Section I. Previous work has indicated that sage grouse Centrocercus wophasianus practice extreme polygyny (Simon 1940; Scott 1942; Patterson 1952; Lumsden 1968). The behavioural interactions that regulate this mating system have remained unclear, as the males' behaviour suggests both territoriality and dominance hierarchy.
Section II. A basic difference between territorial and hierarchical social systems involves the extent to which the constituent individuals' relationships are polarized, rather than reciprocal. In a dominance hierarchy the interactions between individuals are polarized; territorial individuals typically interact reciprocally. Nevertheless, interactions among territorial individuals can incorporate two kinds of polarity: territorial dominance, as each individual dominates his neighbours inside his own territory but is subordinate to them in their territories; and polarized territoriality, when territorial individuals established in preferred areas prevent other territorial individuals from occupying these areas. The indications of reciprocity and polarity in the interactions of male sage grouse are investigated in this paper to clarify the expression of territoriality and dominance hierarchy in their social organization.
Sections III to VI. Sage grouse gather for mating at communal display grounds, or leks, at traditional sites on sagebrush prairie. Although females arrive for mating primarily during 2 or 3 weeks in late March and April, males usually attend the leks regularly from February or March into May. Every morning and evening and often all night the males occupy small territories (13 to 100 m2) defined by boundary zones in which neighbours meet for facing-past encounters and wing-fighting (behaviour patterns are described in Section IV). Within their territories males repeatedly perform an elaborate, stereotyped display, the strut.
I studied three leks with different numbers of attending males (154, 30 and 260), one lek each spring from 1967 to 1969. Time-lapse cinematography was used to record the males' positions and activities.
Females congregate in dense packs at certain sites on a lek, usually in the same places on successive mornings. These sites, termed mating centres, also usually remain in the same locations in successive years.
Section VII. Almost all copulations occurred at these mating centres, within the territories of one or two males, although as many as eighty other males occupied territories around each mating centre. Consequently, each year fewer than 10 per cent of the males completed more than 75 per cent of all copulations. Neighbours occasionally interrupt each other's copulations, but usually only those attempted near or within the boundary zone of facing-past encounters. Therefore, a male's success in mating does not depend on direct prevention of copulations by other males. Instead, a male becomes successful in mating by acquiring a territory at a mating centre.
Section VIII. The behaviour of females arriving at a lek suggests how they might locate the mating centre. The possible cues associated with a mating centre are evaluated for their specificity in identifying the position of the mating centre and for their availability to the females. Although the behaviour of males near a mating centre differed in several respects from that of more peripheral males (for instance, the former strutted more persistently and engaged in much briefer and perhaps slightly more frequent facing-past encounters), these differences apparently depended mostly on the males' proximities to females, rather than on intrinsic differences among the individual males. Most males 2 or more years old, whether near a mating centre or not, responded similarly to the presence of females within their territories.
Since a mating centre ordinarily has a traditional location within a lek, females might learn its position. Only limited guidance could come from the generally smaller territories of males near a mating centre.
Section IX. Reciprocal interactions among males included the limited scope of neighbours' intrusions into each other's territories and neighbours' encounters as equals in boundary zones between their territories. Non-reciprocal, or polarized, relationships resulted from the attraction of males toward a mating centre. Since their more peripheral neighbours tended to encroach beyond their boundary zones, towards the females gathered at a mating centre, the more central males usually initiated most of the encounters with their more peripheral neighbours. The more central males also terminated most of their facing-past encounters, probably as a result of their tendencies to resume strutting nearer the females at the mating centre. When a territorial male disappeared, the vacancy was allocated to a more peripheral neighbour, one farther from the mating centre than the original occupant, without a noticeably increased frequency or intensity of antagonism.
First-year males lag behind older males in the growth of their gonads (Eng 1963). Some yearlings eventually established territories around the edge of a lek about half-way through the mating period, but yearling males were never seen copulating.
Section X. The combination of three processes can explain how a male acquires a territory at a mating centre: (a) the establishment of yearling males on territories around the periphery of a lek; (b) the centripetal movement of territorial males toward the mating centre as vacancies arise; and (c) the tendency for individual males to occupy positions in subsequent years at least as close to the mating centre as previously. The present study has provided evidence for the first two processes. Dalke et al. (1963) obtained some evidence that males usually return to the same lek and often to the same position in successive years. The hypothesis implies that a male's chances for success in mating would increase with increasing age.
Section XI. To clarify the behavioural manifestations of territoriality in sage grouse, a distinction is made between the territorial resident's aggression gradient and his isolation gradient. Male sage grouse occupy largely exclusive territories. Their ability to dominate agonistic encounters declines steeply across a narrow boundary zone. However, these isolation and aggression gradients are not congruent. The shapes of both gradients depend on the interactions of the resident and his neighbours.
Increased external pressure, owing to the attraction of males toward a mating centre, in conjunction with reduced internal resistance, owing to the central males' briefer facing-past encounters, could explain the generally smaller sizes of territories near a mating centre.
The males' interactions, which include both reciprocal and polarized components, suggest polarized territoriality, a form of social organization that merges features from the classical paradigms of both territoriality and dominance hierarchies. Polarized territoriality generates the radially differentiated social structure on a lek.
Section XII. A review of lek behaviour among grouse reveals only quantitative differences among the five species for which information on social organization is available. The lek behaviour of sage grouse represents the extreme development of this behaviour among grouse.