Antarctic krill resource distribution prediction method based on multi-algorithm integration

Abstract

This invention relates to the field of marine biological resource survey technology, specifically disclosing a method for predicting Antarctic krill resource distribution based on multi-algorithm integration. The method includes: acquiring krill acoustic survey density data and multi-source environmental variable data; performing coordinate projection transformation, missing value processing, and grid aggregation on the data; constructing a modeling dataset and performing logarithmic transformation to mitigate the bias of zero-inflation features on model training; calculating the Pearson correlation coefficient and variance inflation factor among various environmental variables; and constructing a correlation-collinearity dual screening criterion by combining krill density correlation ranking. This invention constructs a complementary modeling system of multiple heterogeneous algorithms, utilizing the structural dissimilarity between algorithms to maximize the capture of diverse response patterns between krill density and environmental factors. This effectively suppresses the technical defects of single algorithms exhibiting drastic fluctuations in prediction performance under different sea areas and marine environmental conditions, significantly improving the generalization stability and environmental adaptability of Antarctic krill resource distribution prediction.

Description

Technical Field

[0001] This invention relates to the field of marine biological resource survey technology, and in particular to a method for predicting the distribution of Antarctic krill resources based on multi-algorithm integration. Background Technology

[0002] Antarctic krill (Euphausia superba) is a key species in the Southern Ocean ecosystem. It not only provides an important food source for numerous predators such as whales, seals, penguins, and seabirds, but also plays a vital role in the Southern Ocean's biochemical cycles and the global carbon cycle through vertical migration and biological pumping. With its enormous biomass, Antarctic krill is one of the most important fishery resources in the Southern Ocean. Accurately predicting the distribution of Antarctic krill resources is of great significance for fisheries management and ecosystem protection.

[0003] In existing technologies, due to the scarcity and zero inflation of Antarctic krill survey data, traditional single-species distribution models exhibit significant performance fluctuations under different environmental conditions. They are susceptible to the zero inflation characteristic of Antarctic krill data and the heterogeneity of complex marine environments, resulting in drastic fluctuations in prediction accuracy across different sea areas and resolutions. Furthermore, the lack of a stable performance benchmark leads to inconsistent prediction accuracy. Additionally, in multi-algorithm integration, fixed weight allocation strategies struggle to adapt to the dynamic impact of spatial resolution changes on the prediction performance of each sub-model, causing the prediction bias of the integrated model to gradually accumulate with resolution variations. Moreover, when sub-models with unstable prediction performance and lacking ecological rationality participate in the integration, existing integration frameworks struggle to effectively suppress their interference, ultimately affecting the ecological consistency and regional reliability of Antarctic krill resource spatial distribution prediction results. Therefore, this paper proposes a multi-algorithm integration-based method for predicting Antarctic krill resource distribution to address the aforementioned problems. Summary of the Invention

[0004] To overcome the shortcomings of the prior art, this invention provides a method for predicting the distribution of Antarctic krill resources based on multi-algorithm integration, which can effectively solve the problems involved in the prior art.

[0005] The objective of this invention can be achieved through the following technical solution: This invention provides a method for predicting the distribution of Antarctic krill resources based on multi-algorithm integration, comprising the following steps: Step 1: Obtain krill acoustic survey density data and multi-source environmental variable data. Perform coordinate projection transformation, missing value processing and grid aggregation on the data to construct a modeling dataset and perform logarithmic transformation to mitigate the bias of zero inflation features on model training, effectively reduce data zero inflation bias, and improve model training stability. Step 2: Calculate the Pearson correlation coefficient and variance inflation factor among the environmental variables. Combined with the krill density correlation ranking, construct a correlation-collinearity dual screening criterion to adaptively eliminate redundant variables and retain key ecological driving factors. That is, eliminate highly collinear variables and retain variables that are more strongly correlated with krill density, eliminate variable redundancy, and highlight the core ecological driving factors. Step 3: Construct single sub-models for six heterogeneous algorithms, namely GAM, RF, ANN, XGBoost, MARS and SVM. Through diversity modeling, capture the multi-mode nonlinear relationship between krill density and marine environment, suppress the prediction fluctuations of a single algorithm in heterogeneous sea areas, and use multiple algorithms to complement each other to suppress the prediction fluctuations of a single model. Step 4: K-fold cross-validation is used to calculate the mean absolute error (MAE), root mean square error (RMSE), and coefficient of determination (R²) of each sub-model. Based on performance ranking, usable sub-models are selected, and unstable sub-models that lack ecological rationality are eliminated. Unstable models are also eliminated to ensure the ecological rationality of the integrated model. Step 5: Using a dual weighting strategy based on RMSE and R², the comprehensive weights of the available sub-models are calculated based on the cross-validation results. A weight smoothing factor is introduced to suppress the interference of low-performance sub-models. The weighted fusion is used to obtain the integrated prediction value. Dynamic weighted fusion is used to suppress the interference contribution of inferior models. Step 6: Based on multi-algorithm integration and dynamic weighted fusion technology, output the model performance comparison results, environmental variable importance ranking, partial dependence response curve, and krill resource density spatial distribution map, providing a stable and reliable decision-making basis for fisheries management and ecological protection, and outputting multi-dimensional results to provide a stable and reliable decision-making basis.

[0006] Preferably, step 1 specifically includes: Acoustic data in three frequency bands (38, 70, and 120 kHz) were collected using fish finders mounted on Antarctic krill fishing vessels. Based on the acoustic survey and assessment method recommended by SC-CAMLR, krill resource density data was calculated and output with 1 nautical mile as the basic integral range unit, effectively improving the accuracy and standardization of krill density detection. Simultaneously acquire eleven-dimensional multi-source environmental variable data, including seabed depth, slope, distance from shelf break, sea surface temperature, seabed temperature, sea surface salinity, sea surface height, mixed layer depth, current velocity, distance from sea ice edge, and chlorophyll a concentration. Establish a multimodal feature set across four categories of environmental factors: topography, physical oceanography, sea ice, and organisms. Comprehensively cover key ecological driving factors of krill habitat and enhance model interpretability. All data were uniformly projected to the Antarctic Equal Area Projected Coordinate System EPSG:6932, and missing value imputation and grid aggregation were completed. A logarithmic transformation with the natural constant e as the base was performed on the krill density. By compressing the numerical magnitude of high-density regions, the influence of zero and non-zero observations on model training was balanced, spatial distortion and data bias were eliminated, and the model's fitting stability to zero-inflation data was improved.

[0007] Preferably, step 2 specifically includes: Calculate the Pearson correlation coefficient between any two environmental variables. When the absolute value of the correlation coefficient is greater than 0.7, it is considered highly collinear. Calculate the correlation coefficient between the two highly collinear variables and the krill density after logarithmic transformation. Determine which variables to retain based on the strength of the association with the response variable, effectively eliminating redundant variables and retaining predictive factors with stronger ecological associations. The variance inflation factor was calculated for the environmental variables retained after Pearson screening. A variance inflation factor of less than 10 was used as the threshold for the absence of significant multicollinearity. Redundant variables exceeding the threshold were removed to eliminate the interference of multicollinearity on the estimation of model parameters and improve statistical reliability. Based on the results of Pearson correlation ranking and variance inflation factor test, a dual screening criterion of correlation and collinearity is constructed. Under the premise of retaining the variables most closely related to the ecological driving force of krill density, information redundancy caused by the inherent coupling relationship between environmental variables is adaptively eliminated, so as to achieve a balance between collinearity reduction and ecological information preservation and optimize the quality of feature set.

