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Behavioral Ecology Vol. 9 No. 6: 546-351 The relative importance of size and asymmetry in sexual selection R. ThornhiD' and A. P. M0llerb •Department of Biology, The University of New Mexico, Albuquerque, NM, 87131-1091, USA, and b Laboratoire d'Ecologie, CNRS URA 258, Universite Pierre et Marie Curie, Bat A, 7eme etage,7 quai St. Bernard, Case 237, F-75252 Paris Cedex 05, France Developmental stability reflects the ability of individuals to cope with their environment during ontogeny given their genetic background. An inability to cope with environmental and genetic perturbations is reflected in elevated levels of fluctuating asymmetry and other measures of developmental instability. Both trait size and symmetry have been implicated as playing an important role in sexual selection, although their relative importance has never been assessed. We collected information on the relationship between success in sexual competition and size and asymmetry, respectively, to assess the relative importance of these two factors in sexual selection. Studies that allowed comparison of the relationships for the same traits' size and symmetry and success in sexual competition constituted the data, which totaled 73 samples from 33 studies of 29 species. The average sample-size weighted correlation coefficients between mating success or attractiveness and size and asymmetry, respectively, were used as measures of effect size in a meta-anatysis. Analysis was conducted on samples, studies, and species separately. We found evidence of an overall larger effect of symmetry at the species level of analysis, but similar effects at the sample or study levels. The difference in effect size for character size and character symmetry was larger for secondary sexual characters than for ordinary morphological characters at the level of analysis of samples. The results lend support to the conclusion that symmetry plays an important general role in sexual selection, especially symmetry of secondary sexual characters. Key words: buffering capacity, developmental stability, fluctuating asymmetry, mate choice, meta-analysis. [Behav Exol 9:546-551 (1998)] D evelopmental stability is defined as the ability of individuals to undergo stable development of their phenotype under given environmental conditions (review in Mailer and Swaddle, 1997). An individual's inability to cope with the environment during development is reflected by increased random deviations from perfect symmetry, so-called fluctuating asymmetry, and an increased frequency of phenodeviants (reviews in Graham ct aL, 1993; Miller and Swaddle, 1997; Palmer and Strobeck, 1986; Parsons, 1990). Both environmental and genetic perturbations reduce the ability to control developmental processes and hence increase individual measures of asymmetry (reviewed in Mailer and Swaddle, 1997). Sexual selection arises from reproductive competition among individuals for access to individuals of the choosing sex. Typically, across species, females choose mates, but males also choose mates when they invest parentally, and relative parental investment determines the sex that is most sexually competitive (Darwin, 1871; review in Andersson, 1994). Females may benefit either directly or indirectly from their mate choice (review in Andersson, 1994), and their choice of symmetrical partners may likewise give rise to either direct or indirect fitness advantages (Gangestad and Thomhill, 1997; Mailer, 1990, 1993; Thomhill and Gangestad, 1993; Thomhill and Sauer, 1992; Watson and Thornhill, 1994). For both kinds of benefits, individual mating success is predicted to decrease with increasing asymmetry. Numerous studies of sexual selection in relation to asymmetry have been reported. While some show the predicted negative relationship between mating success and asymmetry (e.g., Harvey and Walsh, 1993; Mailer, 1992; Swaddle and Cuthill, 1994a,b; Thornhill, 1992a,b), others have reported an Address correspondence to A. P. Moller. E-mail: amoUerChalLsnv. jussieuJr. Received 6 October 1997; reviled 20 January 1998; accepted 5 February 1998. © 1998 International Society for Behavioral Ecology absence of any effect (e.g., Fiske et al., 1994; Markow and Ricker, 1992; Ueno, 1994). For example, Andersson and Iwasa (1996) recently stated that "the role of fluctuating asymmetry in sexual selection is debated, and its analysis contains many pitfalls." Similarly, Andersson (1994: 71) stated, in regard to the relationship between low asymmetry and increased mating success or sexual attractiveness, that "more studies of a variety of organisms are needed to clarify how general such patterns may be in sexual selection." Fields with conflicting results are commonplace in biology, and because both consistent and contradictory evidence may follow from perfectly valid studies, disputes cannot be resolved by simple vote counting without considering sample size. A fruitful approach is to use metaanahtic techniques to address the generality of a relationship between two variables, such as sexual selection and asymmetry, and to attempt to understand the factors responsible for heterogeneity among samples (Cooper and Hedges, 1994; Hedges and Olkin, 1985; Rosenthal, 1991). Recently, Mailer and Thornhill (1998), in a meta-analysis of sexual selection in relation to asymmetry in 146 samples from 65 studies of 42 species of all known studies (insects, fish, birds and mammals), found a moderately negative, statistically significant relationship between asymmetry and mating success or attractiveness to the opposite sex (average, sample-size weighted Pearson's product-moment correlation r = —.42 for studies and r = —.34 for species). Moderator variables that explained heterogeneity among studies and species included greater effects for males than for females, when a secondary sexual character rather than an ordinary trait was studied, in experimental as opposed to observational studies, and for traits not involved with mobility as compared to traits affecting mobility. The aim of the present study was to test whether the magnitude of the effect of asymmetry on sexual selection was similar to that of character size per se, which is known from numerous studies to be related to sexual selection (see review in Andersson, 1994). Large males often experience an advantage Thornhill and Mellcr • Size and asymmetry in sexual selection in terms of sexual selection because of their success in malemale competition, or because of superior ability to acquire resources preferred by females (Andersson, 1994). Obviously, we could only include studies in which information on both size and asymmetry was available. The test consisted of pairwise comparisons of the magnitude of a standardized effect size for asymmetry and size of the same characters in the large sample of studies composing the meta-analysis mentioned above. A second objective of this study was to test whether the difference in effect size for character size and symmetry differed between secondary sexual characters and ordinary morphological traits. It has been suggested that an evolutionary history of directional selection gives rise to increased levels of asymmetry (Meller and Pomiankowski, 1993), and some empirical evidence suggests that asymmetry is indeed larger in secondary sexual characters than in ordinary morphological characters (e.g., Meller and Hdglund, 1991). Therefore, choosy individuals or contestants in intrasexual competition should be better able to distinguish between the asymmetry of target individuals when inspecting secondary sexual characters rather than ordinary morphological traits. MATERIALS AND METHODS The data set used for the present study is from Mailer and Thornhill (1998), which was based on (1) a comprehensive search of the literature and of the Internet for information on the relationship between asymmetry and sexual selection, and (2) correspondence between the authors and behavioral ecologists conducting research on this relationship. Because we investigated the relative effect size for symmetry versus character size for the same trait, the only studies included from Mailer and Thornhill (1998) were those that had one or more estimates that allowed calculation of an effect size for the relationship between asymmetry and character size, and mating success or a mate preference, respectively. We were able to obtain unpublished correlation coefficients for character size for a few additional studies that were also included in this study. In all cases of studies used in the present study, data for size and asymmetry are based on the same trait and involve the same individuals and, thus, sample size (see Mellcr and Thornhill, 1998, for further details). All the data are presented in Table 1. Meta-analysis consists of obtaining an estimate of the magnitude of a general effect of interest from