Five scenarios

In a population that is
variable over time, **N**_{e} 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 **smalle****r
numbers** in the series.

Consider five scenarios (**Nc1 **- **Nc5**)
for the change in census count (**N**_{c}) 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 **N**_{e}
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 **N**_{e} 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
****N**_{e}. [**Hint**: The
question asks for an *estimate*, not an exact *calculation*.
What is the numerical relation to scenarios **2 **&
**4 **?]

Consider five scenarios (

Figure & Text material © 2021 by Steven M. Carr