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Presence/absence data and presence-only data are the two customary sources for learning about species distributions over a region. We present an ambitious agenda with regard to the analysis of such data. We illuminate the fundamental modeling differences between the two types of data. Most simply, locations are considered to be fixed under presence/absence data; locations are random under presence-only data. The definition of \"probability of presence\" is incompatible between the two. We are not comfortable with modeling strategies in the literature that ignore this incompatibility and that assume that presence/absence modeling can be induced from presence-only specifications and, therefore, that fusion of presence-only and presence/absence data sources is routine. While, in some cases, data collection may not support this, we propose that, since, in nature, presence/absence is seen at the point locations, presence/absence data should be modeled at point level. If so, we need to specify two surfaces. The first provides the probability of presence at any location in the region. The second provides a realization from this surface in the form of a binary map yielding the results of Bernoulli trials across all locations; this surface is only partially observed. On the other hand, presence-only data should be modeled as a (partially observed) point pattern, arising from a random number of individuals seen at random locations, driven by specification of an intensity function. There is no notion of Bernoulli trials; events are associated with areas. We further suggest that, with just presence/absence data, preferential sampling of locations may arise. Accounting for this, using a shared process perspective, can improve our estimated presence/absence surface as well as prediction of presence. We further propose that preferential sampling can enable a probabilistically coherent fusion of the two data types. We illustrate with two real data sets, one presence/absence, one presence-only, for invasive species presence in New England in the United States. We demonstrate that potential bias in sampling locations can affect inference with regard to presence/absence and show that inference can be improved with preferential sampling ideas. We also provide a probabilistically coherent fusion of the two data sets again with the goal of improving inference for presence/absence. The importance of our work is to encourage more careful modeling when studying species distributions. Ignoring incompatibility between data types and adopting nongenerative modeling specifications results in invalid inference; the quantitative ecological community should benefit from this recognition.

Modelling spatial and temporal patterns in ecology is imperative to understand the complex processes inherent in ecological phenomena. Log‐Gaussian Cox processes are a popular choice among ecologists to describe the spatiotemporal distribution of point‐referenced data. In addition, point pattern models where events instigate others nearby (i.e., self‐exciting behaviour) are becoming increasingly popular to infer the contagious nature of events (e.g., animal sightings). While there are existing R packages that facilitate fitting spatiotemporal point processes and, separately, self‐exciting models, none incorporate both. We present an R package, stelfi, that fits spatiotemporal self‐exciting and log‐Gaussian Cox process models using Template Model Builder through a range of custom‐written C++ templates. We illustrate the use of stelfi's functions fitting models to Sasquatch (bigfoot) sightings data within the USA. The structure of these data is typical of many seen in ecology studies. We show, from a temporal Hawkes process to a spatiotemporal self‐exciting model, how the models offered by the package enable additional insights into the temporal and spatial progression of point pattern data. We present extensions to these well‐known models that include spatiotemporal self‐excitation and joint likelihood models, which are better suited to capture the complex mechanisms inherent in many ecological data. The package stelfi offers user‐friendly functionality, is open source, and is available from CRAN. It offers the implementation of complex spatiotemporal point process models in R for applications even beyond the field of ecology. We introduce the R package stelfi, available from the Comprehensive R Archive Network. This package allows users to fit temporal self‐exciting Hawkes models, spatial and spatiotemporal log‐Gaussian Cox process models and self‐exciting spatiotemporal models. The functionality of stelfi is illustrated using Sasquatch (bigfoot) sightings data shipped with the package.

Malnutrition remains a leading cause of child mortality in Nigeria. The spatial analysis based on areal level approaches could, in reality, conceal variations at smaller units. Using point-referenced data from Nigeria Demographic and Health Survey, we quantify the prevalence of malnutrition among under-five children in Nigeria at 1.63 by 1.63 km spatial resolution, and compute the exceedance probability maps for stunting, wasting and underweight at 20% threshold level using the stochastic partial differential equation approach with Bayesian inference based on integrated nested Laplace approximation. Results show divergence prevalence of the malnutrition indicators among children living in neighbouring locations and that the prevalence of stunting and underweight increase with age. The prevalence of stunting was uneven among children living in Kebbi, Zamfara, Sokoto, Kaduna, Kano, Katsina, Bauchi, Gombe and Taraba states with more concentrations in the northern fringes of some of the states. Except for few locations in about three states, the probability is more than 90% that the prevalence of stunting in all parts of the country exceeds 20% but this was not the case for wasting. The findings can assist in location-specific policy formulation and implementations.