[0008] Preferably, step 2 further includes: Calculate the Pearson correlation coefficient between each environmental variable and the krill density after logarithmic transformation. Based on the absolute value of the correlation coefficient, construct a ranking table of the ecological association strength of candidate predictive factors. Prioritize the identification of environmental driving factors that have statistically significant association with krill resource distribution, realize data-driven identification of key driving factors, and avoid subjective screening bias. A correlation coefficient matrix among environmental variables is constructed. For highly collinear variable pairs with an absolute correlation coefficient greater than 0.7, the pair is sorted according to the established ecological association strength. The pair with a weaker correlation to krill density is removed from each pair of highly collinear variables to achieve a balance between collinearity reduction and ecological information preservation. This maximizes the preservation of ecological association information while eliminating pairwise redundancy. The variance inflation factor is calculated iteratively for the remaining variable set. In each iteration, the variable with the largest variance inflation factor is removed, and the calculation is repeated before entering the next iteration. This process continues until the variance inflation factor of all remaining variables is below 10, ensuring that the final modeling variable set has statistically significant low multicollinearity, eliminating cumulative collinearity effects, and ensuring that the variable set meets the modeling assumptions.

[0009] Preferably, step 3 specifically includes: We constructed single sub-models of six heterogeneous algorithms with different underlying mathematical principles: GAM, RF, ANN, XGBoost, MARS, and SVM (Generalized Additive Model, Random Forest Model, Artificial Neural Network Model, Limiting Gradient Boosting Model, Multivariate Adaptive Regression Spline Model, and Support Vector Machine Model). By utilizing the structural dissimilarity between the algorithms, we maximized the capture of diverse response patterns between krill density and environmental factors, effectively covering multiple potential response relationships such as linear, nonlinear, and interactive effects. Each sub-model employs differentiated parameter configurations optimized for zero-inflation continuous data. These include GAM binding to the Tweedie error distribution to adapt to the peak-heavy-tailed distribution characteristics of krill density, RF using a self-governing aggregation mechanism to reduce the overfitting risk of a single decision tree, and ANN limiting the number of neurons in a single hidden layer to establish a balance between underfitting and overfitting. These measures significantly improve the adaptability and generalization robustness of each model to zero-inflation data. XGBoost employs a tree-by-tree iterative fitting strategy for residuals and binds it to the Tweedie objective function. MARS achieves piecewise linear fitting through automatic basis function selection and pruning mechanisms. SVM constructs a flat hyperplane regression function under the constraint of an insensitive loss function. These six algorithms form a complementary modeling system from multiple paradigm dimensions, including parametric, non-parametric, ensemble learning, and kernel methods. The synergy of these multiple paradigms significantly enhances the adaptability to the heterogeneity of complex marine environments.

[0010] Preferably, step 4 specifically includes: We employ a K-fold cross-validation strategy, dividing the entire dataset into K subsets. Each time, we use K-1 subsets as the training set and the remaining subset as the test set, repeating this process K times to complete the full data round-robin evaluation. This effectively avoids evaluation bias caused by a single partition and improves the robustness of performance estimation. The average absolute error, root mean square error, and coefficient of determination of each sub-model in cross-validation are calculated together. The root mean square error applies a nonlinear penalty to high-bias predictions to highlight the risk of extreme errors, while the coefficient of determination is used to measure the model's share of the spatial variation of krill density. This comprehensively characterizes the model's predictive ability from multiple dimensions and forms a complementary evaluation system. Based on the comprehensive ranking results of the three indicators, the sub-models that rank in the top three in terms of root mean square error and coefficient of determination and whose partial dependence curves maintain sign consistency when spatial resolution changes are prioritized for retention. The excluded algorithms are defined as interference models and removed from the ensemble pool to ensure that the selected models have high accuracy, high interpretability and realistic ecological response.

[0011] Preferably, step 4 further includes: Calculate the cross-fold standard deviation of the root mean square error of each sub-model in K-fold cross-validation, and use the numerical value of this standard deviation to measure the model’s prediction sensitivity to different data subsets. Identify unstable algorithms with abnormally high error in specific spatial partitions or environmental gradient intervals, and effectively eliminate unreliable models with drastic fluctuations in prediction performance. Ecological rationality assessment is conducted based on the morphological consistency of the partial dependence response curves at multiple spatial resolutions. Sub-models that exhibit sign reversal, non-monotonic oscillations, or ecological paradoxes in their response curves at different resolutions are excluded. This ensures that the marginal effects output by the selected models conform to known prior knowledge of krill ecology and that the environmental response relationships output by the models have real ecological meaning. A quantitative admission threshold is established where the mean root mean square error does not exceed the median of the entire model set and the cross-fold standard deviation is lower than the set mean. This threshold, combined with the ecological smoothness of the response curve, forms a double filtering barrier. This ensures that the sub-models finally included in the integration framework simultaneously meet the qualification standards in both statistical prediction accuracy and ecological response authenticity. This dual guarantee ensures that the integrated model is both accurate and conforms to ecological laws.

[0012] Preferably, step 5 specifically includes: Based on the root mean square error of each available sub-model in cross-validation, an error reciprocal weighting strategy is adopted to ensure that the sub-model with the smaller prediction error receives a higher contribution ratio in the integration and fusion, while the model with a larger error is automatically suppressed, ensuring that the high-precision model dominates the prediction results and reducing the overall prediction bias. Based on the determination coefficients of each available sub-model, the explanatory power normalization weighting method is adopted to assign higher fusion weights to the sub-models that characterize the complex relationship between krill density and environmental variables, thereby strengthening the contribution of the real ecological response model and improving the explanatory credibility. Adaptive harmonic normalization is applied to the RMSE weights and R² weights, enabling the sub-models with both high accuracy and strong interpretability to play a leading role in the integration process. This forms a comprehensive weight allocation mechanism that balances statistical error and the realism of ecological response, achieving a balance between accuracy and ecological realism and avoiding distortion caused by single-index optimization.

[0013] Preferably, step 5 further includes: In the process of calculating the comprehensive weight, a nonlinear weight smoothing factor is introduced to adaptively compress and suppress the original weights of the low-performance sub-models, which significantly weakens the interference contribution of the inferior model in the integration and fusion, enhances the robustness of the integration framework against the interference of unstable models, and significantly improves the anti-interference ability of the integration framework against the inferior model. We employ a weighted summation strategy under the dual constraints of accuracy and interpretation to fuse the prediction outputs of each sub-model. This allows the integrated prediction value to achieve optimal fusion based on the dynamic adjustment of the contribution of each sub-model, avoiding the weight bias oriented by a single evaluation index and achieving an intrinsic balance between statistical accuracy and ecological authenticity. The weight combination parameters are independently optimized for different spatial resolution scenarios, enabling the ensemble model to adaptively adjust the fusion ratio of each sub-model according to the resolution change. This effectively eliminates the resolution-dependent cumulative error caused by the fixed weight strategy and the cumulative effect of prediction bias caused by resolution changes.

[0014] Preferably, step 6 specifically includes: The permutation importance assessment method based on root mean square error was adopted. After randomly shuffling each environmental variable, the performance degradation of the ensemble model was calculated, and the normalized ranking of the environmental variables was output to clearly identify the key environmental driving factors that dominate the distribution of krill. The partial dependence response curves between key ecological driving factors and krill resource density are generated. The nonlinear response law and threshold effect of krill density to dominant environmental factors are revealed in a smooth and interpretable visualization, and the nonlinear response law of krill density to environmental factors is revealed intuitively. The study area is discretized into a multi-resolution regular grid system. Environmental variables of each grid cell are extracted and combined into the integrated model to generate raster layers of krill resource density spatial distribution under different spatial resolutions and different survey time phases. The spatial pattern is visualized using ecological color gradation, clearly showing the multi-scale spatiotemporal distribution and dynamic changes of krill resources.

