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

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. The use of ABMs in biology has become widespread over the last few years because of how these models can easily incorporate multiscale data across both time and space. 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. In this talk, we present a mathematical framework for formalizing ABMs which explicitly incorporates features commonly found in biological systems: appearance of agents (birth), removal of agents (death), and locally dependent state changes. We use this framework as a foundation to develop an approach for estimating long-term behavior, such as changes in population density over time, without simulations. Our 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 approach to both a published ABM used to study rib development in vertebrates.