A general mathematical method for predicting spatio-temporal correlations emerging from agent-based models

Author:

Ovaskainen Otso12ORCID,Somervuo Panu1ORCID,Finkelshtein Dmitri3ORCID

Affiliation:

1. Organismal and Evolutionary Biology Research Programme, University of Helsinki, P.O. Box 65, Helsinki FI-00014, Finland

2. Centre for Biodiversity Dynamics, Department of Biology, Norwegian University of Science and Technology, N-7491 Trondheim, Norway

3. Department of Mathematics, Swansea University, Fabian Way, Swansea SA1 8EN, UK

Abstract

Agent-based models are used to study complex phenomena in many fields of science. While simulating agent-based models is often straightforward, predicting their behaviour mathematically has remained a key challenge. Recently developed mathematical methods allow the prediction of the emerging spatial patterns for a general class of agent-based models, whereas the prediction of spatio-temporal pattern has been thus far achieved only for special cases. We present a general and mathematically rigorous methodology that allows deriving the spatio-temporal correlation structure for a general class of individual-based models. To do so, we define an auxiliary model, in which each agent type of the primary model expands to three types, called the original, the past and the new agents. In this way, the auxiliary model keeps track of both the initial and current state of the primary model, and hence the spatio-temporal correlations of the primary model can be derived from the spatial correlations of the auxiliary model. We illustrate the agreement between analytical predictions and agent-based simulations using two example models from theoretical ecology. In particular, we show that the methodology is able to correctly predict the dynamical behaviour of a host–parasite model that shows spatially localized oscillations.

Funder

Jane and Aatos Erkko Foundation

Academy of Finland

Publisher

The Royal Society

Subject

Biomedical Engineering,Biochemistry,Biomaterials,Bioengineering,Biophysics,Biotechnology

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