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). 
• GPA, which is automatically applied on  … – EST_OUTL.txt for 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.
• 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)