A statistical model for quantifying age-reading errors and its application to the Antarctic minke whales

Abstract

A statistical method for quantifying age-reading error, i.e. the extent of bias and inter-reader variability among readers, is introduced. The method assumes the availability of an independent ‘control reader’ who produces reference ages for age-reading structures which are also read by additional readers. This control reader is assumed to provide unbiased or consistently biased age estimates so that the additional readers’ age-reading outcomes can be standardised. Linear structures in bias and variance are incorporated in a conditional probability matrix representing the stochastic nature of age-determination for each reader. A joint likelihood function for the parameters related to age-reading bias, variance and nuisance parameters is defined based on observed age-reading outcomes from both the control and additional readers. The method is applied to data for Antarctic minke whales taken during Japanese commercial (1971/72–1986/87) and scientific (JARPA: 1987/88–2004/05, JARPA II: 2005/06–2010/11) whaling. A total of 250 earplugs selected according to a predetermined protocol were used in the analyses to estimate the inter-reader variation for four Japanese readers. One of the authors acted as the control reader. The Japanese readers and the control reader differed in terms of both the expected age given the true age, and variance in age-estimates. The expected age and random uncertainty in age-estimates differed among the Japanese readers, although the two readers in charge of age-reading for samples taken during Japanese scientific whaling (JARPA and JARPA II) provided quite similar agereading outcomes. These results contribute to analyses using catch-at-age data for this species. It should also be noted that the model and approach in this paper can be applied to populations other than the Antarctic minke whales, if a control reader is available, even retrospectively.