1.The geographic distributions of plant species show marked correlations with the current climate, suggesting that they are likely to shift if climate changes. However, before projecting any such shifts, it is important to establish whether distributions are at equilibrium with the current climate. If they are not, distributional shifts could occur even without climate change, making it difficult to tease apart climate-induced shifts from shifts occurring naturally without climate change.

2.We forecast the geographical distributions of the 10 most common trees occurring in the Iberian Peninsula using a new method that relaxes the species–climate equilibrium assumption implicit in most species distributions models. For each species, we developed a spatially explicit patch occupancy model (SPOM) with climate-dependent extinction rates and with colonization rates that depend on both climate and local seed dispersal. Bayesian methods were used to estimate the colonization, extinction and seed dispersal functions against observed colonization and extinction events recorded in repeat surveys of 46 596 forest plots in the Spanish Forest Inventories (1986–96 and 1997–2007). We then simulated distributional changes between the years 2000–2100.

3.Without climate change, 9 of the 10 species substantially increased in regional frequency. These increases occurred primarily within current ranges, although some species also expanded across their range edges. With climate change, one temperate conifer species and two sub-Mediterranean species would reduce their frequency of occurrence across the studied region, whereas temperate broad-leaved species were unaffected and Mediterranean species were either unaffected or increased their frequency of occurrence.

4.Synthesis. The analysis suggests that these species are substantially out of equilibrium, such that abundances and ranges would increase without climate change. Climate change may increase, decrease, stabilize or shift distributions, in a way that can only be understood by comparing predictions against baseline scenarios that account for these non-equilibrium range dynamics.