PAST - Case study 4 - Shape change through trilobite ontogeny

Case study 4 - Shape change through trilobite ontogeny

Crônier et al. (1998) studied the ontogeny of the Late Devonian phacopid trilobite Trimerocephalus lelievrei from Morocco. Well-separated size classes (growth stages) were identified, and the changing shape of the cephalon through ontogeny was studied using Elliptic Fourier shape analysis. This case study uses the original outline data set, kindly provided by Catherine Crônier.
Drawing by Sam Gon III. Used with permission.

Open the file outlines.dat and commatize if necessary. Each cephalon outline is represented by two columns containing 64 x/y co-ordinate pairs. There are 7 cephala from growth stage A, 16 from stage B, 18 from stage C, 9 from stage D and 1 from stage E.

Using the 'XY graph' option in the Plot menu, inspect one outline from each group. Can you detect any change in shape through ontogeny?

Elliptic Fourier shape analysis

Select all, and run 'Elliptic Fourier' from the Geomet menu. You should get a data matrix containing the Fourier coefficients for all 51 cephala. Click the 'Shape view' button to see how the outlines can be reconstructed from the harmonic modes (the aspect ratio may be distorted in the plots). How many harmonics are needed to get good represention of the shapes?

Principal components analysis

The Elliptic Fourier analysis was the first step in our data reduction. Instead of 128 digitized co-ordinates for each cephalon, we now have 40 Fourier coefficients, normalized with respect to position and size. The second step will be analysis of the coefficients with the aid of PCA.

Use the Copy button under the Elliptic Fourier data matrix. Clear the main spreadsheet (e.g. with 'New' in the File menu) and paste the 51 rows of Fourier coefficients into the empty spreadsheet (Edit menu). Assign different colors to the different size classes (Edit menu), remembering the numbers of cephala contained in each class as given above.

Now choose 'Principal components' in the Multivar menu, using the Var-Covar option. View the loadings, and note how the most important components are related to long-wavelength features (low harmonic number). View the scatter diagram. Can you see any directed shape change through ontogeny?

Stage A: Black dots
Stage B: Red crosses
Stage C: Blue squares
Stage D: Green crosses
Stage E: Purple circle

More information about Elliptic Fourier shape analysis can be found in the manual.