Supporting Information

Male quality, signal reliability and female choice: testing the expectations of inter-sexual selection

Morgan J. McLean, Phillip J. Bishop & Shinichi Nakagawa

MJM: [email protected]

Contents

1. Supplementary Methods...... 3 1.1 Data collection...... 3 1.2 Life history data...... 3 1.3 Publication bias...... 3 1.4 MCMC parameter settings...... 4 1.5. Random effects...... 4 1.6. Additional analysis...... 4 2. Supplementary results...... 5 3. Supplementary figures...... 6 4. Supplementary tables...... 11 5. Supplementary References...... 17

1 1. Supplementary Methods

1.1 Data collection

We collected and were able to use in our analyses 89 individual effect sizes, from 42 published studies (Table S1). The size-preference analyses used 49 of these effect sizes, which represented 24 different species. Of these 49 effect sizes, 17 were from frogs of the family Bufonidae, 14 from the family Hylidae, nine from the family Ranidae, with the remaining nine effect sizes being split amongst six other families. The frequency-size analyses used 18 effect sizes, which represented 15 different species. Of these 18 effect sizes six were from the family Bufonidae, three from the family

Hylidae, three from the family Discoglossidae with the remaining six effect sizes being split amongst

5 other families. The preference-frequency analyses used the remaining 22 effect sizes, which represented 13 species. Of these 22 effect sizes eight were from the family Hylidae, five from the family Bufonidae, three from the family Leptodactylidae, three from the family Discoglossidae with the remaining three all being from different families.

1.2 Life history data

We attempted to gather additional life history data (e.g. body size, longevity, and clutch size) on the species involved in our study, however we only found data for a limited number of species. Thus, the inclusion of these variables would have decreased the already small sample size of our study, and as such we did not include them in the final analyses.

1.3 Publication bias

To test for possible publication bias we calculated a Spearman’s correlation coefficient between effect sizes and corresponding sample sizes (if there is any evidence of a significant correlation between effect sizes and sample sizes then publication bias is present) (Sterne & Egger, 2005).

2 1.4 MCMC parameter settings

This prior has two parameters, V (which specifies variance) and nu (which specifies the degree of belief in V). For the size-preference and preference-frequency models we used V = 1-10 and nu = -1, however the frequency-size models required a stronger prior with the parameters V = 1 and nu =

0.002. To allow us to test the convergence of model parameters we ran each model three times (three

MCMC chains), and we used the same sampling parameter settings for all models. These parameters were: 1) the number of iterations of 108, 2) the thinning interval of 2 × 104 and 3) the number of burn- in of 8 × 107. These settings gave 1,000 samples, which made up our posterior distributions for all parameter estimates. We then confirmed convergence of model parameters applying the Gelman-

Rubin statistic to the three chains (the potential scale reduction factor should be less than 1.1 among model replicates; Gelman & Rubin, 1992). The results presented are from only the first chain of each model.

1.5. Random effects

The number of species for which we found multiple effect sizes was low in all analyses (size- frequency, n = 2, preference-frequency, n = 4, size-preference, n = 11). As a result, the inclusion of species as a random factor may not produce meaningful results. To test this possibility, we repeated the analysis without species as a random factor. However, the results for the fixed effects were qualitatively and quantitatively the same, so the analyses including species were presented in the main text. The heterogeneity estimates for the analyses excluding species effects are presented in table S1.

1.6. Additional analysis

We also calculated the weighted mean effect sizes (i.e. meta-analytic means) for each relationship using subsets of the entire data set. These subsets consisted of studies that provided effect size estimates for at least two of the three relationships. This resulted in four data subsets, one consisting of studies that reported estimates for all three relationships, and three subsets consisting of studies that reported estimates for two of the relationships. Weighted mean effect sizes were then calculated for

3 each relationship in each data set using the rma function from the metaphor statistical package

(Viechtbauer, 2010).

2. Supplementary results

There was no evidence of publication bias in any of the data sets (frequency-size: rs = -0.209 , p =

0.406; preference-frequency: rs = 0.321, p = 0.145; size-preference: rs = -0.060, p =0.683; Fig. S4).

