outliers, a total of 859 males and 902 females were included in the final analysis.

STATISTICAL ANALYSES

Our aim was to determine the degree of constraint that is imposed by shared multivariate genetic (co)variance on the evolution of sexual dimorphism. To facilitate such a comparison across the sexes, the seven logcontrasts, representing seven individual CHCs were individually standardized to have a mean of zero and unitary variance prior to the statistical analyses. Although we recognize a level of contention surrounding such standardization methods and the influence they have on data interpretation (Houle et al. 2011), we chose to standardize in this manner because the traits of interest are log-transformed compositional data points (Aitchison 1986), resulting in a difference scale that can only be meaningfully scaled by the variance (Hansen et al. 2011; Houle et al. 2011); however, we report the raw means and standard deviations of the log-contrast CHCs in Table 1. Directional selection gradients for the seven log-contrast CHCs were estimated using ordinary least squares multiple regression (Lande and Arnold 1983) separately for each sex. To test for differences between the sexes in directional selection, we employed a sequential model-building approach using the same methods outlined in Chenoweth and Blows (2005).

Table 1.  Table showing directional selection gradients for males (βm) and females (βf), the expected response to selection for males and females calculated without (Δzm, Δzf) and with (ΔzmB, ΔzfB) the inclusion of the B matrix and the raw population level means (μ) and standard deviations (σ) for the seven log-contrast CHCs prior to variance standardization. Selection gradients significant at P < 0.05 shown in bold.
Log-contrast CHCβmβfΔzmΔzfΔzmBΔzfBμσ
5,9-C25:2−0.1020.0580.010−0.0020.004−0.0031.710.055
9-C25:10.039−0.119−0.034−0.011−0.012−0.0110.8710.098
9-C26:1−0.0760.1110.0220.0260.0200.0210.3210.102
2-Me-C260.144−0.0230.049−0.0170.0190.0160.4900.187
5,9-C27:2−0.4170.0210.016−0.0190.0070.0030.8420.151
2-Me-C28−0.0540.0580.040−0.0030.0240.0201.2390.123
5,9-C29:21.320−0.1710.050−0.0390.0230.0130.4360.368

Briefly, we constructed a model containing only the linear terms of the quantitative (CHC) and categorical (sex) variables:

image(3)

where M is the measure of binomial mating success, Ci is the log-contrast concentration of the ith CHC, and the term α0sex is an intercept accounting for sex differences in mating success. Model (3) is then compared to the full model (4), which includes the interaction terms between selection gradients and sex for all CHCs, represented by αiCisex in equation (4), becoming:

image(4)

with both models fitted using maximum likelihood (SAS version 9.2; SAS Institute, Cary, NC). To test whether the full model (4) was a better fit than the reduced model (3), we compared differences between −2 log likelihood of the two models using a likelihood ratio test (LRT; df = 7).

The genetic variance–covariance matrix (G) was estimated using WOMBAT (22 February 2011 release; Meyer 2007b), using restricted maximum likelihood (REML) in the multivariate mixed effects model:

image(5)

where, yijk is the trait value of the jth individual, μ is the population mean vector for each trait, d is the effect of experimental day, li is the effect of the ith line, and ɛj(i) is the effect of the jth individual nested within the ith IL. Day was modeled as a fixed effect, whereas all other terms were treated as random. To estimate this model each trait–sex combination was treated as a separate trait resulting in 14 instead of seven traits in the analysis. We used LRTs to compare whether removal of the line term significantly worsened the fit of the model. The separate within-sex matrices were extracted from the full matrix (1) for comparison.

