The art of modelling range-shifting species Jane Elith1*, Michael Kearney2 and Steven Phillips3 1School of Botany, The University of Melbourne, Parkville 3010, Australia 2Department of Zoology, The University of Melbourne, Parkville 3010, Australia and 3AT&T Labs ��� Research, 180 Park Avenue, Florham Park, NJ 07932, USA Summary 1. Species are shifting their ranges at an unprecedented rate through human transportation and environmental change. Correlative species distribution models (SDMs) are frequently applied for predicting potential future distributions of range-shifting species, despite these models��� assumptions that species are at equilibrium with the environments used to train (fit) the models, and that the training data are representative of conditions to which the models are predicted. Here we explore modelling approaches that aim to minimize extrapolation errors and assess predictions against prior biological knowledge. Our aim was to promote methods appropriate to range-shifting species. 2. We use an invasive species, the cane toad in Australia, as an example, predicting potential distri- butions under both current and climate change scenarios. We use four SDM methods, and trial weighting schemes and choice of background samples appropriate for species in a state of spread. We also test two methods for including information from a mechanistic model. Throughout, we explore graphical techniques for understanding model behaviour and reliability, including the extent of extrapolation. 3. Predictions varied with modelling method and data treatment, particularly with regard to the use and treatment of absence data. Models that performed similarly under current climatic condi- tions deviated widely when transferred to a novel climatic scenario. 4. The results highlight problems with using SDMs for extrapolation, and demonstrate the need for methods and tools to understand models and predictions. We have made progress in this direc- tion and have implemented exploratory techniques as new options in the free modelling software, MaxEnt. Our results also show that deliberately controlling the fit of models and integrating infor- mation from mechanistic models can enhance the reliability of correlative predictions of species in non-equilibrium and novel settings. 5. Implications. The biodiversity of many regions in the world is experiencing novel threats created by species invasions and climate change. Predictions of future species distributions are required for management, but there are acknowledged problems with many current methods, and relatively few advances in techniques for understanding or overcoming these. The methods presented in this manuscript and made accessible in MaxEnt provide a forward step. Key-words: cane toad, changing correlations, climate change, extrapolation, invasive species, niche models, novel environments, species distribution models Introduction An increasing number of taxa are undergoing significant range shifts in response to human-assisted dispersal and changes in environmental factors, notably climate (Parmesan 2006). Often these range shifts are into novel environmental space, from both biotic and abiotic perspectives. Correlative occur- rence-based approaches are most commonly applied to the problem of species distribution modelling (Thuiller et al. 2008 Elith & Leathwick 2009), but range-shifting species create two main problems for them: (1) the species records no longer reflect stable relationships with environment, and (2) environ- mental combinations in future scenarios will not have been adequately sampled (Menke et al. 2009). Thus while range- shifting taxa are often the species for which predictions of potential distributions are needed most, they most seriously violate the equilibrium assumption and often require some *Correspondence author. E-mail: j.elith@unimelb.edu.au Correspondence site: http://www.respond2articles.com/MEE/ Methods in Ecology & Evolution 2010, 1, 330���342 doi: 10.1111/j.2041-210X.2010.00036.x �� 2010 The Authors. Journal compilation �� 2010 British Ecological Society

degree of model extrapolation. Clearly, such species represent serious challenges to the field of species distribution modelling (Araujo & Pearson 2005 Thuiller et al. 2005b Dormann 2007 De Marco, Diniz-Filho & Bini 2008). This begs the question, should correlative models be used at all for range-shifting species? Alternative approaches based explicitly on known mechanisms (Kearney & Porter 2009) are likely to be robust under new environmental combinations in new locations but are limited by the availability of data for model parameterization and because their success in predicting range limits relies on the identification of key limiting pro- cesses. By contrast, data required to fit correlative models are widely available at different scales and the models can implic- itly capture many complex ecological responses. Because of this, we anticipate ongoing use of correlative models for range- shifting species. There is no doubt that in using species distribution models (SDMs) for extrapolation we are using them in risky ways so, our approach is to determine the safest way to proceed. Others have considered the same general problem (e.g. Heikkinen et al. 2006 Hijmans & Graham 2006 Pearson et al. 2006 Ficetola, Thuiller & Miaud 2007 Buisson et al. 2009). One popular technique is to generate an ensemble of predictions basedonthestandardapplicationofseveraldifferentmodelling