Embryos in Deep Time: The Rock Record of Biological Development

5. Proportions, Growth, and Taxonomy

92 At the time when little anatomical research of microscopic structures had been done, many people thought that eggs contained fully formed, very small individuals—or homunculi—a theory known as preformism (figure 23). Analogous “animalcules” were assumed for other species. This idea seems ridiculous to us now, but at the time there were no microscopes and evolutionary transformations among organisms were not understood. What is really remarkable, and makes much less sense without a modern acquaintance with biology, is how an egg cell and a spermatozoid can collectively represent the information and capacity to survive and develop into a whole organism. We now know that early ontogeny of complex organisms involves simple cells dividing over and over again, eventually developing into a recognizable organism. It is a magnificent scientific achievement to have discovered this process and the mechanisms behind it at different levels of organization. Usually two aspects of ontogeny, from conception to death, are treated separately: development and growth. Development five Proportions, Growth, and Taxonomy Proportions, Growth, and Taxonomy / 93 concerns cell differentiation and the formation of the basic body pattern, with fundamental structural changes and the first appearance of major features. It starts with conception and ends approximately with the formation of major body tissues. Growth is the later phase of ontogeny during which size increases. This phase builds on the embryonic pattern that has already been laid out during development. Because of the preservational bias of fossilization, most of what paleontology can say about ontogeny concerns growth. Indirectly, it can say much more, as I discuss in later chapters. Growth, in fossils and in living forms, involves changes in size and shape. A major area of research has dealt with grasping the mathematical laws that govern these changes. One of the earliest approaches to accomplish this was presented by the muchadmired scholar D’Arcy Thompson (1860–1948), a professor of zoology at Scotland’s University of St. Andrews. He was also an expert on mathematics and Greek who, among other accomplishments , prepared the standard translation of Aristotle’s Historia animalium. Thompson described his approach in his book On Growth and Form, first published in 1917. He presented transformation grids that were able to synthesize complex form differences in simple geometric terms. A previous and simpler version Figure 23. The “Homunculus,” as illustrated by Nicolas Hartsoekers (1694); the embryo is in the spermium already preformed. Drawing by Madeleine Geiger. 94 / Proportions, Growth, and Taxonomy of these, concerning the differences in the proportions of the human face, can be found in the writings of Albrecht Dürer. Several examples that Thompson used in his transformation grid analyses involved fossils, including a series of fossil horse genera , Archeopteryx, extinct rhinoceroses, and the shoulder girdle of a plesiosaur in a juvenile and an adult. The geometric approach of Thompson drew much attention and praise and influenced other fields of knowledge.1 But it would not be widely implemented for a long time. It was only in recent decades that the proper algorithms to deal with complex geometric information have been developed. Since the 1980s the discipline of geometric morphometrics has flourished, and sophisticated methods and computer programs have been developed to compare different species and trace changes during growth, in the case of vertebrates much of it concerning skulls. In the geometric approach, one records many landmarks and quantiFigure 24. Shoulder girdle of the plesiosaur Cryptocleidus, in young (a) and adult (b) stages. From D’Arcy Thompson’s On Growth and Form (1917). Proportions, Growth, and Taxonomy / 95 fies how the whole is different among species or among stages in a growth series. There are different kinds of landmark-based approaches, each with a different mathematical framework, and they include deformation, superimposition, and linear distance– based methods.2 An alternative and simpler mathematical approach to Thompson ’s geometric one was developed at around the same time. This approach also had a major impact on studies of growth. In 1936 Julian Huxley and Georges Teissier published simultaneously in English and French a paper presenting a simple but elegant equation that summarizes the relationship between two measured quantities. This relationship was expressed as y = xa or in a logarithmic form, log y = a log x, where a is the scaling exponent of the law. The mathematical path of growth, or ontogenetic trajectory, is usually represented as a straight line after logarithmic transformation . The direction or slope and the position or...