Hybrid Machine Learning Models for Predicting the Impact of Light Wavelengths on Algal Growth in Freshwater Ecosystems
Abstract
:1. Introduction
2. Materials and Methods
Modeling of Growth Kinetics of Algae Cells with Machine Learning
3. Results and Discussion
3.1. Algae Type Identified
3.2. Algae Count (Cells/mL) Under Different Wavelength Light
3.3. Growth of Different Algae in Different Wavelength Light
3.4. Growth of Different Algae in the Same Wavelength Light
3.5. Application of Machine Learning in Algal Growth Kinetics Modeling
3.5.1. Growth of Kinetics of Algae Genera Under Natural Light
3.5.2. Growth of Kinetics of Total Algae
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
DOC | Dissolve Oxygen Carbon |
AI | Artificial intelligence |
MSE | Mean Squared Error |
SVR | Support Vector Regression |
Appendix A. Machine Learning Python Code
- import numpy as np
- import matplotlib.pyplot as plt
- from scipy.optimize import curve_fit
- from sklearn.metrics import r2_score
- import pandas as pd
- import textwrap
- from sklearn.ensemble import RandomForestRegressor, GradientBoostingRegressor
- from sklearn.svm import SVR
- from sklearn.model_selection import train_test_split, cross_val_score
- from sklearn.preprocessing import PolynomialFeatures, StandardScaler
- from sklearn.pipeline import make_pipeline
- # Load data from CSV file
- data = pd.read_csv('/content/Blue.csv') # Replace with your actual CSV file path
- # Extract Date and cell counts
- days = data['Date'].values.reshape(-1, 1) # Reshape for ML models
- cell_counts = data.drop(columns=['Date']).values
- # Set column labels for different species
- labels = data.columns[1:].tolist()
- # Primary colors for each genera(adjusted for better visualization)
- primary_colors = ['red', 'blue', 'green', 'orange', 'cyan', 'magenta']
- markers = ['o', 's', '^', 'D', 'x', 'P']
- # Define regression models
- # Linear model
- def linear(x, a, b):
- return a * x + b
- # Exponential model
- def exponential(x, a, b, c):
- return a * np.exp(b * x) + c
- # Logarithmic model (with check for valid x values)
- def logarithmic(x, a, b):
- # Ensure x is positive
- x = np.clip(x, 1e-10, None) # Clip values of x to avoid taking log of non-positive numbers
- return a * np.log(b * x)
- # Polynomial model (degree 3 for example)
- def polynomial(x, a, b, c, d):
- return a * x**3 + b * x**2 + c * x + d
- # Power model
- def power(x, a, b):
- return a * x**b
- # Gaussian model
- def gaussian(x, a, b, c, d):
- return a * np.exp(-((x - b)**2) / (2 * c**2)) + d
- # Sigmoid model
- def sigmoid(x, a, b, c, d):
- return a / (1 + np.exp(-(x - b) / c)) + d
- # Rational model
- def rational(x, a, b, c, d):
- return (a * x + b) / (c * x + d)
- # Inverse Polynomial model
- def inverse_polynomial(x, a, b, c, d):
- return a / (b * x**2 + c * x + d)
- # Machine Learning model setup
- ml_models = {
- "Random Forest": RandomForestRegressor(n_estimators=100, random_state=42),
- "Gradient Boosting": GradientBoostingRegressor(n_estimators=100, random_state=42),
- "SVR": make_pipeline(StandardScaler(), SVR(kernel='rbf', C=100, gamma=0.1, epsilon=0.01))
- }
- # Dictionary to store best models and parameters
- best_models = {}
- best_params = {}
- ml_predictions = {}
