Search

1. The potential for statistical complexity in species distribution models (SDMs) has greatly increased with advances in computational power. Structurally complex models provide the flexibility to analyse intricate ecological systems and realistically messy data, but can be difficult to interpret, reducing their practical impact. Founding model complexity in ecological theory can improve insight gained from SDMs.\ud 2. Here, we evaluate a marked point process approach, which uses multiple Gaussian random fields to represent population dynamics of the Eurasian crane Grus grus in a spatio-temporal species distribution model. We discuss the role of model components and their impacts on predictions, in comparison with a simpler binomial presence/absence approach. Inference is carried out using Integrated Nested Laplace Approximation (INLA) with inlabru, an accessible and computationally efficient approach for Bayesian hierarchical modelling, which is not yet widely used in SDMs.\ud 3. Using the marked point process approach, crane distribution was predicted to be dependent on the density of suitable habitat patches, as well as close to observations of the existing population. This demonstrates the advantage of complex model components in accounting for spatio-temporal population dynamics (such as habitat preferences and dispersal limitations) that are not explained by environmental variables. However, including an AR1 temporal correlation structure in the models resulted in unrealistic predictions of species distribution; highlighting the need for careful consideration when determining the level of model complexity.\ud 4. Increasing model complexity, with careful evaluation of the effects of additional model components, can provide a more realistic representation of a system, which is of particular importance for a practical and impact-focused discipline such as ecology (though these methods extend to applications for a wide range of systems). Founding complexity in contextual theory is not only fundamental to maintaining model interpretability but can be a useful approach to improving insight gained from model outputs.

IP would like to thank the European Commission for the funding (GAP-847014). IP is grateful to the MSCA fellowship that supported his research. MGP thanks the project IMPRESS (RTI2018-099868-B-I00), ERDF, Ministry of Science, Innovation, and Universities - State Research Agency. Species Distribution Models are pivotal for fisheries management. There has been an increasing number of fishery data sources available, making data integration an attractive way to improve model predictions. A wide range of methods have been applied to integrate different datasets in different disciplines. We focus on the use of Integrated Species Distribution Models (ISDMs) due to their capacity to formally accommodate different types of data and scale proportional gear efficiencies. ISDMs use joint modelling to integrate information from different data sources to improve parameter estimation by fitting shared environmental, temporal and spatial effects. We illustrate this method first using a simulated example, and then apply it to a case study that combines data coming from a fishery-independent trawl survey and a fishery-dependent trammel net observations on Solea solea. We explore the sensitivity of model outputs to several weightings for the commercial data and also compare integrated model results with ensemble modelling to combine population trends in the case study. We obtain similar results but discuss that ensemble modelling requires both response variables and link functions to be the same across models. We conclude by discussing the flexibility and requirements of ISDMs to formally combine different fishery datasets. Publisher PDF

This paper proposes a two-stage estimation approach for a spatial misalignment scenario that is motivated by the epidemiological problem of linking pollutant exposures and health outcomes. We use integrated nested Laplace approximation method to estimate the parameters of a two-stage spatio-temporal model – the first stage models the exposures using data fusion while the second stage links the health outcomes to exposures. The first stage is based on the Bayesian melding model, which assumes a common latent field for the different data sources for the pollutants. The second stage fits a GLMM using the spatial averages of the estimated latent field, and additional spatial and temporal random effects. Uncertainty from the first stage is accounted for by simulating repeatedly from the posterior predictive distribution of the latent field. A simulation study was carried out to assess the impact of the sparsity of the data on the monitors, number of time points, and the specification of the priors in terms of the biases, RMSEs, and coverage probabilities of the parameters and the block-level exposure estimates. The results show that the parameters are generally estimated correctly but there is difficulty in estimating the Matèrn field parameters. The effect of exposures on the health outcomes is the primary parameter of interest for spatial epidemiologists and health policy makers, and our results show that the proposed method estimates these very well. The proposed method is applied to measurements of NO2 concentration and respiratory hospitalizations for year 2007 in England. The results show that an increase in NO2 levels is significantly associated with an increase in the relative risks of the health outcome. Also, there is a strong spatial structure in the risks, a strong temporal autocorrelation, and a significant spatio-temporal interaction effect. Publisher PDF

Understanding spatiotemporally varying animal distributions can inform ecological understanding of species' behavior (e.g., foraging and predator/prey interactions) and support development of management and conservation measures. Data from an array of echolocation‐click detectors (C‐PODs) were analyzed using Bayesian spatiotemporal modeling to investigate spatial and temporal variation in occurrence and foraging activity of harbor porpoises (Phocoena phocoena) and how this variation was influenced by daylight and presence of bottlenose dolphins (Tursiops truncatus). The probability of occurrence of porpoises was highest on an offshore sandbank, where the proportion of detections with foraging clicks was relatively low. The porpoises' overall distribution shifted throughout the summer and autumn, likely influenced by seasonal prey availability. Probability of porpoise occurrence was lowest in areas close to the coast, where dolphin detections were highest and declined prior to dolphin detection, leading potentially to avoidance of spatiotemporal overlap between porpoises and dolphins. Increased understanding of porpoises' seasonal distribution, key foraging areas, and their relationship with competitors can shed light on management options and potential interactions with offshore industries.

