A widely used approach to measure selection on a trait is based on selection gradients, first introduced by Robertson (1966) and Price (1970), and subsequently extended by Lande and Arnold (1983). Since then, many estimates of the intensity of selection have been provided and a few meta-analyses on the strength of selection in natural populations have been attempted (e.g., Hoekstra et al. 2001; Kingsolver et al. 2001). A large proportion of such studies concern species with separate sexes, but surprisingly very few of them have focused their attention on differences between selective pressures in the two sexes. Those that have, are mostly driven by the goal of testing whether the pattern of selection in the two sexes are consistent with the observed levels of sexual dimorphism (Price and Burley 1994; Badyaev and Martin 2000; Bjorklund and Senar 2001), under the model proposed by Lande (1980). His model predicts that during an initial rapid phase of evolution, the the mean phenotypes of males and females evolve nearly in parallel in response to selective forces acting on both sexes. Then, if genetic variation for sexual dimorphism exists, a slower phase of evolution ensues in which the mean phenotype of each sex gradually responds to the separate adaptive forces affecting it (Lande 1980).
Recently, a novel framework has been established under the name of intralocus sexual conflict (Rice 1992; Rice and Chippindale 2001; Bonduriansky and Chenoweth 2009): in its simplest form, it occurs when alleles are expressed in both sexes but are selected in opposite directions between the sexes (Rice and Chippindale 2001). Thus, a crucial feature defining this process is the presence of sexually antagonistic (SA) selection: although direct experimental evidence remains scarce, a few studies have produced estimates of sex-specific selection and discussed them under this framework (Chenoweth and Blows 2003; Robinson et al. 2006; Long and Rice 2007; Poissant et al. 2008). Furthermore, data from different species show the presence of sexually antagonistic genetic variation (or a negative genetic correlation) for fitness in the two sexes (Chippindale et al. 2001; Rice and Chippindale 2001; Calsbeek and Sinervo 2004; Fedorka and Mousseau 2004; Foerster et al. 2007; Innocenti and Morrow 2010), supporting the hypothesis that conflict might not be a transient state, but rather results from a combination of sex-specific selection on one or more traits, intersexual genetic correlations and other constraints (e.g., pleiotropy; Mank et al. 2008).
Despite accumulating theoretical and experimental evidence that selective pressures can be, and often are, different in the two sexes, little attempt has been made so far to quantify this difference on a common scale, making it difficult to compare estimates between traits and among different taxonomic levels. We suspect the main reason for the existence of this gap in the literature originates from the discrepancy between the simplicity of the concept of sexually antagonistic selection and a mathematical representation of this measure. An index of sexual size dimorphism is a good example of this discrepancy: it is a deeply studied phenomenon, and its biological meaning is obvious, but it still lacks a standardized measure, despite the considerable effort which has been made to select a single index with the desired properties (Smith 1999; Fairbairn 2007).
In the literature, the intensity of sexually antagonistic selection has generally been regarded as some measure of the difference in selection gradients (Arnqvist and Rowe 2005). This quantity was first formalized by Cox and Calsbeek (2009) in a meta-analysis on the strength of sexually antagonistic selection, with the explicit goal of describing the potential for intralocus sexual conflict, as
where β′M and β′F are the standardized directional selection gradients for a given trait on males and females, respectively. Thus, the greater the difference between the gradients, the larger the value of SAS. However, as noted by the authors (Cox and Calsbeek 2009), this quantity suffers from some major disadvantages. Such a quantity is always positive, so that it is impossible to discriminate between concordant and antagonistic selection. In particular, any given positive value—which should suggest presence of antagonistic selection—can be obtained when β′M and β′F are concordant, or when selection is absent in one sex (because the trait is neutral in one sex or sex limited). To alleviate these problems, the authors qualitatively assess the presence or absence of antagonistic selection using additional criteria, restricting the analysis to the situation in which: the sign of selection gradients differed in the two sexes; the magnitude of selection was greater than an arbitrary threshold; or the gradients were significantly different from zero (Cox and Calsbeek 2009). Overall, we suggest that such a problematic measure may muddle any downstream analysis, and the results of the qualitative adjustments do not justify the complexity of the additional criteria.
