Effect of sampling design on the estimation of length-weight relationship parameter b of Chaemrichthys stigmatias

The length-weight relationship of fish stock is one of the commonly used formulas in fishery ecology study. The length-weight relationship is significant for the assessment of fishery resources. It is often used to estimate the average weight of a given length and estimate the status of the fish stock. The accuracy of the estimates of length-weight relationship parameters for fish stock affects the stock assessment and management. Data obtained with different sampling design may have influence on the estimation of length-weight relationship parameter b of Chaemrichthys stigmatias. In order to find out the affect of sampling season and sample size on the length-weight relationship parameters, this study based on the biological data on the length and weight of C. stigmatias obtained from fishery-independent surveys conducted between 2013 and 2014 in the Yellow River Estuary, examined the influence of sampling designs on the estimation of parameter b of the length-weight relationship of C. stigmatias by using a computer simulation study. Based on the actual situation of fishery resources survey in different seasons, 15 sampling design schemes were simulated, and then the influence of different sampling designs on the estimated body length-weight relationship parameter b was compared by selecting two indexes, namely, relative estimation error and relative deviation. The results showed that the estimation accuracy of the length-weight relationship parameter can be effectively improved with the sample size increasing. The length and weight data in different seasons showed different impacts on the estimation accuracy of the parameter, and the data in summer were particularly important in improving the accuracy and precision of estimation of length-weight relationship parameter b for C. stigmatias. The precision and accuracy of parameter estimates based on the data from more seasons were usually higher than those using data in a single season. Scheme 9 (sampling in summer and winter) performed the best at the same sample size among all the fifteen sampling design schemes. The relative estimation error of parameter b of the length-weight relationship was 2.08%, and the absolute value of the relative bias was 0.71% for scheme 9 at the sample size of 540 individuals. The study indicated that enough biological data from representative seasons that have a great effect on the estimation of the parameter should be obtained when we estimate the length-weight relationship for fish populations like C. stigmatias in the Yellow River estuary. In this paper, using C. stigmatias as an example, the influence of sampling design on the estimation of length-weight relationship parameter was explored, which would provide a reference for the estimation of length-weight relationship parameter of other fish stocks.