Using the Lande (1980) equation, we calculated the predicted response to selection separately for both males (Gm) and females (Gf). Once Δz has been estimated for both sexes, it is possible to calculate the angle between the vector of linear selection for males βm and females βf, and the predicted response within each sex (Δzm and Δzf, respectively), which is a straightforward way of quantifying the degree to which within-sex G rotates the response to selection away from the direction of selection (Blows and Walsh 2008), where the angle is:

image(6)

If θ= 0°, then Δz and β have the same orientation and there is no constraint on the response, whereas θ= 90° corresponds to an absolute constraint (Blows and Walsh 2008). By replacing the vectors of interest in equation (6), we calculated the angle between Δzm and Δzf, to determine the extent to which the expected response to selection differs between the sexes, where θ > 0° indicates that the degree of sexual dimorphism is expected to change.

We then applied the Lande (1980) equation for Gmf, so that:

image(7)

where ΔzmB and ΔzfB is the projected response to selection for males and females when βm and βf are projected through Gmf (Lande 1980). The factor of ½ is to account for equal contributions from both maternal and paternal parents to the autosomal traits the offspring receive (Lande 1980). As described above for the sex-specific estimates of G, we estimated the angle between the vector of directional selection (βm, βf) and the response to selection (ΔzmB, ΔzfB), which is informative of the constraint imposed on each sex due to both the sex-specific G and the between-sex covariance, B. This can then be compared to the angles generated in equation (6) to indicate whether B either intensifies or abates the constraints within a sex.

The vectors Δzm and Δzf represent the response to selection in males and females when βm and βf are, respectively, rotated and scaled by Gm and Gf, and thus were compared to the vectors ΔzmB and ΔzfB, to give the sex-specific change in the response vector as a result of the addition of the between-sex covariance matrix, B. Finally, we compared ∥ΔzmB∥, ∥ΔzfB∥ with ∥Δzm∥, ∥Δzf∥, which allowed us to test how B influences the magnitude of the response to selection (Hansen and Houle 2008), which in our case is measured as changes in units of phenotypic standard deviations (Lynch and Walsh 1998).

We used a bootstrap procedure to determine how the broad patterns we observed in changes in genetic constraints with and without the B matrix might be affected by sampling error. We bootstrapped our dataset by resampling with replacement at the line level and estimating G for each sample, resulting in a total of 1000 replicates each analyzed fitting model (5) in WOMBAT (Meyer, 2007b).

Results

SEXUAL DIMORPHISM AND SELECTION GRADIENTS

The sexes differed significantly in mean log-contrast CHCs (MANOVA: Wilks’λ= 0.238, F7,1753= 799.83, P < 0.001) indicating sexual dimorphism. We detected directional selection in both sexes (Table 1; males; F7,858= 21.02, P < 0.001: females; F7,901= 3.31, P= 0.002); however, the amount of variation accounted for by CHC profile and total strength of selection (vector length of the selection gradients) was much greater in males than in females (Fig. 1; males, R2adj= 0.16, ‖βm‖= 1.40; females, R2adj= 0.02, ‖βf‖= 0.27). Results from our sequential model building approach confirmed significant differences in the strength and direction of sexual selection for these homologous signal traits (Fig. 1; LRT: −2 diff lnL = 156.6, df = 7, P < 0.001). This difference between the sexes in the direction of sexual selection was further evident with an angle of 137.6° between the vectors of linear selection, βm and βf (Fig 1).

Figure 1.

Comparison of the directional selection gradients for males (black bars) and females (gray bars) for seven log-contrast CHCs in Drosophila serrata. Asterisks indicate the presence of significant differences in the strength and direction of the selection gradients between the sexes taken from model (4) (*P < 0.05, **P < 0.01, ***P < 0.001). Top left insert: two-dimensional illustration of the differences in magnitude and direction of the sexual selection vectors (β) between the sexes.

GENETIC CONSTRAINTS

LRTs indicated significant genetic (co)variance for the seven CHCs in males (Gm: diff −2lnL = 4002.9, df = 28, P < 0.001) and females (Gf: diff −2lnL = 4152.2, df = 28, P < 0.001) as well as the full model including both sexes (Gmf: diff −2lnL = 8446.2, df = 105, P < 0.001).