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. area search, binomial point process, continuous sampling, NIMBLE, non-invasive genetic sampling, Poisson point process, spatial capture–recapture, wolverine

This research was supported by a PhD Studentship at the University of St Andrews, jointly funded by NatureScot via the Marine Alliance for Science and Technology for Scotland (MASTS), and the Centre for Research into Ecological and Environmental Modelling. The data were collected as part of research funded by NatureScot (project 015960) and Marine Scotland (projects SP004 and SP02B0) and the Movement Ecology of Flapper Skate (MEFS) project funded by the same organisations. Additional funding was provided from MASTS, in the form of a Small Research Grant, and Shark Guardian. MASTS is funded by the Scottish Funding Council (grant reference HR09011) and contributing institutions. Trends in depth and vertical activity reflect the behaviour, habitat use and habitat preferences of marine organisms. However, among elasmobranchs, research has focused heavily on pelagic sharks, while the vertical movements of benthic elasmobranchs, such as skate (Rajidae), remain understudied. In this study, the vertical movements of the Critically Endangered flapper skate (Dipturus intermedius) were investigated using archival depth data collected at 2 min intervals from 21 individuals off the west coast of Scotland (56.5°N, −5.5°W) in 2016–17. Depth records comprised nearly four million observations and included eight time series longer than 1 year, forming one of the most comprehensive datasets collected on the movement of any skate to date. Additive modelling and functional data analysis were used to investigate vertical movements in relation to environmental cycles and individual characteristics. Vertical movements were dominated by individual variation but included prolonged periods of limited activity and more extensive movements that were associated with tidal, diel, lunar and seasonal cycles. Diel patterns were strongest, with irregular but frequent movements into shallower water at night, especially in autumn and winter. This research strengthens the evidence for vertical movements in relation to environmental cycles in benthic species and demonstrates a widely applicable flexible regression framework for movement research that recognises the importance of both individual-specific and group-level variation. Publisher PDF

Can Bayesian models reveal the underlying processes that drive the lethality of non-state terrorism at a local level? Andre Python, Janine B. Illian, Charlotte M. Jones-Todd and Marta Blangiardo investigate

The classical tools in spatial statistics are stationary models, like the Mat\'ern field. However, in some applications there are boundaries, holes, or physical barriers in the study area, e.g. a coastline, and stationary models will inappropriately smooth over these features, requiring the use of a non-stationary model. We propose a new model, the Barrier model, which is different from the established methods as it is not based on the shortest distance around the physical barrier, nor on boundary conditions. The Barrier model is based on viewing the Mat\'ern correlation, not as a correlation function on the shortest distance between two points, but as a collection of paths through a Simultaneous Autoregressive (SAR) model. We then manipulate these local dependencies to cut off paths that are crossing the physical barriers. To make the new SAR well behaved, we formulate it as a stochastic partial differential equation (SPDE) that can be discretised to represent the Gaussian field, with a sparse precision matrix that is automatically positive definite. The main advantage with the Barrier model is that the computational cost is the same as for the stationary model. The model is easy to use, and can deal with both sparse data and very complex barriers, as shown in an application in the Finnish Archipelago Sea. Additionally, the Barrier model is better at reconstructing the modified Horseshoe test function than the standard models used in R-INLA., Comment: The new version contains major changes and new materials, including a much more appropriate proof of existence of solution to the SPDE

Background: Diagnostics for COVID-19 detection are limited in many settings. Syndromic surveillance is often the only means to identify cases, despite lack of specificity and asymptomatic cases. Rapid antigen testing is inexpensive and easy-to-deploy but concerns remain about sensitivity. We examine how combining these approaches can improve surveillance for guiding interventions. Methods: Community-based volunteers were trained to syndromically assess potential COVID-19 cases in low-income communities in Dhaka, Bangladesh. Rapid antigen tests and PCR validation was performed on 1172 syndromically-identified individuals at their households. Statistical models were fit to predict PCR status using rapid-antigen-test results, syndromic data, and their combination. Model predictive and classification performance was examined under contrasting epidemiological scenarios to evaluate their potential for improving diagnoses. Findings: Models combining rapid-antigen-test and syndromic data yielded equal performance to rapid-antigen-test-only models in the “Agnostic” scenario and performed better under scenarios of “Low Incidence” and “Epidemic Growth”. Under “Epidemic Growth”, the combined model’s false negative rate is 26 (IQR:24-29) percentage points lower than the rapid-antigen-test-only model’s, with a false positive rate

Recent developments in earthquake forecasting models have demonstrated the need for a robust method for identifying which model components are most beneficial to understanding spatial patterns of seismicity. Borrowing from ecology, we use Log‐Gaussian Cox process models to describe the spatially varying intensity of earthquake locations. These models are constructed using elements which may influence earthquake locations, including the underlying fault map and past seismicity models, and a random field to account for any excess spatial variation that cannot be explained by deterministic model components. Comparing the alternative models allows the assessment of the performance of models of varying complexity composed of different components and therefore identifies which elements are most useful for describing the distribution of earthquake locations. We demonstrate the effectiveness of this approach using synthetic data and by making use of the earthquake and fault information available for California, including an application to the 2019 Ridgecrest sequence. We show the flexibility of this modeling approach and how it might be applied in areas where we do not have the same abundance of detailed information. We find results consistent with existing literature on the performance of past seismicity models that slip rates are beneficial for describing the spatial locations of larger magnitude events and that strain rate maps can constrain the spatial limits of seismicity in California. We also demonstrate that maps of distance to the nearest fault can benefit spatial models of seismicity, even those that also include the primary fault geometry used to construct them.

Funding: The Global Challenges Research Fund, the Scottish Funding Council and the Professor Sonia Buist Global Health Research Fund. Most maternal and child deaths result from inadequate access to the critical determinants of health: clean water, sanitation, education and healthcare, which are also among the Sustainable Development Goals. Reasons for poor access include insufficient government revenue for essential public services. In this paper, we predict the reductions in mortality rates — both child and maternal — that could result from increases in government revenue, using panel data from 191 countries and a two-way fixed-effect linear regression model. The relationship between government revenue per capita and mortality rates is highly non-linear, and the best form of non-linearity we have found is a version of an inverse function. This implies that countries with small per-capita government revenues have a better scope for reducing mortality rates. However, as per-capita revenue rises, the possible gains decline rapidly in a non-linear way. We present the results which show the potential decrease in mortality and lives saved for each of the 191 countries if government revenue increases. For example, a 10% increase in per-capita government revenue in Afghanistan in 2002 ($24.49 million) is associated with a reduction in the under-5 mortality rate by 12.35 deaths per 1000 births and 13,094 lives saved. This increase is associated with a decrease in the maternal mortality ratio of 9.3 deaths per 100,000 live births and 99 maternal deaths averted. Increasing government revenue can directly impact mortality, especially in countries with low per- capita government revenues. The results presented in this study could be used for economic, social and governance reporting by multinational companies and for evidence-based policymaking and advocacy. Publisher PDF

