The estimation of the total size of plant or animal populations is of great importance in a variety of biological problems, which may relate to population growth, ecological adaptation, genetic constitution, natural selection and evolution, and so on. Obvious practical consequences are the maintenance of human food supplies and the control of insect pests. For human communities and populations of sessile organisms procedures employing fixed sampling units are available, but for mobile populations other methods must be used. The basic technique, which seems to have been first used by Lincoln (1930) to estimate the total number of duck in North America, and is sometimes referred to as the 'Lincoln Index', is as follows. One catches, marks and releases a certain number of animals taken at random from the population. A further random sample is caught and the proportion of marked animals noted. Then the total number of marked animals released divided by the proportion of marked animals in the sample captured can clearly be used as an estimate of the total population size. The same method was adopted independently by Jackson (1933), who used it for estimating the true density of tsetse flies. Jackson (1937, 1939) subsequently extended his treatment to allow for both birthand death-rates, advocating his 'negative' and ' positive' methods. Further work by Jackson (1940) took into account the effects of migration. Recapture methods have also been successfully applied to populations of Lepidoptera. Dowdeswell, Fisher & Ford (1940) caught, marked and released moths on several different days. On each day the marked insects were classified according to the day on which they had previously been released. Analysis of the data, which could be exhibited in a triangular array, or 'trellis' diagram, gave estimates of the size of the moth population for each day. The interpretation of trellis diagrams was further developed by Fisher & Ford (1947). They estimated daily numbers, taking into account a death-rate which was obtained from the average time interval between marking and recapture. A more detailed application of this procedure was made by D~owdeswell et al. (1949). Although in the various papers cited above effective use has been made of estimates of population size and of birthand death-rates, there has been little discussion for the most part of the precision of the results obtained. Jackson (1937, 1939) obtained both the population estimate and its variance for the 'negative' and 'Positive' methods by fitting a curve