On dominance relations and the structure of animal societies: II. Some effects of possible social factors
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- Landau, H.G. Bulletin of Mathematical Biophysics (1951) 13: 245. doi:10.1007/BF02477920
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In a previous paper (Landau, 1951) it was shown that a society with a dominance relation would rarely tend to be close to the hierarchy in structure if dominance is determined solely by the inherent characteristics of the members. Here we consider the effects of other factors, due to social rank or to the outcome of previous encounters which affected dominance.
The following results are obtained. A uniform bias against reversal of dominance will have no effect on the stationary distribution of the structure of the society. If the probability of dominance is a linear function of the previously established score (number of members dominated), there will be a small tendency for the society to move toward the hierarchy; but this is negligible for large societies. If a member never challenges another whose score exceeds his own by two or more, or if he can never dominate if he should challenge, then the hierarchy is the only stable structure.
From the last result it is concluded that social factors which restrict challenges or the probability of dominance could easily account for societies close to the hierarchy, such as are observed in flocks of domestic hens.
The effectiveness of social bias in establishing hierarchies is much greater in small societies than in large ones.