The power-law nature of individual body size variation

Submitted by editor on 20 November 2015.Get the paper!

The ubiquitous Taylor’s law (TL) scaling between the mean and the variance of species population density was discovered more than half a century ago. The mechanistic basis of TL has been the focal point of research, and little attention was paid to its application other than the sampling design of agricultural pests.

Three years ago, we (Joel E. Cohen, William S. F. Schuster, and the author) asked if TL can be useful in capturing fluctuations across levels of biological organization. Using the oak data of Black Rock Forest, we found TL can be linked to the widely studied density-mass allometry (or “self-thinning law”), which states that greater average body size of individual organisms is associated with lower population density. The combined relationship, called variance-mass allometry, describes the negative correlation between average individual body size and variability of population density. Later it was found that these scaling relationships appear not only in forest trees, but also in animal communities.

A crucial variable that was missing from our formulation is the body size variance among individuals, which has been found to play an important role in regulating population size fluctuation. So the new question I asked is can we extend the universality of TL to individual body mass? Using 57 Long-Term Ecological Research data sets, I confirmed that bigger average individual body mass was correlated with greater individual body mass variation in a power-law fashion, a Taylor’s law for individual body mass (called “mass allometry”) indeed! Tested against the oak trees of Black Rock Forest and fish samples of Lake Kariba, TL, density-mass allometry, and mass allometry yielded a new scaling between the individual body mass variation and population density fluctuation. This scaling quartet successfully incorporated body mass variability at the individual level, and was used to explain the ecological impact of fishing activity on marine stocks.

This appealing scaling framework does not stand without mystery. For example, it is natural to believe that individual body mass variance cannot keep increasing as a power law of the mean body mass, since within-taxon individuals tend to approximate a uniform body size after sexual maturity, reducing individual variation. This intuition was supported by the concave curvilinearity of mass allometry on the log-log scale, but was contradicted by the linearity on the log-log scale observed from majority of data. Mass allometry has the potential to open new doors in searching for the underlying mechanisms of TL, but more efforts are needed to test and understand its empirical generality. 

Meng Xu

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