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Application of Branching Models in the Study of Invasive Species

Author

Listed:
  • Earvin Balderama
  • Frederic Paik Schoenberg
  • Erin Murray
  • Philip W. Rundel

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.

Suggested Citation

  • Earvin Balderama & Frederic Paik Schoenberg & Erin Murray & Philip W. Rundel, 2012. "Application of Branching Models in the Study of Invasive Species," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(498), pages 467-476, June.
    • Handle: RePEc:taf:jnlasa:v:107:y:2012:i:498:p:467-476
    DOI: 10.1080/01621459.2011.641402
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    Cited by:

    1. Baichuan Yuan & Frederic P. Schoenberg & Andrea L. Bertozzi, 2021. "Fast estimation of multivariate spatiotemporal Hawkes processes and network reconstruction," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(6), pages 1127-1152, December.
    2. Francesco Serafini & Finn Lindgren & Mark Naylor, 2023. "Approximation of Bayesian Hawkes process with inlabru," Environmetrics, John Wiley & Sons, Ltd., vol. 34(5), August.
    3. Frederic Paik Schoenberg & Marc Hoffmann & Ryan J. Harrigan, 2019. "A recursive point process model for infectious diseases," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(5), pages 1271-1287, October.
    4. Frederic Paik Schoenberg, 2022. "Nonparametric estimation of variable productivity Hawkes processes," Environmetrics, John Wiley & Sons, Ltd., vol. 33(6), September.
    5. Gresnigt, Francine & Kole, Erik & Franses, Philip Hans, 2015. "Interpreting financial market crashes as earthquakes: A new Early Warning System for medium term crashes," Journal of Banking & Finance, Elsevier, vol. 56(C), pages 123-139.

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