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).