A paper just made available on the American Naturalist website takes a novel and curious perspective on fundamental scaling relationships in ecology. The paper, by Ginzburg and Damuth, is titled The space-lifetime hypothesis: viewing organisms in 4 dimensions, literally. The authors argue that organisms can literally be viewed as four dimensional objects, three spatial and one temporal. While many traits scale with body size, they specifically focus on the well-known finding that metabolic rate scales as the +3/4 power of body mass whereas lifespan goes as the +1/4 power. This makes the product of the two an isometric relationship (m3/4 x m1/4 = m1), such that a doubling in an organisms size predicts a doubling in the energy it metabolizes in a lifetime. While many researchers take this as a consequence of other scaling relationships it is a fundamental role in the 4D view. As they state it, these observations suggest instead that the scaling of lifetimes may reflect a fundamental manner in which organisms of all body masses are ecologically and evolutionarily functionally similar. Thus an organisms energy budget has four dimensions, three spatial (length, area, volume) and one temporal (generation time) that together give m1. If these four dimensions are evenly divided into the isometric scaling of lifetime metabolic rate then each will be m1/4. This predicts that metabolic rate should be m3/4 because energy is taken in through a 3D surface and then allocated to processes that take place in 4 dimensions (the dimension of time plus the 3 dimensional space of the organism). And if metabolic rate is m3/4, the remaining dimension, generation time, should be m1/4 to preserve the isometric scaling lifetime metabolic rate.
The critical role of generation time in ecology and evolution itself is another key component of the 4D argument: Constructing one viable and reproductively capable daughter requires a certain duration (a generation time) that is conveniently viewed as an organisms fourth dimension. So, on average, it takes a generation time of metabolism for a mother to guarantee the existence of her replacement. This establishes the reasoning for why generation time is fundamentally an organisms fourth dimension. Where this argument becomes even less conventional is in the stated lack of a mechanism. In fact, my reading of the paper is that they intend the argument to predict the set of criteria to which any proposed mechanistic explanation of ¾ power scaling in biology must conform. For instance, they predict that progressive reductions in dimensionality, achieved by holding constant generation time, length, etc., should lead to predictable reductions in the exponent. If generation time is held constant then they predict that metabolic rate should be a 2/3 power of mass, rather than ¾, and cite examples where within species metabolic rates have been shown to go as the 2/3 power of mass (if length and generation time are held constant, as with species of same size and lifetime, the scaling should be ½, etc.). But these within species allometries are somewhat contentious issues for some. Because they do not suggest a mechanism, they are not necessarily at odds with existing theories of metabolic scaling that focus on evolutionary constraints such as the space-filling fractal geometry of supply networks in the circulatory and vascular systems of mammals and plants (e.g., West et al. 1997, 1999). The explicitly non-mechanistic argument in the paper adds to its uniqueness but is also where some people may have the greatest trouble with the paper, as we are taught to focus on mechanisms and this nature of dimensional thinking is much more foreign to us (and maybe difficult to interpret at first). The theory makes simple and elegant predictions that should lead readily to either coherence or conflict with some of the existing takes on the topic (note that I'm saying the predictions are simple and elegant but am not saying anything about whether the empirical results are broadly accurate. Its of course too soon to see how these predictions will weather the tests of time. They give some empirical support in the paper). Either way, dimensional thinking is a novel approach in this area that, when combined with the argument for the importance of generation time, makes a fundamental contribution to the literature and will certainly alter future approaches to the subject of scaling in ecology.
