title: Some models describing the distribution of eggs of the parasitePseudeucoila bochei (Hym., Cynip.) over its hosts, larvae ofDrosophila melanogaster.
abstract: Ovipositing females of the cynipid waspPseudeucoila bochei discriminate between parasitized and unparasitized hosts, which results in a far more uniform distribution of eggs over the hosts than would be obtained if oviposition were random (Fig. 1,a0-f0).For the description of the distributions a few models were worked out, which rest on the assumption that the hosts are probed at random. The total number of effective probes made in a larva during the experiment is a random variable with a Poisson distribution and an expectation λ. The chance that at a certain probe an egg will be laid (δ) is dependent on the number of eggs present (j); 1=δ0<δ1≧δ2≧δ3.... In model I it was assumed that the female had only the ability to distinguish parasitized from unparasitized hosts. The chance that an egg will be laid in an unparasitized host when it is probed, δ0, is considered to be equal to 1, while δ1=δ2=...=δn<1 (Fig. 2, 1,a1-f1). When the mean number of eggs present in a host was larger than about 1.1, this model did not describe the distribution of eggs satisfactorily (Fig. 3).It seemed that the ovipositing female is not only able to distinguish parasitized from unparasitized hosts, but also to distinguish thenumber of eggs present in a host. In model II it was assumed that the wasp could distinguish between hosts with 0, 1, and 2 or more eggs: the chance that an egg would be laid in a host containing 2, 3, 4, ... eggs was, hence, the same in this model δ1<δ2=δ3=...=δn(Fig. 2, 1,c2,e2,f2). This model described the distributions of eggs much better (Figs. 4 and 5), but at mean numbers of eggs per host above 2 it was apparently inadequate.Two other models were then tried, in which the chance δ that an egg would be laid in a host decreased with the number of eggs already present (j). In model III (Fig. 2) the chance decreased according to the function δj=δ/j (δ0=1, δ<1). Fig. 1,d3,e3,f3, gives some examples. In model IV the chance δj=δj(δ0=1, δ<1) (see Fig. 1,d4,e4,f4).From the comparison of Figs. 6 and 7 it is clear that model IV gives the best description of the distributions of eggs found.The value of these models is discussed, and plans for both an approach through experimental analysis and simulation models are given. In an Appendix the mathematical derivation of the models is presented.
authors.affiliation: Zoological Laboratory, Department of Animal Ecology, University of Leiden, The Netherlands.|Research Institute for Nature Management, Arnhem, The Netherlands.
authors.forename: K
authors.initials: K
authors.lastname: Bakker
authors.affiliation: Zoological Laboratory, Department of Animal Ecology, University of Leiden, The Netherlands.|Research Institute for Nature Management, Arnhem, The Netherlands.
authors.forename: H J P
authors.initials: HJ
authors.lastname: Eijsackers
authors.affiliation: Zoological Laboratory, Department of Animal Ecology, University of Leiden, The Netherlands.|Research Institute for Nature Management, Arnhem, The Netherlands.
authors.forename: J C
authors.initials: JC
authors.lastname: van Lenteren
authors.affiliation: Zoological Laboratory, Department of Animal Ecology, University of Leiden, The Netherlands.|Research Institute for Nature Management, Arnhem, The Netherlands.
authors.forename: E
authors.initials: E
authors.lastname: Meelis