Steps Towards a Quantitative Analysis of Individuality and its Maintenance: A Case Study with Multi-Agent Systems Alexandra Penn Centre for Computational Neuroscience and Robotics University of Sussex Brighton BN1 9QG UK alexp@cogs.susx.ac.uk Abstract In the context of the study of the evolution of new levels of biological organisation, we present initial work aimed at constructing a metric to detect individuality, or cooperative systems of agents. The metric is based upon the idea that individuals must possess a distinct, reduced set of higher-level variables with respect to the degrees of freedom of their components. Further, in biology, each new level of organisation is a homeostatic entity in its own right, and we argue that the origin of homeostasis amongst a group of entities is the critical point at which they become a new, higher-level, system. We investigate a new measure of the degree of individuality in collective systems of agents, based on calculating the effective number of degrees of freedom in a system, and how this changes with increasing external perturbation. The results of applying the measure to collectives of simulated Kheperas are presented, and the applications to homeostatic and non-homeostatic systems are discussed. 1 Introduction One of the most prominent mechanisms by which organisms have increased in complexity over evolutionary time is transitions in levels of selection, that is, the construction of a new level of individuality from a collective of pre-existing individual organisms (Maynard Smith and Szath- mary, 1995). For example, the origin of multicellularity, insect societies, or eukaryotes. This is clearly a means by which open-ended evolution is achieved in nature, and as such is a dynamic which we would wish to emulate in artificial evolution. In trying to investigate these phenomena in an artificial context, one very quickly comes across an extremely basic problem to be addressed. What is the nature of the entity upon which selection acts? That is, what constitutes an individual? In simulation it is usually the case that the individual is a predefined, static entity with a prescribed set of parameters which can be varied, but no scope for real innovation. By contrast real biological individuals are dynamic physical processes in a constant state of flux, continually metabolising in order to simply exist. It would seem to be a necessary first step in emulating the flexible nature of the individual over biological time to define what we mean by an individual, particularly within the constraints of the living system. Various structural criteria, applicable to both organic and inorganic structures, present themselves: The system possesses a reduced, distinct, set of higher-level system variables