Table 4.
Mixed-effects model analysis of a simulated dataset estimating variance components and regression slopes for nutrient manipulations on fecundity, endoparasite loads, body length, exploration levels and male morph types; N[population] = 12, N[container] = 120 and N[animal] = 960 (N[male] = N[female] = 480). 95% CI (confidence intervals) were calculated by the confint function in lme4. The observation-level variance was obtained by using the trigamma function. In the Morph models, both the observation-level variance and (theoretical) distribution-specific variance were used; note that ones in brackets use the distribution-specific variance for R2 and ICC. ICC[Container] is not a typical ‘repeatability’ but the proportion of variance due to the container effect beyond the population variance.
| fecundity models (log-link) quasi-Poisson mixed models |
parasite models (log-link) negative binomial mixed models |
size models (log-link) gamma mixed models |
exploration models (log-link) gamma mixed models |
morph models (logit-link) binomial (binary) mixed models |
||||||
|---|---|---|---|---|---|---|---|---|---|---|
| model name | null model | full model | null model | full model | null model | full model | null model | full model | null model | full model |
| fixed effects | b [95% CI] | b [95% CI] | b [95% CI] | b [95% CI] | b [95% CI] | b [95% CI] | b [95% CI] | b [95% CI] | b [95% CI] | b [95% CI] |
| intercept | 1.630 [1.379, 1.882] | 1.261 [0.989, 1.532] | 0.766 [0.330, 1.202] | 1.752 [1.282, 2.223] | 2.682 [2.616, 2.689] | 2.737 [2.699, 2.775] | 4.752 [4.555, 4.949] | 4.056 [3.842, 4.269] | −0.108 [−0.718, 0.501] | −0.740 [−1.450, −0.030] |
| treatment (experiment) | — | 0.491 [0.391, 0.591] | — | −0.768 [−0.870, −0.667] | — | 0.033 [0.023, 0.044] | — | 2.007 [1.965, 2.050] | — | 0.840 [0.422, 1.258] |
| habitat (wet) | — | 0.152 [0.055, 0.249] | — | 0.700 [0.599, 0.801] | — | 0.009 [−0.001, 0.019] | — | −0.560 [−0.603, −0.518] | — | 0.414 [0.002, 0.826] |
| sex (male) | — | — | — | −2.198 [−2.511, −1.884] | — | −0.213 [−0.230, −0.196] | — | −1.105 [−1.256, −0.955] | — | — |
| random effects | σ2 | σ2 | σ2 | σ2 | σ2 | σ2 | σ2 | σ2 | σ2 | σ2 |
| population | 0.178 | 0.187 | 0.375 | 0.541 | 0.0026 | 0.0039 | 0.071 | 0.104 | 1.002 | 1.111 |
| container | 0.042 | 0.059 | 1.976 | 0.613 | 0.0140 | 0.0014 | 0.364 | 0.163 | 0.136 | 0.186 |
| observation-level (distribution-specific) | 0.477 | 0.349 | 0.873 | 0.397 | 0.0069 | 0.0064 | 1.664 | 0.118 | 4.010 (3.290) | 4.010 (3.290) |
| fixed factors | — | 0.066 | — | 1.479 | — | 0.0116 | — | 1.393 | — | 0.220 |
 (%) |
— | 9.96 | — | 48.50 | — | 49.54 | — | 78.34 | — | 3.98 (4.57) |
 (%) |
— | 46.95 | — | 86.33 | — | 72.52 | — | 93.34 | — | 27.46 (31.55) |
| ICC[Population] (%) | 25.33 | 31.30 | 11.53 | 34.44 | 11.38 | 33.17 | 3.40 | 26.94 | 19.48 (22.64;) | 20.95 (24.23) |
| ICC[Container] (%) | 5.94 | 9.79 | 60.80 | 39.02 | 59.57 | 12.37 | 17.34 | 42.34 | 2.64 (3.07;) | 3.50 (4.05) |
| AIC | 2498.8 | 2412.3 | 4342.6 | 3920.5 | 3379.9 | 3139.5 | 11223.8 | 9004.3 | 605.5 | 589.6 |