Jane Elith

A working guide to boosted regression trees

1. Ecologists use statistical models for both explanation and prediction, and need techniques that are flexible enough to express typical features of their data, such as nonlinearities and interactions. 2. This study provides a working guide to boosted regression trees (BRT), an ensemble method for fitting statistical models that differs fundamentally from conventional techniques that aim to fit a single parsimonious model. Boosted regression trees combine the strengths of two algorithms: regression trees (models that relate a response to their predictors by recursive binary splits) and boosting (an adaptive method for combining many simple models to give improved predictive performance). The final BRT model can be understood as an additive regression model in which individual terms are simple trees, fitted in a forward, stagewise fashion. 3. Boosted regression trees incorporate important advantages of tree-based methods, handling different types of predictor variables and accommodating missing data. They have no need for prior data transformation or elimination of outliers, can fit complex nonlinear relationships, and automatically handle interaction effects between predictors. Fitting multiple trees in BRT overcomes the biggest drawback of single tree models: their relatively poor predictive performance. Although BRT models are complex, they can be summarized in ways that give powerful ecological insight, and their predictive performance is superior to most traditional modelling methods. 4. The unique features of BRT raise a number of practical issues in model fitting. We demonstrate the practicalities and advantages of using BRT through a distributional analysis of the short-finned eel (Anguilla australis Richardson), a native freshwater fish of New Zealand. We use a data set of over 13 000 sites to illustrate effects of several settings, and then fit and interpret a model using a subset of the data. We provide code and a tutorial to enable the wider use of BRT by ecologists.

Sample selection bias and presence‐only distribution models: implications for background and pseudo‐absence data

Most methods for modeling species distributions from occurrence records require additional data representing the range of environmental conditions in the modeled region. These data, called background or pseudo-absence data, are usually drawn at random from the entire region, whereas occurrence collection is often spatially biased toward easily accessed areas. Since the spatial bias generally results in environmental bias, the difference between occurrence collection and background sampling may lead to inaccurate models. To correct the estimation, we propose choosing background data with the same bias as occurrence data. We investigate theoretical and practical implications of this approach. Accurate information about spatial bias is usually lacking, so explicit biased sampling of background sites may not be possible. However, it is likely that an entire target group of species observed by similar methods will share similar bias. We therefore explore the use of all occurrences within a target group as biased background data. We compare model performance using target-group background and randomly sampled background on a comprehensive collection of data for 226 species from diverse regions of the world. We find that target-group background improves average performance for all the modeling methods we consider, with the choice of background data having as large an effect on predictive performance as the choice of modeling method. The performance improvement due to target-group background is greatest when there is strong bias in the target-group presence records. Our approach applies to regression-based modeling methods that have been adapted for use with occurrence data, such as generalized linear or additive models and boosted regression trees, and to Maxent, a probability density estimation method. We argue that increased awareness of the implications of spatial bias in surveys, and possible modeling remedies, will substantially improve predictions of species distributions.

Predicting species distributions for conservation decisions.

Species distribution models (SDMs) are increasingly proposed to support conservation decision making. However, evidence of SDMs supporting solutions for on-ground conservation problems is still scarce in the scientific literature. Here, we show that successful examples exist but are still largely hidden in the grey literature, and thus less accessible for analysis and learning. Furthermore, the decision framework within which SDMs are used is rarely made explicit. Using case studies from biological invasions, identification of critical habitats, reserve selection and translocation of endangered species, we propose that SDMs may be tailored to suit a range of decision-making contexts when used within a structured and transparent decision-making process. To construct appropriate SDMs to more effectively guide conservation actions, modellers need to better understand the decision process, and decision makers need to provide feedback to modellers regarding the actual use of SDMs to support conservation decisions. This could be facilitated by individuals or institutions playing the role of ‘translators’ between modellers and decision makers. We encourage species distribution modellers to get involved in real decision-making processes that will benefit from their technical input; this strategy has the potential to better bridge theory and practice, and contribute to improve both scientific knowledge and conservation outcomes.

