# Chapter 5: Canonical analysis of principal coordinates (CAP)

Key references

Method: Anderson & Robinson (2003), Anderson & Willis (2003)

#### 5.1 General description

Key references Method: , CAP is a routine for performing canonical analysis of principal co...

#### 5.2 Rationale (Flea-beetles)

In some cases, we may know that there are differences among some pre-defined groups (for example,...

#### 5.3 Mechanics of CAP

Details of CAP and how it is related to other methods are provided by and . In brief, a classica...

#### 5.4 Discriminant analysis (Poor Knights Islands fish)

We will begin with an example provided by Trevor Willis and Chris Denny (; ), examining temperate...

#### 5.5 Diagnostics

How did the CAP routine choose an appropriate number of PCO axes to use for the above discriminan...

#### 5.6 Cross-validation

The procedure of pulling out one sample at a time and checking the ability of the model to correc...

#### 5.7 Test by permutation (Anderson’s irises)

CAP can be used to test for significant differences among the groups in multivariate space. The t...

#### 5.8 CAP versus PERMANOVA

It might seem confusing that both CAP and PERMANOVA can be used to test for differences among gro...

#### 5.9 Caveats on using CAP (Tikus Island corals)

When using the CAP routine, it should come as no surprise that the hypothesis (usually) is eviden...

#### 5.10 Adding new samples

A new utility of the windows-based version of the CAP routine in PERMANOVA+ is the ability to pla...

#### 5.11 Canonical correlation: single gradient (Fal estuary biota)

So far, the focus has been on hypotheses concerning groups and the use of CAP for discriminant an...

#### 5.12 Canonical correlation: multiple X’s

In some cases, interest lies in finding axes through the cloud of points so as to maximise correl...

#### 5.13 Sphericising variables

It was previously stated that CAP effectively “sphericises” the data clouds as part of the proces...

#### 5.14 CAP versus dbRDA

So, how does CAP differ from dbRDA for relating two sets of variables? First, dbRDA is directiona...

#### 5.15 Comparison of methods using SVD

The relationship between dbRDA and CAP can also be seen if we consider their formulation using si...

#### 5.16 (Hunting spiders)

A study by explored the relationships between two sets of variables: the abundances of hunting s...