Incorporating environmental heterogeneity and observation effort to predict host distribution and viral spillover from a bat reservoir

Predicting the spatial occurrence of wildlife is a major challenge for ecology and management. In Latin America, limited knowledge of the number and locations of vampire bat roosts precludes informed allocation of measures intended to prevent rabies spillover to humans and livestock. We inferred the spatial distribution of vampire bat roosts while accounting for observation effort and environmental effects by fitting a log Gaussian Cox process model to the locations of 563 roosts in three regions of Peru. Our model explained 45% of the variance in the observed roost distribution and identified environmental drivers of roost establishment. When correcting for uneven observation effort, our model estimated a total of 2340 roosts, indicating that undetected roosts (76%) exceed known roosts (24%) by threefold. Predicted hotspots of undetected roosts in rabies-free areas revealed high-risk areas for future viral incursions. Using the predicted roost distribution to inform a spatial model of rabies spillover to livestock identified areas with disproportionate underreporting and indicated a higher rabies burden than previously recognized. We provide a transferrable approach to infer the distribution of a mostly unobserved bat reservoir that can inform strategies to prevent the re-emergence of an important zoonosis.

Estimating survival in continuous space from mark-dead-recovery data - Towards a continuous version of the multinomial dead recovery model

Understanding spatially varying survival is crucial for understanding the ecology and evolution of migratory animals, which may ultimately help to conserve such species. We develop an approach to estimate an annual survival probability function varying continuously in geographic space, if the recovery probability is constant over space. This estimate is based on a density function over continuous geographic space and the discrete age at death obtained from dead recovery data. From the same density function, we obtain an estimate for animal distribution in space corrected for survival, i.e., migratory connectivity. This is possible, when migratory connectivity can be separated from recovery probability. In this article, we present the method how spatially and continuously varying survival and the migratory connectivity corrected for survival can be obtained, if a constant recovery probability can be assumed reasonably. The model is a stepping stone in developing a model allowing for disentangling spatially heterogeneous survival and migratory connectivity corrected for survival from a spatially heterogeneous recovery probability. We implement the method using kernel density estimates in the R-package CONSURE. Any other density estimation technique can be used as an alternative. In a simulation study, the estimators are unbiased but show edge effects in survival and migratory connectivity. Applying the method to a real-world data set of European robins Erithacus rubecula results in biologically reasonable continuous heat-maps for survival and migratory connectivity.

A flexible and efficient Bayesian implementation of point process models for spatial capture-recapture data

Spatial capture-recapture (SCR) is now routinely used for estimating abundance and density of wildlife populations. A standard SCR model includes sub-models for the distribution of individual activity centers (ACs) and for individual detections conditional on the locations of these ACs. Both sub-models can be expressed as point processes taking place in continuous space, but there is a lack of accessible and efficient tools to fit such models in a Bayesian paradigm. Here, we describe a set of custom functions and distributions to achieve this. Our work allows for more efficient model fitting with spatial covariates on population density, offers the option to fit SCR models using the semi-complete data likelihood (SCDL) approach instead of data augmentation, and better reflects the spatially continuous detection process in SCR studies that use area searches. In addition, the SCDL approach is more efficient than data augmentation for simple SCR models while losing its advantages for more complicated models that account for spatial variation in either population density or detection. We present the model formulation, test it with simulations, quantify computational efficiency gains, and conclude with a real-life example using non-invasive genetic sampling data for an elusive large carnivore, the wolverine (Gulo gulo) in Norway.

The integrated nested Laplace approximation applied to spatial log-Gaussian Cox process models

Spatial point process models are theoretically useful for mapping discrete events, such as plant or animal presence, across space; however, the computational complexity of fitting these models is often a barrier to their practical use. The log-Gaussian Cox process (LGCP) is a point process driven by a latent Gaussian field, and recent advances have made it possible to fit Bayesian LGCP models using approximate methods that facilitate rapid computation. These advances include the integrated nested Laplace approximation (INLA) with a stochastic partial differential equations (SPDE) approach to sparsely approximate the Gaussian field and an extension using pseudodata with a Poisson response. To help link the theoretical results to statistical practice, we provide an overview of INLA for point process data and then illustrate their implementation using freely available data. The analyzed datasets include both a completely observed spatial field and an incomplete data situation. Our well-commented R code is shared in the online supplement. Our intent is to make these methods accessible to the practitioner of spatial statistics without requiring deep knowledge of point process theory.

