Study area. The Ka Long River originates from the northern edge of Quang Duc Commune, Hai Ha District, located at coordinates 21°36′36′′N and 107°41′2′′E, situated approximately 5 km west of the Bac Phong Sinh border gate. It flows in an east–northeast direction (Fig. 1A) and spans about 16 km in length. This river is situated in a region characterized by a tropical climate featuring a hot and humid summer as well as a cold and dry winter. The average temperature during winter remains below 20°C, whereas in summer, it rises above 25°C. The yearly average humidity stands at 84%, while the annual rainfall varies from 1700 to 2400 mm.

Figure 1. 

The study area in Ka Long (A); Ba Lat (B); and Dinh estuaries (C) in Vietnam. The spatial distribution of the 63; 77; and 54 sampling sites of Ayu, Plecoglossus altivelis, respectively at the three estuaries. Note: the East Sea is otherwise known as the South China Sea.

Ba Lat Estuary is a coastal inlet located in northern Vietnam. It is positioned between Giao Thuy District, Nam Dinh Province (Fig. 1B). The tropical climate of this region experiences two distinct seasons: a dry period extending from November to April, and a rainy season occurring between May and October. The average temperature hovers around 23°C. Annual rainfall levels range from 1650 to 1800 mm, with the rainy season spanning from May to October and the dry season from November to February. The yearly sunshine duration is between 1600 and 1700 hours, while the average relative humidity falls within the range of 80%–90%.

The Dinh estuary is a water body that flows into the East Sea (South China Sea). It stretches across a length of 135 km and covers a drainage basin area of 3109 km². Originating from the elevated E Lam Thong Mountain range bordering Lam Dong Province in the Phan Rang region (Fig. 1C), this river basin experiences a typical tropical monsoon climate characterized by hot and dry conditions, strong winds, and high evaporation rates. The average annual temperature ranges from 26 to 27°C, with rainfall averaging between 700 to 800 mm in Phan Rang and exceeding 1100 mm in mountainous terrains. Air humidity levels fall between 75% and 77%. The climate exhibits two primary seasons: a rainy period from September to November, and a dry season spanning December to August. The coastal zones are abundant in lagoons and bays, offering opportunities for tourism development and aquaculture, particularly shrimp farming, which stands as a pillar of the local fisheries industry.

A total of 117 survey sites were sampled across the two estuaries, comprising 63 samples from the Ka Long estuary collected from September 2021 to December 2021, 77 samples from the Ba Lat estuary collected from March to April 2022, and the remaining 54 samples from the Dinh estuary (Fig. 1) collected from May to June 2022. Sampling was conducted using a small seine net (1 × 4 m, mesh aperture = 1 mm). Specimens were preserved in 5% formalin and then transferred to 80% ethanol. Fish larvae and juveniles were separated under a 10 × 40 magnification dissecting microscope and identified as Ayu based on external morphology following Do et al. (2022a). Water temperature (°C), salinity (ppt), turbidity (NTU), and Chlorophyll-a (mg/m³) were measured at each site using a Water Quality Checker (WQC-22A, TOA DDK). Furthermore, additional data were obtained from Sentinel-2 satellite imagery, with details on preprocessing and sun-glint correction provided in Hedley method sun-glint correction section below.

Elevation. Elevation is a significant factor influencing fish distribution, with higher altitudes generally associated with reduced distribution and vice versa (Ley 2005). Elevation data in the study area (Table 1) ranged from 0–22 m for the Ka Long estuary, 0–42 m for the Ba Lat estuary, and 0–38 m for the Dinh estuary, derived from a Digital Elevation Model (DEM) with a cell size of 10 × 10 m.

Slope. Slope directly impacts surface runoff, with higher slope angles increasing water velocity and affecting flow direction. Slope angle calculations were performed using the DEM spatial analysis tool in ArcGIS 10.8. The slopes of the Ka Long, Ba Lat, and Dinh estuaries exhibited a wide range, of 0–22.6, 0–17.2, and 0–15.24, respectively (Table 1).

Distance from source. The distance from the source is a crucial factor influencing fish distribution and salinity levels in the study area. Areas closer to the sea typically have higher salinity values, leading to increased abundance of fish inland. Details regarding the distance from the source are presented in Table 1.

Mean width. Similar to the distance from the source, the mean width of the estuary is an abiotic factor associated with the presence of fish larvae and juveniles, as estuary width impacts current speed and salinity levels. Previous research in the study area has indicated higher salinity in the bank water region compared to the center of the current (Do and Tran 2023c; Table 1).

Proximity of urban areas. Estuarine areas near urban centers are typically under high pressure from human activities, such as pollution, exploitation, and destruction of fish habitats. Consequently, fish tend to avoid areas in close proximity to urban centers, leading to a more abundant and diverse fish community further away from urban areas.

