Behav Ecol Sociobiol (1994) 35:161-168 © Springer-Verlag 1994 Bo G. Svensson • Erik Petersson Mate choice tactics and swarm size: a model and a test in a dance fly Received: 1 February 1994 / Accepted after revision: 25 June 1994 Abstract In the dance fly Empis borealis (L.) (Diptera: Empididae) females gather to swarm and males visit swarms for mating. A model was constructed, based On previously published data, simulating how males may choose among females of different sizes in swarms of different sizes. The focal question was, what influences the number of individuals in the swarm in this and pos- sibly other swarming insects ? The relationships between original swarm size and both the number of males arriv- ing per minute and the proportion of males mating are both logarithmic. The model predicted that if these rela- tionships were linear, or if males were able to judge ab- solute female size, the mean swarm size should increase and be at least four times as large as those found in the field. The only type of male mate choice strategy that gave rise to very large swarms (> 25) was size-related choice (if males are able to assess the size of a female in relation to the entire population and not merely to the swarm). Furthermore, no swarming behaviour would occur if males mate independently of swarm size. Thus, the numbers of females attending a given swarm site are influenced by male arrival pattern, male preference for larger swarms, the inability of males to judge the abso- lute body size of females, and female polyandry. Males searching for mates seem to prefer larger swarms than females searching for a swarm to join, but the mean swarm size is primarily set by the swarm size preference of females. Optimal swarm size predicted from the mod- el was 4.68 +0.53 females. In order to test model predic- tions, 69 natural swarm sites were studied during one season. The mean swarm size was 4.85_+4.54 females (median 4.03), and about 90% of swarms consisted of 11 females or fewer. Predicted and observed swarm size did not differ significantly. Key words Mate choice - Swarm size • Model Dance fly - Empis borealis B.G. Svensson ([~) • E. Petersson Department of Zoology, Uppsala University, Villav/igen 9, S-752 36 Uppsala, Sweden Introduction Animal mating systems in which members of one sex, usually males, aggregate at certain sites include exam- ples from several taxa such as anuran choruses, avian and mammalian leks, and insect swarms. The number of individuals aggregating varies greatly between, and to a lesser extent within, species. For example, some insect swarms may consist of thousands of individuals, but in other species less than a dozen individuals might be present (Downes 1969; Sullivan 1981; Petersson 1987). Bird leks may be comprised of a few up to hundreds of individuals (Alatalo et al. 1992; Beehler 1987; Bradbury et al. 1989; H6glund and Robertson 1990). Factors that control the number of individuals displaying at the mat- ing aggregation sites are rarely discussed (Parker 1978). In the sage grouse (Centrocercus urophasianus), Brad- bury et al. (1989) evaluated some of the factors con- trolling the numbers of males on different leks. They found that about one third of the daily variation in number of lekking males could be explained by weather variables, female attendance levels, and prior distur- bance by predators. By modelling lek size, Gibson et al. (1990) evaluated the formation of male mating aggrega- tions under female choice. They suggested that males formed clumped distributions if females expressed strong preference either for larger leks or male quality. On the other hand, high travelling costs for females vis- iting leks and high costs to females waiting for mating tended to produce male dispersion. In the midge Chi- ronomus plumosus, the swarm size seems to be set by the opposing effects of predation risk and mating probabili- ty, which are both greatest in small swarms (Neems et al. 1992). Thus, a variety of factors may influence the for- mation of mating aggregations and the number of dis- playing individuals at each aggregation. In the dance fly Empis borealis females gather to swarm and males visit swarms for mating. What con- trols the number of swarming females in this spe- cies? In this paper we answer this question by using previously published data (Svensson and Petersson