The spread of invasive organisms and emerging pathogens often unfolds across spatially heterogeneous landscapes where environmental variation, connectivity, and ecological context shape transmission or establishment dynamics. A longstanding approach to modeling this process has relied on “gravity-type’’ formulations, in which the attractiveness of locations and the flux among them are expressed parametrically, often in proportion to site size or distance. While widely used, gravity models lack an explicit mechanistic basis. In particular, it is unclear whether standard parameterizations capture the true ecological drivers of spread or whether covariates added to improve fit adequately reflect causal pathways. As a result, predictions may be difficult to generalize beyond the specific system or data set to which the model was calibrated.
In this talk, I propose an alternative framework for modeling biological invasions and disease spread that explicitly decomposes the invasion process into three distinct sub-mechanisms: (i) production of propagules at occupied sites, (ii) entrainment of those propagules into physical, ecological, or anthropogenic redistribution pathways, and (iii) successful establishment at uninvaded locations. The key advance is that each component process can be parameterized independently, thereby enabling a fully mechanistic or partially mechanistic formulation. This modular structure naturally accommodates environmental covariates—for example, hydrological connectivity influencing transport, local habitat suitability affecting establishment, or economic activity modulating anthropogenic movement—without ad hoc modifications to the model’s core structure.
I further show that, under reasonable assumptions, the resulting process-based formulation yields a likelihood function for observed invasion times, enabling maximum-likelihood estimation of parameters governing propagule production, transport, and establishment. This allows formal statistical inference, hypothesis testing, and model comparison.
To illustrate the framework, I present a reanalysis of classical data on the spread of zebra mussels (Dreissena polymorpha) through North America. By fitting the model to historical records of first detection, we infer system-specific dispersal pressures, quantify how environmental heterogeneity mediates spread, and demonstrate improved interpretability relative to traditional gravity models. More broadly, this approach provides a principled foundation for forecasting the spread of invasive species and infectious diseases, designing surveillance systems, and evaluating intervention strategies in complex, spatially structured environments.