Description Usage Arguments Details Value Author(s) References Examples

Calculates the number of significant axes from a Principal Components Analysis based on the broken-stick criterion, or adds an equilibrium circle to an ordination diagram.

1 2 | ```
PCAsignificance(pca,axes=8)
ordiequilibriumcircle(pca,ordiplot,...)
``` |

`pca` |
Principal Components Analysis result as calculated by |

`axes` |
Number of axes to calculate results for. |

`ordiplot` |
Ordination plot created by |

`...` |
Other arguments passed to function |

These functions provide two methods of providing some information on significance for a Principal Components Analysis (PCA).

Function `PCAsignificance`

uses the broken-stick distribution to evaluate how many PCA axes are significant. This criterion is one of the most reliable to check how many axes are significant. PCA axes with larger percentages of (accumulated) variance than the broken-stick variances are significant (Legendre and Legendre, 1998).

Function `ordiequilibriumcircle`

draws an equilibirum circle to a PCA ordination diagram. Only species vectors with heads outside of the equilibrium circle significantly contribute to the ordination diagram (Legendre and Legendre, 1998). Vectors are drawn for these species. The function considers the scaling methods used by `rda`

for `scaling=1`

. The method should only be used for `scaling=1`

and PCA calculated by function `rda`

.

Function `PCAsignificance`

returns a matrix with the variances that are explained by the PCA axes and by the broken-stick criterion.

Function `ordiequilibriumcircle`

plots an equilibirum circle and returns a list with the radius and the scaling constant used by `rda`

.

Roeland Kindt (World Agroforestry Centre)

Legendre, P. & Legendre, L. (1998). Numerical Ecology. 2nd English Edition. Elsevier.

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 | ```
library(vegan)
data(dune)
Ordination.model1 <- rda(dune)
PCAsignificance(Ordination.model1)
plot1 <- ordiplot(Ordination.model1, choices=c(1,2), scaling=1)
ordiequilibriumcircle(Ordination.model1,plot1)
``` |

```
Loading required package: tcltk
Loading required package: vegan
Loading required package: permute
Loading required package: lattice
This is vegan 2.5-4
BiodiversityR 2.11-1: Use command BiodiversityRGUI() to launch the Graphical User Interface;
to see changes use BiodiversityRGUI(changeLog=TRUE, backward.compatibility.messages=TRUE)
Warning message:
no DISPLAY variable so Tk is not available
1 2 3 4
eigenvalue 24.79532 18.14662 7.629135 7.152772
percentage of variance 29.47484 21.57136 9.068950 8.502685
cumulative percentage of variance 29.47484 51.04620 60.115145 68.617831
broken-stick percentage 18.67231 13.40916 10.777577 9.023191
broken-stick cumulative % 18.67231 32.08147 42.859047 51.882238
% > bs% 1.00000 1.00000 0.000000 0.000000
cum% > bs cum% 1.00000 1.00000 1.000000 1.000000
5 6 7 8
eigenvalue 5.695027 4.333307 3.199365 2.781865
percentage of variance 6.769826 5.151114 3.803168 3.306874
cumulative percentage of variance 75.387656 80.538770 84.341937 87.648812
broken-stick percentage 7.707402 6.654770 5.777577 5.025697
broken-stick cumulative % 59.589640 66.244410 72.021987 77.047685
% > bs% 0.000000 0.000000 0.000000 0.000000
cum% > bs cum% 1.000000 1.000000 1.000000 1.000000
$radius
[1] 2.051427
$constant
[1] 6.322924
```

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