Table 3.
Summary of models fitted to community-genetic effect size data. Study and residual variance give point estimates for variance components (variance in effect sizes among studies and between effect sizes within studies, respectively, after conditioning on the fixed effects). The percentage of heterogeneity that these effects account for is shown in parentheses. The remaining heterogeneity (100% – study variance% – residual variance%) is attributable to variation within effect sizes (i.e. the measurement error variance). The final three columns give model-checking statistics: the minimum number of effective samples across all parameters (values closer to 1000 indicate a lower degree of autocorrelation within MCMC samples), the maximum absolute autocorrelation of MCMC samples at lag 1 across all parameters (values closer to 0 indicate a lower degree of autocorrelation within MCMC samples) and the maximum potential scale reduction factor across all parameters (PSRF; Gelman–Rubin diagnostic; values closer to 1 indicate better convergence of replicate MCMC chains)
| Effect size measure* | Fixed effects† | Study variance (%) | Residual variance (%) | Effective samples | Auto-correlation | PSRF |
|---|---|---|---|---|---|---|
| d | ∼Intercept | 0.118 (35.5) | 0.018 (5.3) | 1000 | 0.044 | 1.010 |
| d | ∼Outcome level (community/ecosystem) | 0.119 (35.6) | 0.018 (5.4) | 880 | 0.063 | 1.007 |
| d | ∼Outcome type | 0.085 (29.2) | 0.009 (3.1) | 711 | 0.090 | 1.010 |
| d | ∼Intervention size | 0.115 (35.2) | 0.016 (4.9) | 1000 | 0.041 | 1.009 |
| d | ∼Trophic contrast | 0.180 (32.8) | 0.035 (6.4) | 769 | 0.039 | 1.010 |
| d | ∼Sampling strategy | 0.126 (37.0) | 0.018 (5.2) | 717 | 0.055 | 1.007 |
| d | ∼Disparity in sampling scale | 0.111 (33.8) | 0.026 (7.9) | 960 | 0.037 | 1.006 |
| z(r) | ∼Intercept | 0.120 (58.1) | 0.003 (1.6) | 947 | 0.037 | 1.007 |
| z(r) | ∼Outcome level (community/ecosystem) | 0.131 (60.3) | 0.003 (1.5) | 1000 | 0.049 | 1.010 |
| z(r) | ∼Outcome type | 0.150 (63.3) | 0.004 (1.5) | 664 | 0.061 | 1.005 |
| z(r) | ∼Sample unit scale | 0.098 (53.0) | 0.004 (2.0) | 873 | 0.067 | 1.010 |
| z(r) | ∼Sampling strategy | 0.100 (53.6) | 0.004 (1.9) | 1000 | 0.019 | 1.007 |
| z(r) | ∼Genetic diversity type | 0.096 (52.5) | 0.004 (2.1) | 704 | 0.034 | 1.006 |
| z(r) | ∼Locality characteristics | 0.091 (51.1) | 0.004 (2.1) | 828 | 0.049 | 1.007 |
Effect sizes were either standardized mean differences (d) or z-transformed correlation coefficients (z(r)).
Sources of heterogeneity fitted as effects in the meta-analytic models.