Description Usage Arguments Details Value Author(s) References Examples

This function provides a method for CAP that follows the procedure as described by the authors of the ordination method (Anderson & Willis 2003). The CAP method implemented in vegan through `capscale`

conforms more to distance-based Redundancy Analysis (Legendre & Anderson, 1999) than to the original description for CAP (Anderson & Willis, 2003 ).

1 | ```
CAPdiscrim(formula, data, dist="bray", axes=4, m=0, mmax=10, add=FALSE, permutations=0)
``` |

`formula` |
Formula with a community data frame (with sites as rows, species as columns and species abundance as cell values) or distance matrix on the left-hand side and a categorical variable on the right-hand side (only the first explanatory variable will be used). |

`data` |
Environmental data set. |

`dist` |
Method for calculating ecological distance with function |

`axes` |
Number of PCoA axes ( |

`m` |
Number of PCoA axes to be investigated by discriminant analysis ( |

`mmax` |
The maximum number of PCoA axes considered when searching (m=0) for the number of axes that provide the best classification success. |

`add` |
Add a constant to the non-diagonal dissimilarities such that the modified dissimilarities are Euclidean; see also |

`permutations` |
The number of permutations for significance testing. |

This function provides a method of Constrained Analysis of Principal Coordinates (CAP) that follows the description of the method by the developers of the method, Anderson and Willis. The method investigates the results of a Principal Coordinates Analysis (function `cmdscale`

) with linear discriminant analysis (`lda`

). Anderson and Willis advocate to use the number of principal coordinate axes that result in the best prediction of group identities of the sites.

Results may be different than those obtained in the PRIMER-e package because PRIMER-e does not consider prior probabilities, does not standardize PCOA axes by their eigenvalues and applies an additional spherical standardization to a common within-group variance/covariance matrix.

For permutations > 0, the analysis is repeated by randomising the observations of the environmental data set. The significance is estimated by dividing the number of times the randomisation generated a larger percentage of correct predictions.

The function returns an object with information on CAP based on discriminant analysis. The object contains following elements:

`PCoA` |
the positions of the sites as fitted by PCoA |

`m` |
the number of axes analysed by discriminant analysis |

`tot` |
the total variance (sum of all eigenvalues of PCoA) |

`varm` |
the variance of the m axes that were investigated |

`group` |
the original group of the sites |

`CV` |
the predicted group for the sites by discriminant analysis |

`percent` |
the percentage of correct predictions |

`percent.level` |
the percentage of correct predictions for different factor levels |

`x` |
the positions of the sites provided by the discriminant analysis |

`F` |
the squares of the singulare values of the discriminant analysis |

`manova` |
the results for MANOVA with the same grouping variable |

`signi` |
the significance of the percentage of correct predictions |

`manova` |
a summary of the observed randomised prediction percentages |

The object can be plotted with `ordiplot`

, and species scores can be added by `add.spec.scores`

.

Roeland Kindt (World Agroforestry Centre)

Legendre, P. & Anderson, M.J. (1999). Distance-based redundancy analysis: testing multispecies responses in multifactorial ecological experiments. Ecological Monographs 69: 1-24.

Anderson, M.J. & Willis, T.J. (2003). Canonical analysis of principal coordinates: a useful method of constrained ordination for ecology. Ecology 84: 511-525.

Kindt, R. & Coe, R. (2005) Tree diversity analysis: A manual and software for common statistical methods for ecological and biodiversity studies.

https://www.worldagroforestry.org/output/tree-diversity-analysis

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | ```
library(vegan)
library(MASS)
data(dune)
data(dune.env)
Ordination.model1 <- CAPdiscrim(dune~Management, data=dune.env,
dist="bray", axes=2, m=0, add=FALSE)
Ordination.model1
plot1 <- ordiplot(Ordination.model1, type="none")
ordisymbol(plot1, dune.env, "Management", legend=TRUE)
# plot change in classification success against m
plot(seq(1:14), rep(-1000, 14), xlim=c(1, 14), ylim=c(0, 100), xlab="m",
ylab="classification success (percent)", type="n")
for (mseq in 1:14) {
CAPdiscrim.result <- CAPdiscrim(dune~Management, data=dune.env,
dist="bray", axes=2, m=mseq)
points(mseq, CAPdiscrim.result$percent)
}
#
``` |

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