To better understand the progression of heterogeneous breast cancers, four models of progession pathways have been evaluated. The models describe the progression through the grades of ductal carcinoma in situ (DCIS) 1, 2, and 3, and through the grades of invasive ductal carcinoma (IDC) 1, 2, and 3. The first three pathways, termed linear, nonlinear, and branched, describe DCIS as a progenitor of IDC, and grades of DCIS progressing into grades of IDC. The fourth pathway, termed parallel, describes DCIS and IDC as diverging from a common progenitor and progressing through grades in parallel. The best transition rates for the linear, nonlinear, and branched pathways were sought using a random search in combination with a directed search based on the Nelder-Mead simplex method. Parameter values for the parallel pathway were determined with heuristic graphs. Results of computer simulation were compared with clinically observed frequencies of grades of DCIS and grades of IDC that were reported to occur together in heterogeneous tumors. Each of the four pathways could simulate frequencies that resembled, to varying degrees, the clinical observations. The parallel pathway produced the best correspondence with clinical observations. These results quantify the traditional descriptions in which grades of DCIS are the progenitors of grades of IDC. The results also raise the alternative possibility that, in some tumors with both components, DCIS and IDC may have diverged from a common progenitor.