New insights into fish growth parameters estimation by means of length-based methods

Growth studies are an essential instrument in the management of fisheries resources since they contribute to estimates of production, stock size, recruitment and mortality of fish populations. In the event that age becomes too complex to be established through an observation of hard parts (otoliths, scales, opercula, rays, spines and vertebrae), information about the demographic parameters of fish and other animal populations can be obtained by length-frequency analysis. Length-frequency distributions are commonly analyzed by means of histograms, although they present several problems, such as a dependency on the origin, width and number of class intervals, discontinuity of data and fixed bandwidth. This can largely affect the reliability of the estimates, i.e. the results become dependent upon the data massage operated by the user. The main aim of this research study was an attempt to contribute to overcome some of the abovementioned limits. Two algorithms were tested in terms of their capacity to produce accurate estimates of fish growth parameters. The first, the Birgé and Rozenholc algorithm, has recently been proposed for determining the optimal number of intervals to be used for building a regular histogram from available data. The second, the Expectation-Maximization (EM) algorithm, has become a popular tool in statistical computations involving incomplete data, or in similar problems, such as mixture estimation. Monte-Carlo simulations of fish populations having different biological characteristics were generated to test the efficiency of these two algorithms. Two marine species were chosen as representatives of opposing life-histories: the Red mullet (Mullus barbatus Linnaeus, 1758), a fast-growing species, and the European hake (Merluccius merluccius (Linnaeus, 1758), a slow-growing species. A length sample of size n = 100,000 was generated for each species. In order to evaluate the performance of the Birgé and Rozenholc algorithm using samples of different sizes, 100 random datasets containing 100, 200, 500 and 1000 length measurements respectively were extracted from each hypothetical population. Data for each of these 800 length datasets was then partitioned using (i) the method proposed by Birgé and Rozenholc and (ii) the classical interval widths (1 cm for the Red mullet and 2 cm for the European hake). These simulated length-frequency distributions were then analyzed by means of two length-frequency methods: (i) the ELEFAN I method, a non-parametric approach, and (ii) Bhattacharya’s method, a parametric approach. For the present study, a Scilab 4.0 version of the ELEFAN I and the Bhattacharya methods was developed. Since the EM algorithm functions best with samples of size n ≥ 1000, only the 100 random datasets each containing 1000 length measurements were used to run the algorithm. Two length datasets were also used to test the performance of the two algorithms on field data. The results obtained using the two algorithms were very encouraging. The Birgé and Rozenholc algorithm proved to be an easy and efficient method for choosing the number of intervals in a histogram. Nevertheless, the performance of the algorithm with small sized samples needs to be investigated further, especially in the case of slow-growing species. On the other hand, the efficiency of the EM algorithm became evident for the two species considered both with simulated and real length data. The estimates of the demographic parameters obtained by means of the EM algorithm were always better (i.e. there was a less percentage bias) than those used as starting values. In conclusion, the results obtained using the two algorithms seem to be of great interest and their methodological and theoretical contribution to this field could represent a landmark in the enhancement of stock assessment studies.