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#Age backcalculation corrections for verification#
The process of back calculation can be broken down into three steps: verification of the periodicity of annulus formation, establishment of an otolith radius-total body length (OR-TL) relation, and the estimation of size at the time of annulus formation. To standardize age at which size is estimated, or to obtain length-at-age data on ages not included in the sample, back-calculation techniques are often employed to estimate a fish's size at a previous age (Bagenal, 1978). Growth is then described as the change in weight or length over some unit of time. but for this study, however, otoliths were considered the representative hard structure) and with the subsequent assumption that these fish are an unbiased representation of size at that age. Thus, errors in the estimation of growth can lead to erroneous advice to fishery managers concerning the present and possible future status of a population.īy far the most common method of estimating fish growth rate is by estimating the age of individual fish from calcified structures (scales, otoliths, spines, etc. Furthermore, current conservation standards (Gulland and Boerema, 1973 Goodyear, 1993) are dependent upon the rate of individual growth. The average rate at which the fish within the stock increases in weight ultimately determines the level of effort required to extract a desired yield from the stock as a whole (Ricker, 1975). The average rate of growth of an individual fish in a population is critical to age-based stock assessments. Finally, an asymptotically shaped OR-TL was best modeled by the individually corrected Weibull cumulative distribution function when all annuli were used, and when only the last annulus was used. If the OR-TL was exponentially shaped, direct substitution into the fitted quadratic equation resulted in the least error when all annuli were used, and when only the last annulus was used. When the OR-TL was linear, employing a functional regression coupled with the Lee back-calculation equation resulted in the least error when all annuli were used, and also when only the last annulus was used. When the OR-TL was sigmoid shaped and all annuli were used, employing a least-squares linear regression coupled with a log-transformed Lee back-calculation equation (y-intercept corrected) resulted in the least error when only the last annulus was used, employing a direct proportionality back-calculation equation resulted in the least error. Specimen lengths were back-calculated to the last age through measurements between the vertebrae focus and each translucent band for each individual, using the. The best back-calculation technique was directly related to how well the OR-TL model fitted. The accuracy of each of the twenty methods was evaluated by comparing the back-calculated length-at-age and the true length-at-age. using the increments between successive annuli to develop a backcalculated growth curve to age 9, with mean lengths-at-age from age 1 of about 8. Ten different back-calculation equations, two different regression models of radius-length, and two schemes of annulus selection were examined for a total of 20 different methods to estimate size at age from simulated data sets of length and annulus measurements. Four shapes of otolith radius-total length relations (OR-TL) were simulated. We suggest that light body-scale relationships are attainable for many species, obviating concern over which proportional back-calculation method is chosen.Abstract-I simulated somatic growth and accompanying otolith growth using an individual-based bioenergetics model in order to examine the performance of several back-calculation methods. Tighter body-scale relationships in our data sets than in previous studies appear to explain this contradiction. Our results, indicating little or no difference among methods, contradict recent reviews claiming substantial disagreement among methods. Observed lengths were often greater than back-calculated lengths for age-1 golden shiners. Back-calculated lengths generally corresponded well with observed lengths in all pumpkinseeds age-classes and in golden shiners older than 1 year. Likewise, all back-calculation methods produced equivalent results. Differences between OR and GMR body-scale relationships were negligible in both species. Although minor differences were detected in body-scale regressions among lakes, pooling data across lakes yielded linear bodyscale relationships with very high r2.
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Ordinary least-squares regression (OR) was compared with geometric mean regression (GMR) for describing body-scale relationships. 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 lime of annulus formation.