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Understanding community responses to climate is critical for anticipating the future impacts of global change. However, despite increased research efforts in this field, models that explicitly include important biological mechanisms are lacking. Quantifying the potential impacts of climate change on species is complicated by the fact that the effects of climate variation may manifest at several points in the biological process. To this end, we extend a dynamic mechanistic model that combines population dynamics, such as species interactions, with species redistribution by allowing climate to affect both processes. We examine their relative contributions in an application to the changing biomass of a community of eight species in the Gulf of Maine using over 30 years of fisheries data from the Northeast Fishery Science Center. Our model suggests that the mechanisms driving biomass trends vary across space, time, and species. Phase space plots demonstrate that failing to account for the dynamic nature of the environmental and biologic system can yield theoretical estimates of population abundances that are not observed in empirical data. The stock assessments used by fisheries managers to set fishing targets and allocate quotas often ignore environmental effects. At the same time, research examining the effects of climate change on fish has largely focused on redistribution. Frameworks that combine multiple biological reactions to climate change are particularly necessary for marine researchers. This work is just one approach to modeling the complexity of natural systems and highlights the need to incorporate multiple and possibly interacting biological processes in future models.

Turnover, or change in the composition of species over space and time, is one of the primary ways to define beta diversity. Inferring what factors impact beta diversity is not only important for understanding biodiversity processes but also for conservation planning. At present, a popular approach to understanding the drivers of compositional turnover is through generalized dissimilarity modelling (GDM). We argue that the current GDM approach suffers several limitations and provide an alternative modelling approach that remedies these issues.

In functional data analysis, curves or surfaces are observed, up to measurement error, at a finite set of locations, for, say, a sample of n individuals. Often, the curves are homogeneous, except perhaps for individual-specific regions that provide heterogeneous behaviour (e.g. ‘damaged’ areas of irregular shape on an otherwise smooth surface). Motivated by applications with functional data of this nature, we propose a Bayesian mixture model, with the aim of dimension reduction, by representing the sample of n curves through a smaller set of canonical curves. We propose a novel prior on the space of probability measures for a random curve which extends the popular Dirichlet priors by allowing local clustering: non-homogeneous portions of a curve can be allocated to different clusters and the n individual curves can be represented as recombinations (hybrids) of a few canonical curves. More precisely, the prior proposed envisions a conceptual hidden factor with k-levels that acts locally on each curve. We discuss several models incorporating this prior and illustrate its performance with simulated and real data sets. We examine theoretical properties of the proposed finite hybrid Dirichlet mixtures, specifically, their behaviour as the number of the mixture components goes to ∞ and their connection with Dirichlet process mixtures.

With scientific data available at geocoded locations, investigators are increasingly turning to spatial process models for carrying out statistical inference. Over the last decade, hierarchical models implemented through Markov chain Monte Carlo methods have become especially popular for spatial modelling, given their flexibility and power to fit models that would be infeasible with classical methods as well as their avoidance of possibly inappropriate asymptotics. However, fitting hierarchical spatial models often involves expensive matrix decompositions whose computational complexity increases in cubic order with the number of spatial locations, rendering such models infeasible for large spatial data sets. This computational burden is exacerbated in multivariate settings with several spatially dependent response variables. It is also aggravated when data are collected at frequent time points and spatiotemporal process models are used. With regard to this challenge, our contribution is to work with what we call predictive process models for spatial and spatiotemporal data. Every spatial (or spatiotemporal) process induces a predictive process model (in fact, arbitrarily many of them). The latter models project process realizations of the former to a lower dimensional subspace, thereby reducing the computational burden. Hence, we achieve the flexibility to accommodate non-stationary, non-Gaussian, possibly multivariate, possibly spatiotemporal processes in the context of large data sets. We discuss attractive theoretical properties of these predictive processes. We also provide a computational template encompassing these diverse settings. Finally, we illustrate the approach with simulated and real data sets.