It is traditionally accepted that parasitic infections in host populations are aggregative and the negative binomial distribution (NBD) provides the most adequate fit to (Crofton, 1971a, b; Breev, 1972; Anderson and May, 1978; Behnke et al., 1999; Ribas and Casanova, 2005; Stear et al., 2007; Brunner and Ostfeld, 2008). Based on the analysis of occurrence of the different parasite species in hosts a mathematical model of host-parasite relationships, based on the NBD has been constructed (Pavlov, Ieshko, 1986). The model is based on the fact known in probability theory, fact that the NBI can be represented as the mixed Poisson distribution with a random variable having a Gamma distribution. This model assumed that parasite survival is modeled by a Poisson regression model, whereas host resistance obeys the Gamma Probability Law.
«Potato cyst nematode Globodera rostochiensis – potato Solanum tuberosum» host-parasite system is a convenient model for experimental study of host-parasite interactions. In this study an attempt has been made to evaluate the influence of varietal characteristics of potato on infection with G. rostochiensis. Experiments were conducted on susceptible (3 cvs) and resistant (mass reproduction tubers, and elite tubers) to G. rostochiensis potato varieties. The same dosage (10 cysts) was applied in all treatments. Significant differences in the response of potato varieties to infestation were found. The highest and lowest nematode infection rates were found in var. Nevsky and Sudarynya, correspondingly. With the growth of plant resistance to the infection there was observed apparent decreases in the range of numbers variability, variance, and mean values.
For the susceptible potato varieties nematode abundance was modeled by the Gamma Probability Law. For the resistant varieties of the distribution of nematodes corresponded to the NBD. These findings have shown the adequacy of the parasite abundance model proposed by Pavlov and Ieshko (1986) and the prospects of its use for the evaluation of the effectiveness of potato breeding work.
Research was supported by Russian Ministry of Education (№ P 1299).