From Data to Insight: Machine Learning Approaches for Fish Age Prediction in European Hake

Abstract

The European hake (Merluccius merluccius) is a highly sought after, overfished commercial species with a high ecological value. Otolith morphometric characteristics were employed from 150 individuals captured from the Central Aegean Sea (Eastern Mediterranean) using a commercial trawler. Age reading was independently performed by three readers. A multivariate methodology identified the morphometric factors that significantly affect age estimation, and easy to use equations using limited morphological otolith characteristics with a high degree of accuracy were produced as a practical tool for fisheries management. A second tool using ML algorithms produced a highly accurate ML model with the ability to further predict European hake’s age using limited otolith morphometric characteristics. Both tools are important for assessing fish population dynamics, managing sustainable fishing practices, and ensuring the long-term health of marine ecosystems. Practically, the models could be implemented by collecting fish otolith samples, measuring limited morphometric features using imaging techniques, and inputting these measurements into the machine learning model. Both model outputs will allow researchers and fisheries managers to obtain rapid and reliable age estimates without the need for labor-intensive traditional methods. By integrating these models into routine fisheries assessment workflows, stakeholders could make more informed decisions about fish stock assessments and conservation strategies.

1. Introduction

The European hake (Merluccius merluccius) is a demersal species that typically inhabits depths between 70 and 300 m on the continental shelf [1] and upper slope [2,3]. In the Mediterranean Sea, it can be found on both the continental shelf and the upper slope [2,3]. Juvenile European hake gather in nursery areas situated on the continental shelf break [4,5,6,7], while adult fish inhabit a broader depth range extending from the shelf to the upper slope [8,9,10,11]. According to Morales-Nin et al. [12], M. merluccius is a significant demersal finfish in the marine ecosystems of the North Atlantic and Mediterranean Seas. The Cape Breton Gorge on the Atlantic coast of North America divides two M. merluccius stocks, the northern and the southern [13], with the southern stock highly overexploited [14]. The European hake is also one of the most valued and overfished species in Western European fisheries [15]. Its high commercial value has resulted in population declines over the previous 20–40 years as a consequence of fishing pressure from commercial fisheries in the Eastern Mediterranean [16]. In Greek territorial waters, over 1500 tons were caught each year between 1980 and 1985 [17], with annual landings between 1992 and 2019 remaining consistent at roughly 5000 tons [18].

Due to the significance of age estimation for stock assessment and fisheries management, age identification remains essential for the management and conservation of the species [19] and the production of accurate stock assessment models [20]. Age is a crucial biological characteristic for all fish species, since it provides information on their growth rate, mortality, recruitment, and maturity. Growth parameters are also important for estimating the potential of the stock in terms of sizes [21].

Fish age determination is paramount for assessing growth rates, population dynamics, future population trends, and the overall ecological state [22]. Additionally, age and growth assessments of commercial fish species are essential inputs in age-structured assessment models, which are used to evaluate the level and impact of exploitation on fish stocks [23,24]. Scales, otoliths, and vertebrae are used in traditional age categorization methods, but these methods are often time-consuming, labor-intensive, prone to human error [25], and susceptible to environmental influences [26]. Length–frequency distribution analysis is another common technique [27] which, despite offering a rapid evaluation of population age structure, is dependent on assumptions [28]. Despite their shortcomings, otoliths comprise an essential tool for fisheries assessment today [29]. Numerous fields have examined fish otoliths, including fish biology, ecology, age, growth, and fish stock assessment [30,31,32].

Otoliths, also known as ear stones, are three densely paired calcium carbonate (CaCO₃) structures (the sagitta, lapillus, and asteriscus in bony fish) housed in three chambers connected to the inner ear of teleosts, surrounded by a proteinaceous matrix [33]. Their formation starts from the embryonic state and continues throughout the adult’s development in successive layers of CaCO₃ [34]. The otolith’s shape can significantly transform during the fish’s growth in response to both physical and ecological ontogenetic changes, as well as variations in the acoustic environment associated with the various habitats occupied by juveniles and adults [11].

The otolith reading approach is an internationally accepted technique for determining the age of M. merluccius [35], and despite its relatively long lifespan, with the oldest specimen ever reported at 20 years old [1], age interpretation using otolith sections has been established to determine age up to five years [36]. The interpretation of the otolith ring formation employed for the age estimation of M. merluccius exhibits an unusual complexity [37,38,39], posing a number of challenges that include the description of the otolith’s core, presence of false annual rings, and difficulty in ring border interpretation [36,40]. Moreover, it is often challenging to distinguish the first annual ring for M. merluccius due to vertical migrations and the extended spawning season, which results in nearly constant recruitment throughout the year [36,39,41]. Hake otoliths exhibit a series of bands known as checks that lack a consistent, recognizable pattern, making the identification of putative annual markings occasionally difficult [39]. These challenges result in otolith readings that are often open to interpretation, leading to confusion and disagreement among scientists [42]. Although advances in microscopy and otolith preparation techniques, such as burning, thin sectioning, and staining, have improved the optical clarity of the examined structure and produced better precision in age estimation, traditional microscope-based age estimation methods of interpreting the annual growth zones have not evolved significantly over the last century [43].

