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Additional results 1) Assessment of which random factors to include in the multivariate model We tested how much of the variance was explained by our nested random factors of class, family, species and study population. None of the higher order phylogenetic terms (class, family and species) explained any of the variance in weighted mean effect sizes, with only study population explaining any variance at all, and this estimate was very small (0.4%). We dropped each of the higher order taxonomic terms in turn, but this did not explain any additional variance in the next term down, and study population explained no further variance when all other terms had been dropped, suggesting little taxonomic signal in HFC studies. To keep our multivariate models as simple as possible, we only retained the study population random factor, to help account for pseudoreplication of results. To account for the fact that some authors reported correlations for the same trait with more than one of the MLHinc metrics, we included an additional random factor to multivariate models where this new pooled metric was used. This random factor scored the exact trait that was measured, and was nested within study population resulting in a two-factor nested random design. This random factor only accounted for around 0.1% of the variance in a null model of all MLHinc effect sizes, but was retained to help account for pseudoreplication. 2) Sex of individuals Sex of individuals had no directional effect on weighted mean effect sizes (sex modelled as a continuous variable; regression coefficient = -0.003, s.e. = 0.02, t77 = -0.16, P = 0.87), and, when modelled as a categorical variable, effect sizes in females (r = 0.094) and males (r = 0.090) were not significantly different from each other (t263 = 0.22, P = 0.83). 3) Mean effect sizes for fitness versus non-fitness traits Effect sizes were of a similar order of magnitude, and not significantly different, for fitness and non-fitness traits, for both the MLHinc metric (fitness traits r = 0.094, non-fitness traits r = 0.085, t = 0.66, P = 0.48, n = 431 ); and mean d2 (fitness traits r = 0.074, non-fitness traits r = 0.060, t = 0.66, P = 0.51, n = 183). Similarly, when we restricted the analysis to lifehistory traits, fitness and non-fitness traits were of a similar magnitude and not significantly different (MLHinc: fitness traits r = 0.100, non-fitness traits r = 0.088, t = 0.50, P = 0.61, n = 166; mean d2: fitness traits r = 0.098, non-fitness traits r = 0.079, t = 0.46, P = 0.65, n = 61). Model averaging placed a fairly low relative variable importance (Σωi = 0.41) on this categorisation of traits. 4) Comparison of morphological traits in wild versus captive populations It has been suggested that morphological traits in domestic species that have been subject to artificial directional selection should have relatively higher dominance estimates than morphological traits in wild outbred species (Crnokrak and Roff 1995). We tested whether this would translate into larger weighted mean effect sizes for morphological traits in domestic species than for morphological traits in wild outbred species. In fact we found slightly higher mean effect sizes in wild populations (r = 0.064, n = 148) than domestic populations (r = 0.054, n = 63), however this difference was not significant (t46 = 0.02, P = 0.98). 5) Model averaging: wild populations only We repeated the model averaging analysis in the subset of wild populations to determine the relative importance of population demographic history amongst these studies. The best supported model incorporated the fixed factor of trait type, with the null model being the second best supported model (Table S4). Demographic history of the population had a similar effect as captivity status (Σωi = 0.28), and sex had a similar importance as the analysis incorporating all effect sizes (Σωi = 0.29), although the relative variable importance of trait type (Σωi = 0.64) was higher in this analysis, and the importance of publication status was lower (Σωi = 0.29).