The ‘neutral mutation theory’ holds that most amino acid substitutions in evolution are selectively neutral. The known pattern of variation in human haemoglobins can only be made consistent with this theory if the human species has passed through a bottleneck of numbers in the recent past. If this theory is true, estimates of the necessary size and duration of this bottleneck can be made. A theory is developed which leads to an estimate of Yg, n, the number of alleles present in a population which arise between g and n generations ago, and hence to the estimate
where u is the neutral mutation rate and Ne the effective population size, for the probability that a population contains no such alleles. Using data on haemoglobins, this gives an approximate upper limit to the time elapsed since the bottleneck in human numbers. Either such a bottleneck occurred, or the neutral mutation theory is false; data on other proteins will enable a choice between these possibilities to be made.