The spruce budworm and forest: a qualitative comparison of ODE and Boolean models

Raina Robeva, David Murrugarra

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


Boolean and polynomial models of biological systems have emerged recently as viable companions to differential equations models. It is not immediately clear however whether such models are capable of capturing the multi-stable behaviour of certain biological systems: this behaviour is often sensitive to changes in the values of the model parameters, while Boolean and polynomial models are qualitative in nature. In the past few years, Boolean models of gene regulatory systems have been shown to capture multi-stability at the molecular level, confirming that such models can be used to obtain information about the system’s qualitative dynamics when precise information regarding its parameters may not be available. In this paper, we examine Boolean approximations of a classical ODE model of budworm outbreaks in a forest and show that these models exhibit a qualitative behaviour consistent with that derived from the ODE models. In particular, we demonstrate that these models can capture the bistable nature of insect population outbreaks, thus showing that Boolean models can be successfully utilized beyond the molecular level.

Original languageEnglish
Pages (from-to)75-92
Number of pages18
JournalLetters in Biomathematics
Issue number1
StatePublished - Jan 1 2016

Bibliographical note

Publisher Copyright:
© 2016, © 2016 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.


  • Boolean network
  • bistability
  • budworm-forest model
  • discrete dynamical system
  • qualitative dynamics

ASJC Scopus subject areas

  • Statistics and Probability
  • Biochemistry, Genetics and Molecular Biology (miscellaneous)
  • Applied Mathematics


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