In randomly breeding populations, the allelic and genotypic frequencies remain constant from generation to generation and are predicted by the Hardy–Weinberg principle, provided there is no mutation, migration or selection, and the population is infinitely large (see Chapter 6). Population size is finite, however, and many species are structured into several more or less discrete populations (subpopulations or demes) which may be quite small in size. As a consequence there will be changes in allelic frequencies from generation to generation because of sampling error in the production of gametes.

What do we mean by sampling error? Consider a game of coin-tossing in which there is an equal chance of obtaining heads or tails. However, if we toss a coin repeatedly, there is not a sequence of heads, tails, heads, tails, and so on ad infinitum, but rather a random sequence in which there are groupings of heads and tails. Consequently, we would not be surprised if there were not exactly half heads and half tails in a small sample of coin tosses. We would expect the proportion of heads and tails to be distributed in some way around 50%.

Consider the results of a coin-tossing experiment (Fig. 8.1). When the coin was tossed 20 times, the percentage of heads ranged from 25% to 75% in individual trials, and the average across all trials was 49.55%. When the coin was tossed 200 times, the percentage of heads ranged from 42.5% to 57.5%, and the average across all trials was 50%.