An Autoregulatory Model of Forest Insect Population Dynamics and Forest Stand Damage Dynamics in Different Habitats: An Example of Lymantria dispar L.

Abstract

This paper addresses the problem of constructing a mathematical model of population density dynamics and the dynamics of forest areas damaged by spongy moth (Lymantria dispar L.) outbreaks in the United States, Europe, Russia, and Japan. The key variable of the model is either the pest population density or the area of forests damaged by spongy moths during a season. This variable can be considered proportional to the total current pest abundance in the study area. For the purposes of modeling, data from a number of different authors was used (see bibliography), as well as data from surveys conducted at the egg or caterpillar stage. The complexity of modeling the dynamics of L. dispar abundance is largely due to the fact that, when studying the dynamics of spongy moth population density, the values of external factors such as parasites, predators, and the amount of available food are often unknown. A simple model was proposed using only two types of data: population density and monthly weather characteristics. Our analysis demonstrated that, even in the absence of knowledge regarding the characteristics of ecosystem components interacting with the spongy moth population (parasites, predators, and the state of forage trees), it is possible to introduce models that characterize the regulatory processes in the population in terms of (i) the presence of negative and positive feedbacks in the system and (ii) the influence of external weather factors. The system under investigation was described as an autoregressive system, whereby the current state of the population is dependent on its state in previous years. The order of autoregression in the system was estimated using the order of the maximum significant partial autocorrelation function. It was found that the regulation of spongy moth population density was characterized by the presence of two feedback loops: positive feedback between the current population density and the population density in the previous season and negative feedback between the current population density and the population density two years ago. To evaluate the model, its stability margin was calculated and found to be directly proportional to the positive feedback coefficient and inversely proportional to the negative feedback coefficient. The model was demonstrated to explain up to 90% of the observed variance of real data. Although the model coefficients for different local populations (North America, Europe, and Asia) differ, the general form of the equation describing both direct data on population densities and indirect data on pest dynamics characterized by areas of stand damage is consistent. Consequently, the form of the ADL model is general, irrespective of the location of the local population.