Temporal variability in model coefficients: Bupalus piniarius as a case study

Abstract

Given a population dynamics model and a sufficiently long time series of data, the model parameters can be measured in different segments of this series to get respectively different estimates and a model with time-variable parameters. The variations in model parameters can be caused either by variations in the environmental conditions which affect population size, or by mere demographic stochasticity. As an example, a possible approach to the issue is considered for the data on fluctuations in the population density of pine moth (Bupalus piniarius L.) in Germany. To approximate the data, the well-known Moran-Ricker model is used, which has a rich variety of dynamic regimes. Parameter estimation was carried out by the least squares method (along 12 out of 58 values). The analysis of trends in the two series of model coefficients--the maximal growth rate and the coefficient of self-regulation--reveals that the changes in both indexes are low for quite a long period of time (60 years), and the hypothesis of no directed trends in the environment changes turns out statistically plausible.