Proximity of mangrove areas. Mangrove forests offer plentiful food sources, shelters, and ideal spawning conditions for fish. Estuarine areas adjacent to mangrove forests exhibit superior fish distribution and diversity, whereas regions distant from mangroves generally show reduced fish populations and diversity.

Chlorophyll-a. Chlorophyll-a plays a crucial role in determining the distribution of juvenile Ayu in aquatic environments. As an indicator of the presence of phytoplankton, Chlorophyll-a not only provides a rich food source for juvenile fish but also reflects the water quality in their habitat. Areas with high concentrations of Chlorophyll-a typically have good dissolved oxygen levels, which facilitate the growth of fish. Therefore, the abundance of Chlorophyll-a directly impacts the distribution and survival of juvenile Ayu within the ecosystem.

Fish CPUE (catch per unit effort). Fish were captured at wadeable depths (approximately 20 to 100 cm) in the two estuaries employing a seine net (1 × 4 m, 1 mm mesh-aperture) (Kinoshita et al. 1988). Two individuals held the net extended, wading backward in the water from ankle to neck depth along the shoreline for about 50 m within a timeframe of roughly 2 min. Typically, one to two hauls were conducted at each sample station per day. The catch per unit effort (CPUE) was computed as the number of individuals in each haul (about 2 min or 50 m). (Kinoshita et al. 1988).

Hedley method sun-glint correction. Hedley method establishes a linear relationship based on a sample of image pixels rather than solely two image pixels (Kay et al. 2009, 2013). All chosen pixels are integrated in a linear regression of NIR brightness with visible channel brightness.

If the slope of the regression line for channel i is b_i, then all pixels in image channel i can be de-glinted by applying the subsequent equation

R¹_i = R ₁ – b_i (R_NIR – Min_NIR) [1]

This approach relies on a sample of image pixels, eliminating the necessity to mask out non-water pixels like land, clouds, and boats before de-glinting (Busch et al. 2013). The key steps involve:

• Correcting atmospheric effects;
• Opting for one or more representative regions in the image showing a variety of solar flares, along with a homogeneous region free of solar flares. Identify the Min _NIR, which signifies the minimum brightness on the NIR channel within the selected sample;
• Conducting a linear regression analysis on the brightness values of the NIR channel (x-axis) against the brightness of the single channel (y-axis) using the chosen pixels. The slope of the regression line, denoted as b _i , is the key output for channel i.
• Eliminating sun-glint interference from all pixels [1]

The outcomes of the sun-glint adjustment process are demonstrated in Fig. 2 and will subsequently be utilized to extract data for urban and mangrove regions as input variables for the ANFIS model.

Figure 2. 

Satellite images of the study area before (A) and after (B) the pre-processing and sun-glint correction process.

Adaptive neuro fuzzy inference system (ANFIS) is grounded on a fuzzy inference system, trained using an algorithm rooted in neural network principles (Azeem et al. 2000). The ANFIS architecture comprises five layers, illustrated in Fig. 3.

Figure 3. 

Fish CPUE (catch per unit effort) outputs of Ayu, Plecoglossus altivelis, in Vietnam of the Adaptive neuro fuzzy inference system (ANFIS).

Layer 1: This segment is referred to as the fuzzification layer, representing the training data and the initial seven predictor variables for fish, as detailed in Table 1. Adaptive nodes with node functions defined as:

Q¹_i = μA¹_k (X₁) [2]

Parameters {a, b, c} determine the shape of the membership function, termed as the premise parameters

$\mu A_k\left(X_i\right)=\frac{1}{1+{\left|\frac{x-c_i}{a_i}\right|}^{2{\delta }_i}}$ [3]

where i = 1:n, with n being the number of input variables; k representing the clusters and rules count; X₁, X₂… X_n denoting the input nodes; A, B… C as the linguistic labels; and μ (X_n) indicating the membership value.

Layer 2: The second layer is called the rule layer; each node in this layer is a circular node labeled II, responsible for multiplying the incoming signals.

Q²_i = w_i = μA¹_k (X₁) × μA²_k (X₂) × ... × μAⁿ_k (X_n) [4]

Layer 3: Each circular node labeled N in this layer calculates the normalized firing strengths w_i as per the formula [5]:

$Q_i^3=\overline{w_i}=\frac{w_i}{sum\left(w_i\right)}$ [5]

Layer 4: This layer is commonly referred to as the defuzzification layer, where each individual represents an adaptable node.

$Q_i^4=\overline{w_i}{f}_i$ [6]

where f_i = z_ix + r_iy + t_i with f_i is the fuzzy if-then rule; z_i, r_i, and t_i represent the designated parameters, known as the consequence parameters.

Layer 5: The CPUE result of ANFIS is derived from the summation of outcomes acquired for each rule within the defuzzification layer.

