23Allometry refers to the power-law relationship that often occurs between body parts and total 24 body size. Whether measured during growth (ontogenetic allometry), among individuals at 25 similar developmental stage (static allometry) or among populations or species (evolutionary 26 allometry), allometric relationships are often surprisingly tight, and relatively invariant. 27Consequently, it has been suggested that allometry could constrain phenotypic evolution, that 28 is, force evolving species along fixed trajectories. Alternatively allometric relationship may 29 result from selection. Despite nearly a century of active research on allometry, distinguishing 30 between these two alternatives remains difficult partly due to the use of a broad sense 31 definition of allometry where the meaning of relative growth was lost. Focusing on the 32 original narrow-sense definition of allometry, we review evidence for and against the 33 "allometry as a constraint" hypothesis. Although the low evolvability of the static allometric 34 slopes observed in some studies suggests a possible constraining effect of this parameter on 35 phenotypic evolution, the nearly complete absence of knowledge about selection on allometry 36 prevents any firm conclusion. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59
Introduction
42Allometry is the study of the relationship between body size and other organismal traits. 43Allometry is important because variation in a wide variety of morphological, physiological 44 and life history traits are highly correlated with organism size [1,2,3]. These relationships 45 generate intuitive hypotheses for understanding trait variation; for example, the fact that 46 humans are larger than mice can be used to explain why the basal metabolic rate of a human 47 is much higher than the basal metabolic rate of a mouse. In most cases, traits show a non-48 linear relationship with size that is accurately captured by a power relationship of the form z = 49, where the trait value is z, the organism size is x, and a and b are parameters of the 50 relationship. If b = 1, the relationship between the trait and size is linear, a condition referred 51 to as isometry. When b ≠ 1, the relationship is non-linear on the arithmetic scale. For 52 example, the basal metabolic rate in mammals scales with body mass with a coefficient b ≈ 53 0.71 [4]; as a result, for every unit increase in mass, a larger organism will have a smaller 54 increase in basal metabolic rate than a smaller organism. Consequently, humans have a basal 55 metabolic rate 5 to 10 times smaller than a mouse when corrected for body size. The ubiquity 56 of these power-law relationships has led biologists to refer to them as allometric relationships. 57Analyzed on log-transformed data these relationships become linear: log(z) = log(a) + 58 b×log(x), where log(a) and b re...
