An index of per capita recruitment

An index of per capita recruitment (PCR) is proposed such that PCRy-1 = R1(y)/(1-R1(y))e(M) 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 inves tigation of reproductive success and the factors postulated to affect it. T he formulation of PCX is based on the assumptions that: (i) post-recruit mo rtality does not vary over age or between years; (ii) 100% of age-1 animals spawn; (iii) a representative sample of the population is available; and ( iv) the proportion of age-1 animals in the sample can be determined unambig uously. Normal, lognormal and uniform probability distributions of R1, and three levels of M were assumed in order to investigate the resulting distri butions of PCX. Distributions of PCX are skewed toward higher values such t hat 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 un derlying assumptions. PCX is not biased relative to recruits per spawner wh en mortality is constant over all ages and years, and when all age-1 animal s spawn. These conclusions are insensitive to changes in the shape of the f unctional relationship between spawners and recruits. PCR is biased low wit h age-specific decline in mortality and reduction in the proportion of age- 1 spawners. Introducing year-to-year random variability in both mortality a nd proportion of age-1 spawners resulted in broader distributions of PCX re lative to recruits per spawner but did not appear to introduce additional b ias. On average, PCR will underestimate recruits per spawner by 30% if reas onable assumptions are made regarding the variability of mortality and the proportion of age-1 spawners. The effectiveness of PCX to track changes in recruits per spawner over time was confirmed by introducing cycles in the s hape of the functional relationship between spawners and recruits. PCX was also able to track cycles in recruits per spawner after a 20% random sampli ng error was added to the value of R1 used in the calculation of PCX and ye ar-to-year random variability in mortality and proportion of age-1 spawners was introduced, although errors were larger. A time series of PCX for Anta rctic krill (Euphausia superba) sampled in the vicinity of the South Shetla nd Islands from 1979 to 1998 is presented.