We found large differences between the sexes in the predicted responses to directional sexual selection, with an angle between Δzm and Δzf of 116.6° (Fig. 2), which indicates sexually divergent phenotypic evolution of a similar scale to the differences seen in sex-specific selection alone (βm, βf= 137.6°; Fig 1). By contrast, when the predicted responses were calculated using Gmf, the angle between ΔzmB and ΔzfB was reduced to only 15.5°, which suggests close alignment of the sex-specific response vectors, and taken with the differences in the direction of selection between the sexes suggests a strengthening of constraint due to the intersexual genetic covariances in B (Fig 2). A reduction in the angle between the sex-specific response vectors was seen in 998 of 1000 (99.8%) bootstrapped replicates.

Figure 2.

Two-dimensional illustration showing differences in the orientation and magnitude of the expected phenotypic response vectors between males and females (Δz), calculated with and without the inclusion of the between-sex trait covariance matrix, B. (A) The orientation of the male response vector (left) changes little, but the magnitude is decreased, whereas the female response vector (right) shows a large shift in orientation but the change in the magnitude of the response is much smaller than in males. (B) The expected response in males and females is antagonistic without (left), but concordant with (right), the inclusion of B.

As the addition of B produced very different predictions in the extent to which the sexes were expected to diverge in CHC phenotype, we attempted to identify differences in the strength of genetic constraints in each sex separately. To do this we examined the angle between the response vectors with and without the inclusion of B. The response vector for males, Δzm changed very little with the inclusion of B, rotating it by only 16°. The situation was markedly different for females, however, Δzf rotated by 96.5° when B was included in the predicted response. This larger rotation in females was observed in 982 out of 1000 (98.2%) bootstrapped replicates. Similar sex differences were observed when comparing the vector of directional selection, β, to the response to selection, Δz. In males, the angle between βm and Δzm only changed from 62.3° to 65.6° (Fig 3) and an increase was observed only 734 times in 1000 (73.4%) bootstrapped replicates. However, the angle between βf and the expected response in females, Δzf, almost doubled from 39.4° to 77.2° (Fig 3) and this pattern was consistent, being found in 998 of 1000 (99.8%) bootstrapped replicates.

Figure 3.

Two-dimensional illustration of the constraints on the expected response to selection without (left) and with (right) the inclusion of the between-sex covariance matrix, B. (A) In males there is only a small change in the orientation, and (B) in females the shift in orientation away from the vector of directional selection is much larger.

As seen in the analyses of changes in the direction of selection responses, we also observed differences in changes in the length of the response vectors when β was rotated through Gmf. The length of the male response vector decreased by 51% with the inclusion of B (∥Δzm∥= 0.092: ∥ΔzmB∥= 0.046; decrease observed in 100% of the bootstrap replicates); however, the female response vector reduced by only 32% (∥Δzf∥= 0.055: ∥ΔzfB∥= 0.037; decrease observed in only 690 out of 1000 bootstrapped replicates).

Discussion

Using a quantitative genetic model, Lande (1980) was able to show how between-sex covariances, contained within the B-matrix, could slow the evolution of sexual dimorphism. Since its inception, few studies have attempted to estimate B (Meagher 1999; Chenoweth and Blows 2003; Steven et al. 2007; Barker et al. 2010; Lewis et al. 2011) and the extent to which it biases the direction of male and female selection responses is not well understood. We have shown that B significantly alters the predicted response to sexually divergent selection, in this case changing it from a divergent response to one that is essentially concordant. Further, the primary means by which selection responses are biased by B differs between the sexes, suggesting that shared genetic (co)variance may influence trait evolution in males and females in different ways.