Mapping epistemic uncertainties and vague concepts in predictions of species distribution

Most habitat maps are presented as if they were a certain fact, with no indication of uncertainties. In many cases, researchers faced with the task of constructing such maps are aware of problems with the modelling data and of decisions that they make within the modelling process that are likely to affect the output, but they find it difficult to quantify this information. In some cases they attempt to evaluate the modelled predictions against independent data, but the summary statistics have no spatial component and do not address errors in the predictions. It is proposed that maps of uncertainty would help in the interpretation of these summaries, and to emphasize patterns in uncertainty such as spatial clustering or links with particular covariates. This paper reviews the aspects of uncertainty that are relevant to habitat maps developed with logistic regression, and suggests methods for investigating and communicating these uncertainties. It addresses the problems of subjective judgement, model uncertainty and vague concepts along with the more commonly considered uncertainties of random and systematic error. Methods for developing realistic confidence intervals are presented along with suggestions on how to visualize the information for use by decision-makers.

MANAGING LANDSCAPES FOR CONSERVATION UNDER UNCERTAINTY

In ecology, populations may be linked conceptually with landscapes through habitat and spatial population models. Usually, these models deal with single species and treat a range of uncertainties implicitly and explicitly. They assist managers in testing different management scenarios and making strategic decisions. Landscape pattern analysis was the first attempt to deal with multiple species, and it led to a range of landscape management strategies. Advances in landscape ecology, driven largely by the pragmatic needs of conservation, are building approaches to multispecies management that have stronger ecological foundations. However, their treatment of uncertainty is in its infancy. In this paper, we provide examples to illustrate some of these issues. We conclude that one of the most important sources of uncertainty is the choice of the modeling frame. We recommend that landscape planners use different kinds of models, identify important sources of uncertainty that may affect planning decisions, and seek options that are likely to result in tolerable outcomes, despite uncertainty.

Presence‐Only Data and the EM Algorithm

SUMMARY In ecological modeling of the habitat of a species, it can be prohibitively expensive to determine species absence. Presence-only data consist of a sample of locations with observed presences and a separate group of locations sampled from the full landscape, with unknown presences. We propose an expectation-maximization algorithm to estimate the underlying presence-absence logistic model for presence-only data. This algorithm can be used with any off-the-shelf logistic model. For models with stepwise fitting procedures, such as boosted trees, the fitting process can be accelerated by interleaving expectation steps within the procedure. Preliminary analyses based on sampling from presence-absence records of fish in New Zealand rivers illustrate that this new procedure can reduce both deviance and the shrinkage of marginal effect estimates that occur in the naive model often used in practice. Finally, it is shown that the population prevalence of a species is only identifiable when there is some unrealistic constraint on the structure of the logistic model. In practice, it is strongly recommended that an estimate of population prevalence be provided.

Eliciting and integrating expert knowledge for wildlife habitat modelling

Expert knowledge regarding the distribution of sambar deer (Cervis unicolor) in Lake Eildon National Park (LENP), Victoria was used to build a wildlife habitat model to assist with park management. The paper presents two methods for eliciting expert knowledge. These were a quantitative geographical information system (GIS)-based approach using a customised graphical user interface, and a qualitative approach that uses semi-structured interviews. The GIS approach is valuable as it is objective, repeatable and provides a spatial context for knowledge elicitation. Experts were asked to provide estimates of sambar sightings and predicted densities with the assistance of contextual environmental data including terrain, roads, hydrology and rainfall surfaces. The quantitative knowledge elicitation process did not identify any sambar environmental niches in the Park, and the experts disagreed about the location of likely habitat. On the other hand, the qualitative assessment showed very strong expert agreement and a combination of this information and published literature was used to build a habitat map. The results of the analysis indicate that sambar deer occur throughout the entire Park. It is envisaged that the results can be used as baseline information for population modelling and natural resource management in the Park. Elicitation of knowledge is complicated by a number of factors including computer proficiency and study site familiarity. The relatively large cohort used in this study and the inherent inconsistencies that were encountered indicate that wildlife managers should interpret results carefully from habitat models that use only a relatively small cohort of experts.

