Modelling the missing annuli count in North Pacific spiny dogfish (Squalus suckleyi) by nonlinear mixed effects models

Abstract

North Pacific spiny dogfish (Squalus suckleyi, Girard 1854) are aged with annuli count on the second dorsal spine. As this spine grows, enamel at the distal tip is worn away producing a zone of missing annuli. Sixty-seven male and 115 female dogfish specimens were randomly selected from captured specimens taken off the Washington coast in 2005-2006 and their fork lengths measured and spines taken. For the second dorsal spine from each specimen, five measurements were recorded. These measurements permit the estimation of the missing annuli count before the “no wear point” based on the known statistical distribution of annuli count after the “no wear point.” Three diameter measurements were then modeled with nonlinear mixed effects (NLME) models that treated the number of missing annuli count as random effects. Resulting models were compared against Ketchen’s (1975) “no wear point” method. The estimated missing annuli count and the measured spine base diameter fits well with the assumptions of an existing von Bertalanffy growth curve for this species. Ketchen’s method produced an apparent underestimate of the mean missing annuli count for all dogfish with spine diameter at the no wear point less than 1.2 mm and greater than 4.6 mm. The NLME models provide an alternative method to estimate the missing annuli count of north Pacific spiny dogfish based on both sound biological and statistical properties.