Books on statistical ecology?

Question

I know this question was asked before: Reference book for ecological studies but it is not what I am looking for.

What I am looking for is if anyone could recommend a good book (or a canonical reference) on statistical ecology? I have a very good understanding of statistics so the book could really be at any level. I would be using the book to teach myself more about the application of statistics in ecology than anything else so even an introductory book with good/interesting examples would be much appreciated. Also, my research tends to be geared towards Bayesian statistics so a book incorporating Bayesian statistics is even better!

Answer 1

Some good books that I would personally recommend are:

• Hilborn & Mangel (1997) The Ecological Detective: confronting models with data. Princeton University Press.

  This one is more about statistics with ecological examples, but there is nothing wrong about that. This would give a good flavour of how statistics could be used in ecology. Note the date; it won't cover some of the more recent developments or applications.

• M. Henry H. Stevens (2009) A Primer of Ecology with R. Springer.

  Perhaps too basic and not particularly on anything spatial, but it covers the various topics that we'd teach ecologists and illustrates the ecological theory and models with R code.

• B. M. Bolker (2008) Ecological Models and Data in R. Princeton University Press.

  I love this book. It covers topics you will be familiar with given your stats background but applied in an ecological context. Emphasis on fitting models and optimising them from basic principles using R code.

• James S. Clark (2007) Models for Ecological Data: an introduction. Princeton University Press.

  Don't be put off by the "introduction" in the title; this is anything but an introduction. Broad coverage, lots of theory, emphasis on fitting models by hand employing Bayesian approaches (the R lab manual companion discusses writing your own Gibbs samplers for example!)

Not a book, but I'll add this as you specifically mention your interest in Gaussian Processes. Take a look at Integrated Nested Laplace Approximation (INLA), which has a website. It is an R package and has lots of examples to play with. If you look at their FAQ you'll find several papers that describe the approach, particularly:

H. Rue, S. Martino, and N. Chopin. Approximate Bayesian inference for latent Gaussian models using integrated nested Laplace approximations (with discussion). Journal of the Royal Statistical Society, Series B, 71(2):319{392, 2009. (PDF available here).

Answer 2

Jack Weiss (may he rest in peace) was an excellent trained statistician that also really had a good grasp on ecological/environmental principles. He served as an invaluable statistics consultant to ecological/environmental scientists throughout the US and even globally.

Although he doesn't have any books that I'm aware of, his course notes are still available online:

1. Statistical Methods in Ecology [or a 2012 version]

   Course Descrition: This is a course in statistical modeling for ecologists and their kin. We focus on elementary statistical methods, primarily regression, and describe how they can be extended to make them more appropriate for analyzing ecological data. These extensions include using more realistic probability models (beyond the normal distribution) and accounting for situations in which observations are not statistically independent. For each model we consider we will see how to estimate it using both frequentist (when possible) and Bayesian methods. Our emphasis here is on depth rather than breadth. (The other graduate course that I teach, ECOL 562, is a survey course that covers a wide range of statistical methods useful in environmental science. This course focuses on 40% of the material from that course but covers it in greater depth.)

   Familiarity with the standard parametric approaches of statistical analysis such as hypothesis testing is assumed. The course is intended to serve as a transition between what is typically taught in an undergraduate statistics course and what is actually needed to successfully analyze data in ecology and environmental sciences. The ideal enrollee is an upper level undergraduate or beginning graduate student who has already taken an introductory statistics course and wishes to see the modern application of statistics to environmental science and ecology. Topics include:

   - Basic concepts in regression: categorical predictors and interactions
   - Statistical distributions important in ecological modeling: binomial, Poisson, negative binomial, normal, lognormal, gamma
   - Likelihood theory and its applications in regression
   - Bayesian approaches to model fitting
   - Model selection protocols: Information-theoretic alternatives to significance testing
   - Generalized linear models: Poisson regression, negative binomial regression, logistic regression, gamma regression
   - Mixed effects models for analyzing temporally and spatially correlated data
     - Random intercepts and slopes models
     - Multilevel models with 2 and 3 levels
     - Hierarchical Bayesian modeling
     - Nonlinear mixed effects models
     - Mixed effects models with nested and crossed random effects
     - Hybrid mixed effects models with multivariate responses
   

