Phylogenetic PCA for morphological traits

Data

\(n = 18\) lizard species, \(p = 8\) morphological traits, a phylogenetic tree \(T\).

• $ Y_{ij} =$ value of trait \(j\) for species \(i\).
• $ _{ij} = $ scaled trait \(j\) for species \(i\).

Traits :

• mean.L (mean length (mm)),
• matur.L (length at maturity (mm)),
• max.L (maximum length (mm)),
• hatch.L (hatchling length (mm) = ‘à l’éclosion’),
• hatch.m (hatchling mass (g)),
• clutch.S (clutch size = ‘portée’),
• age.mat (age at maturity (number of months of activity)),
• clutch.F (clutch frequency)

##    mean.L matur.L max.L hatch.L hatch.m clutch.S age.mat clutch.F
## Sa   69.2      58    82    27.8   0.572      6.0      13      1.5
## Sh   48.4      42    56    22.9   0.310      3.2       5      2.0
## Tl  168.4     132   190    42.8   2.235     16.9      19      1.0
## Mc   66.1      56    72    25.0   0.441      7.2      11      1.5
## My   70.1      60    81    26.6   0.550      5.4      10      1.0
## Pb   55.2      44    64    24.0   0.304      4.2       8      2.0

Dimension reduction

Regular PCA

Probabilistic PCA

Accounting for phylogeny

Cophenetic variance matrix

## Le chargement a nécessité le package : maps

Comparison cophenetic distance vs PCA distance

Phylogenetic PCA

Comparison cophenetic distance vs phylogenetic PCA distance

Probabilistic phylogenetic PCA

General comparison

Phylogenetic PCA (2nd version: using phyl.pca)