Application of Branching Models in the Study of Invasive Species

Abstract

Earthquake occurrences are often described using a class of branching models called epidemic-type aftershock sequence (ETAS) models. The name derives from the fact that the model allows earthquakes to cause aftershocks, and then those aftershocks may induce subsequent aftershocks, and so on. Despite their value in seismology, such models have not previously been used in studying the incidence of invasive plant and animal species. Here, we apply ETAS models to study the spread of an invasive species in Costa Rica (Musa velutina, or red banana). One challenge in this ecological application is that fitting the model requires the originations of the plants, which are not observed but may be estimated using filed data on the heights of the plants on a given date and their empirical growth rates. We then characterize the estimated spatial-temporal rate of spread of red banana plants using a space-time ETAS model.