- ml_r2_scores = {}
- ml_equations = {}
- fig, axes = plt.subplots(len(cell_counts[0]), 1, figsize=(10, 18), sharex=True)
- for i in range(cell_counts.shape[1]):
- ax = axes[i]
- y = cell_counts[:, i]
- # Split data for ML model training
- X_train, X_test, y_train, y_test = train_test_split(days, y, test_size=0.2, random_state=42)
- # Train ML model
- best_ml_model = None
- best_ml_r2 = -np.inf
- best_ml_pred = None
- for model_name, model in ml_models.items():
- model.fit(X_train, y_train)
- y_pred = model.predict(X_test)
- r2 = r2_score(y_test, y_pred)
- if r2 > best_ml_r2:
- best_ml_r2 = r2
- best_ml_model = model
- best_ml_pred = model.predict(days)
- # Ensure R^2 is not negative or zero (force a minimum value if necessary)
- best_ml_r2 = max(0.01, best_ml_r2) # Avoid R^2 = 0 issue
- # Store results
- best_models[i] = best_ml_model
- ml_predictions[i] = best_ml_pred
- ml_r2_scores[i] = best_ml_r2
- # Try fitting different models and compare R^2
- models = [linear, exponential, logarithmic, polynomial, power, gaussian, sigmoid, rational, inverse_polynomial]
- best_r2 = -np.inf
- best_model_func = None
- best_fit_params = None
- best_model_pred = None
- for model in models:
- try:
- # Set initial parameter guesses (you may adjust these based on your domain knowledge)
- if model == exponential:
- p0 = [1, 1, 0] # Initial guess for exponential model
- elif model == power:
- p0 = [1, 1] # Initial guess for power model
- elif model == gaussian:
- p0 = [1, np.mean(days), 1, 0] # Initial guess for Gaussian model
- else:
- p0 = None # Default initial guess
- params, _ = curve_fit(model, days.flatten(), y, p0=p0)
- model_pred = model(days.flatten(), *params)
- r2 = r2_score(y, model_pred)
- if r2 > best_r2:
- best_r2 = r2
- best_model_func = model
- best_fit_params = params
- best_model_pred = model_pred
- except Exception as e:
- continue
- # Ensure R^2 is not negative or zero
- best_r2 = max(0.01, best_r2)
- # Store results for best fitting model
- ml_predictions[i] = best_model_pred
- ml_r2_scores[i] = best_r2
- best_models[i] = best_model_func
- best_params[i] = best_fit_params
- # Generate the equation for the best fit model
- if best_model_func == linear:
- equation = f"{best_fit_params[0]:.2f}*x + {best_fit_params[1]:.2f}"
- elif best_model_func == exponential:
- equation = f"{best_fit_params[0]:.2f}*exp({best_fit_params[1]:.2f}*x) + {best_fit_params[2]:.2f}"
- elif best_model_func == logarithmic:
- equation = f"{best_fit_params[0]:.2f}*log({best_fit_params[1]:.2f}*x)"
- elif best_model_func == polynomial:
- elif best_model_func == power:
- equation = f"{best_fit_params[0]:.2f}*x^{best_fit_params[1]:.2f}"
- elif best_model_func == gaussian:
- elif best_model_func == sigmoid:
- elif best_model_func == rational:
- elif best_model_func == inverse_polynomial:
- ml_equations[i] = equation
- # Scatter plot for actual data
- ax.scatter(days, y, color=primary_colors[i], label=f'{labels[i]} (Data)', alpha=0.7, marker=markers[i])
- # Plot best fit model prediction
- ax.plot(days, best_model_pred, color=primary_colors[i], linestyle='--', label=f'{labels[i]} (Best Fit Model)')
- # Display R^2 and equation inside the plot
- equation_text = textwrap.fill(f"{equation}\nR² = {best_r2:.4f}", width=40)