Machine learning (ML), a subfield within the broader domain of artificial intelligence (AI), includes knowledge representation, logic models, algorithms, and computational techniques designed to exhibit intelligent behavior [44], with the ability to evaluate large datasets processing a variety of biological and environmental variables [45]. Research has already illustrated how the integration of imaging technology and machine learning could potentially revolutionize fish age identification, providing more precise, efficient, and scalable solutions [46,47]. Robertson and Morison [48] used feed-forward neural networks in conjunction with biological data (fish length, sex, date of capture, otolith weight, and date of capture) and signal (brightness values along transects within sectioned otolith images) to automate the ageing process of nine fish species in Australian waters. Their study showed that biological data can have a positive impact on age prediction. Artificial neural networks (ANNs), Naive Bayes (NB), and Decision Tree (DT) algorithms’ performance in classifying ages was tested by Benzer et al. [49].

Robertson and Morison [50] further assessed ML algorithms to automatically determine the age of several fish species. Fablet and Le Josse [51] used statistical learning to automate the age assessment of Pleuronectes platessa using otolith images. To categorize the age of Gadus morhua and assess the effectiveness of the classifiers considering the morphological aspects and biological attributes of the otoliths, Bermejo [25] employed Support Vector Machines (SVMs). To evaluate age estimations for Perca flavescens, Dub et al. [52] employed Random Forest (RF) analysis with otolith mass, total length, and many temporal and spatial predictor factors. An open-source artificial intelligence framework was created by Politikos et al. [46] to automate the reading of fish ages using otolith or scale images. Benzer et al. [49] evaluated the effectiveness of age classification learning algorithms (Naïve Bayes, Tree-based methods, and RF) on tench (Tinca tinca).

Deep learning models have proven highly effective for age estimation across diverse fish species, marking a significant advancement in automated fishery science and resource management. For example, Moen et al. [53] applied deep learning techniques to extract age data from Greenland halibut (Reinhardtius hippoglossoides) otoliths with greater accuracy than traditional manual methods. Similarly, Politikos et al. [46] employed convolutional neural networks to estimate the age of red mullet (Mullus barbatus) with notable precision, demonstrating the models’ ability to discern complex patterns in fish otoliths. Vabø et al. [54] further expanded the use of deep learning to salmon (Salmo salar) scales, illustrating that these models can effectively analyze scale patterns and yield reliable age estimates. Collectively, these studies underscore the potential of deep learning models to enhance both the accuracy and efficiency of age determination in various fish species, which is vital for sustainable fisheries management and ecological research.

The advent of digital technology, image analysis systems, and shape analysis methodologies has significantly boosted the importance of studies on otolith morphology [55]. The specific benefits include a low cost and relatively high efficiency, making the study of otolith morphometry crucial for stock identification and fisheries management [56]. Instead of requiring laborious manual measurements, image recognition algorithms could be used to non-invasively evaluate features from images, such as length and scale radius [53]. Additionally, using real-time data, ML models have the potential to predict growth patterns [44].

ML algorithms have the potential to implement and/or replace conventional observations and techniques in a variety of industries. This is done to both simplify difficult tasks and improve the accuracy of the results [51]. Marine and freshwater scientists have acquired a strong tendency to apply these accelerated approaches in the studies they conduct in recent years due to their benefits [57]. ML could facilitate improved, informed decision making by automating data analysis and revealing intricate patterns [58], leading to improved efficiency in biological data collection, ultimately promoting sustainable resource management for the European hake.

Despite European hake’s high commercial and significant ecological value, concerns surrounding the interpretation of its age have yet to be resolved. Hence, the aims of the present study were (i) to identify otolith morphometric factors that significantly affect age estimation for European hake, (ii) formulate a simple, reliable, and easy to use model for the age estimation of European hake based on these previous factors, and (iii) with the application of ML methodology, further develop a framework to predict the age of European hake using limited otolith morphometric characteristics.

This manuscript presents a novel approach to predicting the age of European hake by leveraging morphological characteristics of otoliths combined with advanced machine learning techniques. Unlike traditional methods that rely heavily on labor-intensive and subjective visual inspection, this study introduces a dual strategy: easy to use predictive equations for practical, quick assessments and more sophisticated machine learning models for higher accuracy and automation. The integration of machine learning in this context not only improves the precision of age prediction but also offers a scalable solution that can be adapted to other fish species. This approach represents a significant advancement in fisheries science, particularly in enhancing the accuracy and efficiency of age estimation, which is crucial for sustainable fishery management. The novelty lies in the combination of accessible predictive tools and state-of-the-art machine learning methods, bridging the gap between traditional and modern techniques in fish age prediction.

2. Materials and Methods

2.1. Study Area and Sampling Methodology

A total of 150 M. merluccius individuals were collected from the Central Aegean Sea (Eastern Mediterranean) using a commercial trawl vessel with a square mesh coded with a mesh size (bar length) of 28 mm (stretched). Three fishery-independent surveys took place on two consecutive days during May 2021, 2022, and 2023, using the same commercial bottom otter trawl vessel and trawling gear at depths ranging between 62 and 97 m. The trawling speed was approximately 3 knots. In total, 18 hauls of 30 min duration each were conducted in the eastern, western, and central parts of the Pagasitikos Gulf (Figure 1). For each individual, the total length (cm) and total weight (g) (to the nearest 0.01 g) were recorded. A stratified random sampling design was employed with the gulf divided into distinct areas (west, center, and east). Within each stratum, samples were randomly selected to ensure that every part of the stratum had an equal chance of being included, minimizing biases and improving the representativeness of the samples.

