The Mediterranean Basin is a climate change and biological invasion hotspot where recent warming is facilitating the establishment and spread of invasive species, one of which is the highly destructive South American tomato leafminer (Tuta absoluta). This pest recently invaded the Mediterranean Basin where it threatens Solanaceous crops. Holistic approaches are required to project the potential geographic distribution and relative abundance of invasive species and hence are pivotal to developing sound policy for their management. This need is increasing dramatically in the face of a surge in biological invasions and climate change. However, while holistic analyses of invasive species are often advocated, they are rarely implemented.We propose that physiologically-based demographic models (PBDMs) in the context of a geographic information system (GIS) can provide the appropriate level of synthesis required to capture the complex interactions basic to manage invasive species such as T. absoluta. We review the PBDMs for two invasive flies, and use them as a basis for assessing the biological data available for the development of a PBDM for T. absoluta, and in the process identify large data gaps that using the PBDM as a guide can be easily filled. Other components for an ecologically-based management program for this pest (habitat modification, natural and classical biocontrol, pheromones, and others) are also reviewed. The development of a PBDM for T. absoluta would provide the basis for an interdisciplinary agroecological synthesis of the problem and the role different control tactics would play in region-specific control of the pest.