Statistical and Mathematical Ecology
(this site under construction)
The equation displayed represents the probability of extinction
of an ecological population experiencing an Allee effect at low abundances but that
otherwise would grow exponentially at higher abundances. In the equation, the (Greek) letter xi
is the extinction probability, lambda is the per-individual birth rate, mu
is the per-individual death rate, m is the initial population size, and theta
is the population size at which half the population members are
able to reproduce. The expression
turns out to be the summed tail probabilities of a negative binomial
distribution. See: Dennis, B. 1989. Allee effects:
population growth, critical density, and the chance of extinction. Natural
Resource Modeling 3:481-538.
Brian Dennis, Professor Emeritus
Department of Fish and Wildlife Sciences
And
Department of Mathematics and Statistical Science
University of Idaho, USA
Posted here are items of interest (to me at least) concerning
various topics in statistical and mathematical ecology, along with some materials
formerly posted at the now-discontinued webspace for
faculty at University of Idaho.
Comments/questions welcome. I am easy to find.
Online UI courses:
Statistical
Ecology (Wlf/Stat 5550, video course through UI
Engineering Outreach)
Course syllabus
R
Programming (Stat 4270, correspondence course through Independent Study in
Idaho)
Evidential analysis
Data cloning
Allee effects
Logistic model
Book: The R Student Companion, available here, here,
and here.
One of the most
elementary introductions to programming and the R language
for scientific/statistical computing. Examples
from real science!
Read reviews here.
New book
website with scripts, typos here (replaces
the one in the Preface).
Fun With quadratic equations
Golden
rectangle
Quick guide to probability concepts
The normal distribution