[0015] Compared with the prior art, the beneficial effects of the present invention are: 1. This method for predicting the distribution of Antarctic krill resources based on multi-algorithm integration constructs a complementary modeling system of multiple heterogeneous algorithms. By utilizing the structural dissimilarity between algorithms, it maximizes the capture of diverse response patterns between krill density and environmental factors. This effectively suppresses the technical defects of single algorithms in predicting performance that fluctuates drastically under different sea areas and marine environmental conditions, and significantly improves the generalization stability and environmental adaptability of Antarctic krill resource distribution prediction.

[0016] 2. This multi-algorithm integrated method for predicting Antarctic krill resource distribution constructs a correlation-collinearity dual screening criterion by calculating the Pearson correlation coefficient and variance inflation factor between environmental variables and ranking the ecological association strength with krill density. This adaptively eliminates redundant variables while retaining key ecological driving factors, effectively solving the interference of high-dimensional environmental data collinearity on model parameter estimation and ensuring the statistical reliability and ecological interpretability of the prediction model input features.

[0017] 3. The Antarctic krill resource distribution prediction method based on multi-algorithm integration adopts a dynamic dual-weighted fusion strategy based on root mean square error and coefficient of determination. This strategy enables the sub-model with both high prediction accuracy and strong ecological explanatory power to obtain the dominant weight in the integration. At the same time, a nonlinear weight smoothing factor is introduced to adaptively compress and suppress the interference contribution of low-performance sub-models, thereby achieving an inherent balance between statistical accuracy and ecological authenticity in the integration framework and effectively avoiding the problem of prediction bias accumulation caused by fixed weight strategy.

[0018] 4. This method for predicting the distribution of Antarctic krill resources based on multi-algorithm integration establishes a dual filtering barrier by calculating the root mean square error across the standard deviation of the sub-models in cross-validation and combining the morphological consistency of the partial dependence response curves at different resolutions. It eliminates unstable and ecologically unreasonable interference models from two dimensions: statistical prediction stability and ecological response authenticity. This ensures that the sub-models included in the integration framework meet the qualification standards at both the numerical prediction level and the ecological response level, thereby enhancing the robustness of the integrated system against abnormal models. Attached Figure Description

[0019] Figure 1 This is a schematic diagram illustrating the workflow of the Antarctic krill resource distribution prediction method based on multi-algorithm integration of the present invention. Figure 2 This is an overall flowchart of the present invention; Figure 3 This is a ranking chart of the importance of variables in this invention; Figure 4 This is the partial dependency graph of the GAM of this invention; Figure 5 This is the partial dependency graph of the RF of the present invention; Figure 6 This is the partial dependency graph of the ANN of this invention; Figure 7 This is the partial dependency graph of XGBoost in this invention; Figure 8 This is the partial dependency graph of the integration model of this invention; Figure 9 This is a predicted spatial distribution map (5km) of krill in January 2016 based on the present invention. Figure 10 This is a predicted spatial distribution map of krill in January 2016 (10km). Figure 11 This is a predicted spatial distribution map of krill in January 2016 (15km). Figure 12 This is a predicted spatial distribution map of krill in January 2016 (20km). Figure 13 This is a predicted spatial distribution map (5km) of krill in February 2018 based on the present invention. Figure 14 This is a predicted spatial distribution map (10km) of krill in February 2018 based on the present invention. Figure 15 This is a predicted spatial distribution map of krill in February 2018 (15km). Figure 16 This is a predicted spatial distribution map of krill in February 2018 (20km). Detailed Implementation

[0020] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are some embodiments of the present invention, but not all embodiments.

