N

where k is the number of lineages available to coalesce, was a constant since N remains the same over time. If N is instead changing rapidly over time, then the probability of non-coalescence also changes rapidly over time. The result is that the distribution of coalescent times cannot be exponentially distributed when population size is changing over time as it is when population size is constant over time. The waiting time between coalescent events in an exponentially growing population is obtained from the equation:

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