FOG | XYOM-CLIC

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FOG (“Fourier Outlines Graphics”) can enter two different files: coord…_OTL.txt and coord…_OTL_FOG.txt

1/ F O G (“Fourier Outlines Graphics”) — Beta version — Input file: coord_…_OTL.txt

Input data of the FOG module are points of intersection between a manually digitized contour and equally distant RADII emerging from the centroid of the figure.
- HOW TO OBTAIN A coord_…_OTL.txt ?
  - Using the COO module
  - The OTL format can ALSO be obtained also by using the TET module : TET performs the conversion from coord_… .txt (the COO output file) into coord_…_OTL.txt and into coord_…_OTL_DB.txt.

Opening a coord_…_OTL.txt is the first step using FOG: it allows the computing of elliptic Fourier coefficients of each outline (Ao,Co,An,Bn,Cn,Dn — with n = the nth harmonic): then two buttons are made active: the MVA on NEF button and the GRAPH button. They represent two different ways to produce elliptic Fourier coefficients invariant to the position, the size, the orientation of each outline.
The MVA on NEF button normalizes the Fourier coefficients (size, position, orientation, starting point) and allows immediate multivariate analyzes (PCA, DA) on the normalized coefficients.
The button GRAPH adopts another strategy of normalization and allows the visualisation of each step (button VIEWING ). The GRAPH button actually opens a new window with various buttons.

button VIEWING
Using the computed Fourier coefficients (Ao,Co,An,Bn,Cn,Dn), estimated outlines are computed and shown using 400 equally distant points, respecting relative size and initial orientation
button H
Each outline is computed and shown using successively the two, three, four, etc. first harmonics; the POWER is computed at each harmonic
button SF
“SF” means “Size Free” (scaled by perimeter or by square rooted area): estimated outlines are scaled for size by dividing their coordinates by their size
button SF&A
The scaled estimated outlines are rotated along the first principal component of the first outline. Rotation is computed according to Rohlf (1990). These outlines are called ALIGNED ESTIMATED OUTLINES.
button EFA Groups
The mean estimated outline of each GROUP is computed and presented, RESPECTING relative size and initial orientation
button gSP
The mean estimated outline of each GROUP is SCALED for SIZE by dividing its coordinates by its own SIZE
button gSP A
The gSP outlines are ALIGNED according to Rohlf (1990)

In addition, the FOG module allows the following:
– To perform Principal component analysis on normalized coefficients (menu PCA / DA). Button “MVA on NEF”
– To perform Discriminant Analysis on normalized coefficients (menu PCA / DA). Button “MVA on NEF”
– To plot and regress shape variables on size (menu ALLOMETRY). Button “SIZE”- To compute (PHYLIP) and plot (NJPLOT) a NJ classification tree (menu TREE). Button “TREE”

Possible output files are:
– coord_…_OTL_FOG.txt = perimeter, Ao, Co, and elliptic Fourier coefficients computed from observed outlines
– coord_…_OTL_FOGnef.txt = Normalized Elliptic Fourier coefficients
– coord_…_OTL_FOGnefcp.txt = principal components of elliptic Fourier coefficients obtained from normalized coefficients
– coord_…_OTL_PER.txt = perimeters
– coord_…_OTL_ARE.txt = square roots of the areas
– coord_…_OTL_POW.txt = harmonic powers

2/ F O G (“Fourier Outlines Graphics”) — Beta version — Input file: coord_…_OTLFOG.txt

The coord_…_OTL_FOG.txt format is another file which can be used by the module FOG: it contains for each outline the perimeter, Ao, Co and the remaining elliptic Fourier coefficients which were computed using as input the coord_…_OTL.txt file
From there, and as long as the above output files exist in the folder, you can go directly to multivariate and allometry analyses

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Acknowledgements

PHYLIP package by J. Felsenstein, NJPLOT software (Perriere, G. and Gouy, M. (1996) WWW-Query: An on-line retrieval system for biological sequence banks. Biochimie, 78, 364-369), TREEDYN, by F. Chevenet (IRD).