Estimates of Mortality and Population from Survey-Removal Records

The idea that, if a population is exposed to a differential kill of the sexes, the population numbers can be estimated from a knowledge of the sex ratios before and after the kill together with the numbers of the kill was noted first by Kelker [1940; 1943]. The statistical theory of the method was developed by Chapman [1954; 1955]. Quite independently of Kelker's work, Murphy [1952] used a variation of the method. No names seems to have been firmly attached to the procedure-it has been called 'Kelker's method' while Chapman called it a 'dichotomy method' and, later, a 'change-of-composition estimate'. We propose here the term 'survey-removal' estimate as encompassing the two basic aspects involved. \Iuch of the basic data required is already at hand or currently being collected. Harvests or kills are routinely recorded for many populations, and surveys by research and management agencies, primarily for other purposes, are becoming more widespread, e.g., the young sardine surveys of the California Department of Fish and Game (Radovich [1952]), and the North Pacific salmon surveys made as part of the studies in connection with the International North Pacific Fisheries Commission, but used also for management and forecasting purposes. If such surveys and data on the removal by man are available, useful estimates of the mortality rates due to the removals can be computed. Other parameters such as population size can also be estimated if there is auxiliary information oni the populations. The studies and applications of the survey-removal method cited earlier have been based explicitly or implicitly on a mnodel which assumes no natural mortality. This may give satisfactory answers in case the period of removal is short so that the 'before' an-d 'after' surveys are quite close together in time, but is is obviously an un-