An index of per capita recruitment (PCR) is proposed such that Ri PCRy–1 = R1y/(1–R1y)eM where R1 is the proportion of age-1 animals sampled in year y and M is the post-recruit mortality rate. The intent of the index is to facilitate investigation of reproductive success and the factors postulated to affect it. The formulation of PCR is based on the assumptions that: 1) post-recruit mortality does not vary over age or between years; 2) 100% of age-1 animals spawn; 3) a representative sample of the population is available; and 4) the proportion of age-1 animals in the sample can be determined unambiguously. Normal, log-normal and uniform probability distributions of R1, and three levels of M, were assumed in order to investigate the resulting distributions of PCR. Distributions of PCR are skewed toward higher values such that the dynamic range of PCR is largest with high values of R1; increasing M tends to offset this effect but only slightly. A simple population model was then constructed to test the sensitivity of PCR to relaxation of its underlying assumptions. PCR is not biased relative to recruits per spawner when mortality is constant over all ages and years, and when all age-1 animals spawn. These conclusions are insensitive to changes in the shape of the functional relationship between spawners and recruits. PCR is biased low with age-specific decline in mortality and reduction in the proportion of age-1 spawners. Introducing year to year random variability in both mortality and proportion of age age-1 spawners resulted in broader distributions of PCR relative to recruits per spawner but did not appear to introduce additional bias. On average, PCR will under estimate recruits per spawner by 30% if reasonable assumptions are made regarding the variability of mortality and the proportion of age-1 spawners. The effectiveness of PCR to track changes in recruits per spawner over time was confirmed by introducing cycles in the shape of the functional relationship between spawners and recruits. PCR was also able to track cycles in recruits per spawner after a 20% random sampling error was added to the value of R1 used in the calculation of PCR and year to year random variability in mortality and proportion of age-1 spawners was introduced, although errors were larger. A time series of PCR for Antarctic krill sampled in the vicinity of the South Shetland Islands from 1979 through 1998 is presented.

# An index of per capita recruitment

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WG-EMM-99/50

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