Analysis of pine looper population dynamics using discrete time mathematical models

In current publication three time series of pine looper Bupalus piniarius L. (density of eggs per square meter, density of larvae per square meter and density of pupae per square meter) population dynamics are analyzed. Datasets are presented in publication by H. Klomp (1966) and can be found with free access in the Internet (The Global Population Dynamics Database, No 2727, No 2728 and No 2729). For approximation of every time series five models with discrete time (in particular, Moran–Ricker model, and discrete logistic model) were used. All five models describe the influence of self-regulative mechanisms on population dynamics only, and at the same time all models contain the minimal number of unknown parameters. Minimization of total sum of squared deviations between empirical and theoretical trajectories allowed obtaining the best estimations of model parameters. Sets of deviations between empirical and theoretical trajectories were tested for “normality” with zero average (Kolmogorov–Smirnov criteria, and Shapiro–Wilk criteria). Sequences of deviations were also tested for existence of serial correlation (Durbin–Watson criteria). Provided analysis showed that discrete logistic model is a unique model, which gives good approximation of empirical datasets. Thus, it was shown that in the situation being considered the pine looper population dynamics can be explained as a result of influence intra-population self-regulative mechanisms only.