Author(s): D G Chapman
The age distribution of a random sample, or the "catch curve" from a stationary animal or fish population, provides information on the annual survival rate of the population. The usual assumptions imply that the age distribution in such a population is geometric. The best (minimum variance unbiased) estimate of the annual survival rate is X̄[1 + X̄ - (1/n)]-1, X̄ being the mean age and n the sample size. This estimate is compared to the so-called "Jackson" estimate and some modifications of Jackson's estimate. Assumptions basic to regression estimates of the survival rate are considered. A test of the model is given for the particular case where it is suspected that there may be selection against younger ages. With the geometric age distribution there is no unbiased estimate of i, the instantaneous mortality rate, but a nearly unbiased estimate is given by i* = ln [1 + X̄ - (1/n)] - ln X̄ - [(n - 1)(n - 2)/n(t + 1)(n + t - 1)] where t = nX̄.