The probability of speciation on an interaction network with unequal substitution rates

• An interaction network model for speciation is suggested.
• Sampling is done non-uniformly to reflect the possibility of unequal substitution rates.
• Formulas for speciation rates and time until speciation are obtained.

Speciation is characterized by the development of reproductive isolating barriers between diverging groups. A seminal paper of a mathematical model of speciation was published by Orr (1995), extended by Livingstone et al. (2012) to incorporate interaction networks. Here, we further develop the model to take into account the possibility of different substitution rates for network nodes of different connectivity. Mathematically, this amounts to sampling nodes from an undirected graph where the inclusion probability for a given node depends on its degree (number of connecting edges). We establish formulas for the rate of speciation and identify a crucial parameter that is a measure of the deviation from simple random sampling.