Developing a size indicator for fish populations

Abstract

Monitoring temporal and/or spatial variations in fish size-at-age data can often provide fisheries managers with important information about the status of fish stocks and therefore help them identify necessary changes in management policies. However, due to the multivariate nature of size-at-age data, commonly used single-age-based approaches ignore covariance between sizes of different age groups. Different results may therefore be derived when evaluating temporal variations using different age groups for the comparison. The possibility of atypical errors in size-at-age data due to ageing and measurement errors further complicates the comparison. We propose a two-step approach for developing an indicator for monitoring temporal and/or spatial variation in size-at-age data. A robust approach, minimum volume ellipsoid analysis, is used to identify possible outliers in size-at-age data. Then a weighted principal component analysis is applied to the data with the identified outliers down-weighted. An indicator is defined from the resultant principal components for monitoring temporal/spatial variations in size-at-age data. We illustrate the proposed approach with size-at-age data for cod (Gadus morhua) in the northwest Atlantic, NAFO subdivision 3Ps. The overall size-at-age indicator identified shows that the pre-1980 year classes tend to have a much higher size-at-age than the post-1980 year classes.