References on Stochastic Processes
Stephen Ellner, NIH Biocomplexity Short Course
UT Knoxville June 11-14, 2000
General
For the classical material (my first 6 lectures) I like Elementary Applications of Probability Theory by
H.C. Tuckwell (Chapman & Hall), and Introduction to Probability Models by Sheldon Ross (Academic).
The latter is very popular (currently in its 7th edition) but it slants towards engineering applications.
Tuckwell covers all the basics at half the price and gives some biological applications – though not many,
considering that he's a theoretical neurobiologist.
The best place to learn stochastic diffusion theory is Mathematical Population Genetics by W.J. Ewens
(Springer). Sadly this book has gone out of print, but it should be in any good university library.
Handbook of Stochastic Methods by C.W. Gardiner (Springer) also covers it all, but is very terse and
theoretical. Stochastic matrix models are outlined in Caswell's (1989) monograph, and presented in full
detail (for a mathematically inclined audience) in Population Dynamics in Variable Environments by S.
Tuljapurkar (Springer).
According to your orange handout Nisbet & Gurney's Modeling Fluctuating Populations (Wiley, 1982)
is "out of date", but this is rather like calling Shakespeare "obsolete" because we no longer fight with
swords. I don't know any better guide to the systematic and relentless use of approximations for
discovering the main properties of nonlinear stochastic models.
Stochastic Matrix Models and Population Viability Analysis.
Beissinger, S.R. 1995. Modeling extinction in periodic environments: everglades water levels and snail
kite population viability. Ecological Applications 5: 618-631.
Brook, B. W., O’Grady, J. J., Chapman, A. P., Burgman, M. A., Akçakaya, H. R. & Frankham, R. (2000).
Predictive accuracy of population viability analysis in conservation biology. Nature 404, 385–387.
Ellner, S., J. Fieberg, D. Ludwig, M. Mangel, C. Wilcox. 2000. How precise is population viability
analysis? Nature (submitted).
Fieberg, J. and S. Ellner. 2000. When is it meaningful to estimate an extinction probability? Ecology (in
press) [the N=(5 to 10)T rule].
Fieberg, J. and S. Ellner. 2000. Stochastic matrix models for conservation biology: a comparative review
of methods. Ecology Letters (submitted). [PMM vs SFA vs RTM, use of covariates]
Lande, R. and S.H. Orzack. 1988. Extinction dynamics of age-structured populations in a fluctuation
environment. PNAS 85:7418-7421. [diffusion approximation of stochastic matrix models]
Ludwig, D. 1998. Is it meaningful to estimate a probability of extinction? Ecology 10:298-310.
[Computes the depressingly wide confidence interavls for estimates on real data sets].