Human-assisted dispersal has allowed species to cross biogeographical barriers, introducing them to new environments where they interact with novel species assemblages. These non-native species can have negative impacts on native biodiversity (Williamson 1996), and can cause economic damage by becoming pests (Pimentel, Zuniga & Morrison 2005) or disrupting ecosystem services (Cook et al. 2007). To evaluate the potential impacts of these species, and devise management strategies to control them, it is useful to be able to predict their potential distribution and understand the environmental factors that limit this distribution. Species distribution models (SDMs) have often been employed to do this (Real et al. 2008; Strubbe & Matthysen 2009). Where presence–absence data are available, records of non-native species can be mapped onto a grid, and models use environmental covariates to discriminate between grid cells that are occupied and unoccupied. SDMs assume that the species being modelled is at equilibrium with the environment (Guisan & Thuiller 2005), so unoccupied grid cells are unsuitable for the species. This assumption is likely to be violated by spreading non-native species, which have yet to reach all environmentally suitable areas (Václavík & Meentemeyer 2012), and also by range-shifting species responding to environmental change (Elith, Kearney & Phillips 2010), as dispersal limitation may prevent them from keeping pace with the movement of suitable environmental conditions (Menendez et al. 2006; Brooker et al. 2007). Spreading species can therefore be absent from a grid cell due to low environmental suitability or dispersal limitation. The spatial structure of explanatory variables may interact with dispersal limitation to affect model inference (Václavík, Kupfer & Meentemeyer 2012); for example, environmental variables that do not causally influence the distribution of a species may be erroneously identified as limiting the distribution if they occur on a gradient aligned to species’ axis of dispersal.
The need to account for dispersal limitation when modelling the distribution of non-native and range-shifting species has been recognised (Peterson 2003; Guisan & Thuiller 2005; Gallien et al. 2010). Invasion dynamics have been simulated using dispersal models that incorporate environmental suitability (Smolik et al. 2010; Travis et al. 2011), and dispersal models have been used to produce realistic predictions of species’ distributions under climate change scenarios (Engler & Guisan 2009). Despite this, there are few examples of dispersal models being used to influence the fitting of SDMs. Several studies (e.g. Muñoz & Real 2006; Dullinger et al. 2009) have used covariates such as roads that might be related to the transport and introduction of non-native species as proxies for dispersal, while Václavík & Meentemeyer (2009) used propagule pressure calculated from a dispersal model as a covariate. The most direct approach to dealing with the problem of absences due to dispersal limitation was by Elith, Kearney & Phillips (2010) who estimated the maximum area a non-native species could have spread to, and restricted pseudoabsence background points to that area. Despite these techniques, it is still not the state of practice to incorporate dispersal limitation into models of the distribution of spreading species (e.g. Heidy Kikillus, Hare & Hartley 2010; Gormley et al. 2011).
We present a simple new method that accounts for dispersal limitation in the fitting of a SDM. We first construct a dispersal model, and then use this to weight a SDM of the species–environment relationship (SER). In this way, the importance of absences due to dispersal limitation is reduced, so the model fitting procedure is closer to the desired situation where the model discriminates between presences and absences due to suitable and unsuitable environmental conditions, respectively.
We compare the ability of this method with models that do not account for dispersal limitation at parameterising the SER and predicting the future distribution of a simulated non-native species. We explore how both modelling techniques perform when the spatial structure of explanatory variables is varied. Both techniques are then applied to model the distribution of a non-native bird, the common waxbill Estrilda astrild, in the Iberian Peninsula.