In several branches of biology, theories have been formulated which amount to saying that in each cell or in each organism there are a number of ‘targets’, and that changes occur as a consequence of random ‘hits’ on these targets. Such theories are most obviously relevant when explaining the effects of ionising radiations. By a natural extension, similar theories have been put forward to explain ‘spontaneous’ deteriorative changes, particularly those associated with senescence, and for the damaging effects of agents other than radiation.

This chapter introduces the mathematical methods used in developing these theories. There are two devices which are used again and again in target theory, but which have already been met in other contexts; they are as follows:

(1) If you can't calculate the probability that something will happen, calculate the probability that it won't.

(2) If x is small and n large, (1 – x)n ≃ e-nx.

This identity, proved in appendix 6, was used on page 35 to analyse the ‘random’ meetings between a parasite and its host; it is used here to analyse the random collisions of ionising particles with their targets.

If these two devices are borne in mind, no great difficulty should be experienced in coping with the type of problem discussed in this chapter. As an inducement to those with no interest in radiation biology, the same mathematical ideas are used in many other contexts, particularly in ecology.