Colin M. Beale

Regression analysis of spatial data

Many of the most interesting questions ecologists ask lead to analyses of spatial data. Yet, perhaps confused by the large number of statistical models and fitting methods available, many ecologists seem to believe this is best left to specialists. Here, we describe the issues that need consideration when analysing spatial data and illustrate these using simulation studies. Our comparative analysis involves using methods including generalized least squares, spatial filters, wavelet revised models, conditional autoregressive models and generalized additive mixed models to estimate regression coefficients from synthetic but realistic data sets, including some which violate standard regression assumptions. We assess the performance of each method using two measures and using statistical error rates for model selection. Methods that performed well included generalized least squares family of models and a Bayesian implementation of the conditional auto-regressive model. Ordinary least squares also performed adequately in the absence of model selection, but had poorly controlled Type I error rates and so did not show the improvements in performance under model selection when using the above methods. Removing large-scale spatial trends in the response led to poor performance. These are empirical results; hence extrapolation of these findings to other situations should be performed cautiously. Nevertheless, our simulation-based approach provides much stronger evidence for comparative analysis than assessments based on single or small numbers of data sets, and should be considered a necessary foundation for statements of this type in future.

Opening the climate envelope reveals no macroscale associations with climate in European birds

Predicting how species distributions might shift as global climate changes is fundamental to the successful adaptation of conservation policy. An increasing number of studies have responded to this challenge by using climate envelopes, modeling the association between climate variables and species distributions. However, it is difficult to quantify how well species actually match climate. Here, we use null models to show that species–climate associations found by climate envelope methods are no better than chance for 68 of 100 European bird species. In line with predictions, we demonstrate that the species with distribution limits determined by climate have more northerly ranges. We conclude that scientific studies and climate change adaptation policies based on the indiscriminate use of climate envelope methods irrespective of species sensitivity to climate may be misleading and in need of revision.

Improving assessment and modelling of climate change impacts on global terrestrial biodiversity

Understanding how species and ecosystems respond to climate change has become a major focus of ecology and conservation biology. Modelling approaches provide important tools for making future projections, but current models of the climate-biosphere interface remain overly simplistic, undermining the credibility of projections. We identify five ways in which substantial advances could be made in the next few years: (i) improving the accessibility and efficiency of biodiversity monitoring data, (ii) quantifying the main determinants of the sensitivity of species to climate change, (iii) incorporating community dynamics into projections of biodiversity responses, (iv) accounting for the influence of evolutionary processes on the response of species to climate change, and (v) improving the biophysical rule sets that define functional groupings of species in global models.

Incorporating uncertainty in predictive species distribution modelling.

Motivated by the need to solve ecological problems (climate change, habitat fragmentation and biological invasions), there has been increasing interest in species distribution models (SDMs). Predictions from these models inform conservation policy, invasive species management and disease-control measures. However, predictions are subject to uncertainty, the degree and source of which is often unrecognized. Here, we review the SDM literature in the context of uncertainty, focusing on three main classes of SDM: niche-based models, demographic models and process-based models. We identify sources of uncertainty for each class and discuss how uncertainty can be minimized or included in the modelling process to give realistic measures of confidence around predictions. Because this has typically not been performed, we conclude that uncertainty in SDMs has often been underestimated and a false precision assigned to predictions of geographical distribution. We identify areas where development of new statistical tools will improve predictions from distribution models, notably the development of hierarchical models that link different types of distribution model and their attendant uncertainties across spatial scales. Finally, we discuss the need to develop more defensible methods for assessing predictive performance, quantifying model goodness-of-fit and for assessing the significance of model covariates.

Palatability mapping: a koala's eye view of spatial variation in habitat quality

Ecologists trying to understand the value of habitat to animals must first describe the value of resources contained in the habitat to animals and, second, they must describe spatial variation in resource quality at a resolution relevant to individual animal foraging. We addressed these issues in a study of koalas (Phascolarctos cinereus) in a Eucalyptus woodland. We measured beneficial and deterrent chemical characteristics as well as the palatability of trees using a near-infrared spectroscopic model based on direct feeding experiments. Tree use by koalas was influenced by tree size and foliar quality but was also context-dependent: trees were more likely to be visited if they were surrounded by small, unpalatable trees or by large, palatable trees. Spatial autocorrelation analysis and several mapping approaches demonstrated that foliar quality is spatially structured in the woodland at a scale relevant to foraging decisions by koalas and that the spatial structure is an important component of habitat quality.

Protected area networks and savannah bird biodiversity in the face of climate change and land degradation.

The extent to which climate change might diminish the efficacy of protected areas is one of the most pressing conservation questions. Many projections suggest that climate-driven species distribution shifts will leave protected areas impoverished and species inadequately protected while other evidence suggests that intact ecosystems within protected areas will be resilient to change. Here, we tackle this problem empirically. We show how recent changes in distribution of 139 Tanzanian savannah bird species are linked to climate change, protected area status and land degradation. We provide the first evidence of climate-driven range shifts for an African bird community. Our results suggest that the continued maintenance of existing protected areas is an appropriate conservation response to the challenge of climate and environmental change.

