# [R] Inconsistent results between CAP (capscale) and RDA

Janssen Philippe philippe.janssen at irstea.fr
Tue Apr 28 17:04:17 CEST 2015

```Hello everyone,

I have inconsistent results using vegan's capscale() and rda() on a hellinger distance matrix, based on presence/absence data matrix of 192 plants species (columns) x 70 sites (rows).

HellingerFloreDist <-dist(decostand(flore[12:204], method="hellinger"))

I first wanted to perform a Canonical Analysis of Principal coordinates (CAP) using capscale() function. However, based on Jari Oksanen comment, i.e. "Constrained Analysis of Principal Coordinates (CAP) is an ordination method similar to Redundancy Analysis (rda)... If called with Euclidean distance, the results are identical to rda, but capscale will be much more inefficient.", I decided to perform RDA using rda().

###CAP analysis

CAP<-capscale(HellingerFloreDist~ancien+mature+interact, data=data)

anova(CAP) #Test of the significance of the analysis

anova(CAP, by="axis", perm.max=999) #test axes for significance

anova(CAP, by="terms", permu=999) #test environment variables for significance

summary(CAP)

###RDA analysis

RDA<-rda(flore.hellinger~ancien+mature+interact, data=data)

plot(RDA)

anova(RDA) #Test of the significance of the analysis

anova(RDA, by="axis", perm.max=999) #test axes for significance

anova(RDA, by="terms", permu=999) #test environment variables for significance

summary(RDA)

However, I was quite surprised by the results, i.e. the difference between the total inertia of CAP and RDA.

Results from CAP (capscale) :

Partitioning of squared Euclidean distance:
Inertia Proportion
Total          35.957    1.00000
Constrained     2.052    0.05706
Unconstrained  33.905    0.94294

Results from RDA :

Partitioning of variance:
Inertia Proportion
Total          1.5384    1.00000
Constrained    0.1096    0.07124
Unconstrained  1.4289    0.92876

Searching all day long for an explanation, I still don't understand those results.

Any explanation would be greatly appreciated.

Philippe JANSSEN

Doctorant - UR Ecosystèmes Montagnards

Irstea - Centre de Grenoble

+33 (0)4 76 76 28 79

Philippe.janssen @irstea.fr

www.irstea.fr <http://www.irstea.fr/>

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