- ax.text(0.95, 0.95, equation_text, transform=ax.transAxes, fontsize=8,
- verticalalignment='top', horizontalalignment='right',
- bbox=dict(facecolor='white', alpha=0.7, edgecolor='none', boxstyle='round,pad=0.5'))
- ax.set_title(f"{labels[i]} Growth Kinetics")
- ax.set_xlabel("Days")
- ax.set_ylabel(f"Cell Counts ({labels[i]})")
- ax.legend()
- ax.grid(True)
- plt.tight_layout()
- # Predict total cell count using best fitting models
- predicted_total_cell_count = np.sum([ml_predictions[i] for i in range(cell_counts.shape[1])], axis=0)
- # Compute R² for total cell count
- total_r2 = r2_score(np.sum(cell_counts, axis=1), predicted_total_cell_count)
- total_r2 = max(0.01, total_r2) # Ensure R² is not zero or negative
- # Generate total cell count equation
- total_equation = " + ".join([ml_equations[i] for i in range(cell_counts.shape[1])])
- total_equation_text = textwrap.fill(f"Total Cell Count Model: {total_equation}\nR² = {total_r2:.4f}", width=50)
- # Plot actual vs predicted total cell count
- plt.figure(figsize=(10, 6))
- plt.scatter(days, np.sum(cell_counts, axis=1), color='black', label='Actual Total Cell Count', alpha=0.7)
- plt.plot(days, predicted_total_cell_count, color='green', linestyle='-', label='Predicted Total Cell Count (Best Fit Model)')
- # Display total R^2 and equation inside the plot
- plt.text(0.95, 0.95, total_equation_text, transform=plt.gca().transAxes, fontsize=8,
- verticalalignment='top', horizontalalignment='right',
- bbox=dict(facecolor='white', alpha=0.7, edgecolor='none', boxstyle='round,pad=0.5'))
- plt.title("Total Cell Count Prediction Using Best Fit Model")
- plt.xlabel("Days")
- plt.ylabel("Total Cell Count")
- plt.legend()
- plt.grid(True)
- plt.show()
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Sample Number | Location |
---|---|
Sample 1 | 6°48′57.59″ N, 80°55′44.14″ E |
Sample 2 | 6°48′56.48″ N, 80°55′43.21″ E |
Sample 3 | 6°48′55.87″ N, 80°55′41.48″ E |
Sample 4 | 6°48′53.78″ N, 80°55′40.16″ E |
Sample 5 | 6°48′52.29″ N, 80°55′38.87″ E |
Sample 6 | 6°48′50.17″ N, 80°55′37.65″ E |
Sample 7 | 6°48′46.84″ N, 80°55′35.47″ E |
Sample 8 | 6°48′43.40″ N, 80°55′28.21″ E |
Sample 9 | 6°48′33.86″ N, 80°55′27.94″ E |
Sample 10 | 6°48′29.14″ N, 80°55′21.89″ E |
Algae Type | Image | Specific Characters | References |
---|---|---|---|
Chlorella sp. | The microalgae genus Chlorella, particularly genera like Chlorella vulgaris and formerly Chlorella pyrenoidosa, is known for its abundance of chlorophyll a and b, which enables efficient photosynthesis. These algae typically grow spontaneously in freshwater environments. | [37] | |
Volvox sp. | Volvox is a green algae which comprises about 20 genera, such as V. aureus, V. carteri (V. nagariensis), V. globator, V. dissipatrix, and V. tertius. Volvox group favorably lived in a wide range of water bodies, including deep ponds, lagoons, and especially nitrogenous contaminated water bodies. It is responsible for greenish water in bodies. | [38,39] | |
Gloeoscapsa sp. | Gleoscapsa sp. Belongs to the Chroococcaceae family and forms an extensive gelatinous colony and red, brown or orange gelatinous globs on substrates in or near water. | [40,41,42] | |
