Inhibitory cascade

The mathematical expression used to model the inhibitory cascade is 1 + [(a - i)/i](x - 1), where a is the strength of activating developmental factors, i is the strength of inhibitory developmental factors, and x is the number of the lower molar in the tooth row (i.e. M₁, M₂, etc.). The M₂ is always predicted to be exactly one third of the total mandibular molar area in a mammal with the typical eutherian dental formula containing three mandibular molars, with M₁ = i/3a and M₃ = (2a - i)/3a.

An overview of mammal species across various orders found the large majority of them to occupy either a morphospace where M₁ > M₂ > M₃ or one where M₁ < M₂ < M₃, concordant with the inhibitory cascade model. Analysis of a broad range of Mesozoic and early Cenozoic mammaliaform taxa found that about two-thirds of them had molar ratios consistent with the inhibitory cascade's predictions, suggesting a deep evolutionary origin within Mammaliaformes for this developmental mechanism.