| Statistical Programs |
| College of Agricultural and Life Sciences |
University of Idaho |
| Seminar Announcement |
| "Applied Statistics in Agriculture" |
|
Logistic Model of Population Growth, Revisited
Presented By |
| Dr. Brian C. Dennis |
|
Department of Fish and Wildlife Resources and Department of Statistics University of Idaho |
| Tuesday, February 15 3:30 P. M. Ag. Science 62 |
|
The logistic model of population growth appears universally in undergraduate and
graduate ecology textbooks, yet the texts seldom regard it seriously as a scientific hypothesis. Mechanisms described
by ecologists as leading to logistic growth are vague or unclear, and statistical methods used by ecologists for connecting
the logistic to data have been primitive. With biologically plausible mechanisms to serve as hypotheses, and defensible,
realistic statistical methods for fitting and evaluating the model, the logistic could become more than just a toy used
for teaching the concept of limited growth.
In this presentation: (A) I re-examine derivations of the logistic growth model and conclude that ecologists have overlooked a variety of mechanisms that could be adequately described by logistic growth. The logistic model is the quintessential model of invasion. The fundamental idea of the logistic is "something replacing something else": vegetative cover replacing empty space, biomass replacing nutrient, infected individuals replacing uninfected ones, DVD households replacing VHS households. Biological mechanisms producing logistic growth are analogous to an autocatalytic chemical reaction converting a substrate to a product. (B) In addition, I examine a particular stochastic version of the logistic model that seems useful for data analysis. The version is a diffusion process with environmental-type noise. The equilibrium (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. With simulations, I evaluate an approximation, based on singular perturbation, for the full transition probability distribution of the process. The approximation turns out to be accurate and quite helpful for fitting the model to time series data. With the transition distribution in hand, incorporating sampling variability and estimating parameters with data cloning is straightforward. The model has the convenient property that the time intervals between observations can be unequal. Various illustrative examples are given. All interested faculty, staff, and graduate students are invited to attend. |
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