Mendel's use of mathematical modelling: ratios, predictions and the appeal to tradition

The seventh section of Gregor Mendel's famous 1866 paper contained a peculiar mathematical model, which predicted the expected ratios between the number of constant and hybrid types, assuming self-pollination continued throughout further generations. This model was significant for Mendel's argumentation and was perceived as inseparable from his entire theory at the time. A close examination of this model reveals that it has several perplexing aspects which have not yet been systematically scrutinized. The paper analyzes those aspects, dispels some common misconceptions regarding the interpretation of the model, and re-evaluates the role of this model for Mendel himself. In light of the resulting analysis, Mendel's position between nineteenth-century hybridist tradition and twentieth-century population genetics is reassessed, and his sophisticated use of mathematics to legitimize his innovative theory is uncovered.