Book contents
- Frontmatter
- Contents
- Preface
- 1 Introduction and data types
- 2 Using Canoco 5
- 3 Experimental design
- 4 Basics of gradient analysis
- 5 Permutation tests and variation partitioning
- 6 Similarity measures and distance-based methods
- 7 Classification methods
- 8 Regression methods
- 9 Interpreting community composition with functional traits
- 10 Advanced use of ordination
- 11 Visualising multivariate data
- 12 Case study 1: Variation in forest bird assemblages
- 13 Case study 2: Search for community composition patterns and their environmental correlates: vegetation of spring meadows
- 14 Case study 3: Separating the effects of explanatory variables
- 15 Case study 4: Evaluation of experiments in randomised complete blocks
- 16 Case study 5: Analysis of repeated observations of species composition from a factorial experiment
- 17 Case study 6: Hierarchical analysis of crayfish community variation
- 18 Case study 7: Analysis of taxonomic data with discriminant analysis and distance-based ordination
- 19 Case study 8: Separating effects of space and environment on oribatid community with PCNM
- 20 Case study 9: Performing linear regression with redundancy analysis
- Appendix A Glossary
- Appendix B Sample data sets and projects
- Appendix C Access to Canoco and overview of other software
- Appendix D Working with R
- References
- Index to useful tasks in Canoco 5
- Subject index
5 - Permutation tests and variation partitioning
Published online by Cambridge University Press: 05 May 2014
- Frontmatter
- Contents
- Preface
- 1 Introduction and data types
- 2 Using Canoco 5
- 3 Experimental design
- 4 Basics of gradient analysis
- 5 Permutation tests and variation partitioning
- 6 Similarity measures and distance-based methods
- 7 Classification methods
- 8 Regression methods
- 9 Interpreting community composition with functional traits
- 10 Advanced use of ordination
- 11 Visualising multivariate data
- 12 Case study 1: Variation in forest bird assemblages
- 13 Case study 2: Search for community composition patterns and their environmental correlates: vegetation of spring meadows
- 14 Case study 3: Separating the effects of explanatory variables
- 15 Case study 4: Evaluation of experiments in randomised complete blocks
- 16 Case study 5: Analysis of repeated observations of species composition from a factorial experiment
- 17 Case study 6: Hierarchical analysis of crayfish community variation
- 18 Case study 7: Analysis of taxonomic data with discriminant analysis and distance-based ordination
- 19 Case study 8: Separating effects of space and environment on oribatid community with PCNM
- 20 Case study 9: Performing linear regression with redundancy analysis
- Appendix A Glossary
- Appendix B Sample data sets and projects
- Appendix C Access to Canoco and overview of other software
- Appendix D Working with R
- References
- Index to useful tasks in Canoco 5
- Subject index
Summary
In this chapter, we discuss testing hypotheses in a constrained ordination using the Monte Carlo permutation test and two related issues: stepwise selection of a set of explanatory variables and the variation partitioning procedure.
Permutation tests: the philosophy
Canoco has the ability to test the significance of constrained ordination models described in the preceding section, using Monte Carlo permutation tests. These statistical tests relate to a general null hypothesis, stating the independence of the response data (such as community composition) on the values of the explanatory variables (for example environmental factors or human impact). The principles of the permutation test were introduced in Sections 4.11 and 4.12, in an example of testing a regression model and using the simplest possible type of permutation, i.e. completely random permutation.
The null model of the independence between the corresponding rows of the response data table and of the explanatory data table (the rows referring to the same set of cases in both tables) is the basis for the permutation test in Canoco. While the actual algorithm used in Canoco does not employ exactly the approach described here, we use it to better illustrate the meaning of the permutation test.
- Type
- Chapter
- Information
- Multivariate Analysis of Ecological Data using CANOCO 5 , pp. 71 - 91Publisher: Cambridge University PressPrint publication year: 2014