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 Lepoinis 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 r². 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 l 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.