As the COVID-19 pandemic continues to threaten various regions around the world, obtaining accurate and reliable COVID-19 data is crucial for governments and local communities aiming at rigorously assessing the extent and magnitude of the virus spread and deploying efficient interventions. Using data reported between January and February 2020 in China, we compared counts of COVID-19 from near-real time spatially disaggregated data (city-level) with fine-spatial scale predictions from a Bayesian downscaling regression model applied to a reference province-level dataset. The results highlight discrepancies in the counts of coronavirus-infected cases at district level and identify districts that may require further investigation. Funding Statement: This work was supported by Zhejiang University Educational Funding (2020XGZX054), the National Natural Science Foundation of China under Grants (61825205 and 41601001), and The Royal Society, United Kingdom (NF171120). Declaration of Interests: The authors declare no competing interests.

Diagnosis and prognosis of cancer are informed by the architecture inherent in cancer patient tissue sections. This architecture is typically identified by pathologists, yet advances in computational image analysis facilitate quantitative assessment of this structure. In this article, we develop a spatial point process approach to describe patterns in cell distribution within tissue samples taken from colorectal cancer (CRC) patients. In particular, our approach is centered on the Palm intensity function. This leads to taking an approximate-likelihood technique in fitting point processes models. We consider two Neyman-Scott point processes and a void process, fitting these point process models to the CRC patient data. We find that the parameter estimates of these models may be used to quantify the spatial arrangement of cells. Importantly, we observe characteristic differences in the spatial arrangement of cells between patients who died from CRC and those alive at follow up.

The last few decades have seen an increasing interest and strong development in spatial point process methodology, and associated software that facilitates model fitting has become available. A lot of this progress has made these approaches more accessible to users, through freely available software. However, in the ecological user community the methodology has only been slowly picked up despite its obvious relevance to the field. This paper reflects on this development, highlighting mutual benefits of interdisciplinary dialogue for both statistics and ecology. We detail the contribution point process methodology has made to research on biodiversity theory as a result of this dialogue and reflect on reasons for the slow take-up of the methodology. This primarily concerns the current lack of consideration of the usability of the approaches, which we discuss in detail, presenting current discussions as well as indicating future directions. Publisher PDF

This research was funded by EPSRC grants EP/K041061/1, EP/K041053/1, and EP/K041053/2. 1. Spatial processes are central to many ecological processes, but fitting models that incorporate spatial correlation to data from ecological surveys is computationally challenging. This is particularly true of point pattern data (in which the primary data are the locations at which target species are found), but also true of gridded data, and of georeferenced samples from continuous spatial fields. 2. We describe here the R package inlabru that builds on the widely-used R-INLA package to provide easier access to Bayesian inference from spatial point process, spatial count, gridded, and georeferenced data, using integrated nested Laplace approximation (INLA, Rue et al., 2009). 3. The package povides methods for fitting spatial density surfaces and estimating abundance, as well as for plotting and prediction. It accommodates data that are points, counts, georeferenced samples, or distance sampling data. 4. This paper describes the main features of the package, illustrated by fitting models to the gorilla nest data contained in the package spatstat (Baddeley & Turner, 2005), a line transect survey data set contained in the package dsm (Miller et al., 2018), and to a georeferenced sample from a simulated continuous spatial field. Postprint

Funding: EU consolidator’s grant STATEMIG 310820 (SB). Understanding and predicting a species’ distribution across a landscape is of central importance in ecology, biogeography and conservation biology. However, it presents daunting challenges when populations are highly dynamic (i.e. increasing or decreasing their ranges), particularly for small populations where information about ecology and life history traits is lacking. Currently, many modelling approaches fail to distinguish whether a site is unoccupied because the available habitat is unsuitable or because a species expanding its range has not arrived at the site yet. As a result, habitat that is indeed suitable may appear unsuitable. To overcome some of these limitations, we use a statistical modelling approach based on spatio‐temporal log‐Gaussian Cox processes. These model the spatial distribution of the species across available habitat and how this distribution changes over time, relative to covariates. In addition, the model explicitly accounts for spatio‐temporal dynamics that are unaccounted for by covariates through a spatio‐temporal stochastic process. We illustrate the approach by predicting the distribution of a recently established population of Eurasian cranes Grus grus in England, UK, and estimate the effect of a reintroduction in the range expansion of the population. Our models show that wetland extent and perimeter‐to‐area ratio have a positive and negative effect, respectively, in crane colonisation probability. Moreover, we find that cranes are more likely to colonise areas near already occupied wetlands and that the colonisation process is progressing at a low rate. Finally, the reintroduction of cranes in SW England can be considered a human‐assisted long‐distance dispersal event that has increased the dispersal potential of the species along a longitudinal axis in S England. Spatio‐temporal log‐Gaussian Cox process models offer an excellent opportunity for the study of species where information on life history traits is lacking, since these are represented through the spatio‐temporal dynamics reflected in the model. Postprint

We acknowledge the principal investigators who were responsible for collecting and analysing the soil maps (Jim Dallin, Robert John, Kyle Harms, Robert Stallard and Joe Yavitt), the funding sources (National Science Foundation grants DEB021104, 021115, 0212284 and 0212818 and Office of International Science and Engineering grant 0314581, the Smithsonian Tropical Research Institute soils initiative and the Center for Tropical Forest Science) and field assistants (Paolo Segre and Juan Di Trani). Hyperprior specifications for random fields in spatial point process modelling can have a major impact on the results. In fitting log-Gaussian Cox processes to rainforest tree species, we consider a reparameterised model combining a spatially structured and an unstructured random field into a single component. This component has one hyperpa- rameter accounting for marginal variance, while an additional hyperparameter governs the fraction of the variance explained by the spatially structured effect. This facilitates inter- pretation of the hyperparameters and significance of covariates is studied for a range of hyperprior specifications. Appropriate scaling makes the analysis invariant to grid resolution. Postprint