When using only studies that contributed to more than one or the relationships of interest, the meta- analytic means and associated confidence intervals (CIs) showed similar trends compared to the estimates from the full data set (i.e. much overlap in CIs), although some estimates had very large uncertainty due to limited sample sizes (Fig. S5).

4 3. Supplementary figures

Figure S1. The topology of the phylogenetic tree used in the frequency-size analysis. Numbers shown are effect size (correlation coefficient, r) estimates for each node. There is evidence of a phylogenetic signal in this data set.

5 Figure S2. The topology of the phylogenetic tree used in the preference-frequency analysis. Numbers shown are effect size (correlation coefficient, r) estimates for each node. There is no evidence of a phylogenetic signal in this data set.

6 Figure S3. The topology of the phylogenetic tree used in the size-preference analysis. Numbers shown are effect size (correlation coefficient, r) estimates for each node. There is no evidence of a phylogenetic signal in this data set.

7 Figure S4. Funnel plots of each data set, illustrating the variation in effect sizes (correlation coefficient, r) as a function of sample size. a. The frequency-size data set. b. The preference-frequency data set. c. The size-preference data set. The continuous lines represent r = 0, the dashed line represents the mean effect size of the data from the mixed-effects meta-analysis for each data set.

8 Figure S5. Weighted mean effect sizes (meta-analytic means), and associated 95% confidence intervals, CIs (or credible intervals), calculated using only studies that had effect size estimates for more than one relationship, along with the overall results from the complete analysis for comparison.

The dashed lines separate different subsets of the original data set. From top to bottom these are: the entire data set used in the final analysis; the estimate using only studies that had estimates for all three relationships; the estimates using studies that reported both the preference-frequency and size- preference relationships; the estimates using studies that reported the frequency-size and preference frequency relationships; the estimates using studies that reported the frequency-size and size- preference relationships. For all data subsets, the number of contributing studies are given in brackets.

9 4. Supplementary tables

Table S1. Posterior means (percentage) of the estimates of heterogeneity resulting from non- phylogenetic effects (i.e. residual) and from phylogeny for each of our meta-analytic models, when species was not included as a random factor in the analysis. We present heterogeneity estimates for both mixed-effects meta-analyses (MMA) and phylogenetic mixed-effects meta-analyses (PMMA).

