Estimates of survival from the sighting of marked animals

All the methods which have been presented in recent years for the analysis of capturerecapture data have aimed at estimating total population size, survival rates and dilution rates. These methods, whether deterministic or stochastic, all assume that the animals captured on each occasion are a random sample from the whole population. The proportion of marked animals in each sample then contains information about the size of the population at that instant. Darroch (1958, 1959) has shown for a stochastic model that, in the cases where the population is subject to either death or to immigration but not both, the parameters of the population together with their variances and covariances can be very simply estimated. In the more general cases with both death and immigration, he obtains estimation equations which can readily be solved numerically, and suggests that the variances of the estimates can be obtained by standard asymptotic techniques. For a deterministic survival rate Jolly (1963) obtains explicit formulae for population size and survival and dilution rates, and asymptotic formulae for their variance and covariances. This theory has been derived to meet the case where the animals are sampled completely at random. However, for some species, the markings which are applied to render an animal individually identifiable may be visible without capture. For the past thirteen years zoologists from the University of Aberdeen have been carrying out a study of the fulmar petrel (Fulmarus glacialis) on a small island in Orkney, the details of which have been describedby Carrick & Dunnet (1954) andDunnet, Anderson & Cormack (1963). Throughout this study birds have been caught individually on their nests and have been marked by an identifying set of coloured rings on the leg. These rings are clearly visible in flight, so that in years subsequent to marking the continued presence of a bird in the colony may be established without any capture being effected. New individuals may be marked each year by further capture. The aim of this paper is to examine a model applicable to this biological situation. Clearly no useful inference about the population size is possible, but valid estimates of survival rate can be obtained. In ?? 2 and 3 the notation used and the general formulation of the theory are set out. Maximum-likelihood estimates of survival rates are obtained in ? 4, and their asymptotic variances and covariances in ? 5. These are applied to the over-all survival rate and the life span in ? 6. In ? 7, the theory is illustrated for records from the study of fulmars. 2. NOTATION