A Multivariate Maturity Model with a Comparative Analysis of Three Lingcod (Ophiodon elongatus) Stocks

Abstract

In this paper we develop a multivariate analysis of length and age at maturity that includes the univariate maturity model of Schnute and Richards (1990, Can. J. Fish. Aquat. Sci. 47: 24–40) as a special case. In addition, we address the problem of drawing meaningful conclusions from large data sets oriented to fish maturity, and we present statistical tests of such conclusions. We illustrate our approach with comparisons among male and female lingcod (Ophiodon elongatus) from three stocks along the coast of British Columbia, Canada. From the univariate analysis, we demonstrate that male lingcod mature at a smaller size than female lingcod, and that for each sex, size at maturity increases with latitude. From the multivariate analysis, we determine that length and age together provide a better prediction of lingcod maturation than either variate considered alone. The multivariate model is applicable to any situation for which one or more positive variates is asymptotically related to a probability measure in the range (0, 1).