Heterogeneity (%) Analysis Non-phylogenetic Phylogeny

Frequency-size (MMA) 100 -

(PMMA) 52.61 47.39

Preference-frequency (MMA) 100 -

(PMMA) 100 <0.001

Size-preference (MMA) 100 -

(PMMA) 100 <0.001

Table S2: All species and studies used in our analyses, along with associated sample sizes, effect sizes (converted to Pearson’s correlation coefficient, r), and the references of the original publications. Sampl Effect Species Relationship e Size Size (r) Reference size – Alytes obstetricans preference 81 0.889 Lode & Le Jacques, 2003 size- Amietophrynus pardalis preference 34 -0.123 Cherry, 1992 size- Amietophrynus pardalis preference 77 -0.233 Cherry, 1992 size- Amietophrynus pardalis preference 56 -0.068 Cherry, 1992 size- Amietophrynus rangeri preference 81 0.161 Cherry, 1993 size- Amietophrynus rangeri preference 72 -0.003 Cherry, 1993 size- Amietophrynus rangeri preference 39 0.140 Cherry, 1993 size- Anaxyrus americanus preference 132 -0.061 Kruse, 1981 size- Anaxyrus americanus preference 15 -0.086 Sullivan, 1992 10 size- Anaxyrus americanus preference 18 -0.130 Wilbur et al., 1978 size- Anaxyrus boreas preference 171 0.619 Olson et al., 1986 size- Anaxyrus boreas preference 186 0.276 Olson et al., 1986 size- Anaxyrus boreas preference 223 0.101 Olson et al., 1986 size- Anaxyrus cognatus preference 174 0.091 Sullivan, 1983 size- Anaxyrus quercicus preference 49 0.374 Wilbur et al., 1978 size- Anaxyrus quercicus preference 34 0.528 Wilbur et al., 1978 size- Anaxyrus terrestris preference 16 0.110 Wilbur et al., 1978 size- Dendropsophus elegans preference 258 0.329 Bastos & Haddad, 1996 size- Engystomops pustulosis preference 11 0.710 Ryan, 1983 size- Epidalea calamita preference 21 0.438 Arak, 1988 size- Hyla arborea preference 111 0.182 Deorense & Tejedomadueno, 1990 size- Hyla arborea preference 38 0.101 Friedl & Klump, 2005 size- Hyla arborea preference 56 0.070 Friedl & Klump, 2005 size- Hyla chrysoscelis preference 147 0.104 Morris, 1989 size- Hyla chrysoscelis preference 66 0.248 Morris, 1989 size- Hyla chrysoscelis preference 94 0.109 Morris, 1989 size- Hyla chrysoscelis preference 157 0.151 Morris, 1989 size- Hyla versicolor preference 35 0.006 Fellers, 1979 size- Hyla versicolor preference 26 0.359 Gatz, 1981 size- Hyla versicolor preference 56 -0.016 Gatz, 1981 size- Hyperolius marmoratus preference 45 0.364 Dyson et al., 1998 size- Hyperolius marmoratus preference 155 0.155 Dyson et al., 1992 size- Hyperolius marmoratus preference 69 0.256 Dyson et al., 1992 size- Hyperolius marmoratus preference 93 -0.223 Dyson et al., 1992 size- Litoria chloris preference 43 -0.291 Morrison et al., 2001 size- Litoria xanthomera preference 20 -0.420 Morrison et al., 2001 11 size- Oophaga pumilio preference 8 0.300 Prohl, 2003 size- Physalaemus enesefae preference 234 0.150 Tarano & Herrera, 2003 size- Pseudacris crucifer preference 52 0.406 Gatz, 1981 size- Rana clamitans preference 21 0.310 Wells, 1977 size- Rana sylvatica preference 299 0.223 Berven, 1981 size- Rana sylvatica preference 293 0.137 Berven, 1981 size- Rana sylvatica preference 93 0.313 Berven, 1981 size- Rana sylvatica preference 24 0.736 Berven, 1981 ize- Rana sylvatica preference 16 0.887 Berven, 1981 size- Rana sylvatica preference 398 0.238 Howard & Kluge, 1985 size- Rana temporaria preference 40 0.395 Elmberg, 1991 size- Rana temporaria preference 49 0.220 Elmberg, 1991 size- Uperoleia rugosa preference 375 0.287 Robertson, 1986 frequency- Acris crepitans size 238 -0.466 Wagner, 1989 frequency- Alytes cisternasii size 40 -0.698 Marquez, 1995 frequency- Alytes obstetricans size 81 -0.665 Lode & Le Jacques, 2003 frequency- Alytes obstetricans size 15 -0.576 Marquez, 1995 frequency- Amietophrynus rangeri size 31 -0.220 Cherry, 1993 frequency- Anaxyrus americanus size 16 -0.770 Sullivan, 1992 frequency- Anaxyrus americanus size 16 -0.270 Sullivan, 1992 frequency- Anaxyrus americanus size 14 0.050 Sullivan, 1992 frequency- Anaxyrus woodhousii size 15 -0.560 Sullivan, 1992 frequency- Bufo bufo size 20 -0.884 Davies & Halliday, 1978 frequency- Crinia georgiana size 91 -0.774 Smith & Roberts, 2003 frequency- Engystomops pustulosis size 136 -0.530 Ryan, 1980 frequency- Hyla arborea size 41 -0.324 Deorense & Tejedomadueno, 1990 frequency- Hyla chrysoscelis size 30 -0.648 Morris & Yoon, 1989 12 frequency- Metaphrynella sundana size 22 0.167 Lardner & Lakim, 2004 frequency- Oophaga pumilio size 8 0.060 Prohl, 2003 frequency- Physalaemus enesefae size 106 -0.200 Tarano, 2001 frequency- Uperoleia rugosa size 100 -0.710 Robertson, 1986 preference- Acris crepitans frequency 11 -0.185 Ryan et al., 1992 preference- Acris crepitans frequency 10 -0.818 Ryan et al., 1992 preference- Acris crepitans frequency 48 -0.324 Ryan et al., 1992 preference- Acris crepitans frequency 14 -0.724 Ryan et al., 1992 preference- Acris crepitans frequency 11 -0.822 Ryan et al., 1992 preference- Acris crepitans frequency 19 -0.106 Ryan et al., 1992 preference- Alytes cisternasii frequency 72 -0.298 Marquez & Bosch, 1997 preference- Alytes cisternasii frequency 42 0.205 Marquez & Bosch, 1997 preference- Alytes obstetricans frequency 81 -0.789 Lode & Le Jacques, 2003 preference- Anaxyrus americanus frequency 17 -0.461 Howard & Kluge, 1985 preference- Anaxyrus americanus frequency 10 -0.418 Howard & Young, 1998 preference- Epidalea calamita frequency 22 -0.598 Arak, 1988 preference- Hyla intermedia frequency 40 -0.111 Castellano et al., 2009 preference- Incilius valliceps frequency 10 0.000 Wagner & Sullivan, 1995 preference- Metaphrynella sundana frequency 7 -0.804 Lardner & Lakim, 2004 preference- Oophaga pumilio frequency 8 -0.400 Prohl, 2003 preference- Physalaemus enesefae frequency 28 -0.574 Tarano & Herrera, 2003 preference- Physalaemus enesefae frequency 33 -0.153 Tarano & Herrera, 2003

