The analyses revealed that, in the initial phases of range expansion, adding spatial variables always provided better fit than using environmental data alone in Maxent (; figure S1, see also animations in the electronic supplementary material). Under the DNE scenario, models have lower κ values than in their corresponding simulations for the CNE scenario (a) up to 30 time steps. However, ranges expanded continuously in the second scenario, whereas in the first there was a tendency to stabilization below the maximum expected by suitability (b). The relationship between gain in κ values after adding spatial predictors (Δκ values) and range size was independent of the scenario, as the interaction between this factor and range size was not significant (F1,26=1.05; p=0.3144). After accounting for the effect of range size (F1,27=58.5; p<0.001), a significant effect of scenario was detected (F1,27=9.14; p<0.01) and the adjusted mean value of Δκ was actually 10 times higher in the CNE (0.06) than in DNE (0.005; see figure S2 in the electronic supplementary material).
Figure 2 (a) Kappa statistics (open squares, CNE-ENV; filled squares, CNE-ENV-SEVM; open circles, DNE-ENV; filled circles, DNE-ENV-SEVM), (b) range size (squares, CNE; circles, DNE) and (c) residual autocorrelation (Moran's I) in the first distance class for (more ...)
Under CNE, using environmental variables alone overestimates the range in the initial phases of the range expansion (). This occurs because in these initial phases the occurrences are sampled within a restricted part of the range, so there is a systematic bias in sampling environmental suitability values. By including spatial predictors, a better fit was obtained because these additional predictors forced range cohesion independently of the spatial distribution of the environmental suitability. Under the CNE scenario, spatial autocorrelation in the residuals was higher than in the DNE scenario, due to the higher levels of range cohesion within a more concentrated part of the potential range defined by suitability (c). On the other hand, the low levels of spatial autocorrelation in residuals under DNE shows that suitability is enough to ensure accurate predictions and, consequently, this explains why spatial models tend to be ineffective to improve fit in this case (a).
It is well known that biotic interactions and stochastic colonization processes also determine species' range (Heikkinen et al. 2006
; Araújo & Luoto 2007
; Soberon 2007
). Spatial eigenvector mapping and other spatial autocorrelation techniques can account for these processes only if they are spatially structured. Our analyses reveal that adding spatial components can be a promising approach to modelling CNE processes, such as, for instance, those occurring under fast climate change allowing species' range expansion towards new suitable areas. However, they are ineffective under DNE, in which departures from bioclimatic envelopes are caused by local processes related to biotic interactions or metapopulation structure within species' ranges. This is coherent with theoretical expectations based on the origins of autocorrelation in biogeographical data (Diniz-Filho et al. 2003
). So, despite the uncertainty associated with particular SDM techniques (Thuiller 2003
; Araújo & New 2007
) and recent criticisms of the limited transferability of Maxent
(Peterson et al. 2007
; but see Phillips 2008
), our main conclusions must hold in general.
Although further studies are necessary to show how these spatial predictors can be coupled with projected environmental changes, spatial eigenvector mapping is particularly suitable for this task as it allows representing spatial relationships at different spatial scales. Also, they can be easily introduced as new predictors in any SDM, with the advantage of not being intrinsically related to observed species' distribution, as it occurs with autologistic terms (Dormann 2007
). This is in line with recent suggestions that it is necessary to expand SDMs to incorporate other more complex dynamic scenarios in a spatially explicit context.