Methods for quantifying self-organization in biology: a forward-looking survey and tutorial

TL;DR

This paper reviews methods for quantifying self-organization in biological systems, emphasizing the importance of transforming qualitative patterns into quantitative data to better understand and predict collective behaviors.

Contribution

It provides a comprehensive survey of existing techniques for measuring self-organization, including order parameters, correlation functions, and topological data analysis, highlighting future promising directions.

Findings

Survey of methods like order parameters and correlation functions

Discussion of topological data analysis applications

Identification of promising future research areas

Abstract

From flocking birds to schooling fish, organisms interact to form collective dynamics across the natural world. Self-organization is present at smaller scales as well: cells interact and move during development to produce patterns in fish skin, and wound healing relies on cell migration. Across these examples, scientists are interested in shedding light on the individual behaviors informing spatial group dynamics and in predicting the patterns that will emerge under altered agent interactions. One challenge to these goals is that images of self-organization -- whether empirical or generated by models -- are qualitative. To get around this, there are many methods for transforming qualitative pattern data into quantitative information. In this tutorial chapter, I survey some methods for quantifying self-organization, including order parameters, pair correlation functions, and techniques from topological data analysis. I also discuss some places that I see as especially promising for quantitative data, modeling, and data-driven approaches to continue meeting in the future.