Scaling relationships are used to describe ecological patterns within and across individual and population levels. Studies on the mechanisms of these scaling relationships (e.g. Kleiber's law, Taylor's law, and density mass allometry) have facilitated the understanding of how organisms and species operate in nature, such as the metabolic theory of ecology. Among the established patterns, individual variation has been understudied both within and across levels of biological organizations. Individual body size variation is a key evolutionary phenomenon and closely related to ecological diversity and species adaptation. In this meta-analysis, I tested a new mean-variance scaling relationship of individual body mass (called mass allometry) across amphibian, arthropod, bird, fish, mammal, plant, and reptile organisms using 57 Long-Term Ecological Research data sets. Mean, variance, and the mass allometry were calculated and tested at both temporal and spatial scales. I then combined the mass allometry with Taylor's law and density mass allometry to build a new scaling relationship between the variance of individual body mass and variance of population abundance, named density mass variance allometry (DMVA). I analyzed these scaling relationships using fish and forest tree data. Finally, I used DMVA to infer the effect of various fishing strategies on stock fluctuation.
Results/Conclusions
My analysis showed that a power function or a generalized power function describes well the mean-variance scaling of individual body mass, or mass allometry. Mass allometry, Taylor's law, density mass allometry, and density mass variance allometry (DMVA) were confirmed using fish sample data of a freshwater lake and oak tree data from a deciduous forest. Moreover, parameters of DMVA predicted from other three scaling relationships agreed with the corresponding parameters estimated from the data. Using DMVA as a null model, I found analytic evidence that fishing targeted at adult individuals increases population abundance fluctuation. This synthesis shows that integration and extension of existing ecological laws can lead to the discovery of new scaling patterns and complete our understanding of the relation between individual trait and population abundance. The new scaling pattern has potential implication to the diversity-stability relationship at population and community levels.