Dynamic models in research and management of biological invasions.

Invasive species are increasing in number, extent and impact worldwide. Effective invasion management has thus become a core socio-ecological challenge. To tackle this challenge, integrating spatial-temporal dynamics of invasion processes with modelling approaches is a promising approach. The inclusion of dynamic processes in such modelling frameworks (i.e. dynamic or hybrid models, here defined as models that integrate both dynamic and static approaches) adds an explicit temporal dimension to the study and management of invasions, enabling the prediction of invasions and optimisation of multi-scale management and governance. However, the extent to which dynamic approaches have been used for that purpose is under-investigated. Based on a literature review, we examined the extent to which dynamic modelling has been used to address invasions worldwide. We then evaluated how the use of dynamic modelling has evolved through time in the scope of invasive species management. The results suggest that modelling, in particular dynamic modelling, has been increasingly applied to biological invasions, especially to support management decisions at local scales. Also, the combination of dynamic and static modelling approaches (hybrid models with a spatially explicit output) can be especially effective, not only to support management at early invasion stages (from prevention to early detection), but also to improve the monitoring of invasion processes and impact assessment. Further development and testing of such hybrid models may well be regarded as a priority for future research aiming to improve the management of invasions across scales.