A more general index that measures how concordant or discordant directional selection is in the two sexes for a single trait would be of great help but should also show some particular properties: (1) It should be positive when selection is concordant, and negative when discordant (i.e., antagonistic) in the two sexes. (2) It should be zero when selection is absent in one sex, although it must be noted that conflict could occur if strong stabilizing selection is present in that sex (see Day and Bonduriansky 2004). (3) It should be proportional to the absolute intensity of selection. We propose a new index, defined as
that satisfies the requirements described above (Fig. 1). Additionally, it has the desirable properties of being symmetrical and normally distributed for a random set of normally distributed β′M, β′F. | I | is also always included in the interval between the absolute values of the selection gradient in the two sexes, and it coincides with them when β′M=β′F. As a potential drawback, it should be noted that such quantity is not defined when β′M=β′F= 0, even though it makes little sense to estimate how concordant or antagonstic directional selection is when it is absent in both sexes.
A numerical example can better demonstrate the behavior of such an index. Let us assume β′M= 1. If β′F= 1, and selection is therefore completely concordant, then I= 1. With decreasing values of β′F, the index also decreases, reaching 0—selection neither concordant or discordant—when β′F= 0. As β′F changes sign and is now discordant with β′M, I becomes negative indicating antagonistic selection, and reaches −1 when β′F=−1. If the selection gradients are both twice as strong, the index doubles in intensity, accounting for the overall strength of selection.
We applied the new index (2) to the data collected by (Cox and Calsbeek (2009, Appendix B, n = 203) and the results are illustrated in Figure 2. Overall, the index tends to be positive (binomial test = 0.6, P= 0.005), and the correlation between sex-specific selection estimates is positive and significant, although quite low (r= 0.216, P= 0.002). The distribution of the values (Fig. 2A) has a median of 0.025 (mode = 0.012), is nonsignificantly positively skewed (skew = 0.148, P= 0.21) and highly leptokurtic (kurtosis = 5.29, P < 0.001). Overrepresentation of small values of the index indicates that selection tends to be either very small in both sexes or positive/negative in one sex and absent in the other, and underpresentation of higher values indicates a partial lack of highly concordant/antagonistic selective episodes. As a possible interpretation of this result, it should be noted that highly concordant sex-specific selection should—assuming no other constraint—result in rapid evolution of the trait in the direction of selection, whereas strong antagonistic selection can possibly activate processes leading to partial or full “conflict resolution” (e.g., sex-limitation, Bonduriansky and Chenoweth 2009). When considering viability selection, fecundity selection, sexual selection, and net selection separately (Fig. 2B), the mean values of the index do not differ (Kruskal–Wallis rank sum test: χ2= 0.255, df = 3, P= 0.47), but estimates for net selection show higher variance than fecundity and viability selection (Fligner–Killeen test of homogeneity of variances: χ2= 24.32, df = 3, P < 0.001, and bootstrap estimates: see Fig. 2C).
Although Cox and Calsbeek (2009) found a higher level of sexual antagonism for sexual and net selection episodes compared to viability and fecundity selection, this pattern disappears when our index (2) is applied to the same dataset: no difference in the mean intensity of “joint selection” is observed, with median values being generally positive and close to zero. On the other hand, we observed a significant difference in the distributions of the index, with sexual and net selection showing higher variance than viability and fecundity selection. Such a pattern is to be expected given the properties of the two indices employed: using (1), estimates of antagonistic selection will be confounded with those that are concordant in sign but different in intensity; therefore, generally more variable sex-specific estimates will produce a higher overall mean. In contrast, antagonistic selection measured using (2) will produce negative values, clearly distinguishing them from concordant selection. Despite the differences in the results from the two analyses, the conclusions that can be drawn are similar: our results suggest that net selection (and, to some extent, sexual selection) show greater opportunity for sexual conflict, a pattern confirmed also by the larger (albeit marginally nonsignificant) proportion of negative values for these selective episodes (VS = 0.37, FS = 0.26, SS = 0.54, Net = 0.49, χ2= 7.4, df = 3, P= 0.060).
We argue that this simple measure could facilitate comparisons of divergence in the intensity of directional selection in the two sexes across different traits and different taxa, between isolated, diverging populations and possibly applied to polymorphic species. It would also provide a tool to assess the extent to which sexually antagonistic selection persists in populations, harboring potential for the maintenance of intralocus sexual conflict, and contribute to our understanding of the evolution of sexual dimorphism.