rt
Where rexpected(t) was the expected change in daily gobbling activity, Site was the fixed effect for each of the 5 sites, βtemperature was the coefficient for the effect of temperature in matrix Xtemperature, βwind was the coefficient for the effect of wind in matrix Xwind , βbp was the coefficient for the effect of the change in barometric pressure in matrix Xbp , βhumidity was the coefficient for the effect of humidity in matrix Xhumidity , βprecipitation was the coefficient for the effect of precipitation in matrix Xprecipitation , Year was modelled as a random effect, and Units was an offset term used to account for the number of ARUs recording. We modeled the observation process as follows: yt,k,i ~ Poisson(log(Nt)) where yt,k,iwas the logged observed number of gobbles each day(t) at each site during each year . We calculated 95% credible intervals for each parameter estimate of interest. For the random effect of year and to account for process variation, we used a gamma distribution for the priors with a precision of 0.001. For the rest of the parameters, we used a normal distribution with a mean of 0 and a precision of 0.001. We used Markov chain Monte Carlo (MCMC) to estimate the posterior distributions of the model parameters. We generated 3 MCMC chains using a thinning rate of 10,000 iterations per chain and 2,500 burn in values. To check for convergence, we investigated trace plots of the MCMC chains and used Gelman-Rubin statistic to calculate R-values, with R-values less than 1.1 indicating model convergence (Gelman et al. 2004).