Table 1.

Summary of nine key approaches to predicting distribution and abundance under environmental change. Some of these approaches have been applied to empirical data, but others have only been suggested. Columns categorise the different methods with respect to prediction goals, required data inputs, and complexities taken into account and provide a reference to an example of each method. Table entries are discussed in more detail in Appendix S1 in the online supporting information

	Prediction goals		Required data inputs						Complexities taken into account
Approach	Distribution	Abundance	Known occurrences	Values of abiotic and biotic drivers	Vital rates at low density	Effect of intraspecific density on vital rates	Initial abundances at all sites	Dispersal	Living dead populations	Source/sink dynamics	Effects of dispersal on local abundance	Effects of dispersal on distribution	Population cycles	Examples
Classical SDMs	Yes	No	Yes	Yes	No	No	No	No	No	No	No	No	No	Elith & Leathwick (2009)
Abundance-based SDMs (including Poisson process models)	Yes	Yes	Yes	Yes	No	No	No	No	No	No	No	No	No	Fithian & Hastie (2013)
Hybrid SDMs	Yes	Yes	Yes	Yes	Yes	Yes/No	No	Yes/No	Unclear	Unclear	Yes	Yes/No	Yes/No	Dullinger et al. (2012)
Phenology models	Yes	No	No	Yes	No	No	No	No	No	No	No	No	No	Chuine & Beaubien (2001)
Population-based ‘mechanistic’ models	Yes	Yes/No	No	Yes	Yes	Yes/No	No	No	Yes	No	No	No	No	Buckley (2008)
Dynamic range models	Yes	Yes	Yes	Yes	No	No	Yes	No	Unclear	Yes	Yes	Yes	Yes	Schurr et al. (2012)
Demographic range models	Yes	No	No	Yes	Yes	No	No	No	Yes	No	No	No	No	Diez et al. (2014)
Demographic equilibrium abundance models	Yes	Yes	No	Yes	Yes	Yes	No	No	Yes	No	No	No	No	None (suggested in this paper)
Full approach	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	Yes	None

SDM, species distribution models.