[0021] Example 1, please refer to Figure 1 , Figure 2 This invention provides a technical solution: a method for predicting the distribution of Antarctic krill resources based on multi-algorithm integration, comprising the following steps: Step 1: Acquire krill acoustic survey density data and multi-source environmental variable data. Perform coordinate projection transformation, missing value processing, and grid aggregation on the data to construct a modeling dataset and perform logarithmic transformation to mitigate the impact of zero inflation on model training bias, effectively reducing data zero inflation bias and improving model training stability. Acoustic data in three frequency bands (38, 70, and 120 kHz) are collected using a fish finder onboard the Antarctic krill fishing vessel. Based on the acoustic survey assessment method recommended by SC-CAMLR, krill resource density data is calculated and output using 1 nautical mile as the basic integral range unit, effectively improving the accuracy and standardization of krill density detection. Simultaneously acquire data including seabed depth, slope, distance from shelf break, sea surface temperature, etc. Eleven-dimensional multi-source environmental variable data, including seabed temperature, sea surface salinity, sea surface height, mixed layer depth, current velocity, distance from sea ice edge, and chlorophyll a concentration, were used to establish a multimodal feature set across four categories of environmental factors: topography, physical oceanography, sea ice, and organisms. This comprehensively covers key ecological drivers of krill habitats, enhancing the model's interpretability. All data were uniformly projected onto the Antarctic Equal Area Projected Coordinate System EPSG:6932, and missing value imputation and grid aggregation were completed. A logarithmic transformation based on the natural constant e was performed on krill density. By compressing the numerical magnitude of high-density areas, the influence of zero and non-zero observations on model training was balanced, eliminating spatial distortion and data bias, and improving the model's fitting stability to zero-inflation data. The logarithmic transformation of krill density is given by the following formula: ; In the formula, This represents the original krill density value; It should be noted that, using the Simrad EK60 scientific fish finder aboard the Antarctic krill fishing vessel, acoustic echo data were collected at three frequency bands: 38kHz, 70kHz, and 120kHz. Following the acoustic survey and assessment methods recommended by the Scientific Committee on the Conservation of Antarctic Marine Living Resources, noise was removed from the raw acoustic data, target intensity was assigned, and species were identified. Then, using 1 nautical mile as the basic integration distance unit, krill resource density data was calculated and output unitly in grams per square meter. Addressing the common zero-expansion characteristic in krill density data—that is, many survey grid cells showed no krill while a few cells had extremely high densities—a logarithmic transformation with the natural constant e was performed on all density observations. The transformation formula was that the response variable equals the logarithmically transformed krill density plus one. This transformation compressed the numerical magnitude of high-density areas, reducing the dominance of extreme values ​​on model parameter estimation. Simultaneously, eleven-dimensional multi-source environmental variable data were acquired, specifically including data from GEBCO. The data includes seafloor depth from the 2023 Digital Depth Model, slope calculated based on seafloor depth, Euclidean distance between seafloor depth and shelf break location, sea surface temperature, seafloor temperature, sea surface salinity, sea surface height, mixed layer depth, and current velocity from the Copernicus Marine Service, distance from sea ice edge from the same data source, and chlorophyll a concentration. These variables are categorized into four environmental factors: topography, physical oceanography, sea ice, and biota. Together, they constitute a multimodal feature set describing the characteristics of Antarctic krill habitat. All data are uniformly projected onto the Antarctic Equal Area Projection Coordinate System EPSG:6932. This coordinate system uses equal area projection parameters suitable for the Antarctic region, effectively eliminating area distortion problems in high-latitude areas. Missing values ​​are imputed for each data layer after projection, and discrete missing pixels are filled using the spatial nearest neighbor mean method. Grid aggregation is then performed according to the set spatial resolution to achieve spatial matching between environmental variables and krill density data at the same grid cell scale. After the above preprocessing, each grid cell is associated with... A logarithmically transformed krill density value and a complete set of environmental variable vectors are used to fill in missing environmental variables in local areas due to differences in survey coverage or data sources. Multi-temporal monthly average climatological data are used to ensure that all grid cells in the entire study area have complete feature inputs. During the grid aggregation process, modeling datasets with four spatial resolutions of 5 km, 10 km, 15 km and 20 km are generated according to modeling needs to examine performance at different spatial scales. The logarithmically transformed krill density data is used as the model response variable, and the eleven-dimensional environmental variables are used as predictor variables. Together, they form a structured modeling data matrix. Each row in this matrix corresponds to a spatial sampling cell, and each column represents a response variable or a predictor. This data is directly input into the subsequent environmental variable screening and multi-algorithm sub-model construction process. Step 2: Calculate the Pearson correlation coefficient and variance inflation factor among various environmental variables. Combined with the krill density correlation ranking, construct a dual screening criterion of correlation and collinearity. Adaptively eliminate redundant variables and retain key ecological drivers, i.e., eliminate highly collinear variables and retain variables with stronger correlation to krill density, eliminating variable redundancy and highlighting core ecological drivers. Calculate the Pearson correlation coefficient between any two environmental variables; when the absolute value of the correlation coefficient is greater than 0.7, it is considered highly collinear. Calculate the correlation coefficient between each of the two highly collinear variables and the logarithmically transformed krill density. Determine which variables to retain based on the strength of the association with the response variable, effectively eliminating... In addition to redundant variables, predictors with stronger ecological relevance are retained. Variance inflation factors are calculated for environmental variables retained after Pearson screening. A variance inflation factor of less than 10 is used as the threshold for no significant collinearity. Redundant variables exceeding the threshold are removed to eliminate the interference of multicollinearity on model parameter estimation and improve statistical reliability. Combining the results of Pearson correlation ranking and variance inflation factor test, a dual screening criterion of correlation and collinearity is constructed. Under the premise of retaining variables with the closest ecological driving relationship with krill density, information redundancy caused by the inherent coupling relationship between environmental variables is adaptively removed to achieve a balance between collinearity reduction and ecological information retention, and optimize the quality of feature set. Two environment variables and Correlation coefficient between : ; when At that time, the judgment and There is high collinearity between them. In this case, the correlation coefficients between the two variables and the krill density are calculated separately, and the one with the stronger correlation is retained. It should be noted that after constructing the modeling dataset, Pearson correlation coefficients were calculated for all eleven environmental variables. For any two environmental variables, the Pearson correlation coefficient was calculated based on their observation sequences in each spatial sampling unit. A threshold of 0.7 was set for the absolute value of the correlation coefficient. When the absolute value of the correlation coefficient between two variables is greater than 0.7, it is determined that there is high collinearity between them. For each pair of variables that meets the high collinearity criterion, the correlation coefficient between each variable and the krill density after logarithmic transformation was calculated to measure the ecological association strength between each variable and the response variable. The absolute value of the correlation coefficients of the quantities was used to select the variable with a stronger correlation to krill density from each pair of highly collinear variables, while removing the weaker correlation. Guided by statistical significance, this approach initially reduced redundancy caused by the inherent coupling between environmental variables without losing key ecological information. For the set of environmental variables retained after Pearson screening, the variance inflation factor of each variable was further calculated. Specifically, a linear regression was performed on all other retained variables using one environmental variable as the dependent variable. The coefficient of determination of this regression model was obtained, and then the variance inflation factor was calculated. Its value is equal to one minus the reciprocal of the coefficient of determination. The