Otolith Extraction Process and Imaging

In total, 150 sagittal otolith pairs were extracted by locating the otic capsule in the retroventral portion of the neurocranium. A shallow incision was made in the middle part of the otic capsule, which was broken, gently, to expose the sagittal otoliths. Following otolith removal, each otolith was cleaned with distilled water to ensure the removal of biological impurities.

2.2. Otolith Morphometry and Age Classification

Morphometric characteristics were measured from all 300 otoliths. Otolith weight was assessed with the use of a Shimadzu, ATX124R digital scale (to the nearest 0.0001 g). Each otolith was measured under a stereoscope (OLYMPUS, U-TV0.5XC-3, 7H01028, Tokyo, Japan) with the use of the digital image processing software Image J, V1.54 (Philadelphia, PA, USA). Five indices related to otolith size were initially obtained: otolith weight (OW), otolith length (OL), otolith width (OWD), otolith perimeter (OP), and otolith area (OA) (Figure 2).

A further seven dimension indices were also calculated: rectangularity (R), squareness (S), ellipticity (E), roundness (RO), aspect ratio (AR), form factor (F), and circularity (C) (

Table 1. The formulas of the dimension indices that were calculated and their associated sources (otolith weight (OW), otolith length (OL), otolith width (OWD), otolith perimeter (OP), and otolith area (OA)).

Otolith Mophometric Characters	Formula	Reference
rectangularity (R)	$OA/(OL \times OWD)$	[59]
squareness (S)	$OA/(OL \times OWD)$	[60]
ellipticity (E)	$(OL-OWD)/(OL+OWD)$	[61]
roundness (RO)	$4\times OA/\pi \times O{L}^2$	[61]
aspect ratio (AR)	$OL/OWD$	[62]
form factor (F)	$4\times \pi \times OA/O{P}^2$	[61]
circularity (C)	$OP/O{A}^2$	[59]

).

Only left otoliths were utilized for the age identification by reading the growth margins and the determination of allometric relationships, as supported by our results (no significant difference in morphometric characteristics among otolith sides) and the published literature [35]. Otolith preparation included sanding with the use of sandpaper (wetted 400 or 600 grit wet/dry sandpaper) for the removal of material and polishing. The sanding residue was rinsed, and each otolith was submerged in glycerin for viewing [63]. The intersection of the opaque zone and translucent zone was used to define each annual ring. Three readers independently performed the readings of the growth markers in the otolith sections. Each otolith was measured under a stereoscope (OLYMPUS, U-TV0.5XC-3, 7H01028, Tokyo, Japan) with the use of the digital image processing software Image J, V1.54 (Philadelphia, PA, USA). The age reading was performed according to [64]. The age used for model estimation was the mean value from all three readers [43]. To quantify the consistency and reliability of age estimates from the three readers, percent agreement, coefficient of variation (CV), and average percent error (APE) matrices were employed [43,65,66].

2.3. Statistical Analysis

Morphometric comparisons among the left and right sagittal otoliths and among sexes were assessed with the parametric Student’s t and welch tests [67,68] and the non-parametric Mann–Whitney U test [67] using Jamovi (v.2.4.11, Sydney, Australia) [69], at an alpha level of 0.05. Data were previously checked for normality with the Shapiro–Wilk test and for homoscedasticity with Levene’s and Variance ratio tests. The major factors affecting age estimation and their relative importance (p < 0.05) among all recorded measurements were identified by fitting a second-degree stepwise regression using the minimum Bayesian information Criterion (BIC) as a stopping rule, with a forward direction. The Variance Inflation Factor (VIF) was employed for multicollinearity assessment (VIF < 5) [70]. A Pearson correlation was employed to check for potential correlations among different factors.

2.4. Description of ML Algorithms

Following data collection, the data were cleaned, coded, and corrected for errors. The dataset was then divided into a training set and a testing set using a 70%–30% split. Post model training, parameter fine-tuning was carried out to enhance the performance of each model. No preprocessing was applied to the dataset before analysis. Model evaluations and comparisons to determine the best overall performance were conducted using a stratified 5-fold cross-validation with performance metrics.

The models employed included the Stochastic Gradient Descent (SGD), Gradient Boosting, Adaptive Boost (ADA Boost), Random Forest (RF), and Decision Trees (DT).

2.5. Machine Learning (ML)

A predictive analysis using supervised ML algorithms was further employed to identify the principal contributing components that affect the age estimation of European hake from otolith morphometric characteristics, using the visual programming software Orange (version 3.36.2) (Ljubljana, Slovenia) [71] (Figure 3). The data sufficiency for answering the defined research question (age estimation) was assessed with a Sample-size to Feature-size Ratio (SFR) [72].

The contribution of each feature of the best performing model’s prediction was visualized using the SHAP (SHapley Additive exPlanations) approach [73]. The SHAP value measures the impact of each feature on the model’s output. Positive SHAP values, positioned to the right of the center, indicate that the feature positively influences the prediction for the selected class. Conversely, negative SHAP values, to the left of the center, indicate a negative influence on the classification for that class. The colors represent the values of each feature, with red indicating higher feature values and blue indicating lower values. The color range for each feature is determined by all the values present in the dataset.

