Humans are redistributing the world’s biodiversity both indirectly by changing habitats and the climate, and directly by transporting species across natural biogeographical boundaries. Predicting how species will respond to such changes is paramount for formulating effective conservation measures aimed at protecting native biodiversity, economy and human health. Indeed, introduced species can become invasive, and be a main threat to biodiversity and also impose large costs to the economy. Unfortunately, our capacity to accurately predict under which environmental conditions that introduced species will become invasive remains limited. This may be at least partly due to the fact that forecasts of invasion risk typically result from relatively simple correlative models, which integrate information on where a species currently occurs with the dominant climate at these occurrence locations. While this approach generally works well when making forecasts within the area where a species is native, correlations between climate and species occurrence tend to break down when attempting predictions to other areas and time-frames – i.e. when trying to forecast invasion risk under changing climates. Robust predictions of invasion risk may be formulated based on more fundamental, physiologically-informed distribution models. Such mechanistic models do not rely on correlations but use species’ functional traits to characterize the range of environmental conditions tolerable by species. Yet, both real and perceived difficulties in obtaining sufficiently detailed information on species’ ecology and life-history have held back research success in this area. Therefore, FREYA had two overarching Objectives, namely (1) to evaluate predictions of range dynamics derived from correlative versus mechanistic niche modelling techniques, using a multi-species approach, and (2) to assess how ecological and evolutionary processes influence forecasts of invasion risk, using a well-known avian invader as model species. The first objective focusses on a large number of non-native invasive birds while for the second objective, the project concentrates on the ring-necked parakeet. Main conclusions are that overall, mechanistic-physiological model predictive accuracy was moderate to low, as our invasion risk forecasts were prone to both omission and commission errors. Sensitivity analyses revealed a set of key functional traits strongly influencing model accuracy. For comparatively larger avian invaders, estimates of basal metabolic rates, body temperate and body mass are crucial while for smaller birds, feather characteristics such as feather length and plumage depth are important as well. The research on ring-necked parakeets showed that introduced populations were of predominantly Asian ancestry, with differentiation of African native populations occurring through historical evolutionary processes. Within Europe, we identified linear correlations between allele frequencies and environmental variables across a climate spectrum, suggesting rapid selection in response to climatic change within introduced ring-necked parakeet populations, further complicating the modelling of invasion risk. Indeed, mechanistic-physiological models based on European parakeet data (as opposed to native range, Asian data) result in generally more accurate predictions of the current European distribution of this prominent invader. Together, results obtained indicate that complex and parameter hungry mechanistic modelling approaches such as the one applied here may be better suited to uncover processes driving species invasions, rather than for obtaining highly accurate spatial predictions of where invaders are likely to establish and spread.