optimization theories would be generally applicable, even over the enormous size range exhibited by living things (Figure 1). II. ALLOMETRY AND ITS IMPORTANCE TO CREATION RESEARCHERS A. Overview Biophysical optimization is closely linked to allometry, the study of how biological characteristics vary with size in relation to the size of the organism as a whole. As an organism grows, different body parts may grow at different rates. Allometry involves the study of body part sizes as well as temporal characteristics such as heart rate and life span. Allometric relationships are usually expressed in the mathematical form (1) where Y is some biological characteristic, X is some body measurement (total body mass, limb length, etc.), Y0 is a normalization constant, and is an exponent, often some multiple of ¼. The fact that integer multiples of ¼ appear so often in allometric equations has been a long-standing puzzle (Brown et al. 2000). Linear graphs are often used to express allometric relationships, since a power-law function plots as a straight line on a log-log graph. There is a long history of allometric studies going back at least as far as Galileo Galilei, who noted that increasing the linear dimensions of an object by a factor n will cause the object’s surface area to become n2 times larger, but its volume to become n3 times larger (Galilei 1638). Leonardo da Vinci (Minamino and Tateno 2014) observed that the cross sectional area of a tree below a branch point is equal to the sums of the cross-sectional areas above that branch point. A.- G. Greenhill (1881) published a short derivation of the maximum height to which a tree of given proportions could grow without buckling under its own weight. In the 20th century, mathematical biologist D’Arcy Thompson published his book On Growth and Form (1917), which used basic mathematics to describe the shapes and growth of living things. Evolutionary geneticist J. B. S. Haldane (1927) observed that physical constraints placed limits on the sizes of organisms. The term allometry was coined in 1936 in a joint paper by Julian Huxley and Georges Teissier (1936), based upon Huxley’s work in studying growth rates of fiddler crabs (Huxley 1924). Allometry is of interest to creationists for several reasons. Allometric relationships are often used to estimate the sizes of extinct creatures, especially when an entire skeleton is unavailable (Seebacher 2001). Also, creationists have long suggested that unusual anatomical features of ancient humans may somehow be related to extreme longevity. Cuozzo (1998a) suggested that allometric changes in craniofacial features of people who have lived in excess of one hundred years could be responsible for the heavy brow ridges and lower facial heights seen in Neanderthal skulls. A possible problem with this explanation is that a few extant humans have very thick brow ridges, even at younger ages (Rupe and Sanford 2017, Tomkins 2019). Line (2013) suggested that ancient humans may have had robust, thick bones as a necessary engineering constraint for great longevity, rather than the robustness being the result of longevity per se. The robustness in the bones of even Neanderthal children and adolescents (Lubenow 2004) would seem to be consistent with Line’s suggestion. Since a discussion of these differences in the skeletons of ancient humans falls within the domain of allometry, it is worthwhile for creationist paleontologists to be familiar with the subject, especially since evolutionary scientists could misinterpret allometric differences between extinct and extant forms as degrees of evolutionary development between those forms. Finally, it is possible to mathematically derive allometric relationships by assuming that the engineering principles of optimization and efficiency will be characteristics of living things, especially with regard to energy consumption. Such relationships are prima facie evidence for the design of living things. B. Kleiber’s Law Agricultural scientists Max Kleiber and Samuel Brody independently obtained an important empirical allometric relationship. They concluded in Kleiber (1932, 1947, 1961), Brody et al. (1932), and Brody (1945) that for warm-blooded animals like birds or domesticated cattle, the animal’s basal metabolic rate B and body mass M are related by Figure 1. (a) Humpback whales typically have masses of about 30,000 kilograms, and (b) ants have masses of just a few milligrams. Are there fundamental biological principles that are generally valid, even over such an enormous size range? HEBERT Allometric and metabolic scaling 2023 ICC 207
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