Fourier Analysis of Zooecial Shapes in Fossil Tubular Bryozoans
Fourier harmonic amplitudes provide exact characterization of the cross-sectional morphology of fossil tubular bryozoans. The Fourier method resolves a complex zooecial shape into multiple shape components (harmonics), which can be treated as individual morphologic variables. Shape elongation caused by varying zooecial orientation affects only the value of the second harmonic. Fourier harmonic coefficients reveal small changes in model shapes involving different numbers of neighboring zooecia, thickening of zooecial walls, and acanthopore variation. The number (between three and six) of neighboring zooecia controls the gross zooecial shape, as reflected in the third to the sixth harmonic. The sixth harmonic reflects the closest packing of zooecia within a colony, and its mean correlates with the colonial growth form and number of mesopores. Monticules represent the budding centers of a colony: zooecial chambers decrease in maximum diameter and become more densely packed away from the monticules. Ontogenetic changes, from the budding of new zooids to the closest packing of mature individuals, involve variation in gross zooecial form, revealed in the amplitudes of the second to the sixth harmonic. Harmonics above the sixth reflect small-scale sculpturing of the zooecial margin. The mean harmonics of different taxa suggest that Fourier values can be used for multivariate phenetic differentiation. The mean spectra of different growth forms indicate that variation in the second and sixth harmonics results from ontogenetic differences and nonmutational response to external stresses. Comparison of intrageneric variability and intracolonial variability shows that the second and sixth harmonics vary more widely among genetically identical individuals than among evolving taxa, even though the morphologies they reflect have been used as major bio-characters in bryozoan systematics. The higher numbered harmonics, especially the seventh, carry evolutionary information.