Geometric Morphometrics for Biologists
Provides numerous illustrations, including graphical presentations of important theoretical concepts and demonstrations of alternative approaches to presenting results
Geometric Morphometrics for Biologists
Chapter 1 Introduction
Owing largely to developments in measurement theory over the past two decades, there has been remarkable progress in morphometrics. That progress resulted from first precisely defining "shape" and then pursuing the mathematical implications of that definition. We therefore now have a theory of measurement. We offer a critical overview of the recent history of measurement theory, presenting it first in terms of exemplary data sets and then in more general terms, emphasizing the core of the theory underlying geometric morphometrics - the definition of shape. We conclude the conceptual part of this Introduction with a brief discussion of methods of data analysis. The rest of the Introduction is concerned with the organization of this book and where you can find more information about available software and other resources for carrying out the analyses.
geometric morphometrics, shape analysis, landmark coordinates, shape and size
Shape analysis plays an important role in many kinds of biological studies. A variety of biological processes produce differences in shape between individuals or their parts, such as disease or injury, mutation, ontogenetic development, adaptation to local geographic factors, or long-term evolutionary diversification. Differences in shape may signal differences in processes of growth and morphogenesis, different functional roles played by the same parts, different responses to the same selective pressures, or differences in the selective pressures themselves. Shape analysis is an approach to understanding those diverse causes of morphological variation and transformation.
Sometimes, differences in shape are adequately summarized by comparing the observed shapes to more familiar objects such as circles, kidneys or letters of the alphabet (or even, in the case of the Lower Peninsula of Michigan, a mitten). Organisms, or their parts, are then characterized as being more or less circular, reniform, C-shaped or mitten-like. Such comparisons can be extremely valuable because they help us to visualize unfamiliar organisms or to focus attention on biologically meaningful components of shape. However, they can also be vague, inaccurate or even misleading, especially when the shapes are complex and do not closely resemble familiar icons. Even under the best of circumstances, we still cannot say precisely how much more circular, reniform, or C-shaped or mitten-like one shape is than another. When we need that precision, we turn to measurement.
Morphometrics is a quantitative way of addressing the shape comparisons that have always interested biologists. This may not seem to be the case because the morphological approaches once typical of the quantitative literature appeared very different from the qualitative descriptions of morphology; whereas the qualitative studies produce pictures or detailed descriptions (in which analogies figure prominently), morphometric studies usually produced tables with disembodied lists of numbers. Those numbers seemed so highly abstract that we could not readily visualize them as descriptors of shape differences, and the language of morphometrics also seemed highly abstract and mathematical. As a result, morphometrics seemed closer to statistics or algebra than to morphology. In one sense that perception is entirely accurate: morphometrics is a branch of mathematical shape analysis. The way that we extract information from morphometric data involves mathematical operations rather than concepts rooted in biological intuition or classical morphology. Indeed, the pioneering work in modern geometric morphometrics (the focus of this book) had nothing at all to do with organismal morphology; the goal was to answer a question about the alignment of megalithic "standing stones" like Stonehenge ( Kendall and Kendall, 1980 ). Nevertheless, morphometrics can be as much a bran