A spatiotemporal Richards–Schnute growth model and its estimation when data are collected through length-stratified sampling

Abstract

We propose a spatiotemporal generalized von Bertalanffy (vonB) growth model that also includes between-individual (BI) variation and male/female correlation. The generalized vonB model includes the effect of maturation on growth. The model and the methodology are applied to a long time-series of survey observations of age and length for American plaice on the Grand Bank off the northeast coast of Canada. The bias in age-length data due to size selectivity of the survey gear is accounted for. The survey design includes length-stratified age sampling which is a type of response selective sampling design for growth model estimation. We propose and implement a conditional empirical proportion likelihood approach for these data. Neglecting this sampling scheme can lead to seriously biased estimation results. We found that a 6-parameter growth model is necessary for capturing the biphasic growth patterns of the American plaice on the Grand Bank, and the survey gear selectivity and BI variation are important for a good model fit. We proposed an empirically optimal BI variation model for this data. Our estimation results indicate that there are substantial differences in size-at-age for male and female American plaice, and this changes over time and between regions.