The back-calculation of size and growth from otoliths: Validation and comparison of models at an individual level

Abstract

Multiple internal and external tagging experiments tested the applicability of five back-calculation models (Biological Intercept, Modified-Fry, Body Proportional Hypothesis, Time-Varying Growth, and an Age-Effects model) as predictors of individual growth trajectories of two marine cleaning gobies, Elacatinus evelynae and E. prochilos, that were raised in aquaria under conditions that resulted in variable growth. Mixed-effect model analyses of longitudinal records of otoliths and somatic growth collected at the individual level revealed that E. evelynae and E. prochilos produced daily increments on their otoliths for up to two months post-settlement and that the Modified-Fry model provided the most accurate size-at-age estimates despite the presence of age, growth and time-varying growth effects in the dataset. Very large errors in predicted size were produced by the Age-Effects model. The four other back-calculation models all provided slightly biased estimates of back-calculated size-at-age, with the Modified-Fry model providing the least biased estimates. Regardless of bias, both experimental and theoretical evidence indicated that back-calculated size was a better proxy of fish length than otoliths radius. Relationships between fish length and otoliths radius were allometric at the level of individuals, which explained why the Modified-Fry model performed better. However, this allometry was undetectable at the population level. This study represents the first attempt to validate modern back-calculation models using longitudinal data collected and analysed at the individual level. Our results suggest the use of the Modified-Fry model as a conservative approach in routine back-calculations of fish size at age from otoliths.