Summary of results of a linear mixed model explaining variation in egg volume (cm³), including every main effect of interest when population-level variation in female and male helper number were partitioned into their within-mother (Δ) and among-mother (μ) components.

Note that partitioning within-mother (Δ) and among-mother (μ) components might produce bias in the among-mother component [70]; however, this method produces robust estimation of the within-mother component, which the evidence of plasticity is based upon. Sample size and structure were identical to those for Table 1. Model estimates, standard errors (SE) and their 95% confidence intervals (CI (95%)) are provided along with results from likelihood-ratio tests (χ2df = 1 and associated p-values) assessing the statistical significance of each predictor within the full model (i.e., a model containing all of the terms in the table below). Random effect standard deviation: “season” = 0 cm3, “group ID” = 0 cm3, “clutch ID” = 0.070 cm3, “mother ID” = 0.275 cm3. “Heat waves” (days above 35°C), “Clutch size,” and “Egg position” were mean centered and scaled by one standard deviation prior model fit to improve model convergence. Estimates for “Rainfall” and “Rainfall2” given for 100 mm of rainfall (e.g., change in egg volume [cm3] per 100 mm of rainfall). “df” = degrees of freedom for likelihood-ratio tests. This analysis yielded the same conclusions when taking an AIC-based model selection approach (S5 Table).