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

Otso Ovaskainen1,2, Panu Somervuo1, Dmitri Finkelshtein3

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

Journal of the Royal Society, Interface
|October 28, 2020
PubMed
Summary
This summary is machine-generated.

Predicting agent-based model behavior is challenging. This study introduces a new mathematical method to accurately forecast spatio-temporal patterns in these complex systems, improving ecological modeling.

Keywords:
Markov evolutionagent-based modelmarked point processspatio-temporal correlationtheoretical ecology

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Area of Science:

  • Computational and Mathematical Biology
  • Theoretical Ecology
  • Complex Systems Modeling

Background:

  • Agent-based models (ABMs) are crucial for simulating complex phenomena across scientific disciplines.
  • While ABM simulation is feasible, mathematical prediction of their emergent behavior, especially spatio-temporal patterns, remains a significant challenge.
  • Existing mathematical methods have successfully predicted spatial patterns but are limited to special cases for spatio-temporal dynamics.

Purpose of the Study:

  • To present a general and mathematically rigorous methodology for deriving the spatio-temporal correlation structure of individual-based models (IBMs).
  • To extend the predictive capabilities of mathematical approaches to general classes of IBMs for spatio-temporal pattern prediction.
  • To validate the methodology's accuracy against agent-based simulations in ecological models.

Main Methods:

  • Development of an auxiliary model by expanding each agent type into three categories: original, past, and new agents.
  • The auxiliary model tracks both the initial and current states of the primary model.
  • Derivation of spatio-temporal correlations of the primary model from the spatial correlations within the auxiliary model.

Main Results:

  • The proposed methodology successfully derives the spatio-temporal correlation structure for a general class of IBMs.
  • Analytical predictions derived from the methodology show strong agreement with agent-based simulations.
  • The method accurately predicts the dynamics of a host-parasite model exhibiting spatially localized oscillations.

Conclusions:

  • The developed methodology provides a general and rigorous framework for predicting spatio-temporal patterns in agent-based models.
  • This approach significantly advances the mathematical analysis of complex systems, moving beyond predictions limited to spatial patterns or special cases.
  • The successful application to ecological models, including predicting oscillations in a host-parasite system, highlights the methodology's practical utility and broad applicability.