Revealing ecological networks using Bayesian network inference algorithms

Understanding functional relationships within ecological networks can help reveal keys to ecosystem stability or fragility. Revealing these relationships is complicated by the difficulties of isolating variables or performing experimental manipulations within a natural ecosystem, and thus inferences are often made by matching models to observational data. Such models, however, require assumptions-or detailed measurements-of parameters such as birth and death rate, encounter frequency, territorial exclusion, and predation success. Here, we evaluate the use of a Bayesian network inference algorithm, which can reveal ecological networks based upon species and habitat abundance alone. We test the algorithms performance and applicability on observational data of avian communities and habitat in the Peak District National Park, United Kingdom. The resulting networks correctly reveal known relationships among habitat types and known interspecific relationships. In addition, the networks produced novel insights into ecosystem structure and identified key species with high connectivity. Thus, Bayesian networks show potential for becoming a valuable tool in ecosystem analysis.

Lytic activity by temperate phages of Pseudomonas aeruginosa in long-term cystic fibrosis chronic lung infections

Pseudomonas aeruginosa is the most common bacterial pathogen infecting the lungs of cystic fibrosis (CF) patients. The transmissible Liverpool epidemic strain (LES) harbours multiple inducible prophages (LESϕ2; LESϕ3; LESϕ4; LESϕ5; and LESϕ6), some of which are known to confer a competitive advantage in an in vivo rat model of chronic lung infection. We used quantitative PCR (Q-PCR) to measure the density and dynamics of all five LES phages in the sputa of 10 LES-infected CF patients over a period of 2 years. In all patients, the densities of free-LES phages were positively correlated with the densities of P. aeruginosa, and total free-phage densities consistently exceeded bacterial host densities 10–100-fold. Further, we observed a negative correlation between the phage-to-bacterium ratio and bacterial density, suggesting a role for lysis by temperate phages in regulation of the bacterial population densities. In 9/10 patients, LESϕ2 and LESϕ4 were the most abundant free phages, which reflects the differential in vitro induction properties of the phages. These data indicate that temperate phages of P. aeruginosa retain lytic activity after prolonged periods of chronic infection in the CF lung, and suggest that temperate phage lysis may contribute to regulation of P. aeruginosa density in vivo.

Spatiotemporal trends of illegal activities from ranger-collected data in a Ugandan national park

Within protected areas, biodiversity loss is often a consequence of illegal resource use. Understanding the patterns and extent of illegal activities is therefore essential for effective law enforcement and prevention of biodiversity declines. We used extensive data, commonly collected by ranger patrols in many protected areas, and Bayesian hierarchical models to identify drivers, trends, and distribution of multiple illegal activities within the Queen Elizabeth Conservation Area (QECA), Uganda. Encroachment (e.g., by pastoralists with cattle) and poaching of noncommercial animals (e.g., snaring bushmeat) were the most prevalent illegal activities within the QECA. Illegal activities occurred in different areas of the QECA. Poaching of noncommercial animals was most widely distributed within the national park. Overall, ecological covariates, although significant, were not useful predictors for occurrence of illegal activities. Instead, the location of illegal activities in previous years was more important. There were significant increases in encroachment and noncommercial plant harvesting (nontimber products) during the study period (1999-2012). We also found significant spatiotemporal variation in the occurrence of all activities. Our results show the need to explicitly model ranger patrol effort to reduce biases from existing uncorrected or capture per unit effort analyses. Prioritization of ranger patrol strategies is needed to target illegal activities; these strategies are determined by protected area managers, and therefore changes at a site-level can be implemented quickly. These strategies should also be informed by the location of past occurrences of illegal activity: the most useful predictor of future events. However, because spatial and temporal changes in illegal activities occurred, regular patrols throughout the protected area, even in areas of low occurrence, are also required.

Inferring species interaction networks from species abundance data: A comparative evaluation of various statistical and machine learning methods

Abstract The complexity of ecosystems is staggering, with hundreds or thousands of species interacting in a number of ways from competition and predation to facilitation and mutualism. Understanding the networks that form the systems is of growing importance, e.g. to understand how species will respond to climate change, or to predict potential knock-on effects of a biological control agent. In recent years, a variety of summary statistics for characterising the global and local properties of such networks have been derived, which provide a measure for gauging the accuracy of a mathematical model for network formation processes. However, the critical underlying assumption is that the true network is known. This is not a straightforward task to accomplish, and typically requires minute observations and detailed field work. More importantly, knowledge about species interactions is restricted to specific kinds of interactions. For instance, while the interactions between pollinators and their host plants are amenable to direct observation, other types of species interactions, like those mentioned above, are not, and might not even be clearly defined from the outset. To discover information about complex ecological systems efficiently, new tools for inferring the structure of networks from field data are needed. In the present study, we investigate the viability of various statistical and machine learning methods recently applied in molecular systems biology: graphical Gaussian models, L1-regularised regression with least absolute shrinkage and selection operator (LASSO), sparse Bayesian regression and Bayesian networks. We have assessed the performance of these methods on data simulated from food webs of known structure, where we combined a niche model with a stochastic population model in a 2-dimensional lattice. We assessed the network reconstruction accuracy in terms of the area under the receiver operating characteristic (ROC) curve, which was typically in the range between 0.75 and 0.9, corresponding to the recovery of about 60% of the true species interactions at a false prediction rate of 5%. We also applied the models to presence/absence data for 39 European warblers, and found that the inferred species interactions showed a weak yet significant correlation with phylogenetic similarity scores, which tended to weakly increase when including bio-climate covariates and allowing for spatial autocorrelation. Our findings demonstrate that relevant patterns in ecological networks can be identified from large-scale spatial data sets with machine learning methods, and that these methods have the potential to contribute novel important tools for gaining deeper insight into the structure and stability of ecosystems.