S. Mahunka szerk.: Folia Entomologica Hungarica 33/2. (Budapest, 1980)

g For calculating the geometric mean the following equation should be used: (i.e. the n-th root of the product of summation of the catches plus one), -where n is the data number and x is the number of individuals to be caught in each generation. The coefficient of population is able to compare the catching data of light-traps of the same type working at different measuring sites. In addition, it is useful in drawing a parallel between data measured at any generation (KISS, NOWINSZKY, SZABÓ, TÓTH and EKK, 1978), that is, a suitable tool to investigate hypercycles in time and space. In this paper we make an attempt to discover the relations of population dynamics by our coefficient of population for a species of one generation per year: the gipsy moth (Lymantria dispar L.) and, for an other species of two generation per year: the fall webworm moth (Hyphantria cunea Drury). Materials, methods and results We have used the catching data of the Institute for Forest Research (ERTI) obtained by its network (SZONTAGH, 1975). In case of the gipsy moth, we have the time series analysed through 14 years measured at two stations: Sopron and Budakeszi in Hungary. For the study of the fall webworm moth, the data ha/e been taken from four stations: Gerla, Kunfehértó, Tolna and Tompa (stations catching large 'lumber of specimens from year to year). The data of light-traps was kindly made available to us by Dr. P. SZONTAGH, senior researcher. We have calculated the geometric means from data for each measuring stations and generations, after this the coefficient of population were computed by the first equation. The results are compiled in Tables 1 to 5. In the case of the fall webworm moth (two generations per year), we have plotted the P-values of the generations separately as a function of time, later the arithmetic mean of the P-values for four stations, too (Fig. 1). After this, we have a so-called periodogram computed from data of means of the P-values averaged for each station. The latter operation has been made by a micro-electronic computer of the Gothard Astrophysical Observatory of Lóránd Eötvös University (Szombathely). We have plotted the power spectrum values as a function of period (called a periodogram), which are demonstrated in Fig. 2. (For the details of the calculation technique, programme, please send request to G. TOTH.) The periodicity of three generations and less than three are not interpreted because, they are in the neighbourhood of sampling interval, therefore, aliased and associated with noise; on the other hand, they have no significance in entomology. (The expressions: sampling interval and noice associated with others, are referred to the information theory and computer science.) The power spectrum computed from the P-values of four stations shows a periodicity of five generations. Any separately computed spectrums seem of similar nature. Having this, it is concluded that the cycle of the fall webworm moth has a periodicity of five generations. In the case of the gipsy moth we have only a single power spectrum computed from the values of coefficients of population measured and calculated at two observing stations. The results, i.e. the P-values and spectrums are illustrated in Figs. 3 and 4. The most dangerous species for oak-forests, with a tendency to gradations, the gipsy moth have an unequal period for two stations. For the two sites considered, It can be concluded, which is a support to the hypothesis of Szontágh (SZONTAGH 1975, and 1977), that: "... while in highlands and hilly countries the gradations of gipsy moths repeat each other by 8-10 years and collapse by 1 or 2 years, in our oak-forests located at lowlands especially in south-eastern part of Hungary the generations repeat by 3-5 years and the duration of this is 2-3 years." The periodogram computed from data of Sopron (highland) unambiguously shows a periodicity of 9 years. Among this appears a periodicity of 4-5 generations but, at a low level of significance. The values plotted in Fig. 3 verify this conclusion, the periodicity of 9 generations, which is very significant, coincides with the suggestions of Szontágh. The power spectrum computed from data