variance inflation factor was set to be less than... A threshold of 10 is used to determine the absence of significant multicollinearity. Variables with a variance inflation factor (VIF) of 10 or higher are considered to have significant multicollinearity and are therefore removed. An iterative calculation and removal strategy is employed: the VIF of each variable in the current variable set is calculated each time, and the variable with the largest value is removed. The VIF of the reduced variable set is then recalculated, and this process is repeated until the VIF of all retained variables is below 10. This identifies and eliminates the cumulative effect of multicollinearity caused by complex linear relationships between multiple variables. The execution flow of the correlation-multicollinearity dual screening criterion is as follows: First, the Pearson correlation coefficient threshold is used... Value determination is performed to eliminate the pair of highly collinear variables that have a weaker ecological association with krill density, achieving an initial screening based on pairwise correlation. Subsequently, through iterative calculation of the variance inflation factor and threshold discrimination, redundant variables with significant multicollinearity under the multiple linear regression framework are eliminated, achieving a secondary fine screening based on the overall linear relationship. The core of the dual screening criterion is: while retaining the explanatory variables that are most closely related to the ecological driving force of krill density, adaptively eliminating information redundancy caused by the inherent coupling relationship between environmental variables. The final set of retained variables simultaneously satisfies: there is no highly collinear relationship between any two variables, and the variance inflation factor of the entire set is less than 10. Furthermore, step 2 also includes: calculating the Pearson correlation coefficient between each environmental variable and the krill density after logarithmic transformation; constructing an ecological association strength ranking table of candidate predictive factors based on the absolute value of the correlation coefficient; prioritizing environmental driving factors that have a statistically significant correlation with krill resource distribution to achieve data-driven identification of key driving factors and avoid subjective screening bias; constructing a correlation coefficient matrix between environmental variables; for highly collinear variable pairs with a correlation coefficient absolute value greater than 0.7, removing the pair with a weaker correlation to krill density from each pair of highly collinear variables based on the established ecological association strength ranking to achieve a balance between collinearity reduction and ecological information retention; maximizing the retention of ecological association information while eliminating pairwise redundancy; iteratively calculating the variance inflation factor for the remaining variable set; removing the variable with the largest variance inflation factor in each iteration; recalculating and entering the next iteration until the variance inflation factor of all remaining variables is less than 10 to ensure that the final modeling variable set has statistically significant low multicollinearity, eliminate cumulative collinearity effects, and ensure that the variable set meets the modeling assumptions. Calculate the variance inflation factor (VIF) for the screened environmental variables: ; In the formula, For the first The coefficient of determination of a variable in the regression of all other variables, when At that time, it was considered that there was no significant collinearity; It should be noted that for each variable in the eleven-dimensional environmental variables, its observed value sequence across all spatial sampling units is extracted, and correlation analysis is performed with the corresponding unit's response variable value to obtain the Pearson correlation coefficient and its significance level for each variable. Based on the absolute value of the Pearson correlation coefficient, all candidate predictors are sorted in descending order to construct an ecological association strength ranking table. This ranking table intuitively reflects the statistical correlation between each environmental factor and krill resource distribution. Based on this ranking result, environmental driving factors with statistically significant correlations (P-value less than 0.05) and the highest absolute values ​​of correlation coefficients are prioritized as core explanatory variables for subsequent modeling. This data-driven approach identifies key environmental factors that have a dominant controlling effect on krill resource distribution, providing a quantitative basis for ecological association strength for variable retention decisions during collinear reduction processes, and avoiding... Information loss due to subjective screening; constructing a Pearson correlation coefficient matrix among all retained environmental variables, where each element represents the correlation coefficient between two corresponding variables, setting an absolute value threshold of 0.7 as the criterion for high collinearity, traversing the upper triangular region of the correlation coefficient matrix, identifying all high collinear variable pairs that satisfy |r|>0.7, for each high collinear variable pair, according to the previously constructed ecological association strength ranking table, querying the absolute values ​​of the correlation coefficients between the two variables and the response variable, comparing their magnitudes, removing the variable pair with a weaker correlation to krill density, and retaining the one with a stronger ecological association strength, achieving a balance between collinearity reduction and ecological information retention. After this initial screening process traverses all high collinear variable pairs, a reduced variable set filtered by pairwise correlation is obtained, characterized by the absolute value of the correlation coefficient between any two variables not exceeding 0.7. Eliminate significant redundancy among environmental variables from a pairwise correlation perspective, while preserving the variable information most closely related to the ecological drivers of krill resource distribution to the greatest extent possible; for the variable set retained after initial screening using Pearson correlation coefficients, further perform multicollinearity iterative elimination based on variance inflation factor (VIF). Calculate the VIF of each variable in the current variable set. Specifically, construct a linear regression model with the variable as the dependent variable and the remaining variables as independent variables. After obtaining the model's coefficient of determination, calculate the VIF according to the formula: VIF equals one minus the reciprocal of the coefficient of determination. Set a VIF less than 10 as a threshold value. A retention threshold for non-significant multicollinearity is established. In each iteration, the variable with the largest variance inflation factor (VIF) is identified and removed if its value reaches or exceeds 10. Subsequently, the VIF of each variable in the reduced variable set is recalculated, and the above iterative process is repeated, removing the variable with the most severe multicollinearity each time, until the VIF of all retained variables is below 10. This identifies and eliminates the cumulative multicollinearity effect caused by complex linear relationships among multiple variables, ensuring that the variable set finally included in the sub-model construction has low multicollinearity in a statistical sense, meeting the basic assumptions of linear regression modeling. Step 3: Construct single sub-models for six heterogeneous algorithms: GAM, RF, ANN, XGBoost, MARS, and SVM. This diversity modeling captures the multi-mode nonlinear relationship between krill density and the marine environment, suppressing prediction fluctuations of a single algorithm in heterogeneous sea areas. Complementary modeling using multiple algorithms further mitigates prediction fluctuations of a single model. Six heterogeneous algorithm sub-models with different underlying mathematical principles—GAM, RF, ANN, XGBoost, MARS, and SVM (generalized additive model, random forest model, artificial neural network model, extreme gradient boosting model, multivariate adaptive regression spline model, and support vector machine model)—are constructed to maximize the capture of diverse response patterns between krill density and environmental factors, effectively covering linear, nonlinear, and interactive potential response relationships. Each sub-model... Differentiated parameter configurations optimized for zero-inflation continuous data are adopted, including GAM binding the Tweedie error distribution to adapt to the peak-heavy-tailed distribution characteristics of krill density; RF reducing the overfitting risk of a single decision tree through a self-governing aggregation mechanism; ANN limiting the number of neurons in a single hidden layer to establish a balance between underfitting and overfitting, significantly improving the adaptability and generalization robustness of each model to zero-inflation data; XGBoost adopting a tree-by-tree iterative fitting residual strategy and binding the Tweedie objective function; MARS achieving piecewise linear fitting through automatic basis function selection and pruning mechanism; and SVM constructing a flat hyperplane regression function under the constraint of an insensitive loss function. The six algorithms form a complementary modeling system from multiple paradigm dimensions such as parametric, non-parametric, ensemble learning and kernel methods. The synergy of multiple paradigms significantly enhances the adaptability to the heterogeneity of complex