Multiscale Modelling Tool: Mathematical modelling of collective behaviour without the maths

Abstract

Collective behaviour is of fundamental importance in the life sciences, where it appears at levels of biological complexity from single cells to superorganisms, in demography and the social sciences, where it describes the behaviour of populations, and in the physical and engineering sciences, where it describes physical phenomena and can be used to design distributed systems. Reasoning about collective behaviour is inherently difficult, as the non-linear interactions between individuals give rise to complex emergent dynamics. Mathematical techniques have been developed to analyse systematically collective behaviour in such systems, yet these frequently require extensive formal training and technical ability to apply. Even for those with the requisite training and ability, analysis using these techniques can be laborious, time-consuming and error-prone. Together these difficulties raise a barrier-to-entry for practitioners wishing to analyse models of collective behaviour. However, rigorous modelling of collective behaviour is required to make progress in understanding and applying it. Here we present an accessible tool which aims to automate the process of modelling and analysing collective behaviour, as far as possible. We focus our attention on the general class of systems described by reaction kinetics, involving interactions between components that change state as a result, as these are easily understood and extracted from data by natural, physical and social scientists, and correspond to algorithms for component-level controllers in engineering applications. By providing simple automated access to advanced mathematical techniques from statistical physics, nonlinear dynamical systems analysis, and computational simulation, we hope to advance standards in modelling collective behaviour. At the same time, by providing expert users with access to the results of automated analyses, sophisticated investigations that could take significant effort are substantially facilitated. Our tool can be accessed online without installing software, uses a simple programmatic interface, and provides interactive graphical plots for users to develop understanding of their models.

Noise-induced effects in collective dynamics and inferring local interactions from data

“…Despite the simplicity, the model can be applied to contexts of decision making and even collective motion-for example, a group moving in an annulus. Indeed, this model and its extensions have been applied in a wide range of contexts, such as marching locusts [18], fish schooling [14], decision making in animals [28,29] recruitment of cell signalling molecules [30] and even financial markets [31,32].…”

Negative feedback may suppress variation to improve collective foraging performance

“…We conclude by noting that our study highlights the importance of using multiscale modelling to understand collective behaviour [52, 53, 54]. In fact, through mean-field analysis we could not observe the dynamics that justify the use of the negative feedback.…”

“…A Mathematica notebook reproducing the analyses presented herein is available in the GitHub repository https://github.com/DiODeProject/VarianceSuppression. This is supplemented by a notebook for MuMoT [42], an open-source tool for multiscale modelling, which reproduces similar results to those presented herein. The notebook is available online at https://mybinder.org/v2/gh/DiODeProject/MuMoT/master?filepath=DemoNotebooks%2FVariance_suppression.ipynb.…”

“…In this study, we only employed noise-free mean-field analysis and master equations with system-size dependent noise. However, further analysis could include the impact of spatial noise, and time-correlated information and/or interactions [42]. (1) (dashed lines) for both models, the stochastic trajectories show different results for the two models.…”

“…This is supplemented by a notebook for MuMoT [52], an open-source tool for multiscale modelling, which reproduces similar results to those presented herein. The notebook is available online at https://mybinder.org/v2/gh/DiODeProject/MuMoT/master?filepath=DemoNotebooks%2FVariance_suppression.ipynb.…”