Testing the power law model for discrete size data

It is sometimes claimed that different types of size data in biology follow a power law. Here, a formal statistical test of the power law for discrete size data is described. The test is based on embedding the power law in the nonparametric family of distributions for which frequency is nonincreasing with size. A parametric bootstrap is used to assess significance. The test is applied to four data sets concerning the frequency of genera of different sizes. The power law is rejected in three out of four cases.