Bulletin of Mathematical Biology

, Volume 69, Issue 4, pp 1341–1354

A New Method for Calculating Net Reproductive Rate from Graph Reduction with Applications to the Control of Invasive Species

Original Article

DOI: 10.1007/s11538-006-9162-0

Cite this article as:
de-Camino-Beck, T. & Lewis, M.A. Bull. Math. Biol. (2007) 69: 1341. doi:10.1007/s11538-006-9162-0


Matrix models are widely used for demographic analysis of age and stage structured biological populations. Dynamic properties of the model can be summarized by the net reproductive rate R0. In this paper, we introduce a new method to calculate and analyze the net reproductive rate directly from the life cycle graph of the matrix. We show, with examples, how our method of analysis of R0 can be used in the design of strategies for controlling invasive species.


Matrix modelsNet reproductive rateInvasionBiological control

Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  1. 1.Centre for Mathematical Biology and Department of Biological SciencesUniversity of AlbertaEdmontonCanada
  2. 2.Centre for Mathematical Biology and Department of Mathematical and Statistical SciencesUniversity of AlbertaEdmontonCanada