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In this paper we first describe the class of log-Gaussian Cox processes (LGCPs) as models for spatial and spatio-temporal point process data. We discuss inference, with a particular focus on the computational challenges of likelihood-based inference. We then demonstrate the usefulness of the LGCP by describing four applications: estimating the intensity surface of a spatial point process; investigating spatial segregation in a multi-type process; constructing spatially continuous maps of disease risk from spatially discrete data; and real-time health surveillance. We argue that problems of this kind fit naturally into the realm of geostatistics, which traditionally is defined as the study of spatially continuous processes using spatially discrete observations at a finite number of locations. We suggest that a more useful definition of geostatistics is by the class of scientific problems that it addresses, rather than by particular models or data formats.

Understanding and accurately modeling species distributions lies at the heart of many problems in ecology, evolution, and conservation. Multiple sources of data are increasingly available for modeling species distributions, such as data from citizen science programs, atlases, museums, and planned surveys. Yet reliably combining data sources can be challenging because data sources can vary considerably in their design, gradients covered, and potential sampling biases. We review, synthesize, and illustrate recent developments in combining multiple sources of data for species distribution modeling. We identify five ways in which multiple sources of data are typically combined for modeling species distributions. These approaches vary in their ability to accommodate sampling design, bias, and uncertainty when quantifying environmental relationships in species distribution models. Many of the challenges for combining data are solved through the prudent use of integrated species distribution models: models that simultaneously combine different data sources on species locations to quantify environmental relationships for explaining species distribution. We illustrate these approaches using planned survey data on 24 species of birds coupled with opportunistically collected eBird data in the southeastern United States. This example illustrates some of the benefits of data integration, such as increased precision in environmental relationships, greater predictive accuracy, and accounting for sample bias. Yet it also illustrates challenges of combining data sources with vastly different sampling methodologies and amounts of data. We provide one solution to this challenge through the use of weighted joint likelihoods. Weighted joint likelihoods provide a means to emphasize data sources based on different criteria (e.g., sample size), and we find that weighting improves predictions for all species considered. We conclude by providing practical guidance on combining multiple sources of data for modeling species distributions.

Recently developed spatial capture–recapture (SCR) models represent a major advance over traditional capture–recapture (CR) models because they yield explicit estimates of animal density instead of population size within an unknown area. Furthermore, unlike nonspatial CR methods, SCR models account for heterogeneity in capture probability arising from the juxtaposition of animal activity centers and sample locations. Although the utility of SCR methods is gaining recognition, the requirement that all individuals can be uniquely identified excludes their use in many contexts. In this paper, we develop models for situations in which individual recognition is not possible, thereby allowing SCR concepts to be applied in studies of unmarked or partially marked populations. The data required for our model are spatially referenced counts made on one or more sample occasions at a collection of closely spaced sample units such that individuals can be encountered at multiple locations. Our approach includes a spatial point process for the animal activity centers and uses the spatial correlation in counts as information about the number and location of the activity centers. Camera-traps, hair snares, track plates, sound recordings, and even point counts can yield spatially correlated count data, and thus our model is widely applicable. A simulation study demonstrated that while the posterior mean exhibits frequentist bias on the order of 5–10% in small samples, the posterior mode is an accurate point estimator as long as adequate spatial correlation is present. Marking a subset of the population substantially increases posterior precision and is recommended whenever possible. We applied our model to avian point count data collected on an unmarked population of the northern parula (Parula americana) and obtained a density estimate (posterior mode) of 0.38 (95% CI: 0.19–1.64) birds/ha. Our paper challenges sampling and analytical conventions in ecology by demonstrating that neither spatial independence nor individual recognition is needed to estimate population density—rather, spatial dependence can be informative about individual distribution and density.

AIM: During the past decade ecologists have attempted to estimate the parameters of species distribution models by combining locations of species presence observed in opportunistic surveys with spatially referenced covariates of occurrence. Several statistical models have been proposed for the analysis of presence‐only data, but these models have largely ignored the effects of imperfect detection and survey bias. In this paper I describe a model‐based approach for the analysis of presence‐only data that accounts for errors in the detection of individuals and for biased selection of survey locations. INNOVATION: I develop a hierarchical, statistical model that allows presence‐only data to be analysed in conjunction with data acquired independently in planned surveys. One component of the model specifies the spatial distribution of individuals within a bounded, geographic region as a realization of a spatial point process. A second component of the model specifies two kinds of observations, the detection of individuals encountered during opportunistic surveys and the detection of individuals encountered during planned surveys. MAIN CONCLUSIONS: Using mathematical proof and simulation‐based comparisons, I demonstrate that biases induced by errors in detection or biased selection of survey locations can be reduced or eliminated by using the hierarchical model to analyse presence‐only data in conjunction with counts observed in planned surveys. I show that a relatively small number of high‐quality data (from planned surveys) can be used to leverage the information in presence‐only observations, which usually have broad spatial coverage but may not be informative of both occurrence and detectability of individuals. Because a variety of sampling protocols can be used in planned surveys, this approach to the analysis of presence‐only data is widely applicable. In addition, since the point‐process model is formulated at the level of an individual, it can be extended to account for biological interactions between individuals and temporal changes in their spatial distributions.

