N

e 2Ne

where t is the number of generations. Imagine that a population fluctuates in size over three generations as considered in section 3.3. In such a situation the probability of two randomly sampled gene copies not experiencing a coalescence event over the three generations could be approximated by lnc

t

f 1 if

' 1 il

' 1 1

ยป e 2Ne = e1

l 2Ne(t=1) j

. 2Ne(t=2) Jf

where each term in the exponent of e is distinct since the population sizes fluctuate over time. The exponential terms of e can be solved for the effective population size by taking the natural log of both sizes to eliminate e:

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