A PRELIMINARY MATHEMATICAL-MODEL OF THE APPLE TWIG BORER (COLEOPTERA, BOSTRICHIDAE) AND GRAPES ON THE TEXAS HIGH-PLAINS

The apple twig borer, Amphicerus bicaudatus (Say), has a major economic impact on the developing vineyard industry of the Texas High Plains. The life history of this insect has been studied and the potential damage caused by beetles has been calculated. From these data a mathematical model of the interaction of the apple twig borer (ATB) and grape vines has been produced. The model assumes three periods during the year which account for major changes in the ATB-grape vine system. A simple model is presented in which specific functional forms for the relationships between the population densities of ATBs and grape vines are given. Numerical solutions of the model are presented and reflect vineyard practices regarding the removal of pruned canes. The results are discussed in terms of the qualitative behavior of the system.