The spruce budworm and forest

a qualitative comparison of ODE and Boolean models

  • Raina Robeva Department of Mathematics, Randolph-Macon College, Ashland, VA, USA
  • David Murrugarra Department of Mathematics, University of Kentucky, Lexington, KY, USA
Keywords: Boolean network, discrete dynamical system, budworm-forest model, qualitative dynamics, bistability

Abstract

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.

Published
2016-12-01
How to Cite
Robeva, Raina, and David Murrugarra. 2016. “The Spruce Budworm and Forest”. Letters in Biomathematics 3 (1), 75–92. https://doi.org/10.1080/23737867.2016.1197804.
Section
Research