methods (Thuiller 2004 Araujo & New 2007 Marmion et al. 2008 Roura-Pascual et al. 2009), so that the final prediction emphasizes agreement of predictions, and model-based uncer- tainty can be quantified. However, these are not problem free. Unless the candidate set of models are carefully constructed and evaluated, some lack of congruence may be more due to model error (i.e. specification of an unrealistic model) than uncertainty about the correct model. Alternatively, all models can be wrong in the same way, for example, because the species is not in equilibrium so, agreement of models does not guaran- tee correctness. Moreover, there may be a priori knowledge of thebiologyoftheorganismorthenatureofthedatathatrender a particular modelling strategy preferable to others. In this study we instead explore a strategy of interrogating models to assesstheirbehaviourunderdifferentdatatreatmentsandjudg- ingperformancebasedonbiologicallegitimacy. We develop the approach using the case of an invasive spe- cies, the cane toad (Bufo marinus) which is spreading rapidly across Australia since its introduction in 1935 (Phillips, Chip- perfield & Kearney 2008). The cane toad in Australia provides an informative case for exploring these issues, in part because it has previously been modelled in several different ways with qualitatively different outcomes. These include a bioclimatic envelope approach (van Beurden 1981) and a logistic regres- sion model (Urban et al. 2007) based on the current range, a hybrid ecophysiological ��� correlative method Climex (Sutherst, Floyd & Maywald 1995) based on the native range and Aus- tralian occurrences, and a mechanistic model (Kearney et al. 2008) based on physiological tolerances. The potential distri- butions under current climates predicted by these models broadly coincide across eastern and northern Australia but dif- fer in their predictions for southern areas. These differences are problematic for monitoring and management and raise the question: what differences in the model or data drive the differ- ences in prediction? How do such models behave for prediction to changed climates? In exploring these issues with the cane toad, we develop tools and techniques that are generally rele- vant to modelling range-shifting species with correlative approaches. We propose that model uncertainty can be reduced substantially by using ecological and physiological knowledge coupled with model exploration tools to guide model development and evaluation. Materials and methods SPECIES DATA We are interested in the general problem of modelling species not at equilibrium so, we focus on the invaded range, where the cane toad has not yet reached all suitable environments. The species data were identical to those used in Urban et al. (2007) except they included 270 additional records of occurrence collected in 2006 (Fig. 1a and b), and we reduced locally dense sampling by thinning the records to one per 5-km-by-5-km grid cell. In total there were 1183 presence records and 451 absence records. PREDICTOR VARIABLES Eight predictor variables were chosen that had some postulated con- nection to the ecological requirements of the cane toad, and for which pairwise Pearson correlations between variables was less than 0��85 (Booth, Niccolucci & Schuster 1994 Elith et al. 2006): annual mean temperature (clim1), temperature isothermality (clim3), temperature seasonality (clim4), maximum temperature of the warmest month (clim5), mean temperature of the wettest quarter (clim8), annual pre- cipitation (clim12), precipitation of the warmest quarter (clim18) and mean humidity of the warmest quarter (humidity). These were derived at 0��05�� ( 5 km) resolution from the Anuclim (ANU 2009) software package, with the humidity layer being based on dry- and wet-bulb temperatures (Kearney et al. 2008) with a linear 4-week interpolation. We used the moderate climate change scenario pre- sented in Kearney et al. (2008) (SRES marker scenario B1mid, CSIRO mk2), obtained from the software package Ozclim (http:// www.csiro.au/ozclim, last accessed January 2010). A more extreme scenario was obtained by linearly extrapolating the predicted changes for each variable at each grid cell by inflating the change threefold, leading to increases in annual mean temperate above current of 2��8��� 5��4 ��C, and a scenario we will call 20xx. MODELLING METHODS We chose four modelling methods from those currently used for pre- dicting distributions of species (Table 1). Each has a regression-like structure ��� i.e. additive terms within a linear predictor, and most are capable of fitting complex surfaces. With the settings we used (Table 1) boosted regression tree (BRT) and MaxEnt may fit complex models with other settings GAMs are also potentially complex. Spe- cies at equilibrium tend to be well modelled by complex surfaces (Elith et al. 2006), but it is possible that simpler models are more appropriate for range-shifting species. To test this, we fitted the BRT and MaxEnt models with settings found reliable for fitting current distributions (Elith, Leathwick & Hastie 2008 Phillips & Dudik 2008 note use of only hinge features for MaxEnt), and also fitted smoother models (Hastie, Tibshirani & Friedman 2009) by increasing the The art of modelling range-shifting species 331 �� 2010 The Authors. Journal compilation �� 2010 British Ecological Society, Methods in Ecology & Evolution, 1, 330���342