Analysis and Forecast of the <i>Zeiraphera</i> <i>griseana</i> Dynamics Using the Delayed Moran-Ricker Model: the Impact of the Training Sample on Forecast Quality

Abstract

We have applied the Moran–Ricker model with a time lag to describe the dynamics of two populations of larch bud moth. The model takes into account intrapopulation self-regulatory mechanisms. Data on populations inhabiting Switzerland in Graubunden (Baltensweiler, Fischlin, 1988; the Global Population Dynamics Database: Data set 1525) and Oberengadin (Baltensweiler, 1991) locations were used. We have found estimates of model parameter values by minimizing the sum of squared deviations of empirical and model trajectories. The point estimates of the population parameters were shown to satisfy the statistical criteria. The point estimates are located in the region of quasi-periodic oscillations, where, as a rule, they are adjacent to other dynamics modes. Consequently, the variation of population parameters caused by, for example, evolutionary processes or modifying factors influence can change the observed dynamics mode. To test the predictive properties of these models, we use the first part of the data to estimate the parameter values and the rest to compare the real dynamics with the model forecast. As it turned out, the quality of the forecast significantly depends on the nature of the dynamics at the end of the training sample used to estimate the parameters. The best prediction can be obtained if the training sample ends at the population peak phase. In the case of a low abundance phase, the forecast may have an acceptable error, but the nature of the predicted dynamics may change: for example, a shift in the population peak. For Data set 1525, we compare the point estimates obtained from a training sample of different lengths with the dynamic modes of the Moran–Riker model. This allows us to get an insight into the dynamic mode evolution in the Zeiraphera griseana population and to identify transitions from one dynamics mode to another.