Abstract
Cellular automata (CAs) are commonly used to simulate spatial processes in ecology. Although appropriate for modelling events that occur at discrete time points, they are also routinely used to model biological processes that take place continuously. We report on a study comparing predictions of discrete time CA models to those of their continuous time counterpart. Specifically, we investigate how the decision to model time discretely or continuously affects predictions regarding long-run population sizes, the probability of extinction and interspecific competition. We show effects on predicted ecological outcomes, finding quantitative differences in all cases and in the case of interspecific competition, additional qualitative differences in predictions regarding species dominance. Our findings demonstrate that qualitative conclusions drawn from spatial simulations can be critically dependent on the decision to model time discretely or continuously. Contrary to our expectations, simulating in continuous time did not incur a heavy computational penalty. We also raise ecological questions on the relative benefits of reproductive strategies that take place in discrete and continuous time.
Highlights
Cellular automata (CAs) are commonly used to simulate dynamic spatial processes in ecology, contributing to developments in both applied and theoretical research
In the applied literature CAs have been used to simulate the spatial distribution of insect colonies (Perfecto and Vandermeer, 2008; Vandermeer et al, 2008) and the effect of plant-soil feedbacks on relative tree abundance (Mangan et al, 2010), while in microbial ecology, Fox et al (2008) used a CA to investigate the way in which plasmids invade bacterial populations
We investigate the extent of these problems by simulating the same system in continuous and discrete time, taking a continuous time model as our benchmark
Summary
Cellular automata (CAs) are commonly used to simulate dynamic spatial processes in ecology, contributing to developments in both applied and theoretical research. This in turn introduces the need to make additional assumptions in the form of modelling decisions regarding the update scheme used to govern the order in which sites are considered and events take place When these modelling decisions are made carefully, CAs can form appropriate models for discrete time spatial processes. We assume stochastic real world processes that occur in continuous time with exponentially distributed waiting times between events, taking as a case study the asymmetric logistic model of population growth on a lattice (Matsuda et al, 1992) We regard this model as our benchmark and consider discrete time CA simulations as approximations to this model. We describe our experimental protocol, provide findings from our two experiments and conclude with modelling recommendations
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