Analysis of Christmas Bird Count (CBC) data is complicated by the need to account for variation in effort on counts and to provide summaries over large geographic regions. We describe a hierarchical model for analysis of population change using CBC data that addresses these needs. The effect of effort is modeled parametrically, with parameter values varying among strata as identically distributed random effects. Year and site effects are modeled hierarchically, accommodating large regional variation in number of samples and precision of estimates. The resulting model is complex, but a Bayesian analysis can be conducted using Markov chain Monte Carlo techniques. We analyze CBC data for American Black Ducks (Anas rubripes), a species of considerable management interest that has historically been monitored using winter surveys. Over the interval 1966–2003, Black Duck populations showed distinct regional patterns of population change. The patterns shown by CBC data are similar to those shown by the Midwinter Waterfowl Inventory for the United States.
The North American Breeding Bird Survey (BBS) contains data for >700 bird species, but analyses often focus on a core group of ∼420 species. We analyzed data for 122 species of North American birds for which data exist in the North American Breeding Bird Survey (BBS) database but are not routinely analyzed on the BBS Summary and Analysis Website. Many of these species occur in the northern part of the continent, on routes that fall outside the core survey area presently analyzed in the United States and southern Canada. Other species not historically analyzed occur in the core survey area with very limited data but have large portions of their ranges in Mexico and south. A third group of species not historically analyzed included species thought to be poorly surveyed by the BBS, such as rare, coastal, or nocturnal species. For 56 species found primarily in regions north of the core survey area, we expanded the scope of the analysis, using data from 1993 to 2014 during which ≥3 survey routes had been sampled in 6 northern strata (Bird Conservation regions in Alaska, Yukon, and Newfoundland and Labrador) and fitting log-linear hierarchical models for an augmented BBS survey area that included both the new northern strata and the core survey area. We also applied this model to 168 species historically analyzed in the BBS that had data from these additional northern strata. For both groups of species we calculated survey-wide trends for the both core and augmented survey areas from 1993 to 2014; for species that did not occur in the newly defined strata, we computed trends from 1966 to 2014. We evaluated trend estimates in terms of established credibility criteria for BBS results, screening for imprecise trends, small samples, and low relative abundance. Inclusion of data from the northern strata permitted estimation of trend for 56 species not historically analyzed, but only 4 of these were reasonably monitored and an additional 13 were questionably monitored; 39 of these species were likely poorly monitored because of small numbers of samples or very imprecisely estimated trends. Only 4 of 66 “new” species found in the core survey area were reasonably monitored by the BBS; 20 were questionably monitored; and 42 were likely poorly monitored by the BBS because of inefficiency in precision, abundance, or sample size. The hierarchical analyses we present provide a means for reasonable inclusion of the additional species and strata in a common analysis with data from the core area, a critical step in the evolution of the BBS as a continent-scale survey. We recommend that results be presented both 1) from 1993 to the present using the expanded survey area, and 2) from 1966 to the present for the core survey area. Although most of the “new” species we analyzed were poorly monitored by the BBS during 1993–2014, continued expansion of the BBS will improve the quality of information in future analyses for these species and for the many other species presently monitored by the BBS.
The North American Breeding Bird Survey (BBS) provides data that can be used in complex, multiscale analyses of population change, while controlling for scale‐specific nuisance factors. Many alternative models can be fit to the data, but most model selection procedures are not appropriate for hierarchical models. Leave‐one‐out cross‐validation (LOOCV), in which relative model fit is assessed by omitting an observation and assessing the prediction of a model fit using the remainder of the data, provides a reasonable approach for assessing models, but is time consuming and not feasible to apply for all observations in large data sets. We report the first large‐scale formal model selection for BBS data, applying LOOCV to stratified random samples of observations from BBS data. Our results are for 548 species of North American birds, comparing the fit of four alternative models that differ in year effect structures and in descriptions of extra‐Poisson overdispersion. We use a hierarchical model among species to evaluate posterior probabilities that models are best for individual species. Models in which differences in year effects are conditionally independent (D models) were generally favored over models in which year effects are modeled by a slope parameter and a random year effect (S models), and models in which extra‐Poisson overdispersion effects are independent and t‐distributed (H models) tended to be favored over models where overdispersion was independent and normally distributed. Our conclusions lead us to recommend a change from the conventional S model to D and H models for the vast majority of species (544/548). Comparison of estimated population trends based on the favored model relative to the S model currently used for BBS summaries indicates no consistent differences in estimated trends. Of the 18 species that showed large differences in estimated trends between models, estimated trends from the default S model were more extreme, reflecting the influence of the slope parameter in that model for species that are undergoing large population changes. WAIC, a computationally simpler alternative to LOOCV, does not appear to be a reliable alternative to LOOCV.
The Singing‐Ground Survey (SGS) is a primary source of information on population change for American woodcock (Scolopax minor). We analyzed the SGS using a hierarchical log‐linear model and compared the estimates of change and annual indices of abundance to a route regression analysis of SGS data. We also grouped SGS routes into Bird Conservation Regions (BCRs) and estimated population change and annual indices using BCRs within states and provinces as strata. Based on the hierarchical model–based estimates, we concluded that woodcock populations were declining in North America between 1968 and 2006 (trend = −0.9%/yr, 95% credible interval: −1.2, −0.5). Singing‐Ground Survey results are generally similar between analytical approaches, but the hierarchical model has several important advantages over the route regression. Hierarchical models better accommodate changes in survey efficiency over time and space by treating strata, years, and observers as random effects in the context of a log‐linear model, providing trend estimates that are derived directly from the annual indices. We also conducted a hierarchical model analysis of woodcock data from the Christmas Bird Count and the North American Breeding Bird Survey. All surveys showed general consistency in patterns of population change, but the SGS had the shortest credible intervals. We suggest that population management and conservation planning for woodcock involving interpretation of the SGS use estimates provided by the hierarchical model.
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