Scale

This chapter opens with an illustration of the incredible spatial scale over which biological organisms exist and biological processes occur. We find that there are living organisms that differ in length by a factor of a million or more. We then ask how the power needed by mammals to maintain their life processes differs based on their mass. We find that metabolic rate increases at a less than linear rate compared to body mass. Comparing the ratio of a sphere’s surface area to its volume, we argue that this less than linear scaling might result from the requirement of feeding a three-dimensional body over two-dimensional surfaces, suggesting a 2/3-power scaling of metabolic rate with body size. We note, however, that some data suggest metabolic rate scales more steeply than a 2/3 power. We take a detour to explore the problem of fitting a line to a cloud of points, using tools from linear algebra that we first explored in Chapter 6 . Having understood how data were fit to these metabolic scaling models, we ask if there are reasons to expect greater than 2/3 scaling. Exploring the idea of fractal geometry, we suggest that many biological surfaces involved in nutrient absorption have fractal-like scaling. A clever argument by West, Brown, and Enquist suggests that, with such fractal scaling, metabolic rate might scale by as much as a 3/4-power of mass, in accord with some of the data shown previously. We close with an example of how metabolic scaling might have driven modern brewers’ yeasts to produce the alcohol found in beer and wine.