Data analyses
To analyze relationships between colony size and biological parameters of the colonies we used linear mixed models (LMMs) using the R package ‘nlme’ (Bates et al. 2015). Prior to model construction, data from individual species (adult bee counts and biological parameters) were standardized by using z-scores, to allow meaningful comparisons among the different bee species, and effect sizes. The response variable was the number of adult bees per colony, with the external activity, egg-laying rate, food stocks and number of brood cells, and included as fixed effects, and species (five levels) held as random grouping factor.
We considered only simple models (single terms, four competing models). Candidate models were ranked using the dredge function in the R package “MuMIn ” (AICc values – Akaike Information Criterion – corrected for small sample sizes) (Barton, 2019). Models within 2 delta AICc of the model with the lowest AICc value were considered statistically equivalent. Parameter estimates and confidence intervals (95%) of models were constructed using restricted maximum likelihood (REML) and model fit was assessed using marginal R2values (Nakagawa and Schielzeth 2013). In addition to analyses with standardized data (z-scores), simple regression models of the raw data from individual species were used to test relationships between colony size and predictors, using the lm function in the R “car ” package (Fox and Weisberg 2011). Residuals from selected models were visually checked for assumptions of homogeneity of variance and normality using plots.
For obtaining the equations for estimating the colonial sizes according to the measured parameters, a simple regression was used. All analyses were performed in the R software (R Core Team 2018).