Bias in the estimation of krill yield from using a deterministic formulation of the median unexploited spawning biomass

Two Monte Carlo simulation models are currently available to CCAMLR for estimating krill yields according to decision rules that relate spawning stock status to the median unexploited spawning biomass, SB0. The first model has been developed specifically for krill, the krill yield model, while the second is a generalised yield model. The decision rules relate to the effects of a specified long-term annual yield (γ) on (i) the probability of the spawning stock being reduced below a set proportion of SB0 during a projection run (probability of critical depletion) and (ii) the median status of the spawning stock (as a proportion of SB0) at the end of the projection run (level of escapement). The krill yield model uses a biased estimate of SB0 with a method for correcting this bias in the level of escapement. The generalised yield model uses an unbiased estimate of SB0 and, thus, requires no correction.
This paper examines the implications for estimates of krill yield from using the biased estimate of SB0 in the krill yield model compared to the unbiased estimate in the generalised yield model. The results show that the biased estimate of SB0 results in a biased estimate of the probability of critical depletion while the level of escapement is not appreciably sensitive to the method of estimating SB0. This bias in the krill yield model will result in the catch level, γ, given for a set probability of critical depletion will be too high. The relationship between fishing season and spawning season will influence the sensitivity of the krill yield model to this bias. In this case, a greater overlap between fishing season and spawning season will result in less bias occurring.