Data analysis
Our final dataset included time series data for all weather variables (scaled by subtracting variable means from observed values and dividing by the standard deviation) and daily gobbling counts. With the spatially and temporally coupled data, we used state space modeling to evaluate the effects of weather variables on daily gobbling activity. The state space model accounted for correlated observations and included observation error while modeling the influences of weather variables on gobbling activity. We used a hierarchical state space model that allowed us to decompose temporally correlated weather data and gobbling counts into a process variation and observation error (Kery and Schaub 2012). With the weather variables being the parameters of interest, the state space model allowed us to investigate the process variation in gobbling counts relative to stochasticity in the weather variables. We calculated Pearson’s correlation coefficients to test for collinearity between each of our covariates and excluded covariates with a r > 0.60.We fit the state space model within the jagsUI package (Kellner 2018) in program R (R Core team 2020) to estimate the effects of weather on daily gobbling activity.
We fit the Bayesian state space model to counts of daily gobbles (N) at each site (K) during each year (i). We treated daily gobbling counts like counts in a population model but we modeled the abundance of gobbles instead of animals. The process model was:
r expected(t) = Xlog (N[t-1],k,i) + Site(k) + βtemperature * Xtemperature(t,k,i) + βwind * Xwind(t,k,i) + βbp * (Xbp(t,k,i) -Xbp(t-1,k,i) + βhumidity * Xhumidity(t,k,i) + βprecipitation * Xprecipitation(t,k,i) + Year + log(Units)
r t ~ Normal(r expected[t],τprocess)
Log (Nt +1) = log (Nt) +