each of a number of studies, calculating average effects, and elucidating moderator variables that account for heterogeneity among studies. We calculated effect sizes as the Pearson product-moment correlation coefficients, following the procedures outlined in Rosenthal (1991), Hedges and Olkin (1985), and Cooper and Hedges (1994). Effect sizes were reported in the original references in forms other than r (t, F, x* statistics, Mann-Whitney U, Spearman or Kendall rank-order correlations), which were then converted using formulas in Rosenthal (1991). We calculated effect sizes for samples, studies, and spedes by using a sample-size weighted mean of the relevant samples in the study (Rosenthal, 1991). A sample was defined as a single test for an effect The difference in effect size between symmetry and character size per se was tested by first converting the effect size for asymmetry into an effect for symmetry to obtain similar signs for the two measures of effect size by changing the sign of the correlation coefficient for the asymmetry effect size. Hence we decided to work on effect sizes with similar signs for size and symmetry to make the results more intelligible. For example, an effect of size and asymmetry in the same direction, but with a stronger effect for the first variable, should give rise to a consistent positive difference in effect size. Samples within studies and multiple studies of single spedes may lack statistical independence. Traditionally, this problem has been solved by investigating the predictions at the level of samples, studies, and spedes. If qualitatively similar conclusions are reached at all three levels, this implies that the level of analysis is relatively unimportant We are unaware of ways of performing meta-analyses in a phylogenetic framework, although such a solution eventually may become possible. Weighted mean effect sizes were calculated using Fisher's transformation of r to Z, (Sokal and Rohlf, 1996) and calculation of a mean weighted Zn where mean weighted Z,a 1 uyZySw^ where u>j is the weight factor for analysis unit j , with Wj equaling Nj- 3 in the present case (Rosenthal, 1991). The Z\was converted to ? and the significance level of whether r differed significantly from zero was subsequently determined, following Hedges and Olkin (1985), using mean weighted utj = (Nj — S)fl(N — 3), where Nia the sum of the sample sizes in the analysis, and Nj — 3 is summed over all j from 1 to A, which is the number of analysis units (e.g., * = 29 for spedes analysis). Confidence intervals on these r values were calculated using a modification of Hedges and Olkin (1985). The null hypothesis was that the effect size was zero, and lack of overlap of the 95% confidence intervals with zero would reject the null hypothesis. Furthermore, we evaluated the null hypothesis by calculating a standard normal deviate, which has a critical value of 1.96 for statistical significance at the 5% level. Although the effects of symmetry and size in relation to sexual selection were based on the same individuals and thus were dependent, the overall correlation between the two effects was near zero (see Results). Thus, we calculated a confidence interval on the difference between symmetry and size mean weighted Rvalues as the difference in Z,± 1.96/(N — 3k), where 1.96 was the two-tailed critical value of the standard normal distribution; N and k are as described above. Because secondary sexual characters have been suggested to have larger asymmetry than ordinary morphological characters due to a recent evolutionary history of directional selection, we investigated whether the difference in effect size between character size and character symmetry was larger for secondary sexual characters than for ordinary morphological traits. The null hypothesis was that the difference would be zero, and lack of overlap of the 95% confidence interval (C3) with zero would reject the null hypothesis. The characters were classified as being secondary sex traits according to the original source references; the classification is shown in Table 1. RESULTS Statistical independence of effect sixes for symmetry and Unweighted Pearson's correlation coefficients for the correlation between symmetry and a measure of sexual selection and size and a measure of sexual selection were small and insignificant at all three levels of our analysis (samples, n = 73, r « .025, p = .833; studies, n - 33, r = -.007, p = .971; spedes, n = 29, r = .150, p = .441). Analyses haurd on fmpi»« as units of analysis We analyzed the effect size for sexual selection and symmetry and size, respectively, by comparing effect sizes at the levels of samples, studies and spedes. For the 73 samples, the weighted mean effect size for symmetry was r •= .191 (95% CI 0.158, 0.223); the weighted mean effect size for character size was r = .175 (95% (3 0.143, 0.2O9). Both effects were signif- Behavioral Ecology Vol. 9 No. 6 548 Table 1 Species, effect site (Pearson product-moment correlation coefficients) for the relationship between rharartrr size and symmetry, respectively, and a measure of sexual selection, tatmplr size, and type of character for different trwHn Specie* Insects Cotnagrion fnuila Drvsophila mojavtnsis D. mojavtnsis D. nigrospiracula D. nigrospimcula D. pstudoobscura D. pstudoobscura D. pstudoobscura D. pstudoobscura D. pstudoobscura D. simulant D. simulans D. simulans D. simulans D. simulans D. simulans D. simulans Eyprtpocnemts plorons Eypvtpocnevus plorans Ischnura denticolHs I. denticolHs I. dmticolHs Musca donustica M. domtstica M. domtstica M. domtstica M. domtstica M. domtstica At domtstica M. domtstica MjrmeUotettix maculatus Myrmtltotittix maculata Panorpa japonica P. japonica P. japonica P. japonica P. japonica Piatjcjpha caUgata PolybUpharis opaca PotybUpharix opaca Scatophaga sttrcoraria Sepsis cynipsta SienurtUa mtlanura S. mttanura S. mttanura S. mtlanura S. mttanura S. mtlanura S. mdanura S. mtlanura Fish Copadichromis thinos Cjprmodon ptcostnsis Cjprinodon ptcostnsis Birds Anas platyrftynchos Anas platyrhjnchos GalUnago media G. media C media Hirundo rustics H. rustica H. rustica H. rustica Passer domtsticus Pavo cristatus r (size) r (lymmetry) n Character Reference .144 -.146 .783 .042 .085 .215 .113 .107 .121 .533 -.262 -.029 -344 .186 .894 -.733 492 44 44 .028 .041 .029 -.020 .008 .094 -.009 -.095 .033 .183 .041 -.038 -.042 .270 .145 .218 .084 -.078 -.021 -.180 .376 -.172 .096 .105 .041 .174 .045 -.037 -.046 -.114 -.008 -.012 -.048 .2550 .0046 -.1243 .0228 -.0175 .1710 .0174 .4293 .1130 .0380 -.1758 -.1575 -.3951 -.0476 -.0988 -.0842 -.0360 -.0100 -.0500 .2972 .4443 .4245 .0799 .1502 .1192 .6428 .3072 .4422 .3885 3423 .630 .8600 .0980 .4624 .6800 .8390 .8400 -.0301 3200 .8540 3966 .2430 .2210 .1191 .1267 .1740 .3582 3843 3895 .6209 100 100 100 100 100 216 230 95 95 95 100 100 50 50 50 100 100 50 30 30 22 121 25 21 25 55 103 84 87 106 26 33 71 38 69 38 34 26 Wing Bristles Wing Bristles Bristles Wing Arista! branch Wing Bristles Sex comb* Aristal branch Wing Wing Bristles Bristles Bristles Sex comb1 Tibia Tibia Hindwing Forewing Tibia Tibia Tibia Tibia Tibia Wing Wing Wing Wing Stridulator* Stridulator* Wing Wing Wing Wing Pheromone* Tibia color* Wing Wing Wing Tibia Elytra Elytra Elytra Elytra Antenna* Antenna* Antenna* Antenna* Harvey and Walsh (1993) Markow and Ricker (1992) Markow and Ricker (1992) Polak (1997) Polak (1997) Markow and Ricker (1992) Markow and Ricker (1992) Markow and Ricker (1992) Markow et al. (1996) Markow et al. (1996) Markow and Ricker (1992) Markow and Ricker (1992) Markow and Ricker (1992) Markow and Ricker (1992) Markow and Ricker (1992) Markow et al. (19%) Markow et al. (1996) Castro et al. (manuscript) Castro et al. (manuscript) Cordoba-Aguilar (1995) C6rdob*Aguilar (1995) Cordoba-Aguilar (1995) MeUer (1996) Meller (1996) MeUer (1996) Mailer (1996) MeUer (1996) Meller (1996) MeUer (1996) MeUer (1996) MeUer (1998) MeUer (1998) Thornhill (1992b) Thornhill (1992a) Thornhill (1992a) Thorahul (1992b) Thornhill (1992b) Jennions (1996) Poulsen et al. (1994) Poulsen et aL (1994) Liggett et al. (1993) Allen and Simmons (19%) MeUer and Zamora-Munoz MeUeT and Zamora-Munoi MeUer and Zamora-Munoz MeUer and Zamora-Munoz MeUer and Zamora-Munoz MeUer and Zamora-Munoz MeUer and Zamora-Munoz MeUer and Zamora-Munoz -.046 .125 .167 .0520 .4446 -5280 41 153 52 Bower* Skeleton Skeleton Taylor et aL (manuscript) Kodric-Brown (1998) Kodric-Brown (1998) .150 .440 -.244 -.107 .174 .650 -.162 .242 .914 .1400 -5000 -.1888 -.2290 .2732 .4450 .9268 .1500 .1300 .6500 3342 36 36 Tarsus Tarsus Wing Color* Omland (manuscript) Omland (manuscript) Fiske et aL (1994) FiskeetaL (1994) Fiske et al. (1994) MeUer (1992) Meller (1993) MeUer (1994) MeUer (1994) Kimball (1995) Hasegawa (1995) 354 316 .163 368 291 100 100 100 36 100 100 100 22 21 22 61 33 367 390 14 16 Tarsus Tail* Tail* TailWing