Determinants of reproductive success in dominant pairs of clownfish: a boosted regression tree analysis

1. Central questions of behavioural and evolutionary ecology are what factors influence the reproductive success of dominant breeders and subordinate nonbreeders within animal societies? A complete understanding of any society requires that these questions be answered for all individuals. 2. The clown anemonefish, Amphiprion percula, forms simple societies that live in close association with sea anemones, Heteractis magnifica. Here, we use data from a well-studied population of A. percula to determine the major predictors of reproductive success of dominant pairs in this species. 3. We analyse the effect of multiple predictors on four components of reproductive success, using a relatively new technique from the field of statistical learning: boosted regression trees (BRTs). BRTs have the potential to model complex relationships in ways that give powerful insight. 4. We show that the reproductive success of dominant pairs is unrelated to the presence, number or phenotype of nonbreeders. This is consistent with the observation that nonbreeders do not help or hinder breeders in any way, confirming and extending the results of a previous study. 5. Primarily, reproductive success is negatively related to male growth and positively related to breeding experience. It is likely that these effects are interrelated because males that grow a lot have little breeding experience. These effects are indicative of a trade-off between male growth and parental investment. 6. Secondarily, reproductive success is positively related to female growth and size. In this population, female size is positively related to group size and anemone size, also. These positive correlations among traits likely are caused by variation in site quality and are suggestive of a silver-spoon effect. 7. Noteworthily, whereas reproductive success is positively related to female size, it is unrelated to male size. This observation provides support for the size advantage hypothesis for sex change: both individuals maximize their reproductive success when the larger individual adopts the female tactic. 8. This study provides the most complete picture to date of the factors that predict the reproductive success of dominant pairs of clown anemonefish and illustrates the utility of BRTs for analysis of complex behavioural and evolutionary ecology data.

Point process models for presence-only analysis

Summary Presence-only data are widely used for species distribution modelling, and point process regression models are a flexible tool that has considerable potential for this problem, when data arise as point events. In this paper, we review point process models, some of their advantages and some common methods of fitting them to presence-only data. Advantages include (and are not limited to) clarification of what the response variable is that is modelled; a framework for choosing the number and location of quadrature points (commonly referred to as pseudo-absences or ‘background points’) objectively; clarity of model assumptions and tools for checking them; models to handle spatial dependence between points when it is present; and ways forward regarding difficult issues such as accounting for sampling bias. Point process models are related to some common approaches to presence-only species distribution modelling, which means that a variety of different software tools can be used to fit these models, including maxent or generalised linear modelling software.

Detecting extinction risk from climate change by IUCN red list criteria

Anthropogenic climate change is a key threat to global biodiversity. To inform strategic actions aimed at conserving biodiversity as climate changes, conservation planners need early warning of the risks faced by different species. The IUCN Red List criteria for threatened species are widely acknowledged as useful risk assessment tools for informing conservation under constraints imposed by limited data. However, doubts have been expressed about the ability of the criteria to detect risks imposed by potentially slow-acting threats such as climate change, particularly because criteria addressing rates of population decline are assessed over time scales as short as 10 years. We used spatially explicit stochastic population models and dynamic species distribution models projected to future climates to determine how long before extinction a species would become eligible for listing as threatened based on the IUCN Red List criteria. We focused on a short-lived frog species (Assa darlingtoni) chosen specifically to represent potential weaknesses in the criteria to allow detailed consideration of the analytical issues and to develop an approach for wider application. The criteria were more sensitive to climate change than previously anticipated; lead times between initial listing in a threatened category and predicted extinction varied from 40 to 80 years, depending on data availability. We attributed this sensitivity primarily to the ensemble properties of the criteria that assess contrasting symptoms of extinction risk. Nevertheless, we recommend the robustness of the criteria warrants further investigation across species with contrasting life histories and patterns of decline. The adequacy of these lead times for early warning depends on practicalities of environmental policy and management, bureaucratic or political inertia, and the anticipated species response times to management actions.