A combined landmark and outline-based approach to ontogenetic shape change in the Ordovician trilobite Triarthrus becki

Abstract

Landmark based geometric morphometrics has developed as a powerful set of statistical and visual tools for the study of organismal shape. The approach is limited in the kinds of shape information accessible to it, however, by the need to employ discrete homologous landmarks as the basis for comparison. In particular, curves and complex outlines are difficult to study by existing methods. Data of this type may be incorporated into study of shape through the use of semi-landmark methods, which allow information about curved surfaces to be incorporated into the framework of landmark based geometric morphometrics. We present software and statistical approaches needed to carry out combined landmark and semi-landmark analysis. We demonstrate the method and compare it to standard landmark methods with a regression analyses of ontogenetic change in the Ordovician trilobite Triarthrus becki. Abundant landmarks on the cranidium of T. becki allow landmark methods to represent the shape of the organism effectively, making it a good test case for combined landmark and semi-landmark methods. We verify that the patterns of ontogenetic change implied by regression models using varying combinations of landmark and semi-landmark information are consistent with one another. Thus, semi-landmark methods and the standard geometric landmark based methods yield similar information about this ontogenetic shape transformation. This suggests that semi-landmark methods show substantial promise for rigorously testing hypotheses that involve the comparison of shapes when an adequate set of landmarks is lacking.