2.8. Statistical analyses
We studied the size of wasp combs delivered to the nest (recorded by the cameras) in terms of the number of cells, based on the number of cells of the largest diameter (D) and the smallest diameter (d), using the ellipse area formula:
\begin{equation} N\ =\ D/2\ \times\ d/2\ \times\ \pi\nonumber \\ \end{equation}
We used Linear Mixed Models (LMM) to study the variations in size of common-wasp and Asian-hornet combs. Year, breeding phenology (julian date), vespid species, number of nestlings, and age of the nestlings were predictors. Nesting territory was the random factor. To avoid overdispersion in the response variable, we calculated the mean values of cells of the wasp combs delivered each day to each nest.
To assess honey-buzzard prey preferences for vespids species, we used Ivlev’s selectivity index (E) to relate the proportion of prey delivered to nests to the proportion of the same prey available to the environment (Rebollo et al . 2017):
\begin{equation} E=\frac{r-p}{r+p}\nonumber \\ \end{equation}
Where r was the proportion of cells of each wasp species delivered to the nest. This proportion was estimated with the total of comb items recorded by the cameras. The proportion of wasps available in the field (p ) was estimated as the average percentage of workers of each wasp species captured within the 7 traps of each territory sampled. The E index ranges from –1 to + 1. Positive values indicate that honey-buzzards prey upon a species above its availability. We considered a “preferred prey” the species with an E index above zero (Rebollo et al . 2017).
We performed Cumulative Link Mixed Models (CLMM) to study the variations in the proportion of prey items delivered to the nests. We differentiated the 4 main types of prey items (common-wasp, Asian-hornet, reptiles, and birds) as response variables. CLMM models estimate the change in the proportion between the categories of the response variable directly from the number of observations. We explored the age of the nestlings, the study year, and the number of nestlings as predictors.
Finally, we analysed changes in the rate of prey delivery using GLMM with a Poisson error distribution and log link function. The response variable was the daily rate of prey delivery, measured as the account of prey items delivered to the nest each day. We explored the number of nestlings, the age of the nestlings, and the study year as predictors. The random effect was the nesting territory.
In all cases, Akaike’s (1987) information criterion (AIC) was calculated for each model for the model selection process; a smaller AIC indicates a better-fitting model as determined from the parsimony in the number of parameters. We used the cut-off of ΔAIC > 2 units to differentiate models with better explanatory power (Burnham and Anderson 2002). When faced with models having comparable AIC values after the selection process, the model with the lowest AIC value was preferred, even if it was more complex. This decision aimed to enhance the clarity of result interpretation and discussion. In all statistical procedures we considered a level of significance of p < 0.05. All statistical analyses were performed with R software v. 4.2.1 (R Core Team 2022). LMM, CLRM and GLMM analysis were performed with packages stats (R Core Team 2022), lme4 (Bates et al . 2014), nlme (Pinheiro et al . 2022), nnet (Venables and Ripley 2002), ordinal (Christensen 2022) and MuMIn (Barton 2022).