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Data S1 Supplementary methods and results.

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.

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.

Table S3 Meta analytic models of the frequency-size (FS), preference-frequency (PF) and size-preference (SP) data sets.

Figure S1 The topology of the phylogenetic tree used in the frequency-size analysis.

Figure S2 The topology of the phylogenetic tree used in the preference-frequency analysis.

Figure S3 The topology of the phylogenetic tree used in the size-preference analysis.

Figure S4 Funnel plots of each data set, illustrating the variation in effect sizes (correlation coefficient, r) as a function of sample size.

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.

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