A Growth Model for Arctica islandica: The Performance of Tanaka and the Temptation of Von Bertalanffy—Can the Two Coexist?

ABSTRACT Organisms increase in size over time (age) due to excess assimilation over metabolic (respiration) energy demands. Most organisms reach a maximum size with increasing age as gain and loss balance. The von Bertalanffy length-at-age relationship, which is commonly used in fishery assessment calculations, imposes such a maximum size. However, some fished species, such as ocean quahogs, Arctica islandica, are long lived and continue to grow at old age. The Tanaka age-at-length relationship has continued growth at old age, but is rarely used in stock assessment models. A modified form of the von Bertalanffy model is presented, which mimics the continued growth at old age of the Tanaka model by allowing the growth parameter (K) to decline with age. This form is suitable for inclusion in stock assessment models based on von Bertalanffy. The proposed model matches Tanaka curves with precision appropriate for the scatter of data used to fit the curves. The observations of ocean quahog length at age and growth rate from New Jersey and Georges Bank demonstrate the ability of the modified von Bertalanffy relationship to represent continued growth at old age for this fished species. Simulated data generated with continued growth at old age were fit with the Stock Synthesis model (SS3). Results comparing traditional and modified growth relationships showed that the original von Bertalanffy model can reasonably approximate modest nonasymptotic growth as long as the number of observations is sufficient to constrain the parameter values.