Methods in Ecology and Evolution 2016 doi: 10.1111/2041-210X.12707 REVIEW Measuring and interpreting sexual selection metrics: evaluation and guidelines Nils Anthes*,1,InesK.Haderer€ 1,NicoK.Michiels1 and Tim Janicke2 1Animal Evolutionary Ecology Group, Institute for Evolution and Ecology, University of Tubingen,€ Auf der Morgenstelle 28, 2 72076 Tubingen,€ Germany; and Centre d’Ecologie Fonctionnelle et E´volutive, UMR 5175, CNRS, University of Montpellier, 1919 Route de Mende, 34293 Montpellier Cedex 05, France Summary 1. Routine assessments of overall sexual selection, including comparisons of its direction and intensity between sexesorspecies,relyonsummarymetricsthatcapturethe essence of sexual selection. Nearly all currently employed metrics require population-wide estimates of individual mating success and reproductive success. The resulting sexual selection metrics, however, can heavily and systematically vary with the chosen approaches in terms of sampling, measurement, and analysis. 2. Our review illustrates this variation, using the Bateman gradient, a particularly prominent sexual selection metric. It represents the selection gradient on mating success and – given the latter’s pivotal role in defining sexual selection – reflects a trait-independent integrative proxy for the maximum strength of sexual selection. Drawing from a recent meta-analysis, we evaluate potential biases arising from study design, data collection and parame- ter estimation, and provide suggestions to mitigate such biases in future studies. 3. With respect to study design, we argue that currently almost inexistent manipulative studies must complement the dominating correlative studies to inform us about causality in sexual selection. With respect to data collec- tion, we outline how different measures of mating and reproductive success affect the components of sexual (and natural) selection that are reflected in standard summary metrics. With respect to parameter estimation, we show the potential impact of decisions about data inclusion and the chosen quantitative approach on inferences of sex- ual selection and its sex difference. 4. We expect this meta-analytical review to aid future studies in providing less biased and more informative esti- mates of sexual selection. Key-words: Bateman gradient, causality, selection gradient, sex difference, sexual selection components from other forms of selection, accepting a Introduction focus on precopulatory (or pre-spawning) selection episodes Quantifying sexual selection and its effects on trait evolu- (but see section ‘Mating success: definition and meaning’). tion is central to contemporary mating system research. Previous empirical work has been dominated by summary The vastly dominating approach rests on Angus J. Bate- metrics proposed to reflect the opportunity for, and strength man’s (1948) idea to interpret variances in, and the linear of, sexual selection (Table 1). Recent overviews (Jones 2009; relationship between, mating success and reproductive suc- Mobley 2014; Henshaw, Kahn & Fritzsche 2016) accessibly cess as ‘signs’ and ‘causes’ of sexual selection, respectively. summarize their conceptual basis and calculation, and recapit- Later work has formalized his ideas within selection theory ulate a lively debate on the validity of variance-based as well as and clarified the degree to which Bateman’s proxies reflect trait-based metrics to capture sexual selection (refs. in opportunities for, rather than actual, selection (Wade 1979; Table 1), none of which we intend to reiterate or evaluate. Yet, Wade & Arnold 1980; Arnold & Duvall 1994; Jones 2009; while compiling a meta-analysis on sex differences in sexual Table 1). In essence, Bateman metrics echo Darwin’s selection (Janicke et al. 2016), we realized that the existing (1871) conception that sexual selection comprises those empirical work varies remarkably in key aspects of study components of total selection that are mediated through design and analysis. Some approaches can generate inappro- mating success (Arnold 1994). Modern definitions of sexual priate interpretations of sexual selection metrics, or estimates selection also include post-copulatory competition for that are not comparable between sexes, populations, or species. access to gametes. For this review, we stick to ‘mating’ as While earlier work addresses several individual challenges in the anchor that distinguishes sexually selected fitness isolation, we lack a comprehensive and quantitative assess- ment of the methodological pitfalls associated with the quan- *Correspondence author. E-mail: [email protected] tification of routine sexual selection metrics. © 2016 The Authors. Methods in Ecology and Evolution © 2016 British Ecological Society 2 N. Anthes et al. Table 1. Quantitative