2.6. Machine Learning Techniques

2.6.1. Stochastic Gradient Descent

Stochastic Gradient Descent (SGD) is a fundamental optimization algorithm widely used in machine learning for training models. The algorithm updates the model parameters using only a small subset or even a single random sample from the dataset at each iteration [74]. This randomness in selecting data samples introduces noise into the parameter updates, leading to faster convergence and better generalization. By iteratively adjusting the model parameters in the direction that minimizes the loss function, SGD enables the training of complex models efficiently. However, SGD’s stochastic nature requires the careful tuning of learning rates and other hyperparameters to ensure the convergence to the optimal solution [75].

2.6.2. Gradient Boosting

Gradient Boosting is a machine learning technique that builds a predictive model in the form of an ensemble of weak learners, typically Decision Trees, by sequentially minimizing the loss function of the previous model’s residuals. Each subsequent weak learner is trained to correct the errors made by the previous ones, leading to a strong overall model [76]. The algorithm can model inherent, multi-level interactions between environmental variables, is typically unaffected by multi-collinearity, can account for outliers and missing observations, and is well suited for ecological studies exploring predictor importance, particularly those exploring an environment–recruitment relationship [77].

2.6.3. Adaptive Boosting

Adaptive Boosting (AdaBoost) is a popular ensemble learning method that sequentially trains a series of weak learners, typically Decision Trees, by adjusting the weights of misclassified samples at each iteration [78]. AdaBoost has emerged as one of the most popular and successful approaches for completing numerous classification tasks due to its interpretability, flexibility, and accuracy [79]. AdaBoost has been widely used in various machine learning tasks due to its simplicity, effectiveness, and ability to handle both binary and multiclass classification problems [80]. However, there is no information available regarding the usage of AdaBoost to estimate age in fisheries.

2.6.4. Random Forest

Random Forest is a popular ensemble learning technique that builds multiple Decision Trees during training and outputs the mode of the classes (classification) or the mean prediction (regression) of the individual trees [81]. Random Forest combines the simplicity of Decision Trees with the robustness of ensemble learning, resulting in an effective algorithm for both classification and regression tasks [82]. The algorithm has been widely adopted across various domains due to its ability to handle highly dimensional data, nonlinear relationships, and missing values, while mitigating overfitting. Given the diverse threats to marine habitats and biodiversity, ecologists and fisheries scientists are increasingly turning to the Random Forest (RF) model as a potent machine learning technique for species distribution modeling (SDM) in their research [83].

2.6.5. Decision Trees

Decision Trees are fundamental machine learning models that are popular due to their interpretability, ease of understanding, and ability to handle both numerical and categorical data [84]. Decision Trees are classifiers that order examples according to the values of their features before classification. According to [85,86], the classification process starts at the root node, descends hierarchically based on the importance of the features, and establishes consecutive queries that lead to a class label. Decision Trees have been extensively studied and applied in various fields, including medicine, finance, and environmental science [87].

2.7. Assessment of Model Performance

Model performance was assessed using five metrics: namely, the Mean Square Error (MSE) (the average of the squared differences between predicted values and actual target values), Root Mean Square Error (RMSE) (the difference between predicted and actual values), Mean Absolute Error (MAE) (takes the average of absolute errors for a group of predictions and observations as a measurement of the magnitude of errors for the entire group), Mean Absolute Percentage Error (MAPE) (the average magnitude of error produced by a model), and the Coefficient of Determination (R²) (assesses the proportion of variance in the dependent variable explained by the independent variables).

2.7.1. Mean Square Error (MSE)

MSE is a measure used to evaluate the accuracy of a model. It is the average of the squared differences between the observed actual outcomes and the outcomes predicted by the model. Mathematically, it is expressed as follows (Equation (1)):

$$\mathrm{M}\mathrm{S}\mathrm{E}={\displaystyle \frac{1}{n}}{\sum }_{i=1}^n{(yi-\widehat{yi})}^2$$

(1)

where n is the number of observations, yi represents the actual values, and $\widehat{yi}$ represents the predicted values.

Lower MSE values indicate a better fit of the model to the data, as it means that the predictions are closer to the actual values.

2.7.2. Root Mean Square Error (RMSE)

RMSE is a measure used to evaluate the accuracy of a model, similar to MSE, but it provides the error in the same units as the data. RMSE is the square root of the average of the squared differences between the observed actual outcomes and the outcomes predicted by the model. It is expressed as follows (Equation (2)):

$$\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}=\sqrt{{\displaystyle \frac{1}{n}}{\sum }_{i=1}^n{(yi-\widehat{yi})}^2}$$

(2)

where n is the number of observations, yi represents the actual values, and $\widehat{yi}$ represents the predicted values.

RMSE is widely used because it provides a straightforward interpretation of the model’s error magnitude, making it easier to understand and compare the performance of different models. Lower RMSE values indicate a better fit of the model to the data.

