Dominance Hierarchy Calculator
Enter win–loss matrix and calculate ranks
Paste a square matrix where row i, column j = number of times individual i beat individual j.
Leave diagonal as 0. Use spaces or tabs between numbers.
Results
| Individual | David's Score | Normalized Rank | Rank Order |
|---|
The Dominance Hierarchy Calculator computes two of the most widely accepted quantitative measures used in ethology and behavioral ecology:
- Landau's index of linearity h (1975) with de Vries' statistical correction h' (1995)
- David's score (1987) and normalized dominance ranks
These indices are standard in hundreds of peer-reviewed papers on social structure in mammals, birds, fish, insects and primates (de Vries 1995, 1998; Bayly et al. 2006; Bang et al. 2010; Martin & Bateson 2007; Whitehead 2008; Shizuka & McDonald 2012; Schmid et al. 2017).
Dominance hierarchies reduce costly fights by establishing predictable priority of access to resources (food, mates, space). Quantifying them allows researchers to:
- Compare social structures across species, populations, ages, sexes
- Measure effects of hormones, stress, crowding, castration, enrichment
- Assess welfare in farm, zoo and lab animals (pigs, poultry, primates)
- Study coalition formation, nepotism, personality, leadership
- Model disease transmission, foraging efficiency, mating success
Linearity (h') tells how strictly transitive the hierarchy is (0 = egalitarian, 1 = perfect despotism). David's score provides individual rank even in non-linear groups.
More resources → Agri Care Hub | Dominance Hierarchy on Wikipedia
Input format: square matrix of wins (row beats column). Diagonal = 0.
Valid examples:
0 4 7 1
2 0 5 3
0 1 0 6
3 0 2 0
Results explained:
- David's score — relative dominance strength
- Normalized rank — 0 (bottom) to 1 (top)
- h' — linearity (0–1); >0.9 usually considered strongly linear
Landau's index h (1975)
h = [12 / (N³ - N)] × Σ [ (P_i - (N-1)/2)² ]
de Vries' corrected h' (1995) — most commonly used today:
h' = 1 - (number of circular triads / maximum possible circular triads)
David's score (1987) for individual i:
DS_i = Σ W_i + Σ (W_ij / (W_ij + L_ij)) - Σ (L_ji / (W_ji + L_ji))
Where W_i = total wins by i, etc.
Normalization → ranks from 0 (lowest) to 1 (highest).