Effect on Ne of variable population size (Nc) over time:
Five scenarios

In a population that is variable over time, Ne is the harmonic mean of the number of breeding individuals in each generation. The harmonic mean of a series is defined as the inverse of the mean of inverses, and is dominated by the smaller numbers in the series.

Consider five scenarios (Nc1 - Nc5) for the change in census count (Nc) over time. (1) A founding population of 10 individuals that doubles every generation up to 10,000 individuals behaves like a population of N = 55. (2 & 4) Populations that typically comprises 10,000 individuals, but once in 10 (Nc2) or 20 (Nc4) generations undergo a bottleneck to 10, behave like populations ~1/100 or ~1/50 the typical size, respectively. These extreme events may not be evident in populations not subject to long-term study. (3) A population that cycles between 10 and 10,000 individuals by doubling to the peak and then halving to the trough, and repeating, has an even smaller
Ne than a population subject to a single bottleneck. (5) A population that after drastic reduction rebuilds slowly (Ro = 2) to its former size has about one-half the Ne of a population that recovers quickly (Nc4)

Homework: Assume bottlenecks as in scenarios Nc2 & Nc4, where a drastic reduction from 10,000 to 100 occurs once every 100th generation. Estimate Ne. [Hint: The question asks for an estimate, not an exact calculation. What is the numerical relation to scenarios 2 & 4 ?]

Figure & Text material © 2021 by Steven M. Carr