Demographic analysis
We estimated relative population size indices and population trends
(1968-2021) for each of the five breeding populations and across the
entire breeding range using Breeding Bird Survey (BBS) data (Pardieck et
al., 2020). We used a hierarchical over-dispersed Poisson model (Sauer
et al., 2011) to analyze the BBS data. All BBS routes within a 50-km
buffer of a polygon defining one of the breeding populations were
assigned to that breeding population. This breeding population
assignment was then included as the fixed stratum intercept and trend
effects of the log-linear model of the Poisson mean. We estimated
current (2017-2021) population size indices by summarizing posterior
distributions of estimated mean route-level counts that were weighted by
geographic area encompassed by the breeding population polygon and the
proportion of routes in the polygon with American Redstart detections
(Sauer & Link, 2011). Long-term trends in population size were
estimated as the geometric mean of yearly changes from 1968-2021 (Sauer
& Link, 2011). We implemented the hierarchical model in JAGS 4.3.1
(Plummer, 2003) using the jagsUI (Kellner & Meredith, 2021) package in
R (R Core Team, 2022). We assigned vague prior distributions for all
model parameters and hyperparameters. Posterior distributions were
derived from 40,000 simulated values of four chains from the posterior
distribution after an adaptive phase of 20,000 iterations and burn-in of
10,000 samples of the Gibbs sampler and thinning by 3. Markov chains
were determined to have successfully converged based on\(\hat{R}\)<1.1 for posterior estimates of all parameters
(Gelman & Hill, 2007).