D. C., A. L. Q. and F. M. would like to thank the Ministerio de Educación y Ciencia (Spain) for financial support (jointly financed by the European Regional Development Fund) via Research Grants MTM2013‐42323‐P and MTM2016‐77501‐P, and ACOMP/2015/202 from Generalitat Valenciana (Spain). Species distribution models (SDMs) are now being widely used in ecology for management and conservation purposes across terrestrial, freshwater, and marine realms. The increasing interest in SDMs has drawn the attention of ecologists to spatial models and, in particular, to geostatistical models, which are used to associate observations of species occurrence or abundance with environmental covariates in a finite number of locations in order to predict where (and how much of) a species is likely to be present in unsampled locations. Standard geostatistical methodology assumes that the choice of sampling locations is independent of the values of the variable of interest. However, in natural environments, due to practical limitations related to time and financial constraints, this theoretical assumption is often violated. In fact, data commonly derive from opportunistic sampling (e.g., whale or bird watching), in which observers tend to look for a specific species in areas where they expect to find it. These are examples of what is referred to as preferential sampling, which can lead to biased predictions of the distribution of the species. The aim of this study is to discuss a SDM that addresses this problem and that it is more computationally efficient than existing MCMC methods. From a statistical point of view, we interpret the data as a marked point pattern, where the sampling locations form a point pattern and the measurements taken in those locations (i.e., species abundance or occurrence) are the associated marks. Inference and prediction of species distribution is performed using a Bayesian approach, and integrated nested Laplace approximation (INLA) methodology and software are used for model fitting to minimize the computational burden. We show that abundance is highly overestimated at low abundance locations when preferential sampling effects not accounted for, in both a simulated example and a practical application using fishery data. This highlights that ecologists should be aware of the potential bias resulting from preferential sampling and account for it in a model when a survey is based on non‐randomized and/or non‐systematic sampling. Publisher PDF

The authors gratefully acknowledge the financial support from the Knut and Alice Wallenberg Foundation, the Swedish Research Council Grant 2016-04187, and the ÅForsk foundation. Numerous organizations have provided funding, principally the U.S. National Science Foundation, and hundreds of field workers have contributed. The Barro Colorado soil survey was funded by NSFDEB021104, 021115, 0212284, 0212818 and OISE0314581 as well as the STRI Soils Initiative and CTFS. An extension of the popular log-Gaussian Cox process (LGCP) model for spatial point patterns is proposed for data exhibiting fundamentally different behaviors in different subregions of the spatial domain. The aim of the analyst might be either to identify and classify these regions, to perform kriging, or to derive some properties of the parameters driving the random field in one or several of the subregions. The extension is based on replacing the latent Gaussian random field in the LGCP by a latent spatial mixture model specified using a categorically valued random field. This classification is defined through level set operations on a Gaussian random field and allows for standard stationary covariance structures, such as the Matérn family, to be used to model random fields with some degree of general smoothness but also occasional and structured sharp discontinuities. A computationally efficient MCMC method is proposed for Bayesian inference and we show consistency of finite dimensional approximations of the model. Finally, the model is fitted to point pattern data derived from a tropical rainforest on Barro Colorado island, Panama. We show that the proposed model is able to capture behavior for which inference based on the standard LGCP is biased. Postprint

BS was part funded by Engineering and Physical Sciences Research Council–Natural Environment Research Council grant EP/10009171/1. As accessible and potentially vulnerable species high up in the food chain, birds are often used as indicator species to highlight changes in ecosystems. This study focuses on multiple spatially dependent relationships between a raptor (sparrowhawk), a potential prey species (house sparrow) and a sympatric species (collared doves) in space and time. We construct a complex spatiotemporal latent Gaussian model to incorporate both predator–prey and sympatric relationships, which is novel in two ways. First, different types of species interactions are represented by a shared spatiotemporal random effect, which extends existing approaches to multivariate spatial modelling through the use of a joint latent modelling approach. Second, we use a delta–gamma model to capture the semicontinuous nature of the data to model the binary and continuous sections of the response jointly. The results indicate that sparrowhawks have a localized effect on the presence of house sparrows, which could indicate that house sparrows avoid sites where sparrowhawks are present. Postprint

Diagnosis and prognosis of cancer are informed by the architecture inherent in cancer patient tissue sections. This architecture is typically identified by pathologists, yet advances in computational image analysis facilitate quantitative assessment of this structure. In this article, we develop a spatial point process approach to describe patterns in cell distribution within tissue samples taken from colorectal cancer (CRC) patients. In particular, our approach is centered on the Palm intensity function. This leads to taking an approximate-likelihood technique in fitting point processes models. We consider two Neyman-Scott point processes and a void process, fitting these point process models to the CRC patient data. We find that the parameter estimates of these models may be used to quantify the spatial arrangement of cells. Importantly, we observe characteristic differences in the spatial arrangement of cells between patients who died from CRC and those alive at follow up.