preference- Physalaemus enesefae frequency 30 -0.445 Tarano & Herrera, 2003 preference- Pseudacris crucifer frequency 33 -0.394 Forester & Czarnowsky, 1985 preference- Pseudepidalea viridis frequency 30 -0.356 Castellano & Giacoma, 1998 preference- Rana dalmatina frequency 24 -0.735 Lesbarreres et al., 2008

13 Table S3: Meta analytic models of the frequency-size (FS), preference-frequency (PF) and size- preference (SP) data sets. For each data set the results of a mixed-effects meta-analysis (MMA) and a phylogenetic mixed-effects meta-analysis (PMMA) are presented.

Parameter Lower estimate Posterior mean 95% Upper Fixed effects (posterior mode) (sd) CI 95% CI model without phylogeny FS-MMA intercept 0.517 0.522(0.075) 0.393 0.679 PF-MMA intercept 0.451 0.444(0.072) 0.301 0.583 SP-MMA intercept 0.218 0.223(0.048) 0.126 0.312 model with phylogeny FS-PMMA intercept 0.583 0.523(0.139) 0.250 0.766 PF-PMMA intercept 0.446 0.444(0.075) 0.304 0.600 SP-PMMA intercept 0.224 0.219(0.047) 0.126 0.311

Variance Lower component Posterior mean 95% Upper Random effects (posterior mode) (sd) CI 95% CI model without phylogeny FS-MMA species variance <0.001 <0.001 (<0.001) <0.001 <0.001 PF-MMA species variance 0.00271 0.0535 (0.0653) <0.001 0.180 SP-MMA species variance <0.001 <0.001 (<0.001) <0.001 <0.001 FS-MMA residual variance 0.107 0.120 (0.0555) 0.0340 0.230 PF-MMA residual variance 0.00186 0.0848 (0.0676) <0.001 0.219 SP-MMA residual variance 0.0820 0.0936 (0.0258) 0.0498 0.142 model with phylogeny FS-PMMA phylogenetic variance <0.001 <0.001 (<0.001) <0.001 <0.001 PF-PMMA phylogenetic variance 0.00410 0.0948 (0.132) <0.001 0.365 SP-PMMA phylogenetic variance <0.001 <0.001 (<0.001) <0.001 <0.001 FS-PMMA species variance <0.001 <0.001 (<0.001) <0.001 <0.001 PF-PMMA species variance 0.00208 0.0371 (0.0506) <0.001 0.142 SP-PMMA species variance <0.001 <0.001 (<0.001) <0.001 <0.001 FS-PMMA residual variance 0.0830 0.124 (0.0627) 0.0384 0.262 PF-PMMA residual variance 0.00181 0.0567 (0.0598) <0.001 0.174

SP-PMMA residual variance 0.0784 0.0956 (0.0260) 0.0544 0.150

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