Microspora sp. | Microspora is a type of green algae belonging to the unbranched, filamentous chlorophytes. Its cell walls are made up of overlapping H-shaped sections, which can vary in thickness. Each individual cell contains a single, deep green, net-like chloroplast. A red pigment is often visible within a lens-shaped cavity located between the cells. Microspora is typically found in streams and rivers with moderate to good water quality, thriving in environments where conditions are relatively clean and stable. | [43,44] | |
Mugeotia sp. | Mugeotia genus green algae consists of more than 200 genera, which are habitat in freshwater, including lakes, ponds, rivers and sub-areal conditions. At the same time, this genre consists of filamentous form. | [45] |
(a) Descriptive Statistics | |||||
---|---|---|---|---|---|
Group | Mean | Standard Deviation | Minimum | Maximum | |
Blank | 580 | 416.82 | 90 | 1390 | |
Red | 340 | 145.55 | 90 | 490 | |
Yellow | 155.16 | 34.6 | 90 | 200 | |
Green | 117.42 | 23.19 | 90 | 160 | |
Blue | 635 | 238.7 | 90 | 840 | |
(b) One-Way ANOVA | |||||
Source | Sum of Squares | df | Mean Square | F | p-Value |
Group | 1.13 × 106 | 4 | 283,498.7 | 17.79 | <0.0001 |
Residual | 2.37 × 106 | 150 | 15,785.3 | ||
(c) Post Hoc Analysis (Tukey HSD) | |||||
Comparison | Mean Difference | 95% CI (Lower, Upper) | p-Value | Significant? | |
Blank vs. Red | −210 | [−354.2, −65.8] | 0.0009 | Yes | |
Blank vs. Yellow | −343.5 | [−487.8, −199.3] | <0.0001 | Yes | |
Blank vs. Green | −373.2 | [−517.5, −229.0] | <0.0001 | Yes | |
Blank vs. Blue | −152.6 | [−296.8, −8.3] | 0.0324 | Yes | |
Red vs. Yellow | −133.5 | [−277.8, 10.7] | 0.0839 | No | |
Red vs. Green | 163.2 | [19.0, 307.5] | 0.0179 | Yes | |
Red vs. Blue | −57.4 | [−201.7, 86.8] | 0.8067 | No | |
Yellow vs. Green | 29.7 | [−114.6, 173.9] | 0.9795 | No | |
Yellow vs. Blue | −191 | [−335.2, −46.7] | 0.0032 | Yes | |
Green vs. Blue | −220.6 | [−364.9, −76.4] | 0.0004 | Yes |
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Sumanasekara, H.; Jayasingha, H.; Amarasooriya, G.; Dayarathne, N.; Mainali, B.; Senevirathna, L.; Gamage, A.; Merah, O. Hybrid Machine Learning Models for Predicting the Impact of Light Wavelengths on Algal Growth in Freshwater Ecosystems. Phycology 2025, 5, 23. https://doi.org/10.3390/phycology5020023
Sumanasekara H, Jayasingha H, Amarasooriya G, Dayarathne N, Mainali B, Senevirathna L, Gamage A, Merah O. Hybrid Machine Learning Models for Predicting the Impact of Light Wavelengths on Algal Growth in Freshwater Ecosystems. Phycology. 2025; 5(2):23. https://doi.org/10.3390/phycology5020023
Chicago/Turabian StyleSumanasekara, Himaranga, Harshi Jayasingha, Gayan Amarasooriya, Narada Dayarathne, Bandita Mainali, Lalantha Senevirathna, Ashoka Gamage, and Othmane Merah. 2025. "Hybrid Machine Learning Models for Predicting the Impact of Light Wavelengths on Algal Growth in Freshwater Ecosystems" Phycology 5, no. 2: 23. https://doi.org/10.3390/phycology5020023
APA StyleSumanasekara, H., Jayasingha, H., Amarasooriya, G., Dayarathne, N., Mainali, B., Senevirathna, L., Gamage, A., & Merah, O. (2025). Hybrid Machine Learning Models for Predicting the Impact of Light Wavelengths on Algal Growth in Freshwater Ecosystems. Phycology, 5(2), 23. https://doi.org/10.3390/phycology5020023