Extending density surface models to include multiple and double-observer survey data

Spatial models of density and abundance are widely used in both ecological research (e.g., to study habitat use) and wildlife management (e.g., for population monitoring and environmental impact assessment). Increasingly, modellers are tasked with integrating data from multiple sources, collected via different observation processes. Distance sampling is an efficient and widely used survey and analysis technique. Within this framework, observation processes are modelled via detection functions. We seek to take multiple data sources and fit them in a single spatial model. Density surface models (DSMs) are a two-stage approach: first accounting for detectability via distance sampling methods, then modelling distribution via a generalized additive model. However, current software and theory does not address the issue of multiple data sources. We extend the DSM approach to accommodate data from multiple surveys, collected via conventional distance sampling, double-observer distance sampling (used to account for incomplete detection at zero distance) and strip transects. Variance propagation ensures that uncertainty is correctly accounted for in final estimates of abundance. Methods described here are implemented in the dsm R package. We briefly analyse two datasets to illustrate these new developments. Our new methodology enables data from multiple distance sampling surveys of different types to be treated in a single spatial model, enabling more robust abundance estimation, potentially over wider geographical or temporal domains.

Variance Propagation for Density Surface Models

Spatially explicit estimates of population density, together with appropriate estimates of uncertainty, are required in many management contexts. Density surface models (DSMs) are a two-stage approach for estimating spatially varying density from distance sampling data. First, detection probabilities—perhaps depending on covariates—are estimated based on details of individual encounters; next, local densities are estimated using a GAM, by fitting local encounter rates to location and/or spatially varying covariates while allowing for the estimated detectabilities. One criticism of DSMs has been that uncertainty from the two stages is not usually propagated correctly into the final variance estimates. We show how to reformulate a DSM so that the uncertainty in detection probability from the distance sampling stage (regardless of its complexity) is captured as an extra random effect in the GAM stage. In effect, we refit an approximation to the detection function model at the same time as fitting the spatial model. This allows straightforward computation of the overall variance via exactly the same software already needed to fit the GAM. A further extension allows for spatial variation in group size, which can be an important covariate for detectability as well as directly affecting abundance. We illustrate these models using point transect survey data of Island Scrub-Jays on Santa Cruz Island, CA, and harbour porpoise from the SCANS-II line transect survey of European waters. Supplementary materials accompanying this paper appear on-line.

Quantifying the statistical power of monitoring programs for marine protected areas

Marine Protected Areas (MPAs) are increasingly established globally as a spatial management tool to aid in conservation and fisheries management objectives. Assessing whether MPAs are having the desired effects on populations requires effective monitoring programs. A cornerstone of an effective monitoring program is an assessment of the statistical power of sampling designs to detect changes when they occur. We present a novel approach to power assessment that combines spatial point process models, integral projection models (IPMs) and sampling simulations to assess the power of different sample designs across a network of MPAs. We focus on the use of remotely operated vehicle (ROV) video cameras as the sampling method, though the results could be extended to other sampling methods. We use empirical data from baseline surveys of an example indicator fish species across three MPAs in California, USA as a case study. Spatial models simulated time series of spatial distributions across sites that accounted for the effects of environmental covariates, while IPMs simulated expected trends over time in abundances and sizes of fish. We tested the power of different levels of sampling effort (i.e., the number of 500-m ROV transects) and temporal replication (every 1-3 yr) to detect expected post-MPA changes in fish abundance and biomass. We found that changes in biomass are detectable earlier than changes in abundance. We also found that detectability of MPA effects was higher in sites with higher initial densities. Increasing the sampling effort had a greater effect than increasing sampling frequency on the time taken to achieve high power. High power was best achieved by combining data from multiple sites. Our approach provides a powerful tool to explore the interaction between sampling effort, spatial distributions, population dynamics, and metrics for detecting change in previously fished populations.

Movements and behaviour of blue whales satellite tagged in an Australian upwelling system

Knowledge about the movement ecology of endangered species is needed to identify biologically important areas and the spatio-temporal scale of potential human impacts on species. Blue whales (Balaenoptera musculus) are endangered due to twentieth century whaling and currently threatened by human activities. In Australia, they feed in the Great Southern Australian Coastal Upwelling System (GSACUS) during the austral summer. We investigate their movements, occupancy, behaviour, and environmental drivers to inform conservation management. Thirteen whales were satellite tagged, biopsy sampled and photo-identified in 2015. All were genetically confirmed to be of the pygmy subspecies (B. m. brevicauda). In the GSACUS, whales spent most of their time over the continental shelf and likely foraging in association with several seascape variables (sea surface temperature variability, depth, wind speed, sea surface height anomaly, and chlorophyll a). When whales left the region, they migrated west and then north along the Australian coast until they reached West Timor and Indonesia, where their movements indicated breeding or foraging behaviour. These results highlight the importance of the GSACUS as a foraging ground for pygmy blue whales inhabiting the eastern Indian Ocean and indicate the whales’ migratory route to proposed breeding grounds off Indonesia. Information about the spatio-temporal scale of potential human impacts can now be used to protect this little-known subspecies of blue whale.

