No abstract

The development of methods for dealing with continuous data with a spike at zero has lagged behind those for overdispersed or zero‐inflated count data. We consider longitudinal ecological data corresponding to an annual average of 26 weekly maximum counts of birds, and are hence effectively continuous, bounded below by zero but also with a discrete mass at zero. We develop a Bayesian hierarchical Tweedie regression model that can directly accommodate the excess number of zeros common to this type of data, whilst accounting for both spatial and temporal correlation. Implementation of the model is conducted in a Markov chain Monte Carlo (MCMC) framework, using reversible jump MCMC to explore uncertainty across both parameter and model spaces. This regression modelling framework is very flexible and removes the need to make strong assumptions about mean‐variance relationships a priori. It can also directly account for the spike at zero, whilst being easily applicable to other types of data and other model formulations. Whilst a correlative study such as this cannot prove causation, our results suggest that an increase in an avian predator may have led to an overall decrease in the number of one of its prey species visiting garden feeding stations in the United Kingdom. This may reflect a change in behaviour of house sparrows to avoid feeding stations frequented by sparrowhawks, or a reduction in house sparrow population size as a result of sparrowhawk increase.

The importance of multispecies models for understanding complex ecological processes and interactions is beginning to be realized. Recent developments, such as those by Lahoz‐Monfort et al. (2011), have enabled synchrony in demographic parameters across multiple species to be explored. Species in a similar environment would be expected to be subject to similar exogenous factors, although their response to each of these factors may be quite different. The ability to group species together according to how they respond to a particular measured covariate may be of particular interest to ecologists. We fit a multispecies model to two sets of similar species of garden bird monitored under the British Trust for Ornithology's Garden Bird Feeding Survey. Posterior model probabilities were estimated using the reversible jump algorithm to compare posterior support for competing models with different species sharing different subsets of regression coefficients. There was frequently good agreement between species with small asynchronous random‐effect components and those with posterior support for models with shared regression coefficients; however, this was not always the case. When groups of species were less correlated, greater uncertainty was found in whether regression coefficients should be shared or not. The methods outlined in this study can test additional hypotheses about the similarities or synchrony across multiple species that share the same environment. Through the use of posterior model probabilities, estimated using the reversible jump algorithm, we can detect multispecies responses in relation to measured covariates across any combination of species and covariates under consideration. The method can account for synchrony across species in relation to measured covariates, as well as unexplained variation accounted for using random effects. For more flexible, multiparameter distributions, the support for species‐specific parameters can also be measured.

Summary As accessible and potentially vulnerable species high up in the food chain, birds are often used as indicator species to highlight changes in ecosystems. This study focuses on multiple spatially dependent relationships between a raptor (sparrowhawk), a potential prey species (house sparrow) and a sympatric species (collared doves) in space and time. We construct a complex spatiotemporal latent Gaussian model to incorporate both predator–prey and sympatric relationships, which is novel in two ways. First, different types of species interactions are represented by a shared spatiotemporal random effect, which extends existing approaches to multivariate spatial modelling through the use of a joint latent modelling approach. Second, we use a delta–gamma model to capture the semicontinuous nature of the data to model the binary and continuous sections of the response jointly. The results indicate that sparrowhawks have a localized effect on the presence of house sparrows, which could indicate that house sparrows avoid sites where sparrowhawks are present.