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 consistent 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.

Resource selection functions (RSFs) are among the most commonly used statistical tools in both basic and applied animal ecology. They are typically parameterized using animal tracking data, and advances in animal tracking technology have led to increasing levels of autocorrelation between locations in such data sets. Because RSFs assume that data are independent and identically distributed, such autocorrelation can cause misleadingly narrow confidence intervals and biased parameter estimates. Data thinning, generalized estimating equations and step selection functions (SSFs) have been suggested as techniques for mitigating the statistical problems posed by autocorrelation, but these approaches have notable limitations that include statistical inefficiency, unclear or arbitrary targets for adequate levels of statistical independence, constraints in input data and (in the case of SSFs) scale-dependent inference. To remedy these problems, we introduce a method for likelihood weighting of animal locations to mitigate the negative consequences of autocorrelation on RSFs. In this study, we demonstrate that this method weights each observed location in an animal's movement track according to its level of non-independence, expanding confidence intervals and reducing bias that can arise when there are missing data in the movement track. Ecologists and conservation biologists can use this method to improve the quality of inferences derived from RSFs. We also provide a complete, annotated analytical workflow to help new users apply our method to their own animal tracking data using the ctmm R package.

Habitat selection is a fundamental aspect of animal ecology, the understanding of which is critical to management and conservation. Global positioning system data from animals allow fine-scale assessments of habitat selection and typically are analyzed in a use-availability framework, whereby animal locations are contrasted with random locations (the availability sample). Although most use-availability methods are in fact spatial point process models, they often are fit using logistic regression. This framework offers numerous methodological challenges, for which the literature provides little guidance. Specifically, the size and spatial extent of the availability sample influences coefficient estimates potentially causing interpretational bias. We examined the influence of availability on statistical inference through simulations and analysis of serially correlated mule deer GPS data. Bias in estimates arose from incorrectly assessing and sampling the spatial extent of availability. Spatial autocorrelation in covariates, which is common for landscape characteristics, exacerbated the error in availability sampling leading to increased bias. These results have strong implications for habitat selection analyses using GPS data, which are increasingly prevalent in the literature. We recommend that researchers assess the sensitivity of their results to their availability sample and, where bias is likely, take care with interpretations and use cross validation to assess robustness.

Environmental filtering and dispersal limitation can both maintain diversity in plant communities by aggregating conspecifics, but parsing the contribution of each process has proven difficult empirically. Here, we assess the contribution of filtering and dispersal limitation to the spatial aggregation patterns of 456 tree species in a hyperdiverse Amazonian forest and find distinct functional trait correlates of interspecific variation in these processes. Spatial point process model analysis revealed that both mechanisms are important drivers of intraspecific aggregation for the majority of species. Leaf drought tolerance was correlated with species topographic distributions in this aseasonal rainforest, showing that future increases in drought severity could significantly impact community structure. In addition, seed mass was associated with the spatial scale and density of dispersal-related aggregation. Taken together, these results suggest environmental filtering and dispersal limitation act in concert to influence the spatial and functional structure of diverse forest communities.

Movement and location data collected via satellite-linked telemetry tags are often used to inform spatial conservation measures for threatened marine populations. Most applied telemetry studies aim to reconstruct the continuous utilization distribution underlying reported locations to characterize the relative intensity of space use. However, commonly applied space use estimators do not directly estimate the underlying distribution of interest and, perhaps more importantly, ignore correlations in space and time that may bias estimates. Here we describe how geostatistical mixed effects models, which explicitly account for spatial and/or temporal correlation using Gaussian random fields, can be applied to estimate utilization distributions from satellite telemetry data. We use simulation testing to compare the performance of the proposed models with several conventional space use estimators. Our results suggest that geostatistical mixed effects models outperform conventional estimators when the number of tag transmissions changes over time, a common source of bias in satellite telemetry studies that is rarely addressed. We illustrate this approach via application to satellite telemetry location observations collected from 271 large juvenile and adult loggerhead sea turtles in the western North Atlantic from 2004 to 2016. We demonstrate how such models can be used to predict the overall spatial distribution of tagged individuals, as well as seasonal shifts in densities at smaller time scales. For tagged loggerheads, overall predicted densities were greatest in the shelf waters along the US Atlantic coast from Florida to North Carolina, but monthly predictions highlight the importance of summer foraging habitat in the Mid-Atlantic Bight.

We consider determinantal point processes on the d-dimensional unit sphere 𝕊d. These are finite point processes exhibiting repulsiveness and with moment properties determined by a certain determinant whose entries are specified by a so-called kernel which we assume is a complex covariance function defined on 𝕊d × 𝕊d. review the appealing properties of such processes, including their specific moment properties, density expressions and simulation procedures. Particularly, we characterize and construct isotropic DPPs models on 𝕊d, where it becomes essential to specify the eigenvalues and eigenfunctions in a spectral representation for the kernel, and we figure out how repulsive isotropic DPPs can be. Moreover, we discuss the shortcomings of adapting existing models for isotropic covariance functions and consider strategies for developing new models, including a useful spectral approach.