Analysis of cyclic fluctuations in larch bud moth populations with discrete-time dynamic models

Abstract

Data on the population dynamics of the larch bud moth (Zeiraphera diniana Gn.) in the Swiss Alps are analyzed. The analysis is performed with mathematical models of isolated population dynamics in discrete time (such as the Kostitzin model, Skellam model, discrete logistic model, and others), which include minimum unknown parameters. For all analyzed models, the parameters were estimated using data of the Global Population Dynamics Database (nos. 1407 and 6195) by the method of least squares, and sequences of residuals of empirical data and values predicted by model trajectories were analyzed. It is shown that the best approximations are achieved with the Moran-Ricker model and the discrete logistic model. Statistical tests (Kolmogorov-Smirnov, Shapiro-Wilk) show that normal distribution hypotheses of residuals of empirical data and model trajectories for one of the time series (no. 1407) must be rejected; some models display serial correlations in sequences of residuals (according to the Durbin-Watson test). This leads to the conclusion that periodic changes in the larch bud moth population size (no. 1407) can hardly be explained by intrapopulation regulation mechanisms alone. For the other time series (no. 6195), the modified discrete logistic model is shown to be appropriate for explaining population dynamics.