Variation in population size

$$N_e = {1 \over \left[1 - \left\{\prod_{k=1}^t \left(1 - {1 \over {2N_e^{(k)}}}\right)\right\}^{1/t}\right]}$$ (1)

$$\approx {t \over {\sum_{k=1}^t{1 \over N_e^{(k)}}}}$$ (2)

where $N_e^{(k)}$ is the effective size of the population in generation $k$.

If $N_e = 1000$ for $k = 1,2,\cdots9$, but $N_e = 10$ for $k = 10$, $N_e = 83$ versus a mean of 901. Effective size is much more drastically affected by smallest population size than largest population size. Management implication - Populations subject to occasional crashes are more susceptible to random genetic changes than those with relatively stable populations.