Performance evaluation of cetacean species distribution models developed using generalized additive models and boosted regression trees

Species distribution models (SDMs) are important management tools for highly mobile marine species because they provide spatially and temporally explicit information on animal distribution. Two prevalent modeling frameworks used to develop SDMs for marine species are generalized additive models (GAMs) and boosted regression trees (BRTs), but comparative studies have rarely been conducted; most rely on presence-only data; and few have explored how features such as species distribution characteristics affect model performance. Since the majority of marine species BRTs have been used to predict habitat suitability, we first compared BRTs to GAMs that used presence/absence as the response variable. We then compared results from these habitat suitability models to GAMs that predict species density (animals per km2) because density models built with a subset of the data used here have previously received extensive validation. We compared both the explanatory power (i.e., model goodness of fit) and predictive power (i.e., performance on a novel dataset) of the GAMs and BRTs for a taxonomically diverse suite of cetacean species using a robust set of systematic survey data (1991-2014) within the California Current Ecosystem. Both BRTs and GAMs were successful at describing overall distribution patterns throughout the study area for the majority of species considered, but when predicting on novel data, the density GAMs exhibited substantially greater predictive power than both the presence/absence GAMs and BRTs, likely due to both the different response variables and fitting algorithms. Our results provide an improved understanding of some of the strengths and limitations of models developed using these two methods. These results can be used by modelers developing SDMs and resource managers tasked with the spatial management of marine species to determine the best modeling technique for their question of interest.

Understanding the Stochastic Partial Differential Equation Approach to Smoothing

Correlation and smoothness are terms used to describe a wide variety of random quantities. In time, space, and many other domains, they both imply the same idea: quantities that occur closer together are more similar than those further apart. Two popular statistical models that represent this idea are basis-penalty smoothers (Wood in Texts in statistical science, CRC Press, Boca Raton, 2017) and stochastic partial differential equations (SPDEs) (Lindgren et al. in J R Stat Soc Series B (Stat Methodol) 73(4):423–498, 2011). In this paper, we discuss how the SPDE can be interpreted as a smoothing penalty and can be fitted using the package , allowing practitioners with existing knowledge of smoothing penalties to better understand the implementation and theory behind the SPDE approach.

Supplementary materials accompanying this paper appear online.

Discrete versus continuous domain models for disease mapping

The main goal of disease mapping is to estimate disease risk and identify high-risk areas. Such analyses are hampered by the limited geographical resolution of the available data. Typically the available data are counts per spatial unit and the common approach is the Besag-York-Mollié (BYM) model. When precise geocodes are available, it is more natural to use Log-Gaussian Cox processes (LGCPs). In a simulation study mimicking childhood leukaemia incidence using actual residential locations of all children in the canton of Zürich, Switzerland, we compare the ability of these models to recover risk surfaces and identify high-risk areas. We then apply both approaches to actual data on childhood leukaemia incidence in the canton of Zürich during 1985-2015. We found that LGCPs outperform BYM models in almost all scenarios considered. Our findings suggest that there are important gains to be made from the use of LGCPs in spatial epidemiology.

Neural hierarchical models of ecological populations

Neural networks are increasingly being used in science to infer hidden dynamics of natural systems from noisy observations, a task typically handled by hierarchical models in ecology. This article describes a class of hierarchical models parameterised by neural networks - neural hierarchical models. The derivation of such models analogises the relationship between regression and neural networks. A case study is developed for a neural dynamic occupancy model of North American bird populations, trained on millions of detection/non-detection time series for hundreds of species, providing insights into colonisation and extinction at a continental scale. Flexible models are increasingly needed that scale to large data and represent ecological processes. Neural hierarchical models satisfy this need, providing a bridge between deep learning and ecological modelling that combines the function representation power of neural networks with the inferential capacity of hierarchical models.

Integrating data from different survey types for population monitoring of an endangered species: the case of the Eld's deer

Despite its value for conservation decision-making, we lack information on population abundances for most species. Because establishing large-scale monitoring schemes is rarely feasible, statistical methods that combine multiple data sources are promising approaches to maximize use of available information. We built a Bayesian hierarchical model that combined different survey data of the endangered Eld’s deer in Shwesettaw Wildlife Sanctuary (SWS) in Myanmar and tested our approach in simulation experiments. We combined spatially-restricted line-transect abundance data with more spatially-extensive camera-trap occupancy data to enable estimation of the total deer abundance. The integrated model comprised an ecological model (common to both survey types, based on the equivalence between cloglog-transformed occurrence probability and log-transformed expected abundance) and separate observation models for each survey type. We estimated that the population size of Eld’s deer in SWS is c. 1519 (1061–2114), suggesting it is the world’s largest wild population. The simulations indicated that the potential benefits of combining data include increased precision and better sampling of the spatial variation in the environment, compared to separate analysis of each survey. Our analytical approach, which integrates the strengths of different survey methods, has widespread application for estimating species’ abundances, especially in information-poor regions of the world.