Morphometric Tools For Landmark Data: Geometry And Biology

Morphometrics is the statistical study of biological shape and shape change. Its richest data are landmarks, points, such as the bridge of the nose, that have biological names as well as geometric locations. This book is the first systematic survey of morphometric methods for landmark data. The methods presented here combine conventional multivariate statistical analysis with themes from plane and solid geometry and from biomathematics to support biological insights into features of many different organs or organisms. The book begins with a review of the fundamentals of landmarks and a discussion of the thin-plate spline, a new, statistically tractable implementation of the old model of shape change as deformation. This is followed by a critical survey of conventional multivariate morphometrics (the use of interlandmark distances as separate variables). Coordinates for representing landmark configurations without reference to size are then introduced, and their multivariate statistics explored in full. The second half of the book is a survey of the most general and powerful new methods for describing the results of these analyses for both simple and complex landmark configurations. Using diagrams linked to biological interpretation, the text explains and interrelates the geometric features by which morphometric findings can be rendered legible. New tools are demonstrated using a variety of data sets from evolutionary biology, micropaleontology, neuroanatomy, and craniofacial growth.