The split-and-drift random graph, a null model for speciation
The so-called biological species concept gives a static definition of species as a group of interbreeding individuals that are reproductively isolated from other such groups. However, species are constantly evolving, as new groups emerge and lineages cease to interbreed.
To understand this process, we propose to model a set of n populations as the vertices of a graph where edges are drawn between any two populations able to interbreed. We let this graph evolve according to two types of events: fission of populations (vertex cleaving) and loss of interfecundity as a consequence of genetic drift (edge removal). These events lead to the constant formation and destruction of clusters of interbreeding populations, viewed as species in evolution. Rather than a built-in concept, species are recovered as an emergent property of this stochastic model with two parameters: the number n of populations and the ratio r between the fission rate and the edge removal rate.
We prove rigorous mathematical results about some species patterns at stationarity and when r=n^\alpha, we show several phase transitions as \alpha varies. We also use simulations to make predictions about species abundance distributions. This mechanistic yet tractable model can be viewed as a null model of speciation with two generic mechanisms (fission + drift) regardless of any specific biological context.