I am an ecology student and have to deal with 10 or 20 field variables, including species frequencies. I need to screen out what variables are most important in the occurrence of a bird species. What book would tell me the methods to do this?
No book is going to tell you which variable to include and which to exclude. You should have done necessary background research before doing your fieldwork to get an idea of which variables to measure. You could have based those variables on the species life history and/or previous research. Once variables were selected, it is good practice to do a lot of hard thinking about the ecology of the species and develop some a priori models.
Are you trying to model the probability of occurrence for a species? Often researchers assume that a species will be detected if it is at a site. However, detection is never certain. Therefore, we can’t assume detection, non-detection data represent presence-absence data. Further, this imperfect detectability problem also imposes constrains on count data as well. Fortunately, there are all sorts of survey techniques that allow us to collect data that can be used to model and correct for the incomplete detection problem.
There are a new set of techniques based in hierarchical modeling that allow one to untangle the detection process from the occurrence/abundance process. Basically, these models use ancillary data (i.e., distance from transect, time to detection, etc.) or information from repeated surveys (i.e., a series of detection, non-detection or count frequency data at each survey site) to model the detection process. These models provide a framework for modeling both the detection process and the intensity of abundance or occupancy as a latent variable. One of the greatest advantages of the hierarchical modeling framework is the ability to separately model the abundance and detection processes. This allows the effects of a given covariate, on either process, to be disentangled. These techniques result in spatially-explicit models of abundance or occurrence. Such models are attractive because they can be used to understand ecological relationships among animal abundance or occurrence and environmental conditions while accounting for imperfect detection. For species management or conservation purposes, spatially-explicit models of abudance or occurrence can be very valuable. The naive approach is to ignore the problem of incomplete detection and potentially draw wrong inferences about the species' ecological relationships to environmental conditions.
For multivariate techniques and many examples on Ecology you can have a look at:
You can run all procedures on r, but also a nice software for multivariate analysis is CANOCO is one of the most popular tools in statistical modelling of ecological data
The best books for approaching model selection issues like this are by Zuur et al:
- #1) Analyzing ecological data (Zuur et al 2007)
- #2) Mixed models and extension in R (Zuur et al 2009)
Book #1 Contains many case studies, including some on birds, and discusses choosing an appropriate model, model selection with AIC and AICc, and model validation. Book #2 Focuses on mixed models and includes R code for every step in the analyses shown.
Both of these books highlight the importance of choosing an appropriate model - eg, poisson, "quasi-poisson", or negative binomial -- if your response variable is a count, as is often the case with wildlife data. They also address the issue of overdispersion, a major issue with many ecological datasets.
As noted in other responses, key methodologically and philosophically to using AIC is to approach the data with a priori hypotheses that are motivated by the biology of the system and your analysis goals. The bible for AIC is: Model Selection and Multi-Model Inference: A Practical Information-Theoretic Approach by Burnham and Anderson.
A gentler introduction is: Model Based Inference in the Life Sciences: A Primer on Evidence by Anderson. Many of his AIC papers are available on his website.
If you're dealing with count data as your response variable some important papers to look at are:
- "Do not log‐transform count data" (O'Hara and Kotze 2010)
- "Quasi-poisson vs. negative binomial regression: How should we model overdispersed count data?" (JM Ver Hoef and PL Boveng 2007).
- "Why do we still use stepwise modeling in ecology and behavior" (WHITTINGHAM et al 2006)
- "Model selection in ecology and evolution" (Johnson and Omland 2004)
- The journal Behavioral Ecology and Sociobiology recently ran a special issue on using AIC methods.
PDFs of most of these papers can be found online via Google Scholar.
Models such as these don't usually come off-the-shelf. There are general techniques, but you have to adapt them to your use case, and that means you have to get familiar with modeling. The other answers are excellent; for a take on these issues from the Bayesian perspective, see:
- Marc Kery's Introduction to WinBUGS for Ecologists
- Marc Kery's Bayesian Population Analysis
- McCarthy's Bayesian Methods for Ecology
- King et al's Bayesian Analysis for Population Ecology
Kery's first book is an really good introduction.