marine environments. It should be noted that the generalized additive model, as a representative of the parametric modeling approach, correlates the expected value of the response variable with the sum of spline smoothing functions of each environmental variable through a link function. The Tweedie error distribution is chosen to adapt to the peaked, heavy-tailed characteristics of krill density data, which include both zero observations and continuous positive values. The degrees of freedom of the spline functions are automatically determined through cross-validation to achieve a balance between fitting bias and model complexity. Secondly, a random forest model is constructed, generating multiple training subsets from the original data through bootstrap resampling. Each subset independently constructs a decision tree, and at each node of the tree, the optimal splitting variable is selected from a randomly selected feature subset. The number of decision trees... The data set is fixed at 1,000, and the number of features randomly selected during node splitting is set to two. By integrating the prediction results of multiple trees and averaging them, a bootstrap aggregation mechanism is used to reduce the overfitting risk of a single decision tree. Finally, an artificial neural network model is constructed, employing a three-layer feedforward structure with one hidden layer. The number of input layer nodes equals the number of filtered environmental variables, and the number of neurons in the hidden layer is limited to ten to establish a balance between underfitting and overfitting. The output layer is a single krill density prediction value. Backpropagation is used for network training, with a weight decay coefficient set to 0.01 and a maximum of 500 iterations. Limiting model complexity prevents overfitting to small sample data. A limit gradient boosting model is also constructed. Classification and regression trees are used as the basic learners. Model bias is gradually reduced by iteratively fitting the residuals of the previous set tree by tree. Each new tree is fitted to the current prediction residual. The predictions of all trees are then summed to obtain the final output. The number of iterations is set to 500, the learning rate is 0.01, and the maximum tree depth is limited to 5. The objective function is bound to the Tweedie distribution to match the data features of krill density. Overfitting is prevented by controlling the complexity of each tree and the overall ensemble size. A multivariate adaptive regression spline model is constructed. First, a series of piecewise linear basis functions are generated based on environmental variables. The connection points between basis functions are called nodes. Then, a two-stage process of forward selection and backward pruning is used. The strategy determines the optimal combination of basis functions, sets the number of basis function interactions to one (considering only the main effect), sets the maximum number of basis functions to seventeen, and sets the pruning threshold to 0.0001. Finally, the selected basis function set is used to perform piecewise linear fitting on the krill density. A support vector machine model is constructed, with the core objective of finding an optimal hyperplane that keeps the distance from all sample points to the hyperplane within the allowable error range, while keeping the model as flat as possible. Radial basis functions are selected as the kernel function type to capture the nonlinear relationship between environmental variables and krill density. The penalty parameter is set to one, and the insensitive loss threshold is 0.1. By combining slack variables and the insensitive loss function, a trade-off is established between fitting accuracy and model complexity.Six algorithms form a complementary modeling system from multiple paradigm dimensions. The generalized additive model is characterized by a transparent and interpretable additive structure, clearly showing the marginal effect of each environmental factor on krill density. However, it is limited by the preset function form and has limited ability to capture complex high-dimensional interactions. Random forest and extreme gradient boosting belong to the ensemble learning paradigm. The former reduces variance by averaging the prediction results of multiple independent decision trees, while the latter reduces bias by iteratively fitting residuals. Both can automatically handle nonlinear relationships and interactions between environmental variables. Artificial neural networks approximate arbitrarily complex functions through the nonlinear activation function of the hidden layer and have a strong fitting ability, but there is a risk of overfitting on small sample data. Multivariate adaptive regression splines achieve a trade-off between interpretability and flexibility through piecewise linear fitting. Support vector machines construct a flat regression function in a high-dimensional feature space through kernel tricks and have good robustness to outliers. Each of the six algorithms adopts differentiated parameter configurations optimized for zero-inflation continuous data. By utilizing the structural dissimilarity between the algorithms, they maximize the capture of diverse response patterns between krill density and environmental factors. The general form of the Generalized Additive Model (GAM) is: ; In the formula, The response variable is krill density. For link functions, These are the input explanatory variables. It is the spline smoothing function of the explanatory variables. It is the intercept term. This is the residual error term, and the Tweedie error distribution is used in the model; The Random Forest (RF) algorithm uses the bootstrap resampling method during training to randomly sample subsets of data and features from the original dataset. It then uses these sampled data to construct decision trees and finally combines the predictions from all the decision trees to obtain the final result. ; In the formula, For response variables, For the number of decision trees, For the first The prediction results of the decision trees, the number of decision trees (ntree) = 1000, and the number of features randomly selected when splitting nodes (mtry) = 2; A single-hidden-layer neural network is constructed using the backpropagation algorithm in Artificial Neural Networks (ANNs). This network consists of three layers of neurons: an input layer (explanatory variables), a hidden layer (multiple neural nodes), and an output layer (response variables). Its mathematical form can be expressed as: ; In the formula, , It's weight. , is the bias term, g() and f() are activation functions, the number of hidden neurons (size) = 10, the weight decay coefficient (decay) = 0.01, and the maximum number of iterations (maxit) = 500; Extreme Gradient Boosting (XGBoost) uses classification trees and regression trees as base learners, and iteratively adds new trees to correct the residuals of the previous set, thereby gradually reducing model bias. ; In the formula, It is the first Sample The predicted value, It was before The predicted results for each tree. It is the first The model function for the tree is: nrounds = 500, learning rate (eta) = 0.01, maximum tree depth (max_depth) = 5, using the Tweedie loss function; The Multivariate Adaptive Regression Splines (MARS) algorithm divides the feature space into several regions, fits a spline curve to each region, and achieves smooth connection at the region boundaries. Its specific steps are: generating a set of basic functions based on the given variables; applying forward selection or backward elimination methods to select the optimal combination of basic functions; and using the selected basic functions to fit the target variable. ; In the formula, For predicted values, For the intercept term, For the first The coefficients of the basis functions For the first There are 17 basis functions, with the number of interactions (degree) = 1, the maximum number of basis functions (nk) = 17, and the pruning threshold (thresh) = 0.0001. The core idea of ​​Support Vector Machine (SVM) is to find an optimal hyperplane such that the distances from all sample points to this hyperplane are within the allowable error ε, while keeping the model as flat as possible. An insensitive loss function is introduced, allowing for an error between the predicted and true values ​​not exceeding ε without incurring loss. The optimization problem of SVM can be expressed as: ; In the formula, For the weight vector, For the penalty function, and For slack variables, kernel type (kernel) = radial, penalty parameter (cost) = 1, and insensitive loss threshold (epsilon) = 0.1; Step 4: K-fold cross-validation is used to calculate the mean absolute error (MAE), root mean square error (RMSE), and coefficient of determination (R²) of each sub-model. Based on performance ranking, usable sub-models are selected, and unstable sub-models that lack ecological rationality are eliminated. Unstable models are also eliminated to ensure the ecological rationality of the integrated model. Step 5: Using a dual weighting strategy based on RMSE and R², the comprehensive weights of the available sub-models are calculated based on the cross-validation results. A weight smoothing factor is introduced to suppress the interference of low-performance sub-models. The weighted fusion is used to obtain the integrated prediction value. Dynamic weighted fusion is used to suppress the interference contribution of inferior models. Step 6: Based on multi-algorithm integration and dynamic weighted fusion technology, output the model performance comparison results, environmental variable importance ranking, partial dependence response curve, and krill resource density spatial distribution map, providing a stable and reliable decision-making basis for fisheries management and ecological protection, and outputting multi-dimensional results to provide a stable and reliable decision-making basis.

