A model of mate searching and territorial behaviour for “flier” type dragonflies

Abstract

First, the mating system of a “flier” odonate species that continues patrolling without perching,Cordulia aenea amurensis Selys, is briefly reviewed. Adult males of this species search for mates for a long distance along the shore of a pond if male density is very low, but localize their patrol within a short range and defend the ranges if the density is high (Ubukata 1975, 1979). Secondly, a model of mate searching by vision and territoriality for flier dragonflies is proposed. The main assumptions of the model are: (1) a male with a fixed length of visual range (D) patrols with a constant velocity (V) on a straight line; (2) he turns in the opposite direction at 2 fixed points (distance=L); (3) female arrival probability is uniform in both spatial and temporal dimensions; (4) the females stay at the arrival point for a fixed time (C); (5) if a male discovers a female he copulates with her without fail and leaves the line. From the model the following are predicted: if$D > (\sqrt 2 - 1)CV$, the species (type 1) has an optimal length of patrol range even if the female arrival rate is uniform; ifD is smaller than the right hand side of the inequality (type 2), the mating probability becomes higher as the patrol range increases, if there is no other male. On the basis of the above model the concept of an “unusurpable territory” is defined to exist at a given time after the start of patrol and the probability of unusurpability (P) is calculated as a function ofD, V, L, M (male density-1) andT (duration of patrol).P drops abruptly if the length of patrol range (L) exceeds that of unusurpable territory at high male densities. Therefore, there appears to be an optimal length of patrol range when there are other males, agreeing with the data fromC. a. amurensis. Finally, the model is discussed in comparison with some other models.