2.7.3. Mean Absolute Error (MAE)

MAE is a measure used to evaluate the accuracy of a model by averaging the absolute differences between the observed actual outcomes and the predicted outcomes. Unlike MSE and RMSE, MAE does not square the differences, so it is less sensitive to outliers. It is expressed as follows (Equation (3)):

$$\mathrm{M}\mathrm{A}\mathrm{E}={\displaystyle \frac{1}{n}}{\sum }_{i=1}^n\left|yi-\widehat{yi}\right|$$

(3)

where n is the number of observations, yi represents the actual values, and $\widehat{yi}$ represents the predicted values.

MAE provides a straightforward interpretation of the average error magnitude, making it useful for understanding how much the predictions deviate from the actual values on average. Lower MAE values indicate a better fit of the model to the data.

2.7.4. Mean Absolute Percentage Error (MAPE)

Mean Absolute Percentage Error (MAPE) is a measure used to evaluate the accuracy of a model by averaging the absolute percentage errors between the observed actual outcomes and the predicted outcomes. MAPE expresses the error as a percentage, making it easier to interpret the magnitude of errors relative to the actual values. It is expressed as follows (Equation (4)):

$$\mathrm{M}\mathrm{A}\mathrm{P}\mathrm{E}={\displaystyle \frac{1}{n}}{\sum }_{i=1}^n\left|{\displaystyle \frac{yi-\widehat{yi}}{yi}}\right|\times 100$$

(4)

where: n is the number of observations, yi represents the actual values, and $\widehat{yi}$ represents the predicted values.

MAPE is useful for comparing forecast accuracy across different datasets because it provides a percentage-based error. Lower MAPE values indicate a better fit of the model to the data, with values closer to 0% indicating higher accuracy.

2.7.5. Coefficient of Determination (R²)

The Coefficient of Determination is commonly used as a statistical measure that assesses the goodness of fit of a regression model. It indicates the proportion of the variance in the dependent variable that is predictable from the independent variables. It ranges from 0 to 1, with higher values indicating a better fit of the model to the data. It is expressed as follows (Equation (5)):

$${\mathrm{R}}^2=1-{\displaystyle \frac{{\sum }_{i=1}^n{(yi-\widehat{yi})}^2}{{\sum }_{i=1}^n{(yi-\overline{y})}^2}}$$

(5)

where n is the number of observations, yi represents the actual values, $\widehat{yi}$ represents the predicted values, and $\overline{y}$ is the mean of the actual values.

An R² value of 1 indicates that the regression model perfectly predicts the dependent variable, while an R² value of 0 indicates that the model does not explain any of the variance in the dependent variable.

3. Results

A total of 150 M. merluccius individuals (89 females and 61 males) were measured, aged between 1 and 9 years old, with a mean length of 28.23 ± 6.26 cm in total length, and a mean weight of 178.05 ± 138.72 g in total weight (

Table 2. Descriptive statistics: the mean, median, standard deviation (SD), minimum (Min), and maximum (Max) of the recorded age, fish, and otolith measurements from captured individuals.

Variable	N	Mean	Median	SD	Min	Max
Age	150	2.89	3.00	1.58	1	9
Total length (cm)	150	28.23	27.73	6.26	17.15	47.60
Total weight (g)	150	178.05	136.50	138.72	32.28	804.5
Otolith weight (g)	300	0.10	0.09	0.05	0.03	0.30
Otolith perimeter (P)	300	37.83	35.83	9.74	21.41	82.68
Otolith area (A)	300	51.34	47.95	21.45	19.26	121.12
Otolith length (D)	300	13.31	13.15	2.93	8.13	21.22
Otolith width (OW)	300	5.44	5.46	1.09	3.32	8.84
Form factor	300	0.45	0.45	0.07	0.17	0.58
Circularity	300	29.06	28.05	6.24	21.58	71.83
Roundness	300	0.36	0.36	0.02	0.29	0.40
Rectangularity	300	20.90	19.96	8.32	7.87	50.24
Aspect ratio	300	2.44	2.43	0.11	2.20	2.77
Ellipticity	300	155.06	142.03	71.09	54.71	386.98
Squareness	300	0.68	0.69	0.03	0.58	0.74

). Descriptive statistics of the recorded measurements are shown in Table 2.

A significant correlation (R² = 89.6%) was identified between otolith weight and the age of the individuals (Figure 4). The effect of form factor and aspect ratio are also apparent, but are significantly lower compared to weight, thus highlighting the importance of the latter in age estimation for the European hake.

No significant differences were observed in any measured morphometric characteristics between the left and right otoliths (p > 0.05). However, significant differences were found between the sexes (p < 0.05), with females showing significantly higher values in otolith weight, perimeter, area, length, width, circularity, aspect ratio, ellipticity, and rectangularity. Squareness was also higher in females, but this difference was not significant. Males exhibited higher values in form factor and roundness, with a significant difference observed only in form factor.

Using a second-degree stepwise regression model, we identified the main factors (out of 12) that significantly affect age prediction for the European hake. We developed three models: one for the overall population and two separate models for each sex. Each model was optimized, based on the significance (p < 0.05) and collinearity (VIF < 5) of the factors. In all three models, the most impactful factors for age prediction were otolith weight, form factor, and aspect ratio (

Table 3. Second degree standard least squares regression report for the model effects on age estimation, sorted by ascending p-values for the total population, males, and females (the logworth for each model effect is defined as −log10(p-value)). The blue line indicates a significance at the 0.01 level. The Variance Inflation Ratio (VIF) is also indicated.

