Representation of the MMR overlap criteria. The dotted lines correspond to the criteria proposed by Deck et al. (2013), and the collision curve is the approximation of the collision curve for α → 1. We represented in transparent green (p odd) and blue (p even) the first p:p + 1 MMR islands to show the agreement between the proposed overlap criterion and the actual intersections. In this figure, ε = 10^-6.