Badge* Train* (1997) (1997) (1997) (1997) (1997) (1997) (1997) (1997) ThornhiH and Mailer • Size and asymmetry in sexual selection 549 Table 1, continued Species Ptilonorhynchus violacrus Taeniopjgia guttata Tachjdntta bicoior Tttrao utrix Tttrao Utrix Vidua macroura Mammals Homo sapiens Homo sapiens Ourcbia oxtribi r (symmetry) n Character Reference .532 .320 .360 .120 .100 .195 .587 .7489 -.0200 .1500 .0700 -.2500 33 Bower* Plumage* Tail Tarsus Tail feather* Tail* Borgia (1985) Swaddle and Cuthul (1994a) Dunn ct aL (1994) Rintamaki et aL (1997) Rintamakd et al. (1997) Savalli (1998) .420 -.072 .080 .2994 .0754 .3676 61 500 42 Skeleton Thornhill et al. (1995) Manning et al. (1996) Arcese (1994) r(size) 10 21 42 46 7 Breast* Horn* ' Secondary sexual character. icanuy larger than zero (symmetry, statistic = 15.70; size, statistic •= 14.45, p < .001). The effect sizes for symmetry and size were not significantly different, as the 95% (3 of the difference includes zero (-0.026, 0.042). After we divided all samples into those considered to be secondary sexual characters and other characters, we calculated the mean weighted effect size for character size and symmetry. For morphological traits not classified as secondary sexual characters (n = 48), weighted mean effect size for character size was r = .184 (95% CI 0.152,0.210) and for character symmetry r = .174 (95% C3 0.132, 0.200). These means are significantly greater than zero (size, statistic = 12.95; symmetry, statistic = 12.19; all p < .001), and they are not significantly different (95% Q of difference, -0.029, 0.51). For morphological characters classified as secondary sexual characters (n •= 25), weighted mean effect size differed significantly and the effect for character symmetry was larger than the effect size for character size: size, r = .153, 95% d 0.088, 0.216; symmetry, r = .241, 95% a 0.174, 0.299; 95% Q of difference, 0.022, 0.154). Both means exceed zero (size, statistics ™ 6.48; symmetry, statistic = 10.184; all p < .001). Analyses based on studies as units of analysis When analyzed on the basis of the 33 studies, weighted mean effect size for character symmetry was r = .198 (95% CJ 0.152, 0.245); weighted mean effect size for character size was r = .154 (95% a 0.108, 0.201). The means are significantly greater than zero (size, statistic = 8.99; symmetry, statistic «• 1138; all p < .001), and they are not significantly different (95% CI of difference, -0.003, 0.093). Analyses based on species as units of analysis Analysis at the level of the 29 species revealed a weighted mean effect size for character symmetry of r = .219 (95% Q 0.169, 0.260); the weighted mean effect size for character size was r = .140 (95% Q 0.086, 0.191). The means are significantly greater than zero (size, statistic = 7.29; symmetry, statistic »= 11.61; all p < -001), and the means are significantly different (95% a of difference, 0.030, 0.136). In conclusion, the effect size for symmetry was significantly larger than that for character size in analysis across species, but not in the analyses of samples or studies. DISCUSSION Only recendy has fluctuating asymmetry been implied to play a role in sexual selection, with the first study appearing in 1985 (Borgia, 1985). As is the case for all novel approaches and developments in a field, a subsequent surge of interest generates both supportive and contradictory evidence (Hunt, 1997). This is not surprising for evolutionary biology, given that it is a science not generally based on consistent principles. Selection and other evolutionary agents differ between species and in time and space within species. Often in reviews, hypotheses are evaluated by vote-counting procedures without any consideration of sample sizes. Studies will be statistically significant depending on the magnitude of an effect and the sample size. If the power of a statistical test is low, for example, due to small sample size or large within-group variance, we cannot necessarily accept the null hypothesis of no relationship. This is the situation in which meta-analytic approaches become useful because they can help quantitatively assess the magnitude of effects after taking sample size and potential moderator variables into account (Cooper and Hedges, 1994; Hedges and Olkin, 1985; Rosenthal, 1991). We have used this approach to assess the relative importance of size and symmetry in sexual selection. Sample size varied from 7 to 500 across the studies