Robust Bounds on Choosing from Large Tournaments

Tournament solutions provide methods for selecting the "best" alternatives from a tournament and have found applications in a wide range of areas. Previous work has shown that several well-known tournament solutions almost never rule out any alternative in large random tournaments. Nevertheless, all analytical results thus far have assumed a rigid probabilistic model, in which either a tournament is chosen uniformly at random, or there is a linear order of alternatives and the orientation of all edges in the tournament is chosen with the same probabilities according to the linear order. In this work, we consider a significantly more general model where the orientation of different edges can be chosen with different probabilities. We show that a number of common tournament solutions, including the top cycle and the uncovered set, are still unlikely to rule out any alternative under this model. This corresponds to natural graph-theoretic conditions such as irreducibility of the tournament. In addition, we provide tight asymptotic bounds on the boundary of the probability range for which the tournament solutions select all alternatives with high probability.Comment: Appears in the 14th Conference on Web and Internet Economics (WINE), 201

Social rank in schools of juvenile yellowtail, Seriola quinqueradiata

The composition, stability and biotic factors of social rank in juvenile marine fish schools are demonstrated using juvenile yellowtails, Seriola quinequeradiata (Temminck et Schlegel: Carangidae). According to the frequency of aggressive behaviour, members within a school were divided into three categories: dominants (10-20%) intermediates (10-20%) and sub-ordinates (60-80%). Social rank was reset with the same hierarchy composition when dominants and intermediates were combined. Observation of individual aggressive behaviour using a video image analysis system revealed that starvation and an increase in fish densities accelerated aggression only in the dominants. In order to determine the durability of social rank, otoliths of dominant fish in eight experimental groups were labelled and the fish returned to their groups; six dominants appeared after one day and three after one week of rearing, indicating that social rank was maintained for at least one week (binomial distribution; P < 0.05). Total lengths of dominants were larger than tose of subordinates after one day of rearing, whereas dominants were smaller after one week. Social rank of this species is decided upon by individual aggressive tendency, but is not beneficial for feeding or growth

Sexual selection and mating system in Zorotypus gurneyi Choe (Insecta : Zoraptera)

Social behavior of a species in the little-known insect order Zoraptera is described for the first time. Zorotypus gurneyi Choe (Insecta: Zoraptera) is a wing-dimorphic species that lives colonially under the bark of rotting logs in central Panama. Males are larger than females in total body size and fight each other to gain access to females. Highly linear and stable dominance hierarchies exist among males. Higher-ranking males show such agonistic behavior as jerking, chasing, head-butting, hindleg-kicking, and grappling, whereas subordinates often try to avoid contacts. Higher-ranking males, the dominant males in particular, are well recognized by others and relatively free of injuries. Although the dominant males are often the largest, the correlation between body size and dominance rank is not always significant. The mating system of Z. gurneyi is an example of female defense polygyny in which the dominant males obtain the majority of matings (75% on average). Mating success among Z. gurneyi males is much more variable than that of some lekking species.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46900/1/265_2004_Article_BF00164179.pd

Sexual selection and mating system in Zorotypus gurneyi Choe (Insecta: Zoraptera)

Body size is clearly an important factor influencing the outcome of agonistic contests, but is often weakly correlated with dominance ranks in Zorotypus gurneyi Choe (Insecta: Zoraptera). The study of the development and dynamics of dominance relations using artificially constructed colonies show that age, or tenure within the colony, is the prime determinant of dominance among males. Dominance hierarchies become relatively stable within 2 or 3 days and males that emerge later normally begin at the bottom of the hierarchy regardless of size. Males interact much more frequently when they are simultaneously introduced to each other than when they are allowed to emerge at different times. In the latter case, males that emerge late appear to recognize relative dominance of older males and avoid direct contests. Considering the high correlation between dominance rank and mating success, there is a strong selective advantage to males that emerge earlier and such pressure of sexual selection may be responsible for the difference in life history strategies between Z. gurneyi and its sympatric congener, Z. barberi Gurney, in central Panama.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46901/1/265_2004_Article_BF00183473.pd