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.