Extending the Latent Dirichlet Allocation model to presence/absence data: A case study on North American breeding birds and biogeographical shifts expected from climate change.

Understanding how species composition varies across space and time is fundamental to ecology. While multiple methods having been created to characterize this variation through the identification of groups of species that tend to co-occur, most of these methods unfortunately are not able to represent gradual variation in species composition. The Latent Dirichlet Allocation (LDA) model is a mixed-membership method that can represent gradual changes in community structure by delineating overlapping groups of species, but its use has been limited because it requires abundance data and requires users to a priori set the number of groups. We substantially extend LDA to accommodate widely available presence/absence data and to simultaneously determine the optimal number of groups. Using simulated data, we show that this model is able to accurately determine the true number of groups, estimate the underlying parameters, and fit with the data. We illustrate this method with data from the North American Breeding Bird Survey (BBS). Overall, our model identified 18 main bird groups, revealing striking spatial patterns for each group, many of which were closely associated with temperature and precipitation gradients. Furthermore, by comparing the estimated proportion of each group for two time periods (1997-2002 and 2010-2015), our results indicate that nine (of 18) breeding bird groups exhibited an expansion northward and contraction southward of their ranges, revealing subtle but important community-level biodiversity changes at a continental scale that are consistent with those expected under climate change. Our proposed method is likely to find multiple uses in ecology, being a valuable addition to the toolkit of ecologists.