Basis of self-organized proportion regulation resulting from local contacts

One of the fundamental problems in biology concerns the method by which a cluster of organisms can regulate the proportion of individuals that perform various roles or modes as if each individual is aware of the overall situation without a leader. In various species, a specific ratio exists at multiple levels, from the process of cell differentiation in multicellular organisms to the situation of social dilemma in a group of human beings. This study determines a common basis for regulating collective behavior that is realized by a series of local contacts between individuals. In this theory, the most essential behavior of individuals is to change their internal mode by sharing information when in contact with others. Our numerical simulations regulate the proportion of population in two kinds of modes. Furthermore, using theoretical analysis and numerical calculations, we show that asymmetric properties in local contacts are essential for adaptive regulation in response to global information such as group size and overall density. Particle systems are crucial in allowing flexible regulation in no-leader groups, and the critical condition that eliminates overlap with other individuals (the excluded volume effect) also affects the resulting proportion at high densities. The foremost advantage of this strategy is that no global information is required for each individual, and minimal mode switching can regulate the overall proportion. This simple mechanism indicates that proportion regulation in well-organized groups in nature can be realized through and limited to local contacts, and has the potential to explain various phenomena in which microscopic individual behavior results in orderly macroscopic behavior.