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.