Regulatory characteristics of population density dynamics of forest insects and possible reasons for the observed narrow range of such characteristics

To understand regulatory processes in insects, it is proposed here to evaluate regulatory characteristics of various populations. For this purpose, regulatory characteristics were analyzed for many time series of forest insect abundance dynamics and of area of damage to forest stands by forest insects; these characteristics reflect positive and negative feedback in populations. To describe the density dynamics of insect populations, an autoregressive (AR) model is proposed, according to which current population density is determined by its order k: population density in k preceding years. To estimate order k, partial autocorrelation functions of many time series of insect abundance dynamics were used. AR models were constructed for 33 populations of 15 species of phyllophagous insects. It was found that all the examined populations are described rather accurately (with high determination coefficients Radj2) by second-order AR models. Two characteristics of regulatory processes in a population are introduced in this work: coefficient a1 characterizes a positive relation between current population density and its density in the preceding year, and coefficient a2 reflects negative feedback between population densities in years i - 2 and i. It was demonstrated that for all the studied populations, the regulatory coefficients—regardless of a variance of population densities—vary within a relatively narrow range. To discuss reasons for the narrow range of the characteristics of regulatory processes in diverse populations, it is suggested to use indicators of their stability as an ability of a system to restore an equilibrium state that the system left under the influence of perturbing factors. For the analyzed populations, stability margins of second-order AR models were calculated, as were spectra of abundance dynamics of the time series under study. It was shown that the narrow range of regulatory characteristics for the time series of forest insects' population density can be explained by possible existence of oscillatory modes in populations.