The generalization of Gulland’s method: How to estimate maturity ogives when juvenile data are missing while spawner demography is known

Abstract

The proportions of mature individuals at age or length, collectively known as the maturity ogive, are a key population characteristic and serve as critical input to age-disaggregated stock assessments. John Gulland showed in 1964 that it is possible to estimate maturity ogives even when representative data on immature individuals are not available, provided that one can distinguish newly mature individuals (first-time spawners) from those that had matured earlier (repeat spawners). Gulland’s method offers a valuable tool for obtaining information on an unobserved part of a population and is also applicable to other ontogenetic transitions, such as metamorphosis, smolting, ontogenetic niche shifts, and sex change. Here we present a full derivation of Gulland’s method from first principles, applicable to the general case in which the survival of immature, first-spawning, and repeat-spawning individuals may differ. Better observation methods, in particular in sclerochronology and histology, are expected to make meeting this method’s data requirements—i.e., the separation of first-time and repeat spawners—more often achievable, and estimating maturity ogives could serve as an additional incentive for allocating resources to enhanced data collection. With the generalization presented here, we hope to make Gulland’s method better known and more widely accessible.