Source	Logworth		p Value	VIF
		Total population (R2 = 91.0%)
Otolith weight	137.362		<0.0001	1.19
Form factor	3.719		0.0002	1.28
Aspect ratio	2.202		0.0063	1.29
		Males (R2 = 91.6%)
Otolith width	7.820		<0.0001	3.34
Aspect ratio	4.014		0.00010	3.20
Otolith weight	2.149		0.00710	1.08
		Females (R2 = 95.8%)
Otolith weight	52.600		<0.0001	1.00

).

Low collinearity was indicated among model factors (VIF). No lack of fit was detected in any of the models with p > 0.05. The Coefficient of Determination (R²) of the resulting models (Table 3) was higher for the female population but high (over 91%) for all models.

The highest correlation among model effects was exhibited in the relationship between aspect ratio and otolith weight (positive correlation of 0.40), followed by the relationship between aspect ratio and form factor (negative correlation of −0.33), and form factor and otolith weight (negative correlation of −0.18). However, all relationships among otolith measurements (model effects) exhibited relatively low correlations (Figure 5).

A prediction profiler was employed to visualize and assess the importance of each factor and their combined interaction effects for the total population (Figure 6).

The prediction profiler (Figure 6) illustrates the impact and interaction of three factors (namely, otolith weight, form factor, and aspect ratio) on the European hake’s age prediction. The slopes of the lines represent the importance of each factor in the prediction model. The first plot shows a strong positive correlation between otolith weight and age, indicating that as the otolith weight increases, the predicted age of the hake increases significantly. In contrast, the form factor and aspect ratio exhibit a weaker effect on age prediction, with nearly flat slopes indicating minimal influence. Overall, otolith weight is the most influential predictor of age among the three factors.

The resulting prediction formulas for the age estimation of European hake for the total population (Equation (6)), males (Equation (7)), and females (Equation (8)), respectively, were as follows:

Age total pop = 26.3667 × Otolith weight − 1.5265 × Form factor + 0.8032 × Aspect ratio − 0.4406

(6)

Age Males = 2.38822327645761 × Aspect ratio + 6.98697992653868 × Otolith weight + 0.823740010632538 × otolith width − 7.71973993001971

(7)

Age Females = 0.71964654832681 + 28.5858211840073 × Otolith weight

(8)

Linear projection employing principal components and explorative data analysis was employed using the Mean Square Error of k-nearest neighbors’ classifier on the projected two-dimensional data (Figure 7). A lighter color indicates a higher age class and data size of otolith weight.

The linear projection plot in Figure 7 illustrates the relationship between European hake’s age and three biological factors: form factor, aspect ratio, and otolith weight. Fish age between 1 and 10 years is color-coded from blue (younger) to yellow (older). The vectors indicate that form factor is more associated with younger hake, while aspect ratio and otolith weight are increasingly significant in older fish. The plot suggests that as European hake ages, their aspect ratio and otolith weight tend to increase, whereas form factor plays a more crucial role during the younger stages.

The training Sample-size to Feature-size Ratio (SFR) was 50 for the total population, 89 for the females, and 20 for the males (all greater than 10), indicating the presence of sufficient data to answer the defined research question (age estimation) using an ML approach, according to [72].

Model performance was assessed using a total of five metrics, MSE, RMSE, MAE, MAPE, and R². Those metrics were simultaneously employed for model comparison to better assess model performance since each metric has its own strengths and weaknesses (e.g., MSE and RMSE are sensitive to outliers, while MAE and MAPE are not). Lower values in four of the metrics used (MSE, RMSE, MAE, and MAPE) and higher in the fifth (R²) are indicative of better model performance. Based on metric results for the total population, the Stochastic Gradient Descent model achieved the best performance with the lowest MSE, RMSE, MAE, and MAPE, while exhibiting the highest R², followed by Gradient Boosting. In contrast, the Decision Tree model achieved the worst performance, with the opposite trend exhibited for all metrics (Figure 8). Similar results were obtained for females and males, with SGD exhibiting the best performance and DT the worst. The most accurate predictions resulted for the female population, followed by the total and male populations, respectively R² = 93.7 (females), 89.4% (total population), and 80.7% (males).

The SHAP (SHapley Additive exPlanations) summary plot for the total population (Figure 9) illustrated the contribution and importance of three features, namely otolith weight, aspect ratio, and form factor, in predicting the age of European hake. The Y-axis lists these features, while the X-axis shows their SHAP values, indicating each feature’s impact on the model’s output. Positive SHAP values indicate feature contribution to a higher predicted age, and negative values indicate a lower predicted age. The color of each point represents the feature’s value, with blue for low values and red for high values, creating a gradient displaying also intermediate values. Otolith weight exhibited a broad range of SHAP values, highlighting its significant impact on predictions. Aspect ratio displayed a much narrower SHAP value broad range, indicating a significantly lower impact on the model. The form factor exhibited the smallest SHAP value range, indicating a lesser impact compared to the other features. This visualization effectively demonstrated that for the total population, otolith weight is the most influential factor in predicting age, followed by the aspect ratio and form factor. The color gradient aids in understanding how the different values of each feature influence the model’s output, providing a clear, detailed view of the model’s decision-making process.