$Q_i^5=\sum _i\overline{w_i}{f}_i=\sum _i\frac{w_i\times f_i}{sum\left(w_i\right)}=y$ [7]

RMSE is utilized to operate the functional component in the quest for ACO, with m representing the size of the training set:

$\text{RMSE}={\left[\frac{({\sum }_k^n{f}_i-Q_i{)}^2}{m}\right]}^{1/2}$ [8]

Of which, 70% is allocated for training purposes and 30% for validation, resulting in 44, 54, and 38 training instances for Ka Long, Ba Lat, and Dinh estuaries, respectively.

Ant colony optimization (ACO) is a methodology inspired by simulating the behavior of ant colonies in nature, aimed at addressing intricate optimization issues (Lorpunmanee et al. 2007, 2007). In this study, to enhance the ANFIS model’s performance, the rapid hybrid learning method was utilized, incorporating the ACO algorithm to optimize parameters (Zhou et al. 2021). Essentially, ACO is employed to identify the optimal ANFIS parameters.

To replicate ant behavior, artificial ants have been created, each linked to an edge (i; j), the pheromone concentration τ_ij, and the heuristic parameter ϑ_ij on that specific edge. Routes with lower pheromone concentrations will eventually be phased out, leading all ants to converge on a path that typically becomes the shortest route from the ant nest to their food source. Post each iteration, the pheromone on each edge is adjusted based on the formula (Rabiner and Juang 1986):

τ_ij (t +1) = (1 – p) × τ_ij (t) + ∑^m_k=1Δτ^k_ij (t) ∀(i, j) [9]

where, 0 < p ≤ 1 represents the pheromone evaporation rate; and Δτ^k_ij (t) denotes the amount of pheromone that ant k deposits on edge ij, calculated as follows:

$\Delta {\tau }_{ij}^k=\left\{\begin{array}{c}\frac{Q}{f\left(k\right)},\text{ If ant }k\text{ passes through edge }(i,j)\\ 0,\text{ Vice versa }\end{array}\right.$ [10]

where, Q is a constant, and f (k) stands for the objective value in each iteration.

Various values are chosen for optimization to select the suitable input parameter for CPUE estimation (Table 1). The search process concludes upon reaching the predefined maximum number of iterations (three objective functions in the ongoing study). By combining ACOs with ANFIS, the optimal parameters of ANFIS were ascertained to compute fish CPUE across the entire study region.

In this investigation, root mean square error (RMSE), mean absolute error (MAE), coefficient of determination (R²), and receiver operating curve (ROC) were adopted to validate the GA-ANFIS model (Table 2). Results showcasing low RMSE and MAE, along with high R² are deemed as the most favorable outcomes (Do et al. 2022b; Do et al. 2022c; Pham et al. 2023b; Do et al. 2024b; Do 2024a, 2024b, 2024d; Pham and Do 2024; Van Pham et al. 2025).

The investigation expedition gathered CPUE information on Ayu larvae at three river estuaries: Ka Long, Ba Lat, and Dinh, with respective survey tallies of 63, 77, and 54. Nonetheless, the findings revealed the absence of Ayu larvae at the Dinh estuary (Table 1). Consequently, the comprehension of crucial variables and an appropriate rearing habitat for Ayu larvae has become imperative.

The correlation coefficient (R) of the ten chosen variables (Table 1) for scrutinizing larval dispersion is depicted in Fig. 4. Employing the ACO algorithm for search optimization, three variables—temperature, salinity, and turbidity exhibited the highest correlation with Ayu presence (Fig. 4).

Figure 4. 

Correlation coefficient between environmental variables and CPUE (catch per unit effort) of Ayu, Plecoglossus altivelis in Vietnam of Ka Long and Ba Lat estuaries.

The R coefficients for temperature, salinity, and turbidity were 0.47, 0.54, and 0.40 in the Ka Long estuary; and 0.49, 0.50, and 0.42 in the Ba Lat estuary (Fig. 4). Furthermore, other variables like mangrove cover, distance from source, and proximity to urban areas also displayed relatively strong correlation, with R values of 0.45, –0.38, and 0.3 for the Ka Long estuary, and 0.4, –0.49, and 0.34 for the Ba Lat estuary (Fig. 4). These outcomes suggest that landscape and human-induced factors significantly influence species presence, particularly in the context of larvae and juveniles. Conversely, some variables exhibited lesser significance for Ayu presence, such as Chlorophyll-a, and Slope, with R values of 0.13 and –0.15 (Ka Long estuary), and 0.12 and –0.17 (Ba Lat estuary). Hence, the ACO algorithm assisted in discarding redundant and less crucial variables for Ayu larvae distribution, facilitating the selection of the most pertinent variables for the predictive model.