analyzed in this paper (Table 1). The general role of asymmetry in sexual selection has been disputed because several studies have shown no effects, whereas others have demonstrated highly significant effects. In the present study, using studies that include symmetry and size of the same trait in relation to success in sexual competition, we demonstrated that both size and symmetry are significantly and positively related to sexual selection. Our analysis was conducted at three levels. Analysis using all samples for which both size and symmetry effects were available and analysis using means for studies revealed no significant difference between the effect size of symmetry and sexual selection and size and sexual selection. The difference at the species level of analysis, however, was significant, with symmetry having the larger effect size. The sample size for studies (n •= 33) and species (n = 29) were moderate. More research in which investigators include analysis of both size and symmetry in relation to mating success or attractiveness to the opposite sex is needed to more accurately measure the relative importance of size and symmetry in sexual selection. The near-zero correlation between the influences of symmetry versus size on sexual competition indicates that size and symmetry play independent or, as indicated by the analysis at the level of species, weakly similar, roles in the sexual selection systems of different species. The extent to which this may be due to size and asymmetry signaling different kinds of benefits needs careful theoretical and empirical consideration. A study of asymmetry and sexual selection based on a much larger sample of studies revealed an average effect size of 0.34 for species (Moller and Thomhill, 1998), which ia somewhat higher than the value found in the present study (0.219). 550 Hence, the sample used in the present study (because it contained only studies with information on effects of both character size and symmetry) may have been somewhat biased toward a weak effect Obviously, a sample with a weak effect of symmetry would be conservative in the sense that it would make any difference between the effect size of size and asymmetry more difficult to detect. We found a significantly larger difference in effect size between size and symmetry of characters for secondary sexual traits as compared to ordinary morphological traits at the level of sample analysis. Studies and species were not compared because some studies were of only one type of character. It has been suggested that secondary sexual characters demonstrate larger degrees of asymmetry because of a recent evolutionary history of directional selection (Mailer and Hoglund, 1991; Mpller and Pomiankowski, 1993). A larger degree of asymmetry in secondary sexual characters as compared to ordinary morphological traits should be more easily perceived by females and hence give rise to a larger effect size. This prediction was supported by our analyses. Recently, sexual selection was reviewed extensively by Andersson {1994). w n o found considerable evidence for its presence in a wide variety of organisms (see Andersson, 1994: Table 6A). Such compilations of positive evidence are of great value, but summaries of negative and positive studies are even more valuable. The relative importance of sexual selection can be assessed only from quantitative approaches such as meta-analysis. Meta-analysis estimates the overall effect of a relationship in a number of studies and furthermore allows quantitative assessment of the importance of moderator variables presumed to influence the magnitude of a particular relationship. This was the approach used in the present study, which suggests differences in the magnitude of effect sizes for the relative importance of size and symmetry in sexual selection. Although size has been implicated to play an important role in sexual selection (review in Andersson, 1994), our study confirms this. The effect of size in sexual selection, however, is no greater and is perhaps smaller than that of symmetry. In conclusion, the relative importance of character size and symmetry was evaluated meta-anah/tically for all available studies, and the calculations demonstrated significant relationships for both size and symmetry, but symmetry appears to have a slightly greater effect, especially in studies of secondary sexual traits. J. P. 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