Author
- Jean-Pierre Dujardin, IRD, Montpellier
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.
- 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
VIDEO
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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).