Length-at-Age Analysis: Can You Get What You See?

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Abstract
Observations at a single point in time of length-at-age (LAA) for a long-lived rockfish (Sebastes alutus) show that old fish are shorter than intermediate-aged fish. Fitting of a von Bertalanffy growth model to these data produces a systematic trend in the residual of observed versus calculated LAA. We examined how such LAA data can lead to erroneous conclusions about individual growth, and whether asymptotic growth can give rise to such data. We considered two hypotheses: (i) that a time trend in growth rate resulted in larger fish in more recent years and (ii) that there are multiple growth types, where growth and mortality rates are directly related. Using a general growth model that incorporated both (i) and (ii), we show that both hypotheses can generate data identical to those for the rockfish. A single set of LAA data is inadequate for describing individual growth; however, if sufficient data are available, model ambiguity can be resolved and reasonable parameter estimates obtained. Analysis of the rockfish data indicates that (ii) is more likely to explain the observations than (i). We show how fisheries on such species may preclude our understanding these biological relationships.

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