Beaugrand, 1997b

This simulation study explores some conditions leading to transitivity within dominance orders. Combinations of three parameters were varied to study their consequences upon hierarchy formation and upon the degree of linearity of resultant structures. The factors studied were (i) the importance of initial Resource Holding Potentials (RHPs) , (ii) changes brought in RHPs by successive victories and defeats, and (iii) accuracy of RHP assessment made by opponents. Results show that initial differences in RHP always lead to perfectly transitive chains whose rank order reflects the importance of initial differences. Even when simulated animals make important errors while assessing each other during round robin tournaments, emerging dominance structures are perfectly linear and ranks obtained in the structure are highly correlated with initial values in RHPs. Moreover, accumulated experiences of victory and/or defeat alone always lead to perfectly linear hierarchies. Their combination with initial individual differences in RHP led to the same conclusion. Even when assessment was far from being perfect, not only perfect chains were formed but initial values in RHPs significantly influenced rank order when the contribution of victory and defeat to RHP was relatively unimportant. The higher the importance of victory and defeat to RHP as compared to that of initial RHP values, the lower was the correlation between initial RHP values and the ranks order reached by individuals in the resultant hierarchies. In general also, the lower the variation within initial RHPs, the lower was the correlation between initial RHPs and ranks in the hierarchy. At a given level of initial RHP dispersion, increasing the contribution of victory and defeat to RHP diminished the correlation between initial RHP values and obtained ranks. In addition, inaccurate assessment reduced the overall correlation, especially when dispersion of initial RHP values was low and the contribution of victory and defeat was high. These results shed some light on the controversy about the respective roles of initial individual attributes and that of patterns of resolution in the formation of animal hierarchies. We present the emergence of social order within closed systems as those simulated here as a case of self-organization.