Time-series analysis of abundance indices of young fish

Abstract

Abstract Catch-at-age analysis provides estimates of stock size at ages when the fish have reached catchable size. Survey indices contain information about relative cohort size at younger ages. The present analysis is concerned with survey indices of juveniles up to the youngest age where stock estimates, based on time-series analysis of catch-at-age data, are available. A stock estimate at that age from catch-at-age data is also included. A common model of the relationship between stock size and survey indices is combined with the model describing the decline of a stock by natural mortality. Random variations in natural mortality are defined separately from sampling variations and irregular catchability in the survey. The stock size and magnitudes of the random variations are estimated by the Kalman filter, which also provides predictions of future recruitment to the catchable stock. Analysis of observations of Icelandic cod reveals a large deviation from proportionality in the relationship between the index and the stock estimates in the youngest ages, but haddock data are compatible with proportionality. Variations in natural mortality during the second to fourth year of cod and the second to third year of haddock are not a major factor in variations of stock size.