Estimating reaction norms for age and size at maturation with reconstructed immature size distributions: a new technique illustrated by application to Northeast Arctic cod

Reaction norms for age and size at maturation describe the probability of immature fish maturing at a certain age and size. Knowledge of such reaction norms is increasingly important, both for observing and understanding changes in maturation and for calibrating sizeand age-structured population models. Estimating the reaction norms for age and size at maturation by logistic regression requires data on the size and age distribution of immature and maturing fish. To permit such estimation when measurements of the size and age distribution of immature fish are not available, the information can be reconstructed by means of a back-projection procedure. For the reconstruction, only the size and age distribution of maturing fish, or first-time spawners, together with the age-dependent proportion of mature fish, given in the form of maturity ogives, have to be known. The method of Gulland (1964) is used to generate maturity ogives in the absence of data on immature fish. The robustness of the estimation method is demonstrated by analysing artificial data generated with a known reaction norm. Application of the reconstruction method to a set of measurements on Northeast Arctic cod (Gadus morhua) collected between 1933 and 1944 illustrates how the approach allows new information to be extracted from real data.