Inclusion of the B-matrix when predicting sex-specific responses to selection demonstrated the two ways in which multitrait evolution can be affected by genetic covariances; direction and rate (Fig. 2). The correlation between male and female response vectors changed sign (Δzm, Δzf=−0.242, ΔzmB, ΔzfB= 0.958) following the inclusion of B, indicating an overall change in direction between the sexes (Table 1). At the phenotypic level, all seven log-contrast CHCs had selection gradients with opposing signs (Table 1), with six of these also having a significant trait×sex interaction term in model (4), demonstrating they experience sexually divergent selection (Fig. 1). Even though constraints were evident when predicting responses using the sex-specific G matrices, Gm and Gf, five of the seven traits still showed evidence of divergence between the sexes (Table 1). However, when the Lande equation was applied including B, this pattern of sexual divergence was almost removed entirely—only one of seven traits responded in opposing directions.

Overall, B changed the direction of sexual selection in females to a much greater degree than it did in males (Table 1; Fig. 2A). Despite the poor orientation of the male-specific response vector with β in D. serrata (Fig. 3), which is possibly the result of a depletion of multivariate genetic variance in the face of strong open-ended female preferences in this species (Blows et al. 2004), the between-sex trait covariances in B did not greatly alter the direction of the expected male response. The reason for this is likely due to asymmetry within the B matrix. Broad-scale asymmetry in B was certainly evident, the association between corresponding elements of the upper and lower triangles of B was far weaker (matrix correlation: r= 0.23) than the association between the corresponding elements of Gm and Gf (matrix correlation: r= 0.65). Interestingly, we observed a tight association between Gm and the lower triangle of B (matrix correlation: r= 0.73), whereas the same association for Gf was weaker (matrix correlation: r= 0.38). As B shares greater similarity with Gm than it does with Gf, the response is rotated in males to a lesser degree than in females.

Although B biased the direction of the genetic response to a greater extent for females than males, the length of the response vectors changed more for males than females (Fig 2A)—effectively halved in males (Table 1). It is of note that the only existing study for which data are available for comparison shows a similar pattern of constraint. The predicted response to sexual selection for shared life-history traits in the moth, Plodia interpunctella, was influenced by B largely through magnitude changes in males and direction changes in females (Lewis et al. 2011).

When sexually antagonistic selection occurs on a set of shared traits, selection will almost inevitably be stronger on one sex than the other and, assuming a breakdown of intersexual genetic covariances, dimorphism will eventually evolve through greater change in the stronger selected sex (Lande 1980). An interesting observation from our study was that the selection response was derailed to a greater degree in females where selection was weaker. Weaker directional sexual selection on female than male CHCs seems to be a general feature of the D. serrata mating system. For example, consistently less phenotypic variance in mating success was explained by female CHCs than male CHCs in nine independent D. serrata populations (mean r2adj± SD: males, 6.1%± 2.7%; females, 3.9%± 2.5%) (Rundle and Chenoweth 2011). Sex differences in the strength of phenotypic selection are potentially common in nature (Cox and Calsbeek 2009); although whether sexual selection is generally stronger on males than females when it occurs on a shared trait remains to be demonstrated for a wider range of phenotypes than the ones we have studied here. For traits under sexual selection in both sexes, it could be that correlated responses to sexually antagonistic selection tend to be often more maladaptive for females than males.

Although B clearly generates short-term constraints on the evolution of sexual dimorphism, whether those constraints persist over the long-term remains unknown (Barker et al. 2010). Because the trait covariances in B are not actually expressed in any subset of individuals, unlike those in Gm and Gf, they will not be directly subject to selection within a generation, unless selection acts on males and females when they are interacting. Therefore, B may be less stable than Gm or Gf if it is exposed to multivariate stabilizing selection less frequently (Barker et al. 2010). This prediction is based on assumptions of an absence of directional selection, homogeneity between Gm and Gf, and between the individual fitness surfaces (γ) for males and females. As the evolution of sexual dimorphism normally arises due to the presence of disruptive selection (Bonduriansky and Chenoweth 2009; Cox and Calsbeek 2009), which likely leads to differences between Gm and Gf (Meagher 1999; Steven et al. 2007; Lewis et al. 2011), it is unclear how stable B will be when these assumptions are not met. The assumptions of a lack of directional selection and of sexual homogeneity in nonlinear selection are clearly violated for CHCs in D. serrata; directional selection is present and nonlinear sexual selection differs between males and females in many natural populations (Chenoweth and Blows 2005; Rundle et al. 2008; Rundle and Chenoweth 2011). Although data are limited, the structure of Gm for CHCs varies minimally along a latitudinal gradient despite strong divergence in trait means (Hine et al. 2009). Ultimately, statistical comparison of B, Gm, and Gf among natural populations may provide clues into the longer-term stability of B.

