in exactly the same fashion that times to coalescent events are approximated.

When two independent processes are operating, the coalescence model becomes one of following lineages back in time and waiting for an event to happen. The possible events are mutation or coalescence, so the total chance of any event is the sum of the independent probabilities of each type of mutually exclusive event. The total chance of an event occurring while going back in time (increasing t) is then

Time Type of scale event

the sum of the intensities of mutation and coalescence. When an event does occur at a time given by this exponential distribution, it is then necessary to decide whether the event is a coalescence or a mutation. The total chance that the event is either a mutation event or a coalescence event is k9 k(k -1)

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