Bayesian Models for Spatially Explicit Interactions Between Neighbouring Plants

Interactions between neighbouring plants drive population and community dynamics in terrestrial ecosystems. Understanding these interactions is critical for both fundamental and applied ecology. Spatial approaches to model neighbour interactions are necessary, as interaction strength depends on the distance between neighbouring plants. Recent Bayesian advancements, including the Hamiltonian Monte Carlo algorithm, offer the flexibility and speed to fit models of spatially explicit neighbour interactions. We present a guide for parameterizing these models in the Stan programming language and demonstrate how Bayesian computation can assist ecological inference on plant–plant interactions. Modelling plant neighbour interactions presents several challenges for ecological modelling. First, nonlinear models for distance decay can be prone to identifiability problems, resulting in lack of model convergence. Second, the pairwise data structure of plant–plant interaction matrices often leads to large matrices that demand high computational power. Third, hierarchical structure in plant–plant interaction data is ubiquitous, including repeated measurements within field plots, species and individuals. Hierarchical terms (e.g. ‘random effects’) can result in model convergence problems caused by correlations between coefficients. We explore modelling solutions for these challenges with examples representing spatial data on plant demographic rates: growth, survival and recruitment. We show that ragged matrices reduce computational challenges inherent to pairwise matrices, resulting in higher efficiency across data types. We also demonstrate how metrics for model convergence, including divergent transitions and effective sample size, can help diagnose problems that result from complex nonlinear structures. Finally, we explore when to use different model structures for hierarchical terms, including centred and non-centred parameterizations. We provide reproducible examples written in Stan to enable ecologists to fit and troubleshoot a broad range of neighbourhood interaction models. Spatially explicit models are increasingly central to many ecological questions. Our work illustrates how novel Bayesian tools can provide flexibility, speed and diagnostic capacity for fitting plant neighbour models to large, complex datasets. The methods we demonstrate are applicable to any dataset that includes a response variable and locations of observations, from forest inventory plots to remotely sensed imagery. Further developments in statistical models for neighbour interactions are likely to improve our understanding of plant population and community ecology across systems and scales

Form and function in hillslope hydrology : Characterization of subsurface ow based on response observations

Acknowledgements. We are grateful to Marcel Delock, Lisei Köhn, and Marvin Reich for their support during fieldwork, as well as Markus Morgner and Jean Francois Iffly for technical support, Britta Kattenstroth for hydrometeorological data acquisition and isotope sampling, and Barbara Herbstritt and Begoña Lorente Sistiaga for laboratory work. Laurent Pfister and Jean-Francois Iffly from the Luxembourg Institute of Science and Technology (LIST) are acknowledged for organizing the permissions for the experiments and providing discharge data for Weierbach 1 and Colpach. We also want to thank Frauke K. Barthold and the two anonymous reviewers, whose thorough remarks greatly helped to improve the manuscript. This study is part of DFG-funded CAOS project “From Catchments as Organised Systems to Models based on Dynamic Functional Units” (FOR 1598). The article processing charges for this open-access publication were covered by a Research Centre of the Helmholtz Association.Peer reviewedPublisher PD

Point process models for spatio-temporal distance sampling data from a large-scale survey of blue whales

Distance sampling is a widely used method for estimating wildlife population abundance. The fact that conventional distance sampling methods are partly design-based constrains the spatial resolution at which animal density can be estimated using these methods. Estimates are usually obtained at survey stratum level. For an endangered species such as the blue whale, it is desirable to estimate density and abundance at a finer spatial scale than stratum. Temporal variation in the spatial structure is also important. We formulate the process generating distance sampling data as a thinned spatial point process and propose model-based inference using a spatial log-Gaussian Cox process. The method adopts a flexible stochastic partial differential equation (SPDE) approach to model spatial structure in density that is not accounted for by explanatory variables, and integrated nested Laplace approximation (INLA) for Bayesian inference. It allows simultaneous fitting of detection and density models and permits prediction of density at an arbitrarily fine scale. We estimate blue whale density in the Eastern Tropical Pacific Ocean from thirteen shipboard surveys conducted over 22 years. We find that higher blue whale density is associated with colder sea surface temperatures in space, and although there is some positive association between density and mean annual temperature, our estimates are consitent with no trend in density across years. Our analysis also indicates that there is substantial spatially structured variation in density that is not explained by available covariates.Comment: 33 pages 19 figure