Back-calculation of fish length from scales: Empirical comparison of proportional methods

We compared three proportional back-calculation methods for scales using data sets for pumpkinseeds Lepomis gibbosus and golden shiners Notemigonus crysoleucas from 10 southern Quebec lakes, and we validated back-calculations by comparing them with observed lengths at time of annulus formation. Ordinary least-squares regression (OR) was compared with geometric mean regression (GMR) for describing body-scale relationships. Although minor differences were detected in body-scale regressions among lakes, pooling data across lakes yielded linear body-scale relationships with very high r(2). Differences between OR and GMR body-scale relationships were negligible in both species. Likewise, all back-calculation methods produced equivalent results. Back-calculated lengths generally corresponded well with observed lengths in all pumpkinseeds age-classes and in golden shiners older than 1 year. Observed lengths were often greater than back-calculated lengths for age-1 golden shiners. Our results, indicating little or no difference among methods, contradict recent reviews claiming substantial disagreement among methods. Tighter body-scale relationships in our data sets than in previous studies appear to explain this contradiction. We suggest that tight body-scale relationships are attainable for many species, obviating concern over which proportional back-calculation method is chosen.