Basis of Self-organized Proportion Regulation Resulting from Local Contacts (1504.05292v3)

Abstract: 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 knows a whole situation without a leader. A specific ratio exists in various species 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 found a common basis of regulating a collective behavior which is realized by a series of local contacts between individuals. The most essential behavior of individuals in this theory is to change its internal mode through sharing information in contact with others. Our numerical simulations with cellular automata model realize to regulate the ratio of population of individuals who has either two kinds of modes. From the theoretical analysis and numerical calculations, we found that asymmetric properties in local contacts, are essential for adaptive regulation in response to the global information such a group size and whole density. Furthermore, a discrete system is crucial in no-leader groups to realize the flexible regulation, and the critical condition which eliminates overlap with one another (excluded volume effect) also affects the resulting proportion in high density. The foremost advantage of this strategy is that no global information is required for each individual, and only a couple of mode switching can achieve the whole proportion regulation. The simple mechanism say that proportion regulation in well-organized groups in nature can be realized through and limited to local contacts, and has a potential to solve various phenomena that microscopic individuals behaviors connect to macroscopic orderly behaviors.