A proposed, tested, and applied adjustment to account for bias in growth parameter estimates due to selectivity

Abstract

Growth information is important for stock assessments because it gives an indication of spawning stock biomass in the form of weight or fecundity, which is an important indicator of stock status, as well as being important if fitting to length composition data. Sampling for growth characteristics should include all ages and sizes in the population, but data are often only available from fishery-dependent sampling, which can lead to biased estimates of true underlying population growth parameters because of selectivity, which includes both gear selectivity and availability. Two stock assessments with the potential for biased growth because of dome-shaped selectivity and lack of fishery-independent age data are the Gulf and Atlantic menhaden assessments. The objectives of our study were (1) to develop and test a method to estimate unbiased growth parameters regardless of the selectivity of the gear used to sample ages and lengths and (2) to apply the proposed method to fit unbiased population growth parameters for Gulf and Atlantic menhaden. We propose a method to adjust for the bias in the growth curve parameters and account for missing samples at smaller and larger lengths. The proposed method was tested on simulated data and applied to data for Gulf and Atlantic menhaden. Use of the adjustments was robust and resulted in reduced bias in the growth parameter estimates with accuracy being affected by both sample size and variability in mean length at age. Increasing the sample sizes increased the accuracy of the adjustments (i.e., as the coefficient of variation (CV) for length at age increased, the accuracy of the estimates decreased). For Gulf menhaden, the parameters estimated for the unadjusted growth curve were L∞=240.8, k=0.38, t0=−1.14, and CV of length at age=0.06 (assumed constant) with a total sample size of 366,710 from 1977 to 2011. For Atlantic menhaden, the parameters estimated for the unadjusted growth curve were L∞=350.9, k=0.32, t0=−0.83, and CV of length at age=0.12 (assumed constant) with a total sample size of 480,668 from 1955 to 2011. The adjustment for a maximum length of capture had a large impact on the overall growth parameters for both species, while the adjustment for a minimum length of capture had less impact. Bias in the growth curve parameter estimates can be reduced by using the method outlined to account for selectivity.