Summary1. 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 distributions 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 conditions 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 direction 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 information 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.

Species distribution models (SDMs) use spatial environmental data to make inferences on speciesÕ range limits and habitat suitability. Conceptually, these models aim to determine and map components of a speciesÕ ecological niche through space and time, and they have become important tools in pure and applied ecology and evolutionary biology. Most approaches are correlative in that they statistically link spatial data to species distribution records. An alternative strategy is to explicitly incorporate the mechanistic links between the functional traits of organisms and their environments into SDMs. Here, we review how the principles of biophysical ecology can be used to link spatial data to the physiological responses and constraints of organisms. This provides a mechanistic view of the fundamental niche which can then be mapped to the landscape to infer range constraints. We show how physiologically based SDMs can be developed for different organisms in different environmental contexts. Mechanistic SDMs have different strengths and weaknesses to correlative approaches, and there are many exciting and unexplored prospects for integrating the two approaches. As physiological knowledge becomes better integrated into SDMs, we will make more robust predictions of range shifts in novel or non-equilibrium contexts such as invasions, translocations, climate change and evolutionary shifts.

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.

A recently developed integrative framework proposes that the vulnerability of a species to environmental change depends on the species' exposure and sensitivity to environmental change, its resilience to perturbations and its potential to adapt to change. These vulnerability criteria require behavioural, physiological and genetic data. With this information in hand, biologists can predict organisms most at risk from environmental change. Biologists and managers can then target organisms and habitats most at risk. Unfortunately, the required data (e.g. optimal physiological temperatures) are rarely available. Here, we evaluate the reliability of potential proxies (e.g. critical temperatures) that are often available for some groups. Several proxies for ectotherms are promising, but analogous ones for endotherms are lacking. We also develop a simple graphical model of how behavioural thermoregulation, acclimation and adaptation may interact to influence vulnerability over time. After considering this model together with the proxies available for physiological sensitivity to climate change, we conclude that ectotherms sharing vulnerability traits seem concentrated in lowland tropical forests. Their vulnerability may be exacerbated by negative biotic interactions. Whether tropical forest (or other) species can adapt to warming environments is unclear, as genetic and selective data are scant. Nevertheless, the prospects for tropical forest ectotherms appear grim.

Physiological thermal-tolerance limits of terrestrial ectotherms often exceed local air temperatures, implying a high degree of thermal safety (an excess of warm or cold thermal tolerance). However, air temperatures can be very different from the equilibrium body temperature of an individual ectotherm. Here, we compile thermal-tolerance limits of ectotherms across a wide range of latitudes and elevations and compare these thermal limits both to air and to operative body temperatures (theoretically equilibrated body temperatures) of small ectothermic animals during the warmest and coldest times of the year. We show that extreme operative body temperatures in exposed habitats match or exceed the physiological thermal limits of most ectotherms. Therefore, contrary to previous findings using air temperatures, most ectotherms do not have a physiological thermal-safety margin. They must therefore rely on behavior to avoid overheating during the warmest times, especially in the lowland tropics. Likewise, species living at temperate latitudes and in alpine habitats must retreat to avoid lethal cold exposure. Behavioral plasticity of habitat use and the energetic consequences of thermal retreats are therefore critical aspects of species' vulnerability to climate warming and extreme events. macrophysiology | operative temperature | climate sensitivity