Predator-prey temporal overlap models
We fit nine models to examine correlations with tree vole detections as
the dependent variable (three time-bin widths x three time lags
(described below)) and six models using flying squirrels. In each model,
tree vole (or flying squirrel) encounter histories (detection (1) or
non-detection (0)) comprised the dependent binomially distributed
variable and each other species’ detections were independent variables.
At time lag t0 (unlagged), we examined whether nest predator
presence was correlated with tree vole presence. Tree voles used nest
platforms intensively with a high number of detections per day (Linnell
et al., 2018), therefore we interpreted positive correlations as
representing potential attraction of the nest predator to the nest while
tree voles were present.
To examine hypotheses of lagged effects of predator presence on tree
vole presence (t + 1, t + 12 ), we used predator detection in the
previous time step as the independent variables in our t + 1 andt + 12 models. For example, a weasel detected on occasion three
in a t0 encounter history of five occasions (00100) would result
in a t + 1 of 00010. Negative correlations of t + 1 were
thus interpreted as immediate and potentially direct outcomes of the
nest predator’s visit to the tree vole nest platform in the previous
time step. To examine a potential longer-term, up to 12-week, lag in
tree vole response to predator visit at nest site we developed an
independent variable for any previous detection of a predator during the
encounter history. For example, a predator detected during time three of
a 15 occasion encounter history with a t0 of (001000000000000) would
result in 000111111111111 for model t + 12 . Tree vole models
included time lags of t0 , t + 1, t + 12, and flying
squirrel models time lags of t0 and t + 1 .
We made predictions of positive (+), negative (-), or neutral
interactions (=) with the number of symbols indicating the predicted
strength of correlation. We predicted that weasels and owls would be
attracted to nests with tree voles present (t0 ; ++), tree vole
detections immediately following a predator detection would be
negatively correlated (t + 1 ; —) but those
correlations would weaken through time (t + 12 ; -). We
hypothesized that flying squirrels would be weakly attracted to tree
voles at t0 (+) as they potentially use the same nests and that
those effects would remain weak through time at t + 1 (+)
and t + 12 (+). We predicted that birds digging would be
weakly positively correlated with tree vole detections at t0 (+)
as they would be targeting insects in decaying organic materials
prevalent at tree vole nests but that co-occurrence would be incidental
with no effect through time at t + 1 (=) and t + 12(=). For flying squirrels as the dependent variable, we predicted
moderate negative correlations of owls and weasels as we expected these
predators to have stronger correlations with flying squirrels att + 1 (-) and neutral (=) with regards to birds digging.
We used generalized linear mixed models with a logistic link function
for our analyses. To account for spatial and temporal dependence of
observations, we modeled individual nest platforms and the next coarser
bin-width (e.g. 1-week bin-width for 1-day bin-width encounter
histories) as random effects. We represented a priori hypotheses
as fixed effect independent variables (R package MCMCglmm; (Hadfield,
2010; R Core Team, 2018)). We used uniform and multivariate normal
priors for fixed and random effects parameters and used the
inverse-Wishart distribution for variance components of priors. We used
four Markov chains of 200,000 with a burn-in period of 100,000, and set
the thin to 0.02. To assess convergence, we visually evaluated chains
and estimated the Gelman-Rubin convergence diagnostic in the coda
package in R (Brooks & Gelman, 1998; Gelman et al., 2014; Plummer,
Best, Cowles, & Vines, 2006; R Core Team, 2018). We used values of
convergence diagnostics for parameters with < 1.1 indicating
chain convergence. We reported means and 95% credible intervals
(CrI ) of the posterior distributions, and interpreted log odds
coefficients as probability of presence. In addition, we transform some
model output to odds ratios for ease of interpretation.