West, Brown and Enquist's model of allometric scaling again: the same questions remain

The optimal water transport system in plants should maximize hydraulic conductance (which is proportional to photosynthesis) for a given investment in transport tissue. To investigate how this optimum may be achieved, we have performed computer simulations of the hydraulic conductance of a branched transport system. Here we show that the optimum network is not achieved by the commonly assumed pipe model of plant form, or its antecedent, da Vinci's rule. In these representations, the number and area of xylem conduits is constant at every branch rank. Instead, the optimum network has a minimum number of wide conduits at the base that feed an increasing number of narrower conduits distally. This follows from the application of Murray's law, which predicts the optimal taper of blood vessels in the cardiovascular system. Our measurements of plant xylem indicate that these conduits conform to the Murray's law optimum as long as they do not function additionally as supports for the plant body.

Accumulation of noncoding DNA and therefore genome size (C-value) may be under strong selection toward increase of body size accompanied by low metabolic costs. C-value directly affects cell size and specific metabolic rate indirectly. Body size can enlarge through increase of cell size and/or cell number, with small cells having higher metabolic rates. We argue that scaling exponents of interspecific allometries of metabolic rates are by-products of evolutionary diversification of C-values within narrow taxonomic groups, which underlines the participation of cell size and cell number in body size optimization. This optimization leads to an inverse relation between slopes of interspecific allometries of metabolic rates and C-value. To test this prediction we extracted literature data on basal metabolic rate (BMR), body mass, and C-value of mammals and birds representing six and eight orders, respectively. Analysis of covariance revealed significant heterogeneity of the allometric slopes of BMR and C-value in both mammals and birds. As we predicted, the correlation between allometric exponents of BMR and C-value was negative and statistically significant among mammalian and avian orders.

The statistical derivation of Kleiber's 0.75 interspecific mass exponent 'b' is based on an assumption that the mass coefficient 'a' is constant irrespective of a mammal's size and/or species. Analysis of covariance, a statistical technique not based on this assumption, reveals that the mass coefficient is not constant in a series of 7 species (Peromyscus m., mice, rats, cats, dogs, sheep, and cattle) but increases threefold with the size of the animal. THe mass coefficient is a power x mass-2/3, the power being expressed in watts and the mass in kg. (Peromyscus m.: a = 1.91 +/- 0.09; cattle: a = 6.06 +/- 0.14). The intragroup mass exponent is equal to 0.67 +/- 0.03 and is significantly different from 0.75. This study shows that the 0.75 interspecific mass exponent in Kleiber's equation is a statistical artifact and suggests that the data from literature are consistent with the theory of biological similitude of Lambert and Teissier.