Table 2.
Summary of models used in analysis of data on the impact of the three treatments on B. terrestris queens. Table includes details of models used in a model selection process (see Analysis section of the Methods for full details), the specific r packages used, as well as the parameters and estimates from the final or composite models. The importance and reliability of each parameter in the final models was assessed by checking for confidence intervals which did not cross zero (highlighted in bold in the model summaries below).
| Model types | Fixed Factors | Random Factors | R packages used | Final / Composite model | 95% CI | ||||
|---|---|---|---|---|---|---|---|---|---|
| Parameter | Estimate | SE | Lower | Upper | |||||
| Presence or absence of egg laying | GLM, GLMM | Hibernation, Pesticide, Parasite, Thorax | Qcolony, Mcolony | lme4 | Intercept | 5.969 | 5.200 | -4.171 | 16.110 |
| Hibernation | -1.514 | 0.316 | -2.131 | -0.898 | |||||
| Pesticide | -0.628 | 0.313 | -1.240 | -0.017 | |||||
| Thorax | -0.990 | 0.582 | -2.124 | 0.144 | |||||
| Timing of egg laying +* | Cox Regression | Hibernation, P1, P2, Parasite, Thorax | Qcolony, Mcolony | survival | Hibernation | -1.044 | 0.233 | -1.499 | -0.590 |
| P1 | 1.400 | 0.577 | 0.275 | 2.525 | |||||
| P2 | -0.573 | 0.236 | -1.034 | -0.112 | |||||
| Infection | 0.096 | 0.228 | -0.349 | 0.540 | |||||
| Thorax | -0.553 | 0.378 | -1.291 | 0.185 | |||||
| Presence or absence of adult offspring ◊ | GLM, GLMM | Hibernation, Pesticide, Parasite, Thorax | Qcolony, Mcolony | lme4 | Intercept | -0.750 | 0.360 | -1.453 | -0.048 |
| Pesticide | 1.214 | 0.458 | 0.320 | 2.107 | |||||
| Hibernation | 0.963 | 0.495 | -0.003 | 1.928 | |||||
| Weight lost during hibernation† | lm, lme | Hibernation, Parasite, Thorax | Qcolony, Mcolony | nlme | Intercept | 17.895 | 3.284 | 11.491 | 24.298 |
| Hibernation | -5.379 | 0.677 | -6.700 | -4.059 | |||||
| Parasite | 1.323 | 0.676 | 0.006 | 2.641 | |||||
| Thorax | -0.658 | 1.204 | -3.006 | 1.691 | |||||
| Hibernation survival | GLM, GLMM | Hibernation, Parasite, Thorax, PreWeight | Qcolony, Mcolony | lme4 | Intercept | 2.355 | 1.597 | -0.759 | 5.470 |
| Preweight | -7.195 | 2.546 | -12.159 | -2.231 | |||||
| Parasite | 0.447 | 0.497 | -0.522 | 1.415 | |||||
| Hibernation | 0.778 | 2.786 | -4.655 | 6.211 | |||||
| Preweight*Hib. | -6.945 | 5.606 | -17.877 | 3.987 | |||||
| Post-hibernation survival + | Cox Regression | Hibernation, Pesticide, Parasite, Thorax | Qcolony, Mcolony | lme4 | Null model | ||||
| Syrup consumption | lm, lme | Hibernation, Pesticide, Parasite | Qcolony, Mcolony | nlme | Intercept | 0.802 | 0.037 | 0.729 | 0.874 |
| Hibernation | -0.278 | 0.049 | -0.373 | -0.183 | |||||
| Pesticide | 0.024 | 0.488 | -0.927 | 0.974 | |||||
For Cox Regression models, random factors were included as frailty terms48, and model selection was undertaken as described for mixed models.
Timing of egg laying was analysed using a cox regression with proportional hazards. Examination of the residuals showed that the Pesticide factor did not meet the assumption of proportional hazards. To deal with this, the interaction between Pesticide and time was considered, and separate hazard functions were calculated for the period during pesticide exposure (P1: the first 17 days), and for the period after exposure (P2: 17 days - end)48. These two interaction terms were included instead of Pesticide in the model selection process.
For analyses during hibernation, the fixed factor Parasite indicates the exposure of queens to the parasite or a control (as infection status was unknown at this stage). All other analyses including Parasite used data on infection status (whether the queen was successfully infected or not).
Analysis included egg layers only.