Bird group math & stats help

From EEBedia
Revision as of 16:28, 1 April 2008 by ChrisElphick (Talk | contribs) (Demographic modelling and Population viability analysis (PVA))

Jump to: navigation, search

Introduction

This page is designed to provide links to information on statistics and other mathematical topics that might be helpful to students in the bird group. Of course, others are welcome to use the site if it is helpful.

Please note that none of these materials are things that we have generated. Any credit should go to the fine people who have made their materials widely available.

Any comments/questions should be directed to Chris Elphick.

Frequentist methods

On-line software for conducting power analyses can be found here. Please cite it as requested on the web page, if you use it.

More stuff to come as we find it and find time to post it ....

Information theoretic methods

The main text book for this stuff (as it relates to ecology and wildlife biology) is Burnham and Anderson's Model selection and multimodel inference: a practical information-theoretic approach (2002, 2nd Edition).

James Peterson (USGS Coop Unit, U. Georgia) has posted some useful notes on calcuating AIC, model averaging, etc. here

Bayesian methods

Stuff to come as we find it

Demographic modelling and Population viability analysis (PVA)

Probably the best book for understanding how to do PVAs is Morris and Doak's Quantitative Conservation Biology: Theory and Practice of Population Viability Analysis (2002). All of the MATLAB code from their book is available for download here.

Another excellent book, though with more emphasis on teh broader implications of PVA and less on direct implementation is Beissinger and McCullough's Population Viability Analysis (2002) at least ome of which cna be viewed on Google books here.

Kent Holsinger has posted an excellent summary of the basics of PVA here, with explanations of Leslie Lefkovitch matrices, eigenvalues and eigenvectors, sensitivity analysis, etc.

There's a neat site here that helps you see how a Leslie matrix work.

Here's a reading list that I've used to introduce people wanting an introduction to population modeling in birds. (Links may not work unless you have journal access, e.g., via UConn libraries.)

Shaffer, M.L. 1981. Minimum Population Sizes for Species Conservation. BioScience 31: 131-134. (A good starting point for learning about the topic.)

Shaffer, M.L. and F.B. Samson. 1985. Population size and extinction: a note on determining critical population sizes. American Naturalist 125: 144-152.

Crouse et al. 1987. A Stage-Based Population Model for Loggerhead Sea Turtles and Implications for Conservation. Ecology 68: 1412-1423. (A good introduction to the use of sensitivity analysis to guide conservation decisions.)

Beissinger, S.R. 1995. Modeling Extinction in Periodic Environments: Everglades Water Levels and Snail Kite Population Viability. Ecological Applications 5: 618-631. (This paper shows how environmental variables that affect demography can be incorporated into models.)

Elderd, B.D. and M. P. Nott. 2007. Hydrology, habitat change and population demography: an individual-based model for the endangered Cape Sable seaside sparrow Ammodramus maritimus mirabilis. Journal of Applied Ecology 45: 258–268. (Useful because it is an individual-based model - also the species choice is a good one for our lab group.)

Papers from our group's work that might be useful:

Reed, J.M., C.S. Elphick, and L.W. Oring. 1998. Life-history and viability analysis of the endangered Hawaiian stilt. Biological Conservation 84:35-45. (This paper looks at sensitivity analysis in a way that accounts for the feasibility of different management actions, rather than in strictly mathematical terms.)

Ellis, M.M., and C.S. Elphick. 2007. Using a stochastic model to examine the ecological, economic and ethical consequences of population control in a charismatic invasive species: mute swans in North America. Journal of Applied Ecology 44: 312-322. (This paper looks at the ways that demographic models can look at different aspects of the both biological and societal aspects of management decisions involving non-native species.)