Before revision: We give a novel representation of the Moran Genealogy Process, a continuous-time Markov process on the space of size-n genealogies with the demography of the classical Moran process . We derive the generator and unique stationary distribution of the process and establish its uniform ergodicity. In particular, we show that any initial distribution converges exponentially to the probability measure identical to that of the Kingman coalescent. We go on to show that one-time sampling projects this stationary distribution onto a smaller-size version of itself. Next, we extend the Moran genealogy process to include sampling through time.
After revision: We give a novel representation of the Moran Genealogy Process, a continuous-time Markov process on the space of size-n genealogies with the demography of the classical Moran process , sampled through time. To do so, we begin by defining the Moran Genealogy Process using a novel representation. We then extend this process to include sampling through time.