A unified framework for analysis of individual-based models in ecology and beyond

Stephen J Cornell,Yevhen F Suprunenko,Otso Ovaskainen,Panu Somervuo,Dmitri Finkelshtein

doi:10.1038/s41467-019-12172-y

Abstract

Individual-based models, ‘IBMs’, describe naturally the dynamics of interacting organisms or social or financial agents. They are considered too complex for mathematical analysis, but computer simulations of them cannot give the general insights required. Here, we resolve this problem with a general mathematical framework for IBMs containing interactions of an unlimited level of complexity, and derive equations that reliably approximate the effects of space and stochasticity. We provide software, specified in an accessible and intuitive graphical way, so any researcher can obtain analytical and simulation results for any particular IBM without algebraic manipulation. We illustrate the framework with examples from movement ecology, conservation biology, and evolutionary ecology. This framework will provide unprecedented insights into a hitherto intractable panoply of complex models across many scientific fields.

Highlights

Individual-based models, ‘IBMs’, describe naturally the dynamics of interacting organisms or social or financial agents
The mathematical transparency of these models means that we understand their predictions completely and can propose general principles, e.g., regarding the number of resources needed by competing species5 or the processes that destabilise host–parasite dynamics6
Individual-based based models10 faithfully capture the discrete and spatial nature of population dynamics, but these are usually studied by computer simulation1, which only tells us about a limited set of parameter values and not the general model behaviour

Summary

Introduction

Individual-based models, ‘IBMs’, describe naturally the dynamics of interacting organisms or social or financial agents They are considered too complex for mathematical analysis, but computer simulations of them cannot give the general insights required. A more reliable alternative based on a perturbation expansion has been proposed, which gives asymptotically exact results when agents interact over large enough scales, but the algebraic burden for this method remains prohibitive because it requires arduous derivations for each particular model (Fig. 1d). We overcome these difficulties by formulating a unified theoretical framework for a wide class of systems, which allows us to derive general analytical results. We first describe our framework and the mathematical results leading to it, and give three applications that illustrate how our method allows us to answer questions that are not addressable by a simulation approach alone

Methods

Results

Conclusion