[0022] Example 2, as Figure 1 , Figure 2As shown, based on Example 1, this invention provides a technical solution: Step 4 specifically includes: adopting a K-fold cross-validation strategy, dividing the entire dataset into K subsets, using K-1 subsets as the training set and the remaining subset as the test set each time, repeating this K times to complete the full data round-robin evaluation, effectively avoiding evaluation bias caused by a single partition, improving the robustness of performance estimation, jointly calculating the mean absolute error, root mean square error, and coefficient of determination of each sub-model in cross-validation, where the root mean square error applies a nonlinear penalty to high-bias predictions to highlight the risk of extreme errors, and the coefficient of determination is used to measure the model's explanatory share of the spatial variation of krill density, comprehensively characterizing the model's predictive ability from multiple dimensions, forming a complementary evaluation system, and based on the comprehensive ranking results of the three indicators, prioritizing the retention of the sub-models with the top three combined rankings of root mean square error and coefficient of determination and whose biased dependency curves maintain sign consistency when spatial resolution changes, defining the excluded algorithms as interference models and removing them from the ensemble pool, ensuring that the selected models have high accuracy, high explanatory power, and ecological response authenticity; The calculation formulas for each indicator are as follows: ; ; ; In the formula, Indicates the mean absolute error. This represents the root mean square error. For the observed values, For predicted values, As the coefficient of determination, The average of the observed values. The number of samples; It should be noted that a K-fold cross-validation strategy was used to systematically evaluate the performance of the six constructed heterogeneous sub-models. Specifically, the preprocessed and variable-selected modeling dataset was randomly divided into K subsets according to spatial sampling units. The value of K was set to 10 based on the dataset size to ensure that each subset had sufficient sample representativeness. In each iteration, K-1 subsets were used as the training set for sub-model parameter estimation, and the remaining subset was used as the test set to calculate the prediction error. This process was repeated K times, ensuring that each sampling unit participated in exactly one test set evaluation. A data polling mechanism fully utilizes scarce Antarctic krill survey data to obtain unbiased performance estimates of each sub-model on independent test sets, avoiding the evaluation randomness caused by a single training-test split. During cross-validation, three quantitative evaluation indicators—mean absolute error, root mean square error (RMSE), and coefficient of determination—are jointly calculated for each sub-model. Mean absolute error reflects the average deviation between predicted and observed values, and is calculated as the arithmetic mean of the absolute values ​​of prediction errors. RMSE, by taking the square root of the error term, applies a non-linear penalty to high-bias predictions, effectively highlighting the risk of extreme errors. The model is sensitive to abnormally high values ​​in local areas that may occur in krill density prediction. The coefficient of determination (COD) measures the share of the sub-model in explaining the spatial variance of krill density by comparing the model's prediction error with the variation of the observed values. The closer the COD is to 1, the more original information the model retains. These three indicators characterize the predictive performance of the sub-models from different dimensions, forming a complementary evaluation system. Based on the comprehensive ranking of the three indicators, the sub-models with the top three combined root mean square error and COD are prioritized for inclusion in the integration framework. In the specific screening, algorithms with a mean absolute error exceeding the median of the entire model set are first eliminated. Then, the three sub-models with the smallest root mean square error and the largest COD are selected from the remaining algorithms. Furthermore, the candidate sub-models are tested for ecological rationality, requiring that their partial dependency curves maintain the sign consistency of the response shape under different spatial resolutions. That is, the positive or negative relationship between key environmental factors and krill density does not reverse with the change of resolution. Algorithms that fail to meet both the statistical performance threshold and the ecological consistency requirement are defined as interference models and permanently removed from the integration pool to ensure that the final integrated sub-models meet the qualification standards in both prediction accuracy and ecological realism. Furthermore, step 4 also includes: calculating the cross-fold standard deviation of the root mean square error of each sub-model in K-fold cross-validation, using the numerical value of this standard deviation to measure the model's predictive sensitivity to different data subsets, identifying unstable algorithms with abnormally high error in specific spatial partitions or environmental gradient intervals, effectively eliminating unreliable models with drastic fluctuations in predictive performance, conducting ecological rationality assessment based on the morphological consistency of the biased response curve under multiple spatial resolutions, excluding sub-models whose response curves show signs reversal, non-monotonic drastic oscillations, or ecological paradoxes under different resolutions, ensuring that the marginal effect output by the selected model conforms to known prior knowledge of krill ecology, ensuring that the environmental response relationship output by the model has real ecological meaning, establishing a quantitative admission threshold where the mean root mean square error does not exceed the median of the entire model set and the cross-fold standard deviation is lower than the set average, forming a double filtering barrier combined with the ecological smoothness of the response curve, ensuring that the sub-models finally included in the integration framework simultaneously meet the qualification standards in both statistical prediction accuracy and ecological response authenticity, thus providing double assurance that the integrated model is both accurate and conforms to ecological laws; It should be noted that in the K-fold cross-validation process, the cross-fold standard deviation of the root mean square error (RMSE) for each sub-model is calculated to quantitatively measure the model's predictive sensitivity to different data subsets. Specifically, the RMSE values ​​on each fold test set are recorded, forming an error sequence of length K. The standard deviation of this sequence is then calculated as the cross-fold standard deviation. A larger value indicates more drastic fluctuations in the sub-model's predictive performance across different data partitions, suggesting a sudden increase in error within a specific spatial partition or environmental gradient interval. This is achieved by calculating the cross-fold standard deviation for each of the six heterogeneous sub-models and combining the results of each sub-model... The root mean square error (RMSE) is used to construct a statistical performance evaluation matrix. The RMSE reflects the model's average prediction accuracy, while the cross-fold standard deviation reflects the model's spatial prediction stability. Both jointly characterize the reliability of the sub-model in practical application scenarios. Based on this matrix, a quantitative admission threshold is set where the RMSE does not exceed the median of the entire model set and the cross-fold standard deviation is lower than the set mean. This ensures that sub-models entering the subsequent integration process meet the qualification standards in both accuracy and stability statistical dimensions. For candidate sub-models, an ecological rationality assessment based on the partial dependency response curve is further performed. The specific method is as follows: [The text abruptly ends here, likely due to an incomplete sentence or a missing section.] The partial dependence relationships between key environmental factors and krill density were obtained for each sub-model at different spatial resolutions (5 km, 10 km, 15 km, 20 km). Partial dependence response curves were plotted, and the evolution of the curve shape with resolution changes was observed. Ecologically reasonable sub-models should ensure that the response curves maintain sign consistency with resolution changes; that is, the positive or negative regulatory relationship between the same environmental factor and krill density should not reverse with changes in spatial scale. Simultaneously, the curves should exhibit a smooth transition or monotonic trend, avoiding violent oscillations without physical meaning or non-monotonic patterns with alternating extreme points. Sub-models whose response curves at different resolutions show signs reversal, non-monotonic oscillations, or violate prior knowledge of krill ecology are excluded. This assessment does not rely on specific numerical cases but uses the geometric characteristics of the curve shape and ecological consistency for qualitative judgment to ensure that the marginal effects output by the selected models have ecological authenticity. The statistical performance assessment and the ecological rationality assessment are organically combined to form a double filtering barrier. In terms of statistical performance, the root mean square error does not exceed the median of the entire model set and the cross-fold standard deviation is lower than the set mean as the quantitative entry threshold to eliminate sub-models with low prediction accuracy or poor spatial stability.In terms of ecological rationality, the consistency of the morphology of the biased response curve under multiple spatial resolutions is used as a qualitative criterion to eliminate sub-models whose response behavior lacks ecological interpretability. Only sub-models that pass the evaluation of the above two dimensions can be included in the final integration framework. The core advantage of this dual filtering mechanism is that the statistical threshold ensures that the model has reliable predictive ability, and the ecological test ensures that the model's response behavior conforms to the prior knowledge of the domain. Both are indispensable. The sub-models selected by this mechanism not only have a low error level and stable cross-regional generalization ability in numerical prediction, but their output environment-response relationship also has a clear ecological meaning, avoiding the false association or pseudo-correlation that may be generated by purely data-driven black box models. Step 5 specifically includes: Based on the root mean square error of each available sub-model in cross-validation, an error reciprocal weighting strategy is adopted to ensure that the sub-model with the smaller prediction error receives a higher contribution ratio in the integration, while the model with a larger error is automatically suppressed, ensuring that the high-precision model dominates the prediction results and reducing the overall prediction bias. Based on the determination coefficient of each available sub-model, an explanatory power normalization weighting method is adopted to assign higher integration weights to sub-models that characterize the complex relationship between krill density and environmental variables, thereby strengthening the contribution of the ecological response real model and improving the explanatory credibility. The RMSE weight and R² weight are adaptively harmonic normalized to enable the sub-model with both high precision and strong explanatory power to play a leading role in the integration, forming a comprehensive weight allocation mechanism that takes into account both statistical error and ecological response realism, achieving a balance between accuracy and ecological realism, and avoiding distortion caused by single-index optimization. It should be noted that the root mean square error (RMSE) values ​​calculated for each sub-model in the 10-fold cross-validation are extracted, and their reciprocals are used to characterize the positive contribution of prediction accuracy to the weights. That is, the smaller the RMSE of a sub-model, the larger its reciprocal, and the higher its contribution ratio in the ensemble. Conversely, models with larger RMSEs have smaller reciprocals and are automatically suppressed in weight allocation. Mathematically, this gives high-precision models a dominant position while retaining limited participation of low-precision models, avoiding the complete elimination of weak models that might have advantages in certain local gradients. To further stabilize the weight distribution, the calculated RMSE reciprocal sequence is normalized to ensure that the predicted accuracy contributes positively to the weights. The sum of the weights of all available sub-models is equal to one, ensuring that the integrated