Analysis of inconsistencies for the study of dominance: assessing influence of some biological traits on hierarchy in male brown bears

Abstract The structure of social hierarchies is defined by dominance relationships, and a higher hierarchy position has been reported to improve both access to resources and reproductive success. Diverse methods have been proposed to calculate individual rank in an animal population from a matrix of wins and losses in dyads. A procedure for ranking individuals in near-linear rank orders, that minimizes the number of inconsistencies (I) and the total strength of the inconsistencies (SI), has been developed (I&SI method). We present a version of the I&SI algorithm (iDominance) fully implemented using Python v3, that calculates rank orders more efficiently and analyzes the existence of some sets of individuals with interchangeable positions within the ranking and others with fixed positions, from which we identified three dominance groups. We use iDominance to analyze the hierarchy of a semi-free population of male brown bears ( Ursus arctos ) in Cabárceno Nature Park, based upon agonistic interactions observed over two years. We predicted that social rank of brown bears defined by the I&SI method will not be adequately represented by a simple linear hierarchy and should instead be described with a structure of dominance groups. Moreover, we predicted that morphometric, hormonal and behavioral attributes of male brown bears will affect the dominance hierarchy. Our analysis identified three dominance groups: Dominant (3 males), Intermediate (8 males) and Subordinate (16 males). We suggest that in brown bears, a promiscuous solitary species, when aggregating, males maintain a stable dominance hierarchy to diminish social stress. Our results suggest that higher social status is related to greater body mass, longer feet, longer and wider hands, higher testosterone levels and a high rate of mating interruptions. Significance Statement Male brown bears are solitary animals that establish dominance hierarchies during social associations linked to mating season or when resources are abundant. Different methods to define linear dominance have been developed. We assess male brown bear hierarchy using a method already published applying a new computer implementation that defines a non-linear hierarchy and describes dominance groups. Morpho-functional characteristics are discussed, and we observe that dominant bears are heavier, have more testosterone, longer feet and hands, wider hands and interrupts copulations more often.