Whereas our analyses in this study have focussed solely on sex-specific sexual selection, sex-specific natural selection can also influence the evolution of sexual dimorphism (Reeve and Fairbairn 1999; Preziosi and Fairbairn 2000). Spanning the same latitudinal cline within the natural range of D. serrata, along which sexual dimorphism and sexual selection vary, CHC expression also shows a strong correlation with temperature, with the association strongest for males, suggesting CHC blends are under sex-specific natural, as well as sexual, selection in the wild (Frentiu and Chenoweth 2010). Further, an experimental evolution study using a novel diet type showed that while sexual selection tended to increase dimorphism in CHC expression, natural selection decreased it (Chenoweth et al. 2008). It remains to be determined how the response of CHCs to sex-specific natural selection will be affected by B and whether the same sexual asymmetries would be observed.

Despite intersexual genetic correlations (rmf) of a similar size to those detected previously (Table 2), the interpretations in this article differ from previous studies reporting relatively weak constraints on the evolution of CHC sexual dimorphism in D. serrata (Chenoweth and Blows 2003, Chenoweth et al. 2008). By incorporating and examining the role of B, we have shown that considerable constraints on the evolution of sexual dimorphism remain. These constraints were not evident from the intersexual genetic correlation estimates alone. The rmf estimates in this study (Table 2; mean ± SD = 0.59 ± 0.12 [where SD is standard deviation]) are also similar to those found in Poissant et al.'s (2010) meta-analysis for physiological traits (mean ± SD = 0.62 ± 0.07). These estimates are much smaller than those found for morphological (mean ± SD = 0.80 ± 0.03), behavioral (mean ± SD = 0.77 ± 0.09), and developmental (mean ± SD = 0.73 ± 0.05) traits leading to the suggestion that the evolution of sexual dimorphism in physiological traits may be less constrained (Poissant et al. 2010). Our analyses demonstrate how rmf provides only a partial representation of the evolutionary potential of each sex, suggesting it underestimates the degree to which sexual dimorphism is constrained within a population. As is the case for bivariate genetic correlations within a sex (Conner 2003; Blows and Hoffmann 2005; Hansen and Houle 2008; Agrawal and Stinchcombe 2009; Walsh and Blows 2009; McGuigan and Blows 2010), rmf may be a misleading indicator of constraint when traits are expressed in both sexes and multiple correlated traits are under selection.

