# Bird group math & stats help

## Contents

## 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.

## Data presentation

Advice on making graphs here (includes R code).

A link to the an index of chart colors for plotting in R here.

A list of all possible graphical parameters for plotting using R's basic graphics package here.

## Statistics in R

A short guide to making R processes parallel (to speed up processing time) here.

## Jargon

The difference between parameters and variables explained.

## Basic statistics

There's a whole bunch of statistics calculators that might be useful here.

On-line statistics handbook covering introductory stats. Includes examples/SAS code. [1] Please cite as requested.

Information on selecting between alternative statistical methods here.

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

Erdfelder, E., Faul, F., & Buchner, A. G*Power software. Free software for computing statistical power analyses. http://www.psycho.uni-duesseldorf.de/abteilungen/aap/gpower3/

Information for the USGS/NPS "Learn R" course is here (Paul Geissler's site) and here (Tom Philippi's site).

Advice on data transformations here.

A nice explanation of ROC curves here.

## Experimental design

A random (and very incomplete) collection of papers that might be useful:

- Cottingham et al. 2005. Knowing when to draw the line: designing more informative ecological experiments. Front. Ecol. Environ. 3: 145-152. (Compares use of regression vs. ANOVA.)

- Fowler, N. 1990. The 10 most common statistical errors. Bulletin of the Ecological Society of America 71: 161-164. At JSTOR here.

- Guthery, F. S. 1987. Guidelines on preparing and reviewing manuscripts based on field experiments with unreplicated treatments. Wildlife Society Bulletin 15:306

- Heffner, R. A., M. J. Butler, and C. K. Reilly. 1996. Pseudoreplication revisited. Ecology 77:2558–2562.

- Hurlbert, S. H. 1984. Pseudoreplication and the design of ecological field experiments. Ecological Monographs 54:187–211. (Read this, then read it again, then look at it annually to remind yourself ...)

- Lang, T. 2004. Twenty statistical errors even YOU can find in biomedical research articles. Croatian Medical Journal 45: 361-370. On-line here.

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

Some papers on the topic:

Johnson, J.B., and K.S. Omland. 2004. Model selection in ecology and evolution. TREE 19: 101-108.

Stephens et al. 2005. Information theory and hypothesis testing: a call for pluralism. Journal of Applied Ecology 42: 4-12. A response by Lukas et al. is here, and a rejoinder by Stephens et al. here.

Arnold, T.W. 2010. Uninformative parameters and model selection using Akaike's Information Criterion. Journal of Wildlife Management 74:1174-1178. A nice explanation of how to interpret models with delta-AIC<2 properly.

## Bayesian methods

A useful way to successfully implement negative binomial regression here.

## 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 the broader implications of PVA and less on direct implementation, is Beissinger and McCullough's Population Viability Analysis (2002) at least some of which can 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.)

- 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.)