The first step is to sample the coordinates of the research points, and to trace them out in the forest (Fig. 3). The second step is to select windfalls. In the surroundings of each research point, one windfall representing the population investigated is selected. The numbers of research points and sample windfalls depend on the accuracy of the work. It is recommended to select a sample consisting of at least CHIR-99021 ic50 50 windfalls. If there is no windfall in the surroundings of a given research point, an additional research point should be selected according to the presented procedure. After adding research points, it is

checked whether all selected windfalls are distributed randomly. To this aim, Ripley’s K-function is used (e.g. Ripley 1981). After the sample has been selected one should: (1) debark only one half-meter section and count the maternal galleries of I. typographus on each selected P. abies sample stem, (2) calculate the total density of infestation of each of P. abies sample stem by I. typographus using

an appropriate function and (3) estimate of the mean total infestation density of the stem in the area under investigation—calculate the unbiased estimator of the mean and confidence intervals using all sample stems. In SRSWOR, the unbiased estimator of the mean is (Thompson 2002): $$ \bar\barD_\textts = \frac1n\sum\limits_i = 1^n D_\textts_i $$ (5)where \( \bar\barD_\textts \) is the mean total infestation density of the windfall (stand-level); n is a number

of all windfalls in a sample; \( D_\textts_i infestation density of the windfall \( \left( \bar\barD_\textts \right) \) using a sample consisting of at least 50 windfalls, in SRSWOR, a scheme with the normal distribution is used (Cochran 1977). To compute the lower and upper limits of the confidence interval the following formulae are employed (Cochran 1977): $$ H_\textl = \bar\barD_\textts – u_1 – \alpha /2 \fracsd_\textts \sqrt n \sqrt \fracN – nN $$ (6) $$ H_\textu = \bar\barD_\textts + u_1 – \alpha /2 \fracsd_\textts \sqrt n \sqrt \fracN – nN $$ (7)where H l is the lower limit of the confidence interval; H u is the upper limit of the confidence interval; \( \Upphi \left( u_1 – \alpha /2 \right) = 1 – \alpha /2, \) for example, for \( \alpha \) equal 0.05 \( u_1 – \alpha /2 \) is 1.96, \( \Upphi \)—N(0,1), α—significance level; sd ts is the standard deviation of total infestation density of all windfalls in the sample; N is a number of all windfalls in the area investigated.