10.1111jav.01710_nest_Data

10.1111jav.01710_nest_Dat

10.1111jav.01710_Environmental_Data

10.1111jav.01710_Environmental_Dat

Egg volume (cm³) effects on hatchling mass (g).

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: “mother ID” = 0.230 g. (DOCX)</p

Number of helpers at laying predicts the number of helpers during the nestling rearing period.

Mean ± standard deviation (SD) is presented for both male and female helper numbers (dashed line indicates a 1:1 relationship). For female helper number, linear model: N = 271 breeding attempts, β = 0.94 ± 0.017. For male helper number, linear model: N = 271 breeding attempts, β = 0.93 ± 0.022). The data underlying this figure can be found at https://doi.org/10.5281/zenodo.8385995. (TIF)</p

Bivariate model of egg volume (cm³) and maternal provisioning rates (feeds/hour) including the number of helpers as predictors.

This analysis used the full data sets from the egg volume model in Table 1 (490 measures from 271 clutches) and the maternal provisioning rate model in Table 3 (124 measures from 124 broods). Approximately 59 clutches/broods had measures for both egg volume and provisioning rate, while 277 clutches/broods had measures for only one of these 2 metrics. This model was fitted in R using the brms package (v2.34; [72]), using a default prior distribution for random variance components and a normal distribution of mean 0 and standard deviation 100 for fixed effects, and 4 chains of 50,000 MCMC iterations, with 25,000 as initial burn-in and sampling every 10 iterations in each case. Residual variation for maternal provisioning rates was fixed to 0.01 (i.e., no residual variation was left after accounting for differences among clutches). Convergence was assessed via Rhat values, which were always below 1.01 and visual inspection of chain traces. Response terms and fixed effect variables were mean centered and scaled by one standard deviation prior model fit to improve model convergence. “Rainfall” and “Rainfall2” were fitted as orthogonal polynomial, and their estimates are not back transformed in this table (i.e., units do not refer to the real data scale). Mean posterior estimates (“Mean”) and their 95% credible intervals (“95% CI”) are provided. (DOCX)</p

Model selection table for models explaining variation in maternal provisioning rate (feeds/hour), when population-level variation in female and male helper number were partitioned into their within-mother (Δ) and among-mother (μ) components prior to model selection.

Model coefficients (effect sizes ± standard errors) are shown along with number of model parameters (“k”), AIC and ΔAIC. “Heat waves” (days above 35°C) and “Brood size” were mean centered and scaled by one standard deviation prior model fit to improve model convergence. Similarly, “Rainfall” and “Rainfall2” were fitted as orthogonal vectors, and their estimates are not back transformed in this table (i.e., units do not refer to the real data scale). (DOCX)</p

Model selection table for models explaining variation in clutch size (zero-truncated models) after partitioning variation in female and male helper number into their within-mother (Δ) and among-mother (μ) components.

Models including female or male helper number components received similar support from the data that the intercept-only model. Model coefficients (effect sizes ± standard errors) are shown along with number of model parameters (“k”), AIC and ΔAIC. “Clutch order” was mean centered and scaled by one standard deviation prior model fit to improve model convergence. (DOCX)</p

Summary of results of a linear mixed model explaining variation in maternal provisioning rate (feeds/hour), 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 3. 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” = 0.92 feeds/hour, “group ID” = 0 feeds/hour, “mother ID” = 0 feeds/hour. “Heat waves” (days above 35°C) and “Brood size” 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 maternal provisioning rate [feeds/hour] 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 (S11 Table).</p

Egg volume (cm³) effects on egg mass (g).

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: “mother ID” = 0.021 g. (DOCX)</p

Sliding window analysis for the effect “heat waves” (days above 35°C) on egg volume.

See Section A in S1 File above for methods and interpretation. (a) Effect of the best-supported “heat waves” index (i.e., that calculated for 0–13 days prior to egg laying) on egg volume when tested within the baseline model. Raw data points in black and regression line (± SE) in blue. (b) AIC support (i.e., the difference in AIC between a given sliding window model and the baseline model) for all possible sliding windows of >4 days in length within the 80 days before egg laying. The darker the color of the tiles, the stronger the support for a given window. (c) Histogram showing the AIC support for the best-supported heat wave index windows arising from 25 randomisations (i.e., the distribution of AIC support expected if no relationship exists between the heat waves index and egg volume). The blue dashed line illustrates the AIC support achieved using the best-supported window from the real data set. The data underlying this figure can be found at https://doi.org/10.5281/zenodo.8385995. (TIF)</p