| Statistical Programs |
| College of Agriculture and Life Sciences |
University of Idaho |
| Seminar Announcement |
| "Applied Statistics in Agriculture" |
|
Properties of a Stochastic Logistic Equation
Presented By |
| Dr. Brian C. Dennis |
|
Department of Fish and Wildlife Resources and Department of Statistics University of Idaho |
| Tuesday, November 9 3:30 P. M. Ag. Science 62 |
|
The logistic population growth equation appears in virtually every ecology textbook. Yet,
it has the reputation of being a "toy model" intended as a simple teaching concept, but not intended for describing real
population systems. In this presentation, I argue that adding one ingredient --stochasticity-- transforms the model into a
frequently useful data analysis tool. The resulting model, of logistic growth with environmental-type noise, is a stochastic process known as a diffusion process. The concept of carrying capacity is no longer a point equilibrium, but rather is a gamma probability distribution. Many statistical properties of the model can be derived as formulas. I explore various approximation schemes for the full time-dependent probability distribution of the process; the schemes are helpful for fitting the model to time series data. Various examples that use the model for statistical analysis of population time series are developed. |
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