EAPSI:Developing periodic life cycles through interspecies competition

Meissen Emily P, Tucson AZ

Investigators

Abstract

Population cycles occur in many plants and animals; however the causes of these cycles are usually unknown. For example, although there are 13- and 17-year cicadas in the United States which exhibit periodic outbreaks in their populations every 13 or 17 years, cicadas in Japan are prevalent every summer and lack such periodicity. The understanding of population cycles is important to managing fisheries and crops, protecting endangered species, and dealing with species invasions and the spread of epidemics. In this research, the causes of periodic life cycles will be investigated through a model of two competing populations. When isolated, the populations do not exhibit periodic outbreaks; however, when together, the interactions between them cause both to develop periodic outbreaks similar to those of the famous 13- and 17-year cicadas found in the eastern United States. This research will be done at the University of Miyazaki in Japan with Professor Ryusuke Kon, a leading researcher of periodicity in population dynamics. The equilibria and cycles of the discrete-time matrix model and their stabilities will be determined, first through numerical exploration and then analytically. A bifurcation analysis of the system will also be done to determine dynamics' dependence on the model parameters. In addition to a basic linear stability analysis, some specific methods of analysis may include using Lyapunov functions, the Lyapunov-Schmidt reduction, and/or center-manifold theory. The dynamics of the model, particularly the stable equilibria which correspond to phenomena likely to be found in nature, will then be related to existing organisms. This NSF EAPSI award is funded in collaboration with the Japan Society for the Promotion of Science.