As regards authors Linda Altieri and Fedele Greco, the research work underlying this paper was partially funded by an FIRB 2012 [grant number RBFR12URQJ]; title: Statistical modelling of environmental phenomena: pollution, meteorology, health and their interactions) for research projects by the Italian Ministry of Education, Universities and Research. This work presents advanced computational aspects of a new method for changepoint detection on spatio-temporal point process data. We summarize the methodology, based on building a Bayesian hierarchical model for the data and declaring prior conjectures on the number and positions of the changepoints, and show how to take decisions regarding the acceptance of potential changepoints. The focus of this work is about choosing an approach that detects the correct changepoint and delivers smooth reliable estimates in a feasible computational time; we propose Bayesian P-splines as a suitable tool for managing spatial variation, both under a computational and a model fitting performance perspective. The main computational challenges are outlined and a solution involving parallel computing in R is proposed and tested on a simulation study. An application is also presented on a data set of seismic events in Italy over the last 20 years. Postprint

Spatial statistics are widely used in studies of ecological processes in plant communities, especially to provide evidence of neutral or non‐neutral mechanisms that might support species coexistence. The contribution of such statistics has been substantial, but their ability to identify any links between underlying processes and emergent patterns is not certain. We investigate the ability of a number of spatial statistics to distinguish theorized mechanisms of species coexistence (spatial and temporal niche differentiation, neutrality, the Janzen–Connell effect and heteromyopia) in a simulated plant community. We find that individual statistics differ substantially in their sensitivity to these mechanisms, with those based on nearest neighbour species identities being the most sensitive. These differences are largely robust to changes in the strength of the modelled mechanisms when simulated independently and in combination. The spatial signal of niche differentiation is always distinct in simulations that combine mechanisms. Synthesis. We describe full spatial signals of modelled coexistence mechanisms that are observed consistently across statistics and simulated strengths and combinations of mechanisms, and identify a set of spatial statistics that holds particular promise for empirical studies designed to investigate mechanisms of these kinds.

Coming up with Bayesian models for spatial data is easy, but performing inference with them can be challenging. Writing fast inference code for a complex spatial model with realistically‐sized datasets from scratch is time‐consuming, and if changes are made to the model, there is little guarantee that the code performs well. The key advantages of R‐INLA are the ease with which complex models can be created and modified, without the need to write complex code, and the speed at which inference can be done even for spatial problems with hundreds of thousands of observations. R‐INLA handles latent Gaussian models, where fixed effects, structured and unstructured Gaussian random effects are combined linearly in a linear predictor, and the elements of the linear predictor are observed through one or more likelihoods. The structured random effects can be both standard areal model such as the Besag and the BYM models, and geostatistical models from a subset of the Matérn Gaussian random fields. In this review, we discuss the large success of spatial modeling with R‐INLA and the types of spatial models that can be fitted, we give an overview of recent developments for areal models, and we give an overview of the stochastic partial differential equation (SPDE) approach and some of the ways it can be extended beyond the assumptions of isotropy and separability. In particular, we describe how slight changes to the SPDE approach leads to straight‐forward approaches for nonstationary spatial models and nonseparable space–time models. Locked until 5.7.2019 due to copyright restrictions. This is the peer reviewed version of an article, which has been published in final form at [https://doi.org/10.1002/wics.1443]. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.

Summary Many ecological questions could gain insight from linking variation in spatial structure to explanatory variables. Although methods that make these links have been developed in the statistical literature, they have been used rarely in ecology. We present an approach that considers point patterns from different sources (e.g. multiple plots or species) as replicates of the spatial processes of interest. Using an integrated two-step procedure, the method uses a linear mixed-effects modelling framework to explain variation in the spatial structure of the replicated patterns with categorical and continuous predictors. Inferences on the strength of the relationships between the predictors and spatial structure are made on the basis of a semi-parametric bootstrap procedure that accounts for the dependency among spatial scales and, if required, among replicates. We illustrate the approach with three simulated examples. These demonstrate that replicated analyses can increase the performance of spatial point pattern analyses, allow analysis of sparse patterns (e.g. rare species) and help identify the drivers of variation among spatial point patterns. The paucity of ecological studies that utilize replicated point pattern analysis may be due partly to a lack of familiarity with the methods. By highlighting the options available, we hope to encourage greater use of these methods by ecologists in the future.

Since 2009, Nigeria has been the scene of numerous deadly terrorist attacks perpetrated by the terrorist group Boko Haram. In response to this threat, stakeholders in the fight against terrorism have deployed various counterterrorism policies, the costs of which could be reduced through efficient preventive measures. Statistical models able to integrate complex spatial dependence structures have not yet been applied, despite their potential for providing guidance to assess characteristics of terrorist attacks. In an effort to address this shortcoming, we use a flexible approach that represents a Gaussian Markov random field through stochastic partial differential equation and model the fine-scale spatial patterns of the lethality of terrorism perpetrated by Boko Haram in Nigeria from 2009 to 2014. Our results suggest that the lethality of terrorist attacks is contagious in space and attacks are more likely to be lethal at higher altitudes and far from large cities.

Summary 1. We highlight an emerging statistical method, integrated nested Laplace approximation (INLA), which is ideally suited for fitting complex models to many of the rich spatial data sets that ecologists wish to analyse. 2. INLA is an approximation method that nevertheless provides very exact estimates. In this article, we describe the INLA methodology highlighting where it offers opportunities for drawing inference from (spatial) ecological data that would previously have been too complex to make practical model fitting feasible. 3. We use INLA to fit a complex joint model to the spatial pattern formed by a plant species, Thymus carnosus, as well as to the health status of each individual. 4. The key ecological result revealed by our spatial analysis of these data, relates to the distance-to-water covariate. We find that T. carnosus plants are generally healthier when they are further away from the water. 5. We suggest that this may be the result of a combination of (1) plants having alternative rooting strategies depending on how close to water they grow and (2) the rooting strategy determining how well the plants were able to tolerate an unusually dry summer. 6. We anticipate INLA becoming widely used within spatial ecological analysis over the next decade and suggest that both ecologists and statisticians will benefit greatly from working collaboratively to further develop and apply these emerging statistical methods. Publisher PDF

The first author was supported by the European Union under a IEF Marie-Curie Action. Accurate estimation of tree biomass is necessary to provide realistic values of the carbon stored in the terrestrial biosphere. A recognized source of errors in tree above-ground biomass (AGB) estimation is introduced when individual tree height values (H) are not directly measured but estimated from diameter at breast height (DBH) using allometric equations. In this paper we evaluate the performance of 12 alternative DBH : H equations and compare their effects on AGB estimation for three tropical forests that occur in contrasting climatic and altitudinal zones. We found that fitting a 3-parameter Weibull function using data collected locally generated the lowest errors and bias in H estimation, and that equations fitted to these data were more accurate than equations with parameters derived from the literature. For computing AGB, the introduced error values differed notably among DBH : H allometric equations, and in most cases showed a clear bias that resulted in either over- or under-estimation of AGB. Fitting the three-parameter Weibull function minimized errors in AGB estimates in our study and we recommend its widespread adoption for carbon stock estimation. We conclude that many previous studies are likely to present biased estimates of AGB due to the method of H estimation. Publisher PDF

