If N identical abelian anyons each with individual statistics α α (that is, the system picks up a phase e i α α when two individual anyons undergo adiabatic counterclockwise exchange) all fuse together, they together have statistics N 2 α α . This can be seen by noting that upon counterclockwise rotation of two composite anyons about each other, there are N 2 pairs of individual anyons (one in the first composite anyon, one in the second composite anyon) that each contribute a phase e i α α . An analogous analysis applies to the fusion of non-identical abelian anyons. The statistics of the composite anyon is uniquely determined by the statistics of its components.