Introduction

The rate at which a population can spread across space is likely a key determinant of how well species are able to respond to climate change (Pacifici et al., 2015). Until recently, almost all projections of species’ future distributions have largely ignored the process of population spread (Travis et al., 2013). For more than a decade, the field of climate envelope modelling relied almost exclusively on projections that made one of two extreme assumptions in relation to population spread: no dispersal vs. unlimited dispersal (Bateman et al., 2013), implying either that a species would be unable to colonise any newly suitable regions or that it would be able rapidly to reach all of the newly available suitable climate space. Recognising the potential limitations of this approach, some authors have considered ‘partial dispersal scenarios’ (Bateman et al., 2013) that rely on average dispersal distance and the number of dispersal events in a given time frame (Hannah et al., 2005; Schloss et al., 2012; Visconti et al., 2015) in order to make predictions for how well large numbers of species are likely to be able to track a shifting climate.

However, over the last few years, increasing recognition of the importance of ecological and evolutionary dynamics of range shifts has resulted in calls for the development of a new generation of models for forecasting biodiversity futures (Dormann et al., 2012; Schurr et al., 2012; Travis et al., 2013), and dispersal has been highlighted as a critical process for inclusion (Huntley et al., 2010). This call is being met, and there has already been a proliferation of models for biodiversity forecasting that incorporate increased biological realism [see Lurgi et al. (2015) for a recent review of such models]. These models represent ecological and evolutionary processes in differing degrees of detail. Thus, we already possess a good theoretical understanding of key determinants of spread rate. The main reason for the continued incorporation of reduced ecological realism in models forecasting the dynamics of large numbers of species is likely the lack of sufficient high‐quality ecological data for parameterisation, rather than the lack of appropriate, and sufficiently efficient, modelling approaches. A key challenge will be to use these models for anything more than a relatively small set of species for which we have the required data for parameterisation (e.g. Nathan et al., 2011; Bullock et al., 2012). We need approaches for making the best possible use of the considerable available ecological data that exist across many species, given that they are sparse and patchy in nature. Here, we introduce the concept of using a trait‐space approach for understanding how spread rates will vary across a wide and realistic range of life histories.

Biological traits are not assembled at random in species, but show various degrees of covariation which reflect evolutionary optimal strategies and physical constraints (Bielby et al., 2007). An understanding of how traits are combined may enable one to make inferences about the biological traits of poorly known species, while accounting for the biological variation observed in nature. Trait‐based approaches have become used increasingly in several ecological fields including biodiversity‐provisioned ecosystem services (Suding et al., 2008; Dìaz et al., 2013), assessing species’ intrinsic vulnerability to extinction (Purvis et al., 2000; Cardillo et al., 2006; González‐Suárez & Revilla, 2013) and phylogenetic comparative analyses (FitzJohn et al., 2009; Santini et al., 2015). All these fields have made a different use of traits, but share a focus on biological traits rather than species.

In this study, we develop a novel approach to determine which life‐history traits are the best predictors of spread rate and also illustrate how we can use the method to determine the proportion and types of species within a defined (e.g. taxonomic) group that are likely to have insufficiently high rates of spread to keep pace with climate change. We use the life‐history data available across terrestrial mammal species to fit a multivariate trait‐space model. Terrestrial mammals exhibit very diverse ecologies, and are one taxon for which a good amount of ecological information is available (Jones et al., 2009). Yet, we have the complete data needed to model spread for few terrestrial mammal species. While certain traits (e.g. body mass) are better documented, ecological variables related to dispersal or demographic parameters are lacking or poorly known for most species, and when available are often uncertain. The model that we develop is able to predict missing trait value combinations based on our knowledge of traits’ covariation in mammals. Having a large number of spread rates for virtual species, representing life histories that are realistically constrained, offers opportunities for addressing important fundamental and applied questions. Crucially, adopting this approach removes the need to have complete sets of life‐history data for many species; instead, a statistical description of trait space, including the covariation between different traits, can be derived from the patchy data that are available across many species.

By generating large sets of virtual species (trait value combinations), each with its complete life‐history data, we then use two well‐established demographic modelling approaches – analytical integrodifference equations (IDEs; Neubert & Caswell, 2000) and the individual‐based model (IBM) RangeShifter (Bocedi et al., 2014a) – to project spread rates for a large number of species. We use the two, quite different modelling approaches (Travis et al., 2011) to ascertain the robustness of our trait‐space method. To demonstrate the utility of this novel method, we then: