**Size** and **shape** computation from your digitisation data.

**Input:**

Data for characterisation are always RAW COORDINATES, except if “OTHER” has been selected

If “OTHER” has been selected, data are linear measurements between anatomical landmarks.

Remark: “raw coordinates” are the coordinates as saved after a digitisation session by XYOM.

**Output:**

For each individual, characterisation analyses provide:

- A GLOBAL SIZE ESTIMATOR
- centroid size (CS), if from landmarks (LM),
- perimeter (PER) or square root area (ARE), if from pseudolandmarks (outlines)
- “log-size” if data are “OTHER” (linear measurements between LM)

- A number of SHAPE DESCRIPTORS
- Orthogonal Projections (ORP) of aligned specimens, if from landmarks,
- Normalized Elliptic Fourier coefficients (NEF). if from pseudolandmarks (outlines)
- Log-Shape-Ratios (LSR) if data are linear measurements between anatomical points (traditional morphometrics). See: Mosimann JE (1970) Size allometry: size and shape variables with characterizations of the lognormal and generalized gamma distributions. J Am Stat Assoc 65:930–945.

**If Input = raw coordinates of anatomical LANDMARKS (LM) **

**or **

**If Input = raw coordinates of LM + SL (semilandmarks)**

ANALYSES

**GPA**(Generalized Procrustes Analysis)**PCA**(Principal component analysis) using (automatically) as input the**rotated specimens**after orthogonal projection (ORP)**DA**(Discriminant analysis) using (automatically) as input the**principal components**(PC) of the ORP.

OUTPUT

**Reports****Graphics**- GPA Cuantile boxes for centroid size
- Raw, Translated, Scaled, and Rotated landmarks
**Mean objects**(rotated landmarks averaged by groups)- PCA, DA Factor map of the two first multivariate variables.

**Files (**from folder**…_ANALYSES_landmarks_SUBDIVISION_…)**- Raw coordinates of landmarks (landmarks.txt)
- Centroid size (…- CS.txt)
- Rotated (or aligned) specimens (… – ROTATED.txt)
- Orthogonal Projection of aligned specimens (… – ORP.txt)
**Principal components of ORP (… – PC.txt)**- Euclidean distances between PCs (… –
**ED**.txt) - Discriminant analysis of PC, discriminant factors (… – DF.txt)
- Mahalanobis distances (… –
**Mahalanobis distances**– .txt)

**If Input = raw coordinates of pseudoLANDMARKS (outlines)**

ANALYSES

**EFA**(Elliptic Fourier analysis), which generates two important outputs for subsequent analyses:- (1) … – EST_OUTL.txt, the
**estimated coordinates after EFA** - (2) …- the
**Normalized Elliptic Fourier coefficients**(… – NEF.txt).

- (1) … – EST_OUTL.txt, the
**GPA**, which is automatically applied on**graphical outputs****PCA**, automatically using as input the**… – NEF.txt**data**DA**, automatically using as input the**principal components of NEF**(… – PCs.txt).

OUTPUT

**Reports****Graphics**:- Graphical comparison of outlines, using estimated outlines (…_EST_OUTL.txt)
- Usual graphics after GPA
- Especially:
**Mean objects**(rotated landmarks averaged by groups)

**EFA (…_PER.txt):****Quantile****boxes for perimeter****EFA (…PC.txt on NEF)PCA, DA: Factor map of the two first PC.****EFA (…DF.txt from …PC.txt): Factor map of the two first DF.**

- Graphical comparison of outlines, using estimated outlines (…_EST_OUTL.txt)
**Files (**from folder:**_ANALYSES_outlines_SUBDIVISION_…)**- Coordinates of pseudolandmarks (outlines.txt)
- Perimeter (… – PER.txt)
- Square Root area (… – ARE.txt)
- Estimated coordinates after EFA (… – EST_OUTL.txt)
- (Centroid sizes)
- (ROTATED)
- (ORP)
**Normalized Elliptic Fourier Coefficients**(… – NEF.txt)**Principal components (of NEF) (… – PCs.txt)**- Euclidean
**distances**between principal components (… –**ED**.txt)

**If Input = linear measurements between landmarks (traditional morphometrics)**

ANALYSES

**Log transformation**-> log-data = log(1+ data)**log-size**of specimen**x**-> average of log-transformed characters describing**x****log-shape-ratios (LSR)**-> centered log-data**PC of logShape Ratios**<- last PC = 0 removed.

OUTPUT

**Files**- shape variables (PCs of LSR))
- global size estimate (log-size)