Estimating the Long-term Behavior of Biologically Inspired Agent-based Models

TL;DR

This paper develops a probabilistic framework to estimate the long-term behavior of complex agent-based models, incorporating biological features like birth and death, and applies it to models including the Game of Life and vertebrate rib development.

Contribution

It extends existing methods to include biologically realistic features and provides a way to predict long-term dynamics without extensive simulations.

Findings

Framework successfully models population changes over time.

Applied to Game of Life and rib development models with promising results.

Enables analysis of long-term behavior efficiently.

Abstract

An agent-based model (ABM) is a computational model in which the local interactions of autonomous agents with each other and with their environment give rise to global properties within a given domain. As the detail and complexity of these models has grown, so too has the computational expense of running several simulations to perform sensitivity analysis and evaluate long-term model behavior. Here, we generalize a framework for mathematically formalizing ABMs to explicitly incorporate features commonly found in biological systems: appearance of agents (birth), removal of agents (death), and locally dependent state changes. We then use our broader framework to extend an approach for estimating long-term behavior without simulations, specifically changes in population densities over time. The approach is probabilistic and relies on treating the discrete, incremental update of an ABM via "time steps" as a Markov process to generate expected values for agents at each time step. As case studies, we apply our extensions to both a simple ABM based on the Game of Life and a published ABM of rib development in vertebrates.