Finding an appropriate order for a hierarchy based on probabilistic dominance

Methods of ranking individuals in a dominance hierarchy that use transitivity of relationships may obscure irregularities. Furthermore, these methods use only a small proportion of the information available from dominance encounters. This paper presents an intuitively appealing and easily implemented alternative to existing methods for ordering dominance data, developed from the work of Batchelder et al. (1992 Journal of Mathematical Psychology36, 185-212). The procedure presented here is based on a mathematical model of paired comparisons and it involves only simple estimation procedures. We illustrate its use with data on dominance among red deer Cervus elaphus, stags. The results indicate that dominance relationships are well characterized by the scale values that the model provides, and, because the method provides predictions for all pairings of animals, dominance predictions also exist for pairs of animals that have yet to be observed. Moreover, the dominance outcomes predicted by the model using the order scale are highly correlated with actual dominance observations at all levels. Overall, the procedure described provides a solution to the problem of identifying an appropriate order for a near-linear dominance hierarchy. Copyright 1999 The Association for the Study of Animal Behaviour.

[1]  William H. Batchelder,et al.  Dynamic paired-comparison scaling , 1992 .

[2]  E. Solberg,et al.  Statistical models of transitive and intransitive dominance structures , 1998, Animal Behaviour.

[3]  R. Beilharz,et al.  Social position and behaviour of dairy heifers in yards , 1963 .

[4]  R. A. Bradley,et al.  RANK ANALYSIS OF INCOMPLETE BLOCK DESIGNS , 1952 .

[5]  D. Wood‐Gush.  The behaviour of the domestic chicken: A review of the literature , 1955 .

[6]  Ivan D. Chase,et al.  Models of hierarchy formation in animal societies , 1974 .

[7]  M. Kendall.  Further contributions to the theory of paired comparisons , 1955 .

[8]  Kimberly A. Jameson,et al.  Numerical scaling techniques for evaluating generative models of orthographies , 1996 .

[9]  Michael C. Appleby,et al.  The probability of linearity in hierarchies , 1983, Animal Behaviour.

[10]  Geoffrey J. Iverson,et al.  Thurstonian psychophysics: Case III , 1987 .

[11]  M. Appleby.  The Consequences and Causes of High Social Rank in Red Deer Stags , 1982 .

[12]  Martin W. Schein,et al.  Social dominance relationships in a herd of dairy cattle , 1955 .

[13]  Nancy Alvarado.  NEW FINDINGS ON THE CONTEMPT EXPRESSION , 1996 .

[14]  L. Thurstone.  A law of comparative judgment. , 1994 .

[15]  R. A. Bradley,et al.  RANK ANALYSIS OF INCOMPLETE BLOCK DESIGNS THE METHOD OF PAIRED COMPARISONS , 1952 .

[16]  T. Clutton‐Brock,et al.  The logical stag: Adaptive aspects of fighting in red deer (Cervus elaphus L.) , 1979, Animal Behaviour.

[17]  De,et al.  Finding a dominance order most consistent with a linear hierarchy: a new procedure and review. , 1998, Animal behaviour.

[18]  A. Kimball Romney,et al.  The implications of social structure for dominance hierarchies in red deer, Cervus elaphus L , 1992, Animal Behaviour.

[19]  J. M. Roberts,et al.  Modeling hierarchy: Transitivity and the linear ordering problem , 1990 .

[20]  William H. Batchelder,et al.  The statistical analysis of a thurstonian model for rating chess players , 1979 .

[21]  F. Carroll,et al.  Social dominance in a herd of Angus, Hereford, and Shorthorn cows. , 1966, Animal behaviour.

[22]  J. Yellott.  The relationship between Luce's Choice Axiom, Thurstone's Theory of Comparative Judgment, and the double exponential distribution , 1977 .

[23]  B. Cole.  Dominance hierarchies in leptothorax ants. , 1981, Science.

[24]  Robert Boyd,et al.  A method for assigning cardinal dominance ranks , 1983, Animal Behaviour.

[25]  Evolution of Behaviour , 1959, Nature.

[26]  Teh-Hsing Wei,et al.  The algebraic foundations of ranking theory , 1952 .

[27]  T. Clutton‐Brock,et al.  Red Deer: Behavior and Ecology of Two Sexes , 1992 .

[28]  C. Drews.  THE CONCEPT AND DEFINITION OF DOMINANCE IN ANIMAL BEHAVIOUR , 1993 .

[29]  R. May,et al.  The Evolution of Behaviour , 1982 .