Legendre shape descriptors and shape group determination of specimens in the Cymbella cistula species complex

Abstract

Ten Legendre shape descriptors were calculated for 66 specimens in the Cymbella cistula species complex from the Great Lakes. One-hundred x,y co-ordinates were used to calculate the width function W(x)=∑b P(x) to obtain the Legendre coefficients (b) as shape descriptors. Principal components analysis (PCA) was performed on Legendre shape descriptors for the whole valve outline, to determine a shape gradient. A second PCA was performed on Legendre shape descriptors for the dorsal side of the valve outline. From this, nine shape groups were determined. From multiple discriminant analysis (DA), all but the third and eigth shape groups had near-perfect specimen assignment. Misassigned specimens from these shape groups were assigned instead to adjacent groups in PCA shape space. Overall, a curved trajectory in PCA shape space may relect the degree of valve shape complexity. That is, there is a progression in PCA shape space form dorsally semicircular and somewhat arcuate to crescentic with a ventrally gibbous midvalve region. The distinct shape groups found indicated that several species may be present in the C. cistula complex.