metrics commonly used to characterize sexual selection and mating systems independent of specific traits, and references dis- cussing their calculation and interpretation (modified and extended from Klug et al. 2010 and Mobley 2014) Metric Description Key references Opportunity for selection (I) Intra-sexual variance in relative reproductive Crow (1958), Wade (1979), Arnold & success. Its square root captures the upper limit of Wade (1984b) and Jones (2009) total linear selection on standardized traits Opportunity for sexual selection (Is) Intra-sexual variance in relative mating success. Its Wade (1979), Wade & Arnold (1980), square root captures the upper limit for mating Jones (2009); recent reviews in differentials m’, i.e. the covariance between Klug et al. (2010), Krakauer et al. (2011), standardized traits and mating success Jennions, Kokko & Klug (2012) and Evans & Garcia-Gonzalez (2016) Bateman gradient (bss) Linear slope of a least squares regression of relative Arnold & Duvall (1994), Andersson & reproductive success on relative mating success, Iwasa (1996) and Jones (2009) describing the average fitness gain associated with each additional mating. Technically represents a selection gradient on mating success, often seen to reflect the average ‘strength’ of directional sexual selection pffiffiffiffi b Jones index (s’max)Calculatedasss Is. Defines the upper limit for Jones (2009) and Henshaw, sexual selection differentials in units of phenotypic Kahn & Fritzsche (2016) standard deviations (=maximum standardized sexual selection differential) Morisita index (Id) Observed variance in mating (or reproductive) Morisita (1962) success relative to the expected variance under uniform mate acquisition probabilities Index of resource monopolization (Q) Ratio of observed to maximum variance in mating Ruzzante et al. (1996) (or reproductive) success Upper limit to the opportunity for selection Estimated maximum gain in reproductive success in Lorch (2005) idealized mating interactions, independent of mate fecundity We scrutinize the quantification of (sex differences in) sexual Study design selection metrics with respect to three components: the under- lying study design (section ‘Study design’), data collection (sec- This section treats pitfalls that researchers encounter when tion ‘Data collection’), and parameter estimation (section designing a study to quantify sexual selection. We discuss the ‘Parameter estimation’). For each component, we discuss pit- degree to which Bateman gradients reflect causality, the need falls during data acquisition, analysis, and interpretation, to estimate sexual selection across a meaningful range of mat- where possible quantify their empirical prevalence and statisti- ing frequencies, and the significance of field vs. laboratory cal consequences using our meta-analysis database (Janicke studies. et al. 2016), and propose guidelines to help prevent these prob- lems in future studies. CAUSALITY VS. CORRELATION IN BATEMAN GRADIENTS Throughout, we exemplify those issues with a focus on the Bateman gradient (bss), representing a widely used integrative Arnold & Duvall’s (1994) path diagrammatic view of sexual proxy of sexual selection (Klug et al. 2010). Contrary to purely selection focuses on two multiplicative fitness components. variance-based proxies such as I and Is (Table 1), Bateman The mating differential, m’ (as defined by Jones 2009), quanti- gradients are considered to reliably capture the overall direc- fies the covariance between candidate traits and mating suc- tion and intensity of, and sex difference in, sexual selection cess, and thus identifies traits that aid individuals in increasing (Jones et al. 2005; Janicke et al. 2016). One proxy directly access to mates. The sexual selection gradient or Bateman gra- derived from the Bateman gradient, the Jones index s’max, dient, bss, quantifies the expected fitness gain associated with shows particularly good performance (Henshaw, Kahn & each additional mating, averaged across the investigated mat- Fritzsche 2016; Table 1) and captures upper limits to sexual ing success range. Their product, m’ bss, describes the standard- selection differentials on any given trait (Jones 2009). We wish ized sexual selection differential on a given trait (Jones 2009). to stress that our methodological arguments extend to all other While both fitness components are routinely quantified in cor- recently advocated metrics of sexual selection (Table 1) that relative studies, we argue that they capture sexual (vs. other share a necessity to quantify individual reproductive success forms of) selection only if they signify causality. We focus our and individual mating success in a population. This includes argumentation on the Bateman gradient, but note that the