Statistical analysis
Data analysis was done in R, version 3.4.0 (R Core Team 2017). To investigate the probability of predator detection and mobbing behaviour in red kites, we used mixed effect cox-proportional hazard models with both a binary success variable and a time-to-event variable as response, and date-ID and nest-ID as random effects (coxme function; R package coxme; Therneau 2018). As detection of the decoy predator and mobbing behaviour represent different processes, we analysed the two processes in separate models using detection success (binary) together with time-to-detection as responses to model detection probability (detection model) and capture success (binary) together with time-to-capture to model mobbing intensity (capture model). This allowed for differentiation between factors affecting detection probability and capture probability.
Brood size and age (of the oldest nestling) on the day of the exposure trial, rodent activity index, and food supplementation were included as focus predictors in both models. Mean daily precipitation (Source: MeteoSchweiz), ambient temperature (measured at the beginning of the exposure trial), wind (binary: low vs. high, recorded at the beginning of the exposure trial), distance between decoy predator and red kite nest, and year (categorical) entered as fixed control variables. In the capture model, we included three more control variables potentially affecting capture probability: proximity to trees, disturbance, and whether repeated trials on the same nest within the same season had been performed (denoted as “repetition”). All numeric explanatory variables were centred and scaled before including them in the analyses. The initial models included all two-way interactions between focus variables. Age of nestlings was added as a quadratic term, whereby orthogonal polynomials were used to avoid collinearity. Interactions and quadratic terms with 95 % CI of effect sizes overlapping zero were excluded by backward elimination, while all main effects remained in the model. Effects with 95 % CI not overlapping zero were considered as important effects.