2. Statistics for Environmental Science [or a 2007;2012 version]

   Course Descrition: An introduction to statistical methods for ecology and environmental science. This is a topics course. Our emphasis here is on breadth rather than depth. (The other graduate course I teach takes an in-depth approach to the topics covered in the first third of this course.) Familiarity with the standard parametric approaches of statistical analysis such as hypothesis testing is assumed. The course is intended to serve as a transition between what is typically taught in an undergraduate statistics course and what is actually needed to successfully analyze data in ecology and environmental sciences. The ideal enrollee is an upper level undergraduate or beginning graduate student who has already taken an introductory statistics course and wishes to see the modern application of statistics to environmental science and ecology. Topics include:

   - Overview of regression
   - Likelihood theory and its applications in regression
   - Generalized linear models
   - Analysis of temporally correlated data
   - Mixed effects models
   - Generalized estimating equations
   - Bayesian methods
   - Generalized additive models
   - Survey sampling methods
   - Machine learning methods
   - Survival analysis
   - Contingency table analysis
   - Analysis of extreme values
   - Structural equation models
   

3. Statistics for Ecology & Evolution

   Course Description: This is a course in statistical modeling for ecologists and their kin. We focus on elementary statistical methods, primarily regression, and describe how they can be extended to make them more appropriate for analyzing ecological data. These extensions include using more realistic probability models (beyond the normal distribution) and accounting for situations in which observations are not statistically independent. Topics include:

   - Experiments in ecology
   - Statistical distributions important in ecological modeling: binomial, Poisson, negative binomial, normal, lognormal, gamma, and exponential
   - Likelihood theory and its applications in regression
   - Bayesian approaches to model fitting
   - Model selection protocols: Information-theoretic alternatives to significance testing
   - Generalized linear models: Poisson regression, negative binomial regression, logistic regression, and others
   - Regression models for temporally and spatially correlated data: random coefficient models (multilevel models) and hierarchical Bayesian modeling
   

4. Ecology 145—Statistical Analysis

   ECOL 145 is intended to be an intense introduction to the analysis of ecological data. Its target audience consists of highly motivated graduate students and upper level undergraduates in biologically-related disciplines who ideally have data of their own to analyze. This is a serious, hands-on course not suitable for dilettantes or those who wish to merely audit and observe. We focus on the use of two modern statistical packages, R and WinBUGS, and use them to tackle real data sets with all their foibles. The closer you are to carrying out your own research and analyzing your own data the more useful this course should turn out to be.

   The perspective of the course is that probability models are best thought of as data-generating mechanisms and in keeping with this viewpoint we use likelihood-based methods to directly model ecological data. Data sets are from the published literature, from my own consulting projects, or are supplied by students who are enrolled in the course. If you have data you need to get analyzed you are welcome to submit it to me for use in class exercises. Topics include:

   - Statistical distributions important in ecological modeling: binomial, Poisson, negative binomial, normal, lognormal, gamma, and exponential
   - Likelihood theory and its applications in regression
   - Generalized linear models: Poisson regression, negative binomial regression, logistic regression, and others
   - The perils of significance testing—multiple comparison adjustments and the false discovery rate
   - Model selection protocols: likelihood ratio tests, Wald tests, and information-theoretic alternatives to significance testing
   - Goodness of fit for GLMs: deviance statistics, extensions of R2, Pearson chi-square approaches
   - Regression models for temporally and spatially correlated data: random coefficient models (multilevel models) and the method of generalized estimating equations
   - Bayesian approaches to data analysis
   - Hierarchical Bayesian modeling using WinBUGS and R
   

I'm sure there is a ton of overlap between courses, but his notes (and R code) are available for each of these courses and should prove to be very useful to most people visiting this post.

Answer 3

Some good ecology books based in Bayesian statistics are:

Kery, M. 2010. Introduction to WinBUGS for Ecologists: Bayesian approach to regression, ANOVA, mixed models and related analyses. Academic Press.

Kery, M., and M. Schaub. 2011. Bayesian Population Analysis using WinBUGS: A hierarchical perspective. Academic Press.

Royle, J.A. and R.M. Dorazio. 2008. Hierarchical Modeling and Inference in Ecology: The Analysis of Data from Populations, Metapopulations, and Communities. Academic Press

I also find Zuur et al. (2009) very useful.

Zuur, A., E. N. Ieno, N. Walker, A. A. Saveliey, and G. M. Smith. Mixed Effects Models and Extensions in Ecology with R. Springer.