Bias and Bias Correction in Fish Recruitment Prediction

Abstract

A lognormal error is usually assumed in the traditional stock–recruitment (SR) analysis. In this paper, I demonstrate that a positive bias results when an SR model with lognormal error is used for fish recruitment prediction. Not only is this bias exponentially dependent on the structure of the model's residual variance and the historical SR data, it is also dependent on the specific value of spawner biomass used. I then derive a bias correction that is asymptotically unbiased with a finite-sample bias that is practically zero. Data from two Pacific salmon populations, southeast Alaska pink salmon Oncorhynchus gorbuscha and Chilko Lake sockeye salmon O. nerka, are used to demonstrate this approach. The results show that the relative bias is about 10% for a spawning biomass within the historical range and that the bias is substantial outside that data range. However, with the proposed bias correction, the bias is negligible both within (<0.1%) and outside of (<0.3%) the data range.