Linf of grey mullets from the Cross River Estuary, Nigeria

The Non-Parametric Scoring Dataset from ELEFAN In the electronics of FiSAT-based growth analysis, non-parametric scoring constitutes a core step in the procedure for estimating the von Bertalanffy Growth Function (VBGF) from length-frequency data (Pauly, 1987). The scoring dataset generated by ELEFAN is a quantitative representation of how well candidate growth parameter pairs (K, L∞) match the observed modes of the empirical length-frequency distribution without requiring direct ageing information. Understanding the structure and interpretation of this dataset is essential for both parameter estimation and subsequent statistical modelling. At its core, the ELEFAN algorithm evaluates the alignment between hypothesised growth curves (parameterised by K and L∞) and the empirical peaks (modes) of the monthly length-frequency data. This evaluation is summarised in a non-parametric score matrix, sometimes called the “scoring surface”. The matrix can be described as follows. Structure of the ELEFAN scoring dataset Axes: The two principal dimensions correspond to a grid of candidate growth parameter pairs. In the present application, K values ranged from 0.51 yr⁻¹ to 10.0 yr⁻¹ (20 discrete values), and L∞ values ranged from ~17 cm to ~53 cm (20 discrete values). Each cell in the matrix is uniquely defined by a pair (K, L∞). Entries (Scores): The scalar value S(K, L∞) stored in each cell represents the non-parametric score computed by ELEFAN, which quantifies the agreement between the theoretical growth trajectory and the observed length-frequency modes. Higher scores indicate better alignment and thus greater biological plausibility under the data. The score is dimensionless and typically ranges from ~0 to 1. Interpretation of high scores: The highest score in the matrix identifies the discrete global optimum, i.e. the (K, L∞) pair that best explains the observed modes. In this case, ELEFAN identified K = 0.51 yr⁻¹ and L∞ = 27.80 cm as the discrete maximum (score = 0.1690). Surface topology: Beyond the single peak, the scoring dataset often reveals ridges, plateaus, and local maxima that may represent alternative growth parameterisation hypotheses or artefacts of limited data resolution. For instance, a secondary high-score peak was observed at K ≈ 3.42 yr⁻¹ and L∞ ≈ 17.54 cm, suggesting possible population heterogeneity or sampling bias. Downstream use: The complete scoring surface is used for more advanced analyses—such as Gaussian Process smoothing, uncertainty quantification, curvature diagnostics and ridge detection. These help turn the ELEFAN table into an interpretable and continuous parameter space rather than a discrete grid.