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We introduce a new random graph model motivated by biological questionsrelating to speciation. This random graph is defined as the stationarydistribution of a Markov chain on the space of graphs on $\{1, \ldots, n\}$.The dynamics of this Markov chain is governed by two types of events: vertexduplication, where at constant rate a pair of vertices is sampled uniformly andone of these vertices loses its incident edges and is rewired to the othervertex and its neighbors; and edge removal, where each edge disappears atconstant rate. Besides the number of vertices $n$, the model has a singleparameter $r_n$.  Using a coalescent approach, we obtain explicit formulas for the firstmoments of several graph invariants such as the number of edges or the numberof complete subgraphs of order $k$. These are then used to identify fivenon-trivial regimes depending on the asymptotics of the parameter $r_n$. Wederive an explicit expression for the degree distribution, and show that underappropriate rescaling it converges to classical distributions when the numberof vertices goes to infinity. Finally, we give asymptotic bounds for the numberof connected components, and show that in the sparse regime the number of edgesis Poissonian.

The split-and-drift random graph, a null model for speciation