Frequency distributions of parasites in a population of three-spined sticklebacks,Gasterosteus aculeatusL., with particular reference to the negative binomial distribution

All three species of parasites found in sticklebacks from Priddy had overdispersed distributions, similar in shape to host–parasite distributions described by other authors. The distributions of both Echinorhynchus clavula and Diplostomum gasterostei were fitted closely by the negative binomial. The values of k were similar for both species, being always less than unity; the Diplostomum distributions were more overdispersed and therefore had higher values of p . The Schistocephalus distributions were mostly described by the log normal, but the high percentage infection and relatively low overdispersion meant that the fit was often not close. There was also some truncation at the upper end. The relationship between the parameters of the negative binomial ( p and k ) and the shape and parameters of the original distribution have been investigated, both theoretically and with respect to the distributions of the stickleback parasites.In general p varied as the overdispersion and k as the percentage infection. The advantages of an overdispersed distribution to the host and parasite populations are discussed and related to the life cycles of the parasites. I am most grateful to Dr H. D. Crofton for his help and encouragement during this study, and to the staff of the Computer Unit, University of Bristol for their assistance with programming problems. This work was supported by a Science Research Council research studentship and a NATO studentship.