A class of distributions applicable to the description of the number of nematodes parasitizing birds.

We define the class of bivariate binomial distributions as Poisson distributions transformed by a binomial dilution and mixing with a gamma distribution. They are used to study the number of nematodes, considering the sex ratio, parasitizing birds.

Estimation of distribution parameters of some avian parasites.

Occurrence of nematodes (mostly dominating and common species of Porrocaecum ensicaudatum and P. semiteres) in host populations of birds (Turdus merula, T. philomelos, Sturnus vulgaris and Scolopax rusticola) was summarized in frequency distributions, and tests of agreement with the Poisson model as well as the modified binomial have been computed. Comparisons of the observed frequencies with the expected ones showed the high values (3--257) of the coefficient of dispersion, the so-called "overdispersion", characteristic for the negative binomial which is an extension of the Poisson model. A nearly perfect fitness of the counted (observed) with the expected frequencies was found for S. vulgaris both in the analysis of nematode metapopulation and their common species of P. ensicaudatum. Some deviations from the expectations were found for tracing of all nematode species distributions in T. merula, T. philomelos. On the other hand, the same model (negative binomial distribution according to moment method) has fitted quite well to each for common or dominating nematode species.

Population dynamics in the co-culture of Shigella flexneri 1b original strain and its antigenic 3b mutant carrying a prophage.

The antigenic mutant Shigella flexneri 3b showed selective prevalence when subcultured with the original strain 1b. Mathematical analysis of such co-cultures showed that the dynamics of bacterial growth may be described by equations of the Lotka-Volterra type. The analysis of serial cultivations suggests that parameters of the equations may be realizations of random variables characterizing strains and media. The mutant carries a prophage lethal for the original strain. Distinctive features of the growth of these strains alone and in co-culture may be successfully explained by the differences in growth parameters, without phage inference. The concurrence model connected only with the existence of the phage is not sufficient. A complete description of the dynamics of the co-culture is obtained by the connection of the assumptions of two models: strains in competition and growth of strains with phage, given the random character of the parameters.