The effect of tied rank numbers on the linearity of dominance hierarchies.

The occurence of tied rank numbers in dominance hierarchies is discussed, especially its effect on the linearity of the hierarchy. This linearity is measured with Landau's index, that is calculated for several hierarchies with tied ranks on one, two of three levels. Linearity is mostly affected by ties in small groups with many ties. A distinction is made between a hierarchy of individuals and hierarchical levels. The phenomenon of despotism is called an extreme case of tied ranks. It is proposed to regard hierarchies with a linearity in a continuous scale.