Phylogenetic and spatial distribution of abundance change

To plot abundance change across a phylogeny, we derived species-level rates of change in abundance from the taxonomic (species and genera) and phylogenetic random effects. We incorporate uncertainty in species-level trend prediction by estimating the CI threshold by which a species would be considered to have increased or decreased. For instance, a negative trend at an 80% CI threshold would be considered stronger evidence of decline than a negative trend at a 20% interval threshold. We derive four asymptotic CI thresholds (20%, 40%, 60% and 80%) using the uncertainty (s.d.) from the phylogenetic random effect and a series of z-scores (0.25, 0.52, 0.84 and 1.28).

To plot abundance change across space, we focus solely on one abundant and iconic species, the American robin T. migratorius, as site-level trend variability is high at the community level (that is, community trends across space are rarely significant). To produce abundance change predictions for the American robin across space, we expanded the BioTIME spatial Haversine distance matrix (describing distances between each time series) by supplementing it with a gridded extent covering North America. This new grid had a latitudinal range of 20 to 60 and 1° spacing (for example, 15, 16 and so on), and longitudinal range of −130 to −60 with 1° spacing. This new matrix allows us to estimate expected covariance (similarity) in abundance trends for any pair of 1° cells across North America. We then derived the average rate of change in abundance across all hierarchical and correlative random effects, and used population-level trend uncertainty to derive the selection of CI thresholds described above.