Plant invasions that arise from human introductions of new species to a region, or from range expansion of some native plant species, can profoundly affect biodiversity and alter the structure and function of ecosystems. Although preventive strategies may be an effective way to limit plant invasions, they are difficult to achieve because adequate descriptions of biological and environmental characteristics are often lacking, and truly predictive models of invasive biology have been elusive. On the basis of a history of repeated plant introductions and the absence of a general predictive theory, it may be best to assume that plant invasions will continue. This paper explores ways to empirically study and to predict plant invasions through a study of the invasion process. Several approaches are explored, such as species demography, DNA analysis, and geographic information system reconstructions, to characterize source and satellite populations and factors that influence the spread of these populations.

The Moran model in population genetics may also be regarded as an invasion process (or voter model) on the complete n-graph. Tracing lines of ancestry is equivalent to studying the dual process. Using this technique certain results concerning lines of ancestry can be derived very rapidly.