A Tournament Metaphor for Dominance Hierarchy

We explore the possibility of using Ramanuja-charyulu’s tournament metaphor to get new dominance indices. This graph theoretic approach leads to two dimensionless rating measures, a power-weakness ratio (PWR) and a normalized power-weakness difference (nPWD). Three popular dominance indices already in use are the Clutton-Brock et al.’s index (CBI), David’s score (DS) and frequency-based dominance index (FDI), and weshall show that CBI and FDI are ratio scales like PWR, and DS is an interval scale like nPWD. Unlike the PWR which can become singular (i.e. it ranges from zero to infinity), the nPWD ranges from –1 to +1. The new dominance indices yield unique scores and ranks and can be used interchangeably as they have a monotonic one-to-one relationship.