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