Allomeric Variation. 1. The Theory and Some Consequences

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Abstract
Allomeric variation is the tendency for variability in morphological traits to decrease as the size (number of parts) increases. Such a trend is supported by the commonly observed negative correlation between the CV [coefficient of variation] and size of anatomically similar traits. The mechanistic basis for allomery is probably the decreasing contribution to variation of random events or noise as the number of parts increases. The principle of allomery is elaborated and an attempt is made to integrate it with observations from the literature on stress physiology and developmental genetics in animals. The physical-chemical basis of phenotypic randomness or noise is explored and a theory is proposed that associates noise with random molecular motion. One of the genetic corollaries of this explanation for allomery is the possibility that the random contribution to the variance of traits (VR/VP) should decrease and the additive genetic component should increase in a series of similar traits ranked in order of decreasing CV. Another consequence of the theory should be the phenotypic partitioning of relatively homozygous and heterozygous genotypes as CV decreases; homozygotes should occur with greater frequency in the tails of phenotypic distributions; heterozygotes should occur near the mean with increasing frequency. Some of the predictions that follow from this theory are heritability should increase as CV decreases for uncanalized morphometric traits: stress should lower intracellular order and viscosity, thus increasing randomness (VR), producing an increase in CV and bilateral asymmetry; the magnitude of the random component of variation should be proportional to absolute temperature; extreme individuals should be more asymmetrical than typical individuals and the strength of this effect should be inversely related to the CV.