where N is the population size and t is the number of generations. For example, 0.955 = 0.77.
Based on Frankel and Soulé 1981
| Generations | ||||
|---|---|---|---|---|
| Population size (N) | 1 | 5 | 10 | 100 |
| 2 | 0.75 | 0.24 | 0.06 | <<0.01 |
| 6 | 0.917 | 0.65 | 0.42 | <<0.01 |
| 10 | 0.95 | 0.77 | 0.60 | <0.01 |
| 20 | 0.975 | 0.88 | 0.78 | 0.08 |
| 50 | 0.99 | 0.95 | 0.90 | 0.36 |
| 100 | 0.995 | 0.975 | 0.95 | 0.60 |
We can see that although a population of 10 individuals may retain 95% of its genetic variation after one generation (or after one bottleneck), with random genetic drift for 10 generations only 60% of the variation is likely to be retained, and after 100 generations virtually all the original genetic variation would be lost. A similar pattern exists for the loss of alleles; after many generations of random genetic drift, small populations will usually retain only one allele for a given gene (Table 5.4). In the language of genetics, the gene will have been fixed for that allele. In sum, random genetic drift in a population that remains small for many generations is much more likely to lead to a loss of genetic diversity than is a single bottleneck from which a population recovers quickly.
Table 5.4 Expected number of alleles remaining after t generations for a population of six individuals with 2, 4, or 12 alleles for a gene, assuming equal frequency of each allele.
Based on Frankel and Soulé 1981
| Number of alleles | |||
|---|---|---|---|
| Generations | m = 2 | m = 4 | m = 12 |
| 0 | 2.00 | 4.00 | 12.00 |
| 1 | 1.99 | 3.87 | 7.78 |
| 2 | 1.99 | 3.55 | 5.88 |
| 8 | 1.67 | 2.18 | 2.64 |
| 20 | 1.24 | 1.36 | 1.44 |
| ∞ | 1.00 | 1.00 | 1.00 |
If drift erodes genetic diversity then will mutation simply replenish it? Probably not. The problem is a severe imbalance between the rates at which the two processes operate. A population bottleneck can deplete genetic diversity from a population during just a few generations if the bottleneck is narrow enough. In contrast, it has been estimated that 105–107 generations are required to regenerate allelic diversity for a single gene (Lande and Barrowclough 1987). The genetic machinery of a cell is remarkable at avoiding “copying errors” and thus we cannot rely on mutation to replenish genetic diversity over time scales of conservation concern; preventing bottlenecks and excessive genetic drift by keeping populations of “healthy” size is our best approach.
Effective Population Size
To estimate the effects of bottlenecks and random genetic drift, as presented in Tables 5.2 and 5.3, we made some simplifying assumptions: that the organism is diploid, sexually reproducing, and has nonoverlapping generations; that the population is of constant size, has equal numbers of females and males, random mating, and no migration; that reproductive success of all individuals is the same; and that no mutation or natural selection occurs. Of course these assumptions are violated in any natural population. But making these simplifying assumptions allows us to avoid a major complexity: the difference between total or census population size (the actual number of individuals in a population) and the effective population size. To take a very simple example, let us return yet again to bison. Consider a population of 100 bison in which 25 are too young to breed and 15 adults are infertile, so 60 is the number of breeding adults and therefore the effective size of the population. In practice, the issue is more complicated. What if most of those breeding age adults are females (or males)? We have violated the assumption of equal sex ratios. Bison are of course large‐bodied and long‐lived creatures with overlapping generations. Bison moreover do not mate indiscriminately – some pairings are more successful than others, especially skewed among the bulls.
These biological realities mean that effective population size is usually much lower than actual (or census) population size. Effective population size is a very important concept in conservation biology. We will begin with a definition and then show two examples of how to calculate effective population size (see Frankham et al. 2009 for further details). First the definition: the effective population size (Ne ) of a population is the number of individuals in a theoretically ideal population (i.e. one that meets all the assumptions stated earlier) that would have the same magnitude of random genetic drift as the actual population. Now let us explore how biological realities reduce effective population size relative to census size.
Example 1. Population fluctuations. The effective size of a population that is fluctuating through time (as most do) is less than the actual population size. In this case, Ne is estimated to be the harmonic mean of the actual size of each generation (Hartl and Clark 1997). Mathematically,
In words, the harmonic mean is the reciprocal of the average of reciprocals of the population size for each of t generations. This method of estimating an effective population gives more weight to smaller population sizes. For example, the Ne for three generations (t = 3) in which N1 = 1000, N2 = 10, and N3 = 1000, would be
