Intraspecific Competition in the Population of Danaus plexippus (L.)
We propose and analyze a model to describe the population cycles of the monarch butterfly. The annual migration of the monarch involves four generations with mixed reproductive strategies in each generation. Members of generations 1 through 3 (occasionally 4) migrate from the over-wintering site in central Mexico to breeding grounds that extend as far north as the northern United States and southern Canada. A portion of the third generation and all members of the fourth generation begin their return to the over-wintering grounds in August through October where they enter reproductive diapause for several months. We developed a discrete time model in which two different fecundity functions are used in several ways to model the reproductive strategies of each generation. The fecundity functions are selected from broad classes of functions used in ecology. The selection of the type of fecundity function used with each generation is based on biological observations. The objectives of our research are multiple and include the study of the generationally dependent intraspecific competition and its effect on the pool size of migrants as well as the persistance of the overall butterfly populations. The stage structure used in modeling the monarch butterfly dynamics and their generationally-dependent reproductive strategies naturally support fluctuating patterns and multiple attractors. The implications of these fluctuations and attractors on the long-term survival of the monarch butterfly population is explored analytically and through simulations. The impact of our work on conservation biology is discussed.
Roberto Sáenz, University of Texas at El Paso
Julie Stein, New College of Florida
Aziz Yakubu, Howard University
Laura Jones, Cornell University
Nancy Tisch, Cornell University