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
6 - Similarity measures and distance-based methods
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 many multivariate methods, one of the first steps is to calculate a matrix of similarities (resemblance measures) either between the cases or between the variables. Although this step is not explicitly done in all the methods, in fact each of the multivariate methods works (even if implicitly) with some similarity measure. The linear ordination methods can be related to several variants of Euclidean distance, while the unimodal (weighted averaging) ordination methods can be related to chi-square distances. The resemblance functions are reviewed in many texts (e.g. Orloci 1978; Gower & Legendre 1986; Ludwig & Reynolds 1988; Legendre & Legendre 2012), so here we will introduce only the most important ones.
In this chapter, we will use the following notation: we have n cases (e.g. relevés), containing m response variables (e.g. species). Yik represents the value (abundance) of the k-th variable (k = 1, 2,…, m) in the i-th case (i= 1, 2,…, n). In this chapter, we will also refer to (response) variables of the analysed data table as species, to reflect the common nature of data and increase the readability of the text.
- Type
- Chapter
- Information
- Multivariate Analysis of Ecological Data using CANOCO 5 , pp. 92 - 111Publisher: Cambridge University PressPrint publication year: 2014