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 ...
Highlights
The spruce budworm, Choristoneura fumiferana (Clements), is the most serious defoliator of spruce (Picea spp.) and balsam fir (Abies balsamea) trees in the boreal forest of North America
We study Boolean approximations of a classical ordinary differential equations (ODE) model of the budworm–forest dynamics that was developed and analysed in Ludwig et al (1978)
The ODE model developed in Ludwig et al (1978) for the dynamics of the budworm– forest interaction is a three-variable system based upon the dynamics of the budworm population size and the state of the forest
Summary
The spruce budworm, Choristoneura fumiferana (Clements), is the most serious defoliator of spruce (Picea spp.) and balsam fir (Abies balsamea) trees in the boreal forest of North America. That Boolean models can be bistable was first established in Veliz-Cuba and Stigler (2011), followed by work on Boolean approximations of ODE models that preserve bistability (Hinkelmann & Laubenbacher, 2011; Robeva & Yildirim, 2013) All of these results were obtained for systems at the molecular level where much of the system’s dynamics are known a priori to be close to Boolean (e.g. genes are either on or off, proteins are either made or not, etc.). A question regarding the general suitability of Boolean models at the population level deserves attention and the ability of such models to capture biologically meaningful states of bistability, as in the case of the budworm–forest system, is of particular interest Answering these questions was the main motivator for the work presented here.
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