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Allometric growth is found in many tagging systems online. That is, thenumber of new tags (T) is a power law function of the active population (P), orT P^gamma (gamma!=1). According to previous studies, it is the heterogeneity inindividual tagging behavior that gives rise to allometric growth. These studiesconsider the power-law distribution model with an exponent beta, regarding1/beta as an index for heterogeneity. However, they did not discuss whetherpower-law is the only distribution that leads to allometric growth, orequivalently, whether the positive correlation between heterogeneity andallometric growth holds in systems of distributions other than power-law. Inthis paper, the authors systematically examine the growth pattern of systems ofsix different distributions, and find that both power-law distribution andlog-normal distribution lead to allometric growth. Furthermore, by introducingShannon entropy as an indicator for heterogeneity instead of 1/beta, theauthors confirm that the positive relationship between heterogeneity andallometric growth exists in both cases of power-law and log-normaldistributions.

Heterogeneity and Allometric Growth of Human Collaborative Tagging Behavior