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Classic therapeutic strategies try to prevent the nucleation and spread of amyloid fibrils, whilst diffusible oligomers have emerged as promising drug targets affecting downstream pathogenic processes. We developed a generic protein aggregation model and validate it against measured compositions of fibrillar and non\u2010fibrillar assemblies of ataxin\u20103, a protein implicated in Machado\u2013Joseph disease. The derived analytic rate\u2010law equations can be used to 1)\u2005identify the presence of parallel aggregation pathways and 2)\u2005estimate the critical sizes of amyloid fibrils. The discretized population balance supporting our model is the first to quantitatively fit time\u2010resolved measurements of size and composition of both amyloid\u2010like and oligomeric species. 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