A New Paradigm for the Analysis and Interpretation of Growth Data: The Shape of Things to Come

Abstract

The process of growth is basic to all organisms, and studies of growth have long been a subject of concern to ornithologists. At a workshop held at the recent meeting of the American Ornithologists' Union (1821 August 1986), a series of presentations and subsequent discussions laid the foundation for what we feel to be a new paradigm for studying growth. The strengths of this new paradigm lie in its potential for more detailed quantitative comparisons of growth in general and intraspecific comparisons in particular. It is our purpose to summarize the major aspects of this paradigm and to provide information on its development. The paradigm was derived mainly from studies of birds, but should have broad applicability to studies of a variety of organisms. Growth was first studied qualitatively by describing developmental stages in chronological series. This was followed by quantitative formulations that considered growth as the net result of simultaneous anabolic and catabolic processes. Many of these early concepts (e.g. Huxley 1932, von Bertalanffy 1957) still influence current thinking. A third stage was introduced by Ricklefs (1967), based on a graphical method of fitting data to S-shaped or sigmoid growth models. This methodology, applied to interspecific comparisons, has contributed significantly to our understanding of the meaning of the patterns of variation in avian growth-particularly from an evolutionary point of view (Ricklefs 1983). The new paradigm is also based on the fitting of data to sigmoid models but is directed more toward questions that involve intraspecific as well as interspecific comparisons. The Richards sigmoid growth function (Richards 1959) and its expression in terms of parameters with specific biological meaning (Bradley et al. 1984, Brisbin et al. 1986b) have been of basic importance to the new growth paradigm. These approaches now allow independent quantitative assessments of three biologically meaningful aspects of growth: (1) size, the upper or asymptotic limit; (2) rate, a measure of the time required for specified growth increments to take place; and (3) shape, a quantitative measure describing