Survival of new mutations: branching processes

Abstract

In the previous chapter, we gave methods yielding exact solutions to some critical problems. While the calculations may have seemed laborious, they are easily adapted for the computer, provided the population size is fairly small. For large populations, these calculations are beyond the computer’s capacity and different methods are required. Usually, such ‘large-population’ methods yield approximate answers only. However, other things being equal, the inaccuracy should be smallest when the population size is very large. If, then, large-population methods give reasonably accurate results for fairly small populations, for which exact results are available, we can be confident a fortiori that these methods are satisfactory for large populations; sometimes this can be confirmed in other ways. In practice, the accuracy varies with the problem under consideration. Hence a systematic checking, problem by problem, of results is essential.

Full many a flower is born to blush unseen, And waste its sweetness on the desert air.

Thomas Gray, Elegy in a Country Churchyard