### THE ANALYSIS OF SOCIAL DOMINANCE MATRICES WITH MATMAN

H. de Vries

*Ethology & Socio-ecology Group, Department of Comparative Physiology, Utrecht University, Utrecht, The Netherlands*

At least three topics are important in the analysis of social dominance relationships between the individuals living in a social group:

**The linearity test**. Do the individuals form a linear dominance hierarchy? That is: how can one test statistically that the linearity in the set of dominance relationships is significantly strong?
**The linear ordering problem**. If the linearity is significant, how can the individuals be ordered into a (nearly) linear rank order?
**The unidirectionality test**. Is the exchange of dominance interactions among each pair of individuals sufficiently unidirectional?

I will present a recently developed test of linearity in a set of
dominance relationships that contains unknown or tied relationships.
Next I will briefly discuss an algorithm for finding the (near) optimal
ranking of individuals based on two criteria: minimization of the
number of reversals and minimization of the total strength of the
reversals. If time allows I will discuss a statistical test of
unidirectionality. These three methods are part of the newest version
of MatMan, a program for the analysis of sociometric matrices and
behavioural transition matrices. A previous version of MatMan is
described in *Behaviour* (125:157-175, 1993).

Paper presented at *Measuring Behavior '96*, International Workshop on Methods and Techniques in Behavioral Research, 16-18 October 1996, Utrecht, The Netherlands