| Statistical Programs |
| College of Agriculture | University of Idaho |
| Seminar Announcement |
| "Applied Statistics in Agriculture" |
| Chaos and Quasiperiodicity in an Insect Population Presented By |
| Dr. Brian Dennis |
| Department of Fish and Wildlife Resources and Division of Statistics University of Idaho |
| Tuesday, November 19 3:30 P. M. Ag. Science 62 |
| Chaos is confirmed in laboratory populations of the flour beetle Tribolium. An interdisciplinary team, consisting of two population biologists, a mathematician, and myself, have designed, conducted, and analyzed experiments to study the nonlinear dynamics of population fluctuations in the flour beetle arising from interactions between the life stages. A nonlinear demographic model (system of difference equations) was used to predict the population dynamics and to establish the experimental protocol. With the adult mortality rate experimentally set high, the dynamics of animal abundance changed from equilibrium to quasiperiodic cycles to chaos as adult stage recruitment rates were experimentally manipulated. These transitions in dynamics correspond to those predicted by the mathematical model. Phase-space graphs of the data and model attractors, along with point and interval estimates of Lyapunov exponents, provide the first convincing evidence of transition to chaos in ecological populations. While the presentation will emphasize some of the unusual statistical aspects of the study, a major feature of the study was that biological experiments, mathematical modeling, and statistical analyses were thoroughly integrated. |
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