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Many pathogens rely on the mobility of their hosts for dispersal. In order to understand and predict how a disease can rapidly sweep across entire continents, illuminating the contributions of host movements to disease spread is pivotal. While elegant proposals have been made to elucidate the spread of human infectious diseases, the direct observation of long-distance dispersal events of animal pathogens is challenging. Pathogens like avian influenza A viruses, causing only short disease in their animal hosts, have proven exceptionally hard to study. Here, we integrate comprehensive data on population and disease dynamics for low-pathogenic avian influenza viruses in one of their main hosts, the mallard, with a novel movement model trained from empirical, high-resolution tracks of mallard migrations. This allowed us to simulate individual mallard migrations from a key stopover site in the Baltic Sea for the entire population and link these movements to infection simulations. Using this novel approach, we were able to estimate the dispersal of low-pathogenic avian influenza viruses by migrating mallards throughout several autumn migratory seasons and predicted areas that are at risk of importing these viruses. We found that mallards are competent vectors and on average dispersed viruses over distances of 160 km in just 3 h. Surprisingly, our simulations suggest that such dispersal events are rare even throughout the entire autumn migratory season. Our approach directly combines simulated population-level movements with local infection dynamics and offers a potential converging point for movement and disease ecology.

Investigation of species abundance has become a vital component of many ecological monitoring studies. The primary objective of these studies is to understand how specific species are distributed across the study domain, as well as quantification of the sampling efficiency for detecting these species. To achieve these goals, preselected locations are sampled during scheduled visits, in which the number of species observed at each location is recorded. This results in spatially referenced replicated count data that are often unbalanced in structure and exhibit overdispersion. Motivated by the Baltimore Ecosystem Study, we propose Bayesian hierarchical binomial mixture models, including Binomial Conway-Maxwell Poisson (Bin-CMP) mixture models, that formally account for varying levels of spatial dispersion. Our proposed models also allow for variable selection of model covariates and grouping of dispersion parameters through the implementation of reversible jump Markov chain Monte Carlo methodology. Finally, using demographic covariates from the American Community Survey, we demonstrate the effectiveness of our approach through estimation of abundance for the American Robin (Turdus migratorius) in the Baltimore Ecosystem Study.

Vector autoregressive (VAR) models have become a staple in the analysis of multivariate time series and are formulated in the time domain as difference equations, with an implied covariance structure. In many contexts, it is desirable to work with a stable, or at least stationary, representation. To fit such models, one must impose restrictions on the coefficient matrices to ensure that certain determinants are nonzero; which, except in special cases, may prove burdensome. To circumvent these difficulties, we propose a flexible frequency domain model expressed in terms of the spectral density matrix. Specifically, this paper treats the modeling of covariance stationary vector-valued (i.e., multivariate) time series via an extension of the exponential model for the spectrum of a scalar time series. We discuss the modeling advantages of the vector exponential model and its computational facets, such as how to obtain Wold coefficients from given cepstral coefficients. Finally, we demonstrate the utility of our approach through simulation as well as two illustrative data examples focusing on multi-step ahead forecasting and estimation of squared coherence.