Based on the survey outcomes and CPUE data, in the presently reported study, the values of the three most critical variables were categorized into five levels ranging from very low to very high (Table 3). The “very high” ranges for temperature, salinity, and turbidity are 21–25°C, <13‰, and <10 NTU, respectively.

For the temperature variable: When the temperature falls below 13°C and ranges between 13–15°C, the CPUE of Ayu fish larvae is observed at notably low levels as indicated in Table 3. In these temperature intervals, the activity and growth of Ayu fish larvae might face inhibition. As the temperature escalates to 15–19°C, the CPUE steadily increases to a moderate level. This particular temperature range proves to be relatively conducive for the requirements of Ayu larvae, enabling them to engage in active behaviors, forage effectively, and reproduce reasonably well. The most favorable temperature range identified for the Ayu species is situated between 19–25°C. It is evident that deviations towards excessively low or high temperatures in comparison to this range result in a decline in CPUE.

For the salinity variable: Among the array of environmental factors, salinity emerges as one of the most critical elements influencing the distribution patterns of the Ayu species. When the salinity surpasses 25‰, the CPUE is notably low, while salinity levels ranging from 20‰–25‰ correspond to a low CPUE level, as depicted in Table 3. Conversely, salinity values oscillating within 13‰–15‰ and below 13‰ are acknowledged as the optimal range for the thrivingness and well-being of Ayu larvae, facilitating their active engagement in foraging and successful reproduction.

Regarding the turbidity variable: The outcomes delineated in Table 3 underscore a negative correlation between turbidity levels and the likelihood of Ayu presence. The optimal turbidity threshold for this species is determined to be below 18 NTU, with an even more preferable level falling below 10 NTU, as illustrated in Table 3. This prescribed range of turbidity stands as the ideal milieu for Ayu larvae, ensuring adequate illumination, food availability, and fostering optimal conditions for their various activities.

In general, Table 3 effectively demonstrates how environmental parameters, such as temperature, salinity, and turbidity, exert a profound influence on the CPUE levels of Ayu larvae. Instances of temperatures deviating from the suitable range, salinity exceeding the permissible threshold, or turbidity levels registering at extremes will induce stress, curtail growth prospects, and elevate mortality rates among the larvae, consequently leading to a substantial alteration in their spatial distribution within the region.

The integration of ACO has enhanced the predictive capability of the ANFIS model in estimating the CPUE of fish in the Ka Long and Ba Lat estuaries. The delineation of Ayu fish larvae CPUE distribution consists of 5 categories, spanning from 0.35 to 732.28 individuals/haul at Ka Long and from 0.6 to 218.50 individuals/haul at Ba Lat (Fig. 5). At the Ka Long and Ba Lat estuaries, the mean CPUE values for fish are 105.10 and 52.86 individuals/haul, respectively (Fig. 5, Table 4).

Figure 5. 

Map of predicted Ayu fish CPUE (catch per unit effort) of Ayu, Plecoglossus altivelis, in Vietnam distribution based on the hybrid ACO-ANFIS model. (A) Ka Long estuary, and (B) Ba Lat estuary.

The prognostic outcomes derived from the ACO-ANFIS model reveal that the CPUE of fish in the Ka Long estuary surpasses that in the Ba Lat estuary. Nevertheless, the CPUE distribution of Ayu larvae in the Ba Lat estuary displays a more uniform pattern in contrast to the distribution observed in the Ka Long estuary (Fig. 5). This discrepancy in distribution could potentially be attributed to the significant difference between the minimum and maximum CPUE values.

The efficacy of the ACO-ANFIS model in predicting the CPUE of Ayu species is illustrated in Fig. 6 and Table 5.

Figure 6. 

ROC curve for evaluating the performance of the ACO-ANFIS prediction model. (A) Ka Long estuary, and (B) Ba Lat estuary.

The computational findings demonstrate that the hybrid model attains commendable performance levels, with R²_train values of 0.84 and 0.81 at the Ka Long and Ba Lat estuaries, respectively. Furthermore, for the subset of samples utilized for assessment, the model exhibits strong predictive accuracy, with R²_test values of 0.79 and 0.75 at the Ka Long and Ba Lat estuaries, respectively.

The predictive capability of the ACO-ANFIS model at the Ka Long estuary outperforms that at the Ba Lat estuary, potentially due to more concentrated sampling procedures, as indicated in Table 5 by RMSE values of 7.00 and 5.54 individuals/haul at the Ka Long and Ba Lat estuaries, respectively. Moreover, the receiver operating characteristic curve was employed to assess the ANFIS model integrated with the ACO algorithm, yielding AUC values of 0.804 and 0.793 at the Ka Long and Ba Lat estuaries, respectively (Fig. 6). These findings suggest that the ACO-ANFIS hybrid model is well-suited for forecasting the presence of Ayu fish larvae in the estuaries of Vietnam.