On the estimation of the absolute population size from the distribution of captures in the MRR-experiment on the example of the fritillary butterflies of genus Boloria (Insecta, Lepidoptera, Nymphalidae)

The absolute size of an animal population is estimated from the experiments with marked specimens. Populations of butterflies are usually studied by the Jolly – Seber method, which uses the stochastic model as a mathematical basis. However, the initial data that correspond to the minimum requirements for sample size, periodicity and proportionality of captures are not always possible to obtain. In such cases, it remains to estimate the absolute number by one of the known laws of frequency distribution. In this article we consider the techniques of estimation of the absolute population size. The original samples were obtained by the mark-recapture method according to the Jolly-Seber scheme in insular local populations of fritillary butterflies of the genus Boloria. Studies were carried out in the mires Blizkoe and Osokovoe in Kivach Reserve in the summer of 1995, 1996 and 2016. In total, 261 imagos of B. freija and 3628 of B. aquilonaris were marked; the number of recaptures was 274 and 968, respectively. Poisson and geometric distributions were taken as theoretic platforms. The general task was to determine the number of individuals that were not captured based on the proportion of marked specimens in the sample. A script is proposed for calculating the absolute size and its confidence intervals for Poisson and geometric distributions as well as estimating the adequacy of empirical frequencies to theoretic models in the language R. It was established that the Poisson model assuming an equal probability of capture of any specimen is more adequate to the experimental data. The conformity of the empirical frequencies to the Poisson distribution can be considered as a measure of isolation of the population. The Poisson values of the absolute size were similar to the estimates by the Jolly – Seber model, which presumes the existence of inbound and outbound streams of individuals. It calls in question the recommendations for initial choosing certain methods for "closed" and "open" populations. The geometric model is used to describe the processes with non-constant probability of events, i. e. it should better correspond to the "open" Jolly – Seber system. But in practice this model gave highly inflated values, especially when applied to larger samples.