[Analysis of cyclic fluctuations in larch bud moth populations by means of discrete-time dynamic models]

Analysed are the data of larch bud moth (Zeiraphera diniana Gn.) fluctuations in Swiss Alps. The analysis applies simplest mathematical models of isolated population dynamics (in particular, Kostitzin model, Skellam model, the discrete logistic model, and some other ones), which include the minimal number of unknown parameters. The parameters have been estimated, for all the models in hand, by the least-squares method, to fit certain data from the Global Population Dynamics Database (N 1407 and N 6195), the sequences of the data deviations from the model trajectories being treated as well. The best approximations are shown to be achieved with Moran-Ricker model and the discrete logistic model. Statistical criteria (Kolmogorov-Smirnov and Shapiro-Wilk tests) reveal that the hypotheses of normal distribution of residuals must be rejected for one of the time series (N 1407); some models demonstrate serial correlations in the sequence of residuals (according to Durbin-Watson test). This leads to the conclusion that periodic fluctuations in the larch bud moth population (N 1407) can hardly be explained by self-regulation mechanisms alone. For another time series (N 6195), the modified discrete logistic model has appeared to be acceptable as a mode of fluctuations.