Table 2.  The genetic variance–covariance matrix, Gmf for seven log-contrast CHCs. Top left panel: Gm with variances in bold along the diagonal, covariances below the diagonal, and correlations above the diagonal. Bottom right panel: Gf with variances in bold along the diagonal, covariances below the diagonal, and correlations above the diagonal. Bottom left panel: the between-sex covariance matrix (B). Top right panel: the between-sex between-trait correlations. The correlations in bold along the diagonal are equal to the intersexual genetic correlation, rmf.
  MaleFemale
5,9C25:29C25:19C26:12MeC265,9C27:22MeC285,9C29:25,9C25:29C25:19C26:12MeC265,9C27:22MeC285,9C29:2
Male5,9C25:20.2360.4270.255 0.2920.4870.4460.4800.6530.4780.212 0.2840.5670.303 0.273
 9C25:10.1110.2840.194 0.1020.3860.1950.149 0.1880.6100.296 0.0490.3110.056−0.166
 9C26:10.0890.0750.519 0.1470.4330.4830.518 0.4480.5130.743 0.0570.6280.443 0.447
 2MeC260.0920.0350.0690.4230.2080.4820.189−0.0620.0310.0750.4880.1710.051 0.136
 5,9C27:20.1820.1590.240 0.1040.5940.4060.823 0.2320.2210.074 0.2570.6890.331 0.215
 2MeC280.1400.0670.224 0.2020.2020.4160.497 0.3490.3980.342 0.1240.4440.472 0.256
 5,9C29:20.0810.0280.129 0.0430.2200.1110.120 0.3020.2160.205 0.2910.6840.4730.456
Female5,9C25:20.1810.0570.184−0.0230.1020.1280.0600.3240.6370.249 0.2220.4840.535 0.406
 9C25:10.1160.1630.185 0.0100.0860.1290.038 0.1820.2510.486 0.0100.5320.316 0.393
 9C26:10.0760.1170.397 0.0360.0420.1640.053 0.1050.1810.550−0.0660.4410.209 0.413
 2MeC260.0900.0170.027 0.2070.1300.0520.066 0.0830.003−0.0320.4280.2790.604 0.366
 5,9C27:20.1920.1150.314 0.0770.3690.1990.165 0.1920.1850.228 0.1270.4840.549 0.728
 2MeC280.1060.0210.230 0.0240.1840.2190.118 0.2190.1140.112 0.2850.2750.519 0.556
 5,9C29:20.085−0.0570.206 0.0560.1060.1050.101 0.1480.1260.196 0.1530.3230.2560.408

Intersexual genetic covariances for CHCs are in part affected by X-linked loci (Chenoweth and Blows 2003, Chenoweth et al. 2008). Although it is unclear how the B matrices due to X-linked and autosomal effects would be expected to differ, for the IL approach we adopted in this study, X-linked genetic variance is included in both the sex-specific variances as well as the between-sex genetic covariances. This is not the case for paternal half-sibling analysis because males are heterogametic. Although breeding designs are available that can isolate X-linked from autosomal genetic variance (e.g., the double first-cousin design; Fairbairn and Roff 2006), they require very large sample sizes (Meyer 2007a). Ultimately multi-founder quantitative trait locus (QTL) (e.g., MacDonald and Long 2007) or genome-wide association mapping approaches may prove more useful for disentangling sex-linked from autosomal factors on the intersexual covariance structure of sexually shared traits.

It has been widely recognized that a population's response to multivariate selection is limited by the genetic variance available in the direction of selection (Schluter 1996; Hansen and Houle 2008; Agrawal and Stinchcombe 2009; Kirkpatrick 2009; Walsh and Blows 2009). The degree to which the sexes are constrained by shared genetic variance follows a similar thread. Through the incorporation of B we have provided a more complete parameterization of the predicted response to selection for shared traits and showed that the bias introduced can be severe; changing the selection response from one that increases divergence between the sexes to one that sees the shared traits evolving in similar directions, largely at the expense of females sexual fitness. A more complete understanding of genetic constraints on the evolution of sexual dimorphism will require a move beyond single trait measures such as rmf, thus far the mainstay of quantitative genetic studies of constraints on the evolution of sexual dimorphism.

Associate Editor: M. Reuter

ACKNOWLEDGMENTS

We would like to thank Howard Rundle for supplying a proportion of the ILs used, and R. de Bruyn, C. Latimer, D. Petfield, and B. Rusuwa for technical assistance in the laboratory. We would also like to thank M. Reuter, D. Fairbairn, and two anonymous reviewers for comments and suggestions on an earlier version of the manuscript. This research was supported by funding from the Australian Research Council awarded to SFC and the Swedish Research Council (Vetenskapsrådet) to TPG.

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