This study was supported by the FP7-PEOPLE-2013-IEF Marie-Curie Action – SPATFOREST. Tree data from BCI were provided by the Center for Tropical Forest Science of the Smithsonian Tropical Research Institute and the primary granting agencies that have supported the BCI plot tree census. Data for the liana censuses were supported by the US National Science Foundation grants: DEB-0613666, DEB-0845071, and DEB-1019436 (to SAS). Soil data was funded by the National Science Foundation grants DEB021104, DEB021115, DEB0212284 and DEB0212818 supporting soils mapping in the BCI plot. 1. Prediction of carbon dynamics in response to global climate change requires an understanding of the processes that govern the distribution of carbon stocks. Above ground biomass (AGB) in tropical forests is regulated by variation in soil fertility, climate, species composition and topography at regional scales, but the drivers of fine-scale variation in tropical forest AGB are poorly understood. The factors that control the growth and mortality of individual trees may be obscured by the low resolution of studies at regional scales. 2. In this paper, we evaluate the effects of soil nutrients, topography and liana abundance on the fine-scale spatial distribution of AGB and density of trees for a lowland tropical moist forest in Panama using additive regression models. 3. Areas with larger values of AGB were negatively associated with the presence of lianas, which may reflect competition with lianas and/or the association of lianas with disturbed or open canopy patches within forests. AGB was positively associated with soils possessing higher pH and K concentrations, reflecting the importance of below-ground resource availability on AGB independently of stem density. 4. Synthesis: Our results shed new light the factors that influence fine-scale tree AGB and carbon stocks in tropical forests: liana abundance is the strongest predictor, having a negative impact on tree AGB. The availability of soil nutrients was also revealed as an important driver of fine-scale spatial variation in tree AGB. Postprint

This paper introduces a new method for performing computational inference on log-Gaussian Cox processes. The likelihood is approximated directly by making novel use of a continuously specified Gaussian random field. We show that for sufficiently smooth Gaussian random field prior distributions, the approximation can converge with arbitrarily high order, while an approximation based on a counting process on a partition of the domain only achieves first-order convergence. The given results improve on the general theory of convergence of the stochastic partial differential equation models, introduced by Lindgren et al. (2011). The new method is demonstrated on a standard point pattern data set and two interesting extensions to the classical log-Gaussian Cox process framework are discussed. The first extension considers variable sampling effort throughout the observation window and implements the method of Chakraborty et al. (2011). The second extension constructs a log-Gaussian Cox process on the world's oceans. The analysis is performed using integrated nested Laplace approximation for fast approximate inference., 22 Pages, 8 figures

This work is partially supported by Research Councils UK We consider spatial point pattern data that have been observed repeatedly over a period of time in an inhomogeneous environment. Each spatial point pattern can be regarded as a “snapshot” of the underlying point process at a series of times. Thus, the number of points and corresponding locations of points differ for each snapshot. Each snapshot can be analyzed independently, but in many cases there may be little information in the data relating to model parameters, particularly parameters relating to the interaction between points. Thus, we develop an integrated approach, simultaneously analyzing all snapshots within a single robust and consistent analysis. We assume that sufficient time has passed between observation dates so that the spatial point patterns can be regarded as independent replicates, given spatial covariates. We develop a joint mixed effects Gibbs point process model for the replicates of spatial point patterns by considering environmental covariates in the analysis as fixed effects, to model the heterogeneous environment, with a random effects (or hierarchical) component to account for the different observation days for the intensity function. We demonstrate how the model can be fitted within a Bayesian framework using an auxiliary variable approach to deal with the issue of the random effects component. We apply the methods to a data set of musk oxen herds and demonstrate the increased precision of the parameter estimates when considering all available data within a single integrated analysis. Postprint

While much research in ecology has focused on spatially explicit modelling as well as on measures of biodiversity, the concept of spatial (or local) biodiversity has been discussed very little. This paper generalises existing measures of spatial biodiversity and introduces a family of spatial biodiversity measures by flexibly defining the notion of the individuals’ neighbourhood within the framework of graphs associated to a spatial point pattern. We consider two non-independent aspects of spatial biodiversity, scattering, i.e. the spatial arrangement of the individuals in the study area and exposure, the local diversity in an individual’s neighbourhood. A simulation study reveals that measures based on the most commonly used neigh-bourhood defined by the geometric graph do not distinguish well between scattering and exposure. This problem is much less pronounced when other graphs are used. In an analysis of the spatial diversity in a rainforest, the results based on the geometric graph have been shown to spuriously indicate a decrease in spatial biodiversity when no such trend was detected by the other types of neighbourhoods. We also show that the choice neighbourhood markedly impacts on the classification of species according to how strongly and in what way different species spatially structure species diversity. Clearly, in an analysis of spatial or local diversity an appropriate choice of local neighbourhood is crucial in particular in terms of the biological interpretation of the results. Due to its general definition, the approach discussed here offers the necessary flexibility that allows suitable and varying neighbourhood structures to be chosen. Postprint