A visualization of the Decision Tree model (the first five levels are displayed), employed by splitting the data into nodes by class purity (using the Kullback–Leibler divergence) for the total population, indicated the mode of classification of each age class for the total population (Figure 10). The Decision Tree Model showed a detailed Decision Tree for the determination of European hake’s age based on otolith characteristics. The tree displayed the first five levels of depth and used three main features for classification (otolith weight, aspect ratio, and form factor). The output of the tree classification used a combination of otolith weight, aspect ratio, and form factor at different levels to make increasingly fine-grained age classifications. The leaf nodes provided the estimated fish age (mean ± standard deviation) along with the number of instances in each category. The tree structure suggested that otolith weight is the most important feature for initial age determination, with aspect ratio and form factor providing additional refinement for certain age groups. Age classifications ranged from approximately 1.6 to 8.1 years, with younger fish having lighter otoliths and older fish having heavier ones.

Tree classification (Figure 10) functioned by initially placing all the fish data at the topmost root node. From here, the information branched out based on a decision made about a single feature value, such as otolith weight (e.g., ≤0.0992 g). The tree continuously partitioned the data into increasingly homogenous subgroups based on age by selecting the most effective feature value split at each junction. This process was iterated until the subgroups reached a sufficient level of uniformity in terms of age. The text boxes within the tree represent the features used for branching and their corresponding split values. For instance, the root node made a decision based on otolith weight with a threshold of 0.0992 g. European hake with otolith weights lower than or equal to this value were directed to the left branch, while those exceeding it went to the right branch. The terminal nodes at the bottom, known as leaf nodes, displayed the predicted average age and standard deviation for the fish within that particular subgroup. By following the branching pathway from the root node down to a leaf node based on a specific fish’s otolith values, it is possible to trace the decision-making process of the model in the prediction of age.

4. Discussion

Our research provides a valuable preliminary exploration into the application of otolith morphometric features for age estimation in European hake. This study introduces an innovative approach that offers a precise and efficient alternative to traditional methods, which are often labor-intensive and prone to human error. The advancements presented here hold potential for improved population assessments and more effective management strategies for this commercially significant species. Additionally, the findings offer a foundation for future exploration of machine learning applications in other marine species, potentially leading to the development of generalized age prediction models. This aligns with contemporary trends in fisheries science, where advanced computational methods are increasingly applied to address complex ecological and biological challenges.

Our results provided two practical tools for fisheries management by estimating fish age from otolith morphometric characteristics. The first tool was an easy to use equation with a high degree of accuracy (R²= 91.0%, RMSE = 0.479), using only otolith weight, form factor, and aspect ratio to predict European hake’s age. The second tool was a highly accurate ML model (R² = 89.4%, RMSE = 0.507) with the ability to further predict European hake’s age using the same inputs (otolith weight, form factor, and aspect ratio). Both tools are important for assessing fish population dynamics, managing sustainable fishing practices, and ensuring the long-term health of marine ecosystems. Practically, the models could be implemented by collecting fish otolith samples, measuring limited morphometric features using imaging techniques, and inputting these measurements into the machine learning model. Both model outputs will allow researchers and fisheries managers to obtain rapid and reliable age estimates without the need for labor-intensive traditional methods. By integrating these models into routine fisheries assessment workflows, stakeholders could make more informed decisions about fish stock assessments and conservation strategies.

The starting point of the stock assessment often consists of research that focuses on the life-history traits of fish species [88]. Consequently, otolith reading procedures that are validated through international standards and standardized could be an effective tool to advance our understanding of those issues that fishery biologists continue to vigorously address. Otolith reading-based M. merluccius ageing research can yield extremely valuable information since it is widely acknowledged that accurate data on the age structure of the catch is crucial for stock evaluation. Fish age can be inferred from otolith morphological and morphometric properties, demonstrated to be age-related [89]. Age estimation is a fundamental step in comprehending the biology and dynamics of fish populations and a significant element in numerous fisheries models [90]. The need for increased use of otolith morphometry to predict age due to age estimations being essential to the studies of stock assessments, population dynamics, and growth has been emphasized [91]. As a result, continuous monitoring programs and stock assessments could benefit and increase their efficiency.

Our multivariate approach with the employment of a second-degree stepwise regression model resulted in the formulation of an easy to use equation with a high degree of accuracy (high Coefficient of Determination and low RMSE) to predict European hake’s age using limited morphological otolith characteristics. According to [92], otolith morphology and morphometry are useful methods for identifying fish species and estimating age, with a significant impact on fishery science and management [90], linked to ontogenetic alterations [93,94] and spatial temporal migration [95]. Both internal and external factors control variations in the size and shape of otoliths as the fish grows [24,96,97], such as ecological and biological variables [98], depth [99], water temperature [99], salinity [94], and food supply [100], with an age-related tendency towards a progressively complex shape. However, the finer details can be influenced by environmental factors, especially those related to feeding level, which can range from starvation to ad libitum [100], and food availability [101]. According to [102], there is a strong association between otolith ring number and length. Furthermore, the application of ML algorithms in the present study produced a framework using the SGD algorithm that predicted age groups with a high accuracy and low error, demonstrating the potential usefulness of otolith morphometry in deciphering fish age. Otolith weight was by far the most significant factor for age determination in both the approaches that were employed similarly to previous work [103,104,105], suggesting a strong correlation between the two, as also suggested by other researchers.

