First of all, the results of our modelling effort gives potential distributions for future doubled CO2 equilibrium GCM-scenarios for 80 tree species. Let's assume that CO2 concentrations will double from pre-industrial levels by 2100. By potential distribution we mean that the habitat becomes suitable for a species to colonize around 2100, provided that the GCM predicted climate of the future is accurate and our model (DISTRIB) captures all relevant attributes pertaining to the current distribution of the species.
Please note here that we merely use the results of the GCM-climate scenarios - we have no control on its outputs - also, like with all models, ours (DISTRIB) has several assumptions and limitations.
So, if species x has increased its range in our maps on one of the GCM scenarios, say GISS, it would be accurate to assume that: if climate were to change as defined by the GISS model, then the suitable habitat for colonization for x could expand according to the DISTRIB model by around 2100. We would like to stress here that our model is not predicting migration of species x - but rather the movement of suitable habitat for that species. In order to predict migration, our model has to take into account several additional factors like fragmentation of landscapes, competition with other species, and other possible inhibiting and accelerating factors, which are beyond the scope of DISTRIB.
In addition to the geographic range-shifts, our model predicts the potential change in abundance (importance value) of species. Some species could potentially increase in abundance in some areas and decrease in other areas under future climates. The same caveats outlined above for geographic distributions apply to interpreting changes in abundance.
See our 1998
Ecological Monographs paper (citation)
if you want details. Possible barriers to migration and simulating migration
through time are being explored in a related
study. Also see FAQ for some more answers to questions on this topic.