1. Spatial management of marine ecosystems requires detailed knowledge of spatio-temporal mechanisms linking physical and biological processes. Tidal currents, the main driver of ecosystem dynamics in temperate coastal ecosystems, influence predator foraging ecology by affecting prey distribution and ecology. The mechanistic links between tidal currents and how they influence predator–prey behaviour and interactions at a fine scale are poorly understood. 2. Studies of fine-scale changes in oceanography, prey and predator behaviour with tidal currents require repeated surveys of the same location over brief time-scales. Such data are highly temporally and spatially autocorrelated and require appropriate analytical tools. 3. We used functional data analysis (FDA), specifically functional principal component analysis (FPCA), to analyse repeated, fine-scale, survey data collected in the North Sea. FPCA was used to explore the relationship between the behaviour of an important North Sea prey species (sandeel Ammodytes spp.) and a vulnerable surface-foraging predator (black-legged kittiwake Rissa tridactyla) with fine-scale tidally driven changes in bio-physical characteristics (temperature stratification and maximumsubsurface chlorophyll concentration). 4. The FPCA indicated that sandeels were aggregated close to the surface at maximum ebb (ME) currents. Surface-feeding kittiwakes were also found in highest numbers during ME in locations of both high subsurface chlorophyll concentration and shallow sandeel aggregations. We suggest that the combination of a well-stratified water column with the movement of tidal currents over uneven topography results in surface aggregations of sandeels which kittiwakes exploit. 5. Synthesis and applications. Functional Data Analysis provides a useful tool for examining spatio-temporal patterns in natural ecosystems. In combination with fine-scale repeated survey design, we identified the importance of tide in driving prey behaviour and hence predator foraging behaviour. This has implications both for critical marine habitat identification for Marine Protected Area selection and for fisheries stock assessments. We therefore recommend that tidal aspects should be taken into account when designing marine surveys in temperate coastal ecosystems both to ensure the best identification of critical marine habitat and to improve the accuracy of fish stock assessments.

Summary 1. Attempts to infer underlying ecological process from observed patterns in ecology have been widespread, but have generally relied on first-order (non-spatial) community characteristics such as the species abundance distribution (SAD). This measure has become an important test of several theories of species coexistence, but has proved unsuccessful in distinguishing between them. 2. Spatially explicit data are increasingly available for a range of ecological communities, and analysis methods for these data are well developed. However, relatively little work has investigated the potential of these data for similar inference about mechanisms of coexistence. 3. In this study, we systematically investigate the spatial and non-spatial signals of simulated ecological processes. We include neutral, niche, lottery, Janzen–Connell and heteromyopia models, deriving and comparing first- and second-order measures for the patterns they generate. 4. We find that the SAD is unable to distinguish reliably between underlying models, with random variation in its shape concealing any systematic differences. 5. A new second-order summary measure of spatial structure derived in this paper, in contrast, proves highly sensitive to the type of ecological interaction being modelled, and is robust to random variation. 6. Synthesis. A simple summary measure of the spatial structure of plant communities is presented and found to be a more powerful indicator of underlying process in simulated data than a widely used first-order measure, the SAD. The potential for answering important ecological questions using spatial statistics, particularly concerning mechanisms of coexistence in diverse communities, appears to be great.

The anchovy/sardine complex is an important fishery resource in some of the largest upwelling systems in the world. Synchronous, but out of phase, fluctuations of the two species in distant parts of the oceans have prompted a number of studies dedicated to determining the phenomena, atmospheric and oceanic, responsible for the observed synchronicity and the biological mechanisms behind the population changes of the two species. Anchovy and sardine are of high commercial value for the fishing sector in Greece; this study investigates the impact of large-scale climatic indices on the anchovy/sardine complex in the Greek seas using fishery catches as a proxy for fish productivity. Time series of catches for both species were analysed for relationships with teleconnection indices and local environmental variability. The connection between the teleconnection indices and local weather/oceanic variation was also examined in an effort to describe physical mechanisms that link large-scale atmospheric patterns with anchovy and sardine. The West African Summer Monsoon, East Atlantic Jet and Pacific–North American (PNA) pattern exhibit coherent relationships with the catches of the two species. The first two aforementioned patterns are prominent atmospheric modes of variability during the summer months when sardine is spawning and anchovy juveniles are growing. PNA is related with El Nino Southern Oscillation events. Sea Surface Temperature (SST) appears as a significant link between atmospheric and biological variability either because higher temperatures seem to be favouring sardine growth or because lower temperatures, characteristic of productivity-enhancing oceanic features, exert a positive influence on both species. However at a local scale, other parameters such as wind and mesoscale circulation describe air–sea variability affecting the anchovy/sardine complex. These relationships are non-linear and in agreement with results of previous studies stressing the importance of optimal environmental windows. The results also show differences in the response of the two species to environmental forcing and possible interactions between the two species. The nature of these phenomena, e.g., if the species interactions are direct through competition or indirect through the food web, remains to be examined.

The 2010 biodiversity target agreed by signatories to the Convention on Biological Diversity directed the attention of conservation professionals toward the development of indicators with which to measure changes in biological diversity at the global scale. We considered why global biodiversity indicators are needed, what characteristics successful global indicators have, and how existing indicators perform. Because monitoring could absorb a large proportion of funds available for conservation, we believe indicators should be linked explicitly to monitoring objectives and decisions about which monitoring schemes deserve funding should be informed by predictions of the value of such schemes to decision making. We suggest that raising awareness among the public and policy makers, auditing management actions, and informing policy choices are the most important global monitoring objectives. Using four well-developed indicators of biological diversity (extent of forests, coverage of protected areas, Living Planet Index, Red List Index) as examples, we analyzed the characteristics needed for indicators to meet these objectives. We recommend that conservation professionals improve on existing indicators by eliminating spatial biases in data availability, fill gaps in information about ecosystems other than forests, and improve understanding of the way indicators respond to policy changes. Monitoring is not an end in itself, and we believe it is vital that the ultimate objectives of global monitoring of biological diversity inform development of new indicators.

