The validity of different methods in the backcalculation of the lengths of roach—a comparison between scales and cleithra

The backcalculated lengths of roach Rutilus rutilus obtained with three different proportional methods [body proportional (BPH) and scale proportional hypotheses (SPH), Fraser—Lee] were compared. In the BPH and SPH methods both scales and cleithra were used, while the Fraser—Lee method was used with scales only. The validity of the results was evaluated by comparing the results with observed lengths within one cohort. Both body—scale and body-cleithrum relationships were best described by a power function ( r ²= 0·83). The backcalculated lengths of roach at age 1 varied from 51 mm (SPH, scales and cleithra) to 72 mm (Fraser—Lee), a 30% difference. In within-cohort comparisons, the difference compared with observed lengths was smallest in BPH (<4% with few exceptions). The linear Fraser—Lee method overestimated (up to 5%) the lengths at young ages and underestimated the lengths at older ages (3–5%). In SPH the difference with observed length was 12% at highest. The length estimates by SPH were more affected by the age—structure of the sample than the estimates by BPH, which suggested that Lee's phenomenon was present. This was tested by backcalculating the lengths at the age of 2 years for roach, separately from different age-groups. The backcalculated lengths declined with the increasing age of fish used in the calculations. The phenomenon was strongest in SPH and weakest in Fraser—Lee. The results suggested that in the backcalculation of the lengths of roach, BPH method gives the most reliable results. Considering the other methods, Fraser—Lee should be used rather than SPH.