Spatial process models are being increasingly employed for analyzing data available at geocoded locations. In this article, we build a hierarchical framework with multivariate spatial processes, where the outcomes are “mixed” in the sense that some may be continuous, some binary and others may be counts. The underlying idea is to build a joint model by hierarchically building conditional distributions with different spatial processes embedded in each conditional distribution. The idea is simple and the resulting models can be fitted to multivariate spatial data using straightforward Bayesian computing methods such as Markov chain Monte Carlo methods. Bayesian inference is carried out for parameter estimation and spatial interpolation. The proposed models are illustrated using housing data collected in the Walmer district of Port Elizabeth, South Africa. Inferential interest resides in modeling spatial dependencies of dependent outcomes and associations accounting for independent explanatory variables. Comparisons across different models confirm that the selling price of a house in our data set is relatively better modeled by incorporating spatial processes.

Customary modeling for continuous point-referenced data assumes a Gaussian process that is often taken to be stationary. When such models are fitted within a Bayesian framework, the unknown parameters of the process are assumed to be random, so a random Gaussian process results. Here we propose a novel spatial Dirichlet process mixture model to produce a random spatial process that is neither Gaussian nor stationary. We first develop a spatial Dirichlet process model for spatial data and discuss its properties. Because of familiar limitations associated with direct use of Dirichlet process models, we introduce mixing by convolving this process with a pure error process. We then examine properties of models created through such Dirichlet process mixing. In the Bayesian framework, we implement posterior inference using Gibbs sampling. Spatial prediction raises interesting questions, but these can be handled. Finally, we illustrate the approach using simulated data, as well as a dataset involving precipitation measurements over the Languedoc-Roussillon region in southern France.

Occupancy models are popular for estimating the probability a site is occupied by a species of interest when detection is imperfect. Occupancy models have been extended to account for interacting species and spatial dependence but cannot presently allow both factors to act simultaneously. We propose a two‐species occupancy model that accommodates both interspecific and spatial dependence. We use a point‐referenced multivariate hierarchical spatial model to account for both spatial and interspecific dependence. We model spatial random effects with predictive process models and use probit regression to improve efficiency of posterior sampling. We model occupancy probabilities of red fox (Vulpes vulpes) and coyote (Canis latrans) with camera trap data collected from six mid‐Atlantic states in the eastern United States. We fit four models comprising a fully factorial combination of spatial and interspecific dependence to two‐thirds of camera trapping sites and validated models with the remaining data. Red fox and coyotes each exhibited spatial dependence at distances >0.8 and 0.4 km, respectively, and exhibited geographic variation in interspecific dependence. Consequently, predictions from the model assuming simultaneous spatial and interspecific dependence best matched test data observations. This application highlights the utility of simultaneously accounting for spatial and interspecific dependence.

The global emergence of Batrachochytrium dendrobatidis (Bd) has caused the extinction of hundreds of amphibian species worldwide. It has become increasingly important to be able to precisely predict time to Bd arrival in a population. The data analyzed herein present a unique challenge in terms of modeling because there is a strong spatial component to Bd arrival time and the traditional proportional hazards assumption is grossly violated. To address these concerns, we develop a novel marginal Bayesian nonparametric survival model for spatially correlated right‐censored data. This class of models assumes that the logarithm of survival times marginally follow a mixture of normal densities with a linear‐dependent Dirichlet process prior as the random mixing measure, and their joint distribution is induced by a Gaussian copula model with a spatial correlation structure. To invert high‐dimensional spatial correlation matrices, we adopt a full‐scale approximation that can capture both large‐ and small‐scale spatial dependence. An efficient Markov chain Monte Carlo algorithm with delayed rejection is proposed for posterior computation, and an R package spBayesSurv is provided to fit the model. This approach is first evaluated through simulations, then applied to threatened frog populations in Sequoia‐Kings Canyon National Park.