We consider spatial point patterns that have been observed repeatedly in the same area at several points in time. We take a maximum pseudolikelihood approach (besag :1976) to parameter estimation in the context of Gibbs processes (Stoyan et al., 1995, Illian et al., 2008). More specifically, we discuss pair-wise interaction processes where the conditional intensity has a log-linear form and extend existing models by expressing the intensity and the interaction terms in the pseudolikelihood as a sum of fixed and random effects, where the latter accounts for variation over time. We initially derive a Strauss process model with mixed effects. As this model is too simplistic in the given context, we further consider a more general model that allows for inter-group differences in intensity and interaction strength and has a more flexible interaction function. We apply the approximate Berman–Turner device (Baddeley and Turner, 2000) to a generalised linear mixed model with log link and Poisson outcome rather than a simple generalised linear model. Estimates are obtained using existing software for generalised linear mixed models based on penalised quasi-likelihood methods (Bresow and Clayton, 1993). The approach is applied to a data set detailing the spatial locations of different types of muskoxen herds in a fixed area in Greenland at different points in time within several years (Meltofte and Berg, 2004). Copyright © 2009 John Wiley & Sons, Ltd.

Recent research suggests the coupling of climatic fluctuations and changes in biological indices that describe species richness, abundance and spatiotemporal distribution. In this study, large-scale modes of atmospheric variability over the northern hemisphere are associated with chlorophyll-a concentration in the Mediterranean. Sea level atmospheric pressure, air temperature, wind speed and precipitation are used to account for climatic and local weather effects, whereas sea surface temperature, sea surface height and salinity are employed to describe oceanic variation. Canonical Correlation Analysis was applied to relate chlorophyll concentration to the above-mentioned environmental variables, while correlation maps were also built to distinguish between localized and distant effects. Spectral analysis was used to identify common temporal cycles between chlorophyll concentration and each environmental variable. These cycles could be interpreted as mechanistic links between chlorophyll and large-scale atmospheric variability. Known teleconnection patterns such as the East Atlantic/Western Russian pattern, the North Atlantic Oscillation, the Polar/Eurasian pattern, the East Pacific/North Pacific, the East Atlantic jet and the Mediterranean Oscillation are found to be the most important modes of atmospheric variability related to chlorophyll-a concentration and distribution. The areas that are mostly affected are near the coasts and areas of upwelling and gyre formation. The results also suggest that this influence may arise either through local effects of teleconnection patterns on oceanic features or large-scale changes superimposed onto the general circulation in the Mediterranean.

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 figures

The key operation in Bayesian inference, is to compute high-dimensional integrals. An old approximate technique is the Laplace method or approximation, which dates back to Pierre- Simon Laplace (1774). This simple idea approximates the integrand with a second order Taylor expansion around the mode and computes the integral analytically. By developing a nested version of this classical idea, combined with modern numerical techniques for sparse matrices, we obtain the approach of Integrated Nested Laplace Approximations (INLA) to do approximate Bayesian inference for latent Gaussian models (LGMs). LGMs represent an important model-abstraction for Bayesian inference and include a large proportion of the statistical models used today. In this review, we will discuss the reasons for the success of the INLA-approach, the R-INLA package, why it is so accurate, why the approximations are very quick to compute and why LGMs make such a useful concept for Bayesian computing., 28 pages, 7 figures

As regards author Linda Altieri, the research work underlying this paper was partially funded by a FIRB 2012 grant (project no. RBFR12URQJ; title: Statistical modeling of environmental phenomena: pollution, meteorology, health and their interactions) for research projects by the Italian Ministry of Education, Universities and Research. This work introduces a Bayesian approach to detecting multiple unknown changepoints over time in the inhomogeneous intensity of a spatio-temporal point process with spatial and temporal dependence within segments. We propose a new method for detecting changes by fitting a spatio-temporal log-Gaussian Cox process model using the computational efficiency and flexibility of integrated nested Laplace approximation, and by studying the posterior distribution of the potential changepoint positions. In this paper, the context of the problem and the research questions are introduced, then the methodology is presented and discussed in detail. A simulation study assesses the validity and properties of the proposed methods. Lastly, questions are addressed concerning potential unknown changepoints in the intensity of radioactive particles found on Sandside beach, Dounreay, Scotland. Postprint

1. The effects of neighbours on the growth of individual plants are fundamental to dynamics in plant populations and can be described by means of mathematical functions, so-called competition kernels, in formal spatiotemporal models. Little is known about the form and components such functions should have. 2. We evaluate some properties of kernel functions using data on the growth of Arabidopsis thaliana plants in replicated, even-aged stands of many individuals. Because of the essential non-independence of plant growth in stands, we employed a Bayesian hierarchical modelling approach to estimate values and uncertainties of kernel parameters in location-dependent models of interacting plants. 3. During the experiment plant size and a simple measure of neighbourhood crowding became strongly correlated, plants tending to be small where local crowding was intense, indicating that local competition was an important process in the growth of the plants. 4. Competitive interactions between plants of different sizes were strongly asymmetric, the larger individual acquiring a disproportionately greater share of resources. Competition increased with plant size and attenuated rapidly at distances of a few centimetres, but the exact shape of the attenuation function was less important. 5. Kernel functions with the same kind of structural features were similar in their predictive ability. However, a simple zone-of-influence model, based on overlap of pairs of individuals, with competition favouring the larger individual, was arguably the most parsimonious. 6. Neighbourhood competition in stands of even-aged plants may be successfully captured with relatively simple kernel functions. The results should inform and enhance the formal theory of spatiotemporal plant population and community dynamics. Bayesian hierarchical modelling is a powerful tool with which to analyse complex, spatially dependent data, and has potential as a widely applicable statistical approach for plant ecology.

Acquisition and transfer of algae from distant polar locations to research facilities in the northern hemisphere may take several months, at which point the algae may be non-viable and in a deteriorated state. This study explores the effectiveness of 3% (w/v) Benomyl fungicide (Benlate) pre-treatments, on fungal "spoilage", viability and biochemical status of algae collected from terrestrial and freshwater habitats at Signy Island, maritime Antarctic. The results allow recommendations concerning sampling procedures and species selection for the ex-situ study of Antarctic algae to be made. The three algal taxa examined showed that although the fungicide was not necessary for successful transfer of viable specimens, it had a positive effect on viability. Prasiola crispa is suggested as a target organism for future ex-situ physiological studies.