A theory on the temporal pattern of operational sex ratio: the active-inactive model.

A game model is presented that explains a schedule of male reproductive activity during the breeding season. The main assumptions are: reproductively active males wait for females in a 'mating arena'; females arrive when they are ready to mate; each female mates with a single mate, then leaves; all males that are reproductively active on a given day have the same chance of mating with available females; each male is not reproductively active every day, but alternates between sexually active and inactive states; active males have a higher daily mortality than inactive males; and each male chooses daily whether it will be reproductively active or inactive, thereby maximizing its lifetime mating success. The Nash equilibrium of this noncooperative differential game is solved by using dynamic programming. The number of active males each day during the season can be calculated if the female arrival schedule, mortalities of active and inactive males, and annual survivorship of males are given. The model predicts that 1) numbers of active males and fertilizable females will be correlated if the number of arrivals of fertilizable females varies among days; 2) the operational sex ratio (the ratio of reproductively active males to fertilizable females) decreases through the season; 3) the rate of decrease in the operational sex ratio during the early part of the season is the same as the mortality rate of inactive males; and 4) the operational sex ratio fluctuates during the later part of the season and increases toward the end of the season.-from Authors