When it comes to estimating the fish age, machine learning has exhibited high accuracy, flexibility, and scalability, often surpassing conventional techniques [49]. Large amounts of data can be processed quickly using age estimation based on a few chosen otolith parameters [106]. Conventional techniques, such the manual inspection of otoliths and the visual inspection of exterior features, can be labor-intensive, time-consuming, and subject to subjectivity. On the other hand, machine learning algorithms are capable of precisely and efficiently predicting age and sex by analyzing a big dataset of information. According to [89], machine learning categorization is a method that has the potential to significantly impact conservation and stock assessment projections.

The interpretation of otolith growth markings is frequently a challenging endeavor, in which subjectivity rises with the intricacy of the otolith’s structural structure [107]. The interpretation of hake otoliths is challenging due to the abundance of macrostructures. Thin transparent zones (TTZs) are common and likely represent brief physiological and/or environmental events. The difficulty of identifying such otoliths generally rises with fish size [107]. It is thought that the prolonged spawning season contributes to the complexity of hake otolith macrostructure and growth variability [42,108]. Varying ring patterns originate from the nearly constant recruiting that occurs throughout the year because of multiple spawning. Otolith interpretation is made more challenging by the sexual dimorphism in growth rates and the various ring patterns, depending on the hatching time and location, which also contributes to the disparities between different otolith readers. The initial annual ring’s placement (first annulus), the other rings’ characterization as annual or false, and the interpretation of the edges are the three main challenges in otolith age estimation. These issues, according to [36], may be caused by a few generally well-marked false rings that frequently appear before, during, or after the first annulus deposition. As a result, it is extremely challenging to recognize the first annual ring, which is the biggest source of uncertainty in hake otolith age readings.

Expert readers manually extract age information from otoliths by counting the daily or annual development zones under a microscope or from high-resolution images [109]. The process of determining fish age is dependent on the reader’s experience, the ability to recognize the first annual ring, the otolith axis used for measurements, and the fish’s date of birth [110], resulting in frequent differentiation of readers’ estimates. To address this problem, findings from different readers or from readings by the same reader are compared to comprehend observed differences. Nonetheless, implementing this procedure is prohibitively costly, time-consuming, and labor-intensive [111]. Since fewer fish may be age-analyzed as a result, monitoring programs are forced to rely more heavily on growth-at-age models in order to ascertain the age composition of fish populations [64]. This emphasizes the necessity for automated tools that otolith experts could use to enable a more efficient study in their facilities. Additional research and widespread implementation of these methods could be advantageous for each of these domains. By assessing stock conditions along with offering reliable species classification, this approach could contribute to the goal of sustainable fisheries [112]. Moreover, the use of image recognition algorithms could lessen the need for laborious manual measurements by non-invasively evaluating features like length and scale radius from photographs.

Fish age determination using otolith imaging has proven to be an important tool for fisheries management, offering reliable data leading to the estimation of critical trends in fish biology and population dynamics [109]. Fisheries programs have been obliged to restrict the quantity of fish specimens analyzed and rely on model estimations to assess the age composition of fish populations due to the high expenses associated with data collection and age interpretation [64]. This highlights the need for automated techniques to determine fish age. Our results indicated that the application of ML algorithms may assist in fish age recognition and become an asset for experts in age reading.

The significance of this research transcends the European hake, offering a foundation for the broader application of machine learning in fisheries science. This approach may facilitate the development of generalized age prediction models that are applicable across various species. As fisheries management increasingly relies on data-driven strategies, the integration of advanced computational techniques, as exemplified in this study, is poised to play a critical role in addressing the complex challenges associated with sustainable fishery practices and biodiversity conservation.

5. Conclusions

The present study identified the main contributing otolith morphometric factors that significantly affect the age estimation for European hake, namely, otolith weight, form factor, and aspect ratio. Three easy to use equations with a high degree of accuracy were further produced and are readily applicable for most stakeholders. With the application of ML methodology, a framework was further developed for the prediction of European hake’s age from otolith morphometrics. The integration of imaging technology, employed to assess otolith morphology, and statistical analyses offers a powerful approach to fish age identification, with high accuracy, a reduction in labor, and the enabling of large-scale assessments. Age and growth studies could utilize otolith morphometry in age estimation, resulting in time and cost reductions, while generating reliable data. To guarantee a thorough prediction, an accurate assessment, and overall sustainable stock exploitation, it is also crucial to consider the relationships and interactions between the environmental elements in the aquatic ecosystem. By the careful selection of datasets and model evaluation, ML could address biases and overcome the drawbacks of traditional approaches that rely on subjective judgments. With age estimation being essential to studies of the stock assessments and population dynamics of the European hake, the present study indicates the potential for accurate age estimation and the expedition of the assessment process, providing researchers and fisheries managers with trustworthy data for conservation and sustainable resource management. Our manuscript provides a valuable preliminary exploration into the application of machine learning for the otolith-based ageing of European hake. Despite its limitations, the study offers a robust starting point that can significantly contribute to the field and guide subsequent research efforts. Future studies could employ larger sample sizes to validate and extend our findings. The current study lays the groundwork and provides a proof-of concept, which is crucial for securing funding and resources for larger-scale research.