predictions have a unified dimensional benchmark. A second set of weight vectors is calculated using an explanatory power normalization weighting method. The coefficient of determination reflects the share of each sub-model in explaining the spatial variation variance of krill density; the closer its value is to one, the more fully the model can characterize the complex response relationship between environmental variables and krill density. In practice, the coefficient of determination values ​​obtained from cross-validation of each sub-model are directly extracted, preserving the explanatory power differences inherent in their original values ​​to avoid introducing additional transformations that could distort information. Subsequently, a normalization operation is performed on the coefficient of determination sequence to normalize the sum of the explanatory power weights of each sub-model to one. This approach allows sub-models that can more fully capture the nonlinear interactions of environmental factors and more accurately fit the peak heavy-tailed distribution characteristics of krill density to receive higher fusion weights. This strengthens the contribution ratio of ecological response realism within the ensemble framework, complementing the accuracy weights based on root mean square error. The accuracy weights based on root mean square error and the explanatory power weights based on the coefficient of determination are adaptively harmonic and normalized to form a comprehensive weight allocation mechanism that balances statistical error and ecological response realism. In practice, for each usable sub-model, its accuracy weight and explanatory power weight are added to obtain the unnormalized comprehensive score of that model, without introducing additional hyperparameters, thus ensuring fairness. The summation method reflects the equal importance of the two indicators in the integrated decision-making. Then, the unnormalized comprehensive scores of all sub-models are summed, and normalization is completed by dividing the scores of each model by the sum to obtain the final comprehensive weight vector. This harmonization strategy allows sub-models with both low prediction error and high explanatory share to play a leading role in the integration, while the weights of models that perform well only in a single dimension are appropriately adjusted. Through the above mechanism, the integration framework establishes an intrinsic balance between statistical accuracy and ecological authenticity, avoiding the risk of ecological distortion of the response curve due to one-sided optimization of the root mean square error, while preventing the sacrifice of the prediction robustness of extreme values ​​in the pursuit of the coefficient of determination. Furthermore, step 5 also includes: introducing a nonlinear weight smoothing factor in the comprehensive weight calculation process to adaptively compress and suppress the original weights of low-performance sub-models, significantly weakening the interference contribution of inferior models in the integration process, enhancing the robustness of the integration framework against unstable models, significantly improving the integration framework's ability to resist interference from inferior models, using a weighted summation strategy under the dual constraints of accuracy and interpretation to fuse the prediction outputs of each sub-model, so that the integrated prediction value achieves optimal fusion based on the dynamic adjustment of the contribution of each sub-model, avoiding weight bias oriented by a single evaluation index, achieving an intrinsic balance between statistical accuracy and ecological authenticity, and independently optimizing the weight combination parameters for different spatial resolution scenarios, so that the integration model adaptively adjusts the fusion ratio of each sub-model according to the resolution change, effectively eliminating the resolution-dependent cumulative error caused by the fixed weight strategy, and eliminating the cumulative effect of prediction bias caused by resolution changes; Weights are calculated based on RMSE. The smaller the RMSE, the higher the model's prediction accuracy, and the higher the weight should be assigned. ; In the formula, Representation Model RMSE, This represents the set of models used. For the model The root mean square error (RMSE) value; The weights are calculated based on R². The larger R² is, the stronger the model's interpretability, and the higher the weights should be assigned. ; In the formula, Representation Model R², For the model The R² value; Overall weight calculation: ; In the formula, Representation Model Based on RMSE weights, Representation Model Weights based on R² Representation Model Based on RMSE weights, Representation Model Weights based on R²; The final prediction of the ensemble model is a weighted sum of the predictions from each sub-model: ; In the formula, For the model The overall weight, For the model The predicted value; It should be noted that, based on the calculated comprehensive weight vector of each sub-model, a nonlinear mapping function is set. This function applies a strong compression effect when the weight value is below a preset threshold, and maintains an approximately linear response when the weight value is above the threshold, thus significantly weakening the interference contribution of inferior models. The strength parameter of the smoothing factor is adaptively determined based on the dispersion of model performance in cross-validation; the more dispersed the performance distribution, the greater the compression strength. Through this mechanism, the effective weights of sub-models with persistently low prediction accuracy or severely distorted ecological response curves in the integration process are compressed to a negligible level, while the weights of high-performing models remain basically unchanged. This enhances the robustness of the integration framework against unstable models, ensuring that the final prediction results are dominated by high-quality sub-models and reducing the risk of abnormal models contaminating the spatial distribution layer. The calculated comprehensive weight vector is used as the fusion coefficient of each sub-model, and the krill density prediction values ​​output by multiple sub-models on the same spatial grid cell are weighted linearly combined. The accuracy constraint is reflected in the high sensitivity of the weights to the inverse of the root mean square error, allowing models with high prediction accuracy to account for a larger proportion of the contribution. The interpretation constraint is reflected in the weights' relationship with the coefficient of determination. The direct dependence on the original values ​​prioritizes models that can reasonably characterize the ecological response relationship between environmental factors and krill density. The combined effect of the dual constraints enables the integrated predictions to achieve optimal fusion based on the dynamic adjustment of the contributions of each sub-model. This avoids ecological distortion or extreme value prediction instability caused by the one-sided weight allocation under the guidance of a single evaluation index, and improves the generalization reliability of the integrated model under different marine environmental gradients. For the modeling datasets at four resolutions of 5 km, 10 km, 15 km and 20 km, the complete process of steps 1 to 5 is executed respectively, and the comprehensive weight vector of each available sub-model in each resolution scenario is calculated independently. Since there are systematic differences in the prediction performance of each algorithm at different spatial scales, such as some algorithms overfitting severely at fine resolutions but improving performance at coarse resolutions, the independent optimization strategy allows the integrated weights to be adaptively adjusted with the resolution. This allows sub-models that perform well at a specific scale to obtain higher fusion weights, effectively eliminating the cumulative effect of prediction bias caused by resolution changes when using a fixed weight strategy, and ensuring that the integrated model always maintains better prediction performance and ecological consistency in multi-scale application scenarios. Step 6 specifically includes: using a permutation importance assessment method based on root mean square error, calculating the performance decay of the ensemble model after randomly shuffling each environmental variable, outputting the normalized environmental variable importance ranking results, clearly identifying the key environmental driving factors that dominate krill distribution, generating partial dependence response curves between each key ecological driving factor and krill resource density, revealing the nonlinear response law and threshold effect of krill density to the dominant environmental factors in a smooth and interpretable visualization method, intuitively revealing the nonlinear response law of krill density to environmental factors, discretizing the study area into a multi-resolution regular grid system, extracting the combination of environmental variables from each grid unit and inputting it into the ensemble model, generating a raster layer of krill resource density spatial distribution under different spatial resolutions and different survey time phases, and realizing the visualization output of spatial pattern in an ecological color scale manner, clearly showing the multi-scale spatiotemporal distribution and dynamic changes of krill resources; It should be noted that after the ensemble model was built, a permutation importance assessment method based on root mean square error was used to quantify and rank the contributions of each environmental variable. Specifically, keeping the response variable constant, the observation sequence of a certain environmental variable in the modeling dataset was randomly shuffled to disrupt its true correlation with krill density. The shuffled dataset was then input into the trained ensemble model to calculate the root mean square error. The difference between the root mean square error in the original dataset and the root mean square error after shuffling is the permutation importance measure for that variable. This process was repeated ten times independently for each environmental variable to eliminate sampling fluctuations caused by random shuffling. The average of the ten differences was taken as the final importance score. The importance scores of all variables were min-max normalized to compress them into the [0, 1] interval, resulting in a normalized importance ranking that allows direct comparison across variables. This ranking quantitatively reveals the dominance of each environmental driving factor in the prediction of krill resource distribution. To reveal the marginal response relationship between key environmental factors and krill resource density, partial dependence response curves were generated for the top three environmental variables in the normalized importance ranking. The calculation method for the partial dependence plot was as follows: keeping other environmental variables constant, the target variable was divided into fifty grid points at equal intervals within its observed range. For each grid point, all sample values ​​of that variable in the dataset were replaced with the value of that point, while other variables retained their original observed values. The input is used to calculate the predicted value of krill density in the integrated model. The average of all sample predicted values ​​is taken as the partial dependence response value corresponding to that grid point. Finally, the expected change trend of the predicted value of krill density from the minimum to the maximum value of the target variable is displayed in the form of a smooth line graph. This intuitively presents the nonlinear response law of krill density to the dominant environmental factors, including the monotonicity direction of the response curve, the existence of a threshold effect, and key ecological characteristics such as the response saturation range. The study area is discretized into a regular grid system. According to the spatial resolution set during modeling, prediction grid layers of four scales (5 km, 10 km, 15 km, and 20 km) are generated respectively. For each grid cell, the spatial data of the preprocessed environmental variables are used to calculate the predicted value. Eleven environmental variable values ​​were extracted from the data layer. After undergoing the same logarithmic transformation and standardization as the modeling data, a complete feature vector was input into the integrated model. The logarithmic scale krill density prediction value of the unit was calculated, and then restored to the original density dimension through exponential inverse transformation. The above prediction process was executed for different survey phases to generate multi-temporal and multi-resolution raster layers of krill resource density spatial distribution. When outputting, an ecological color gradient scheme was used for visualization rendering. The gradient from red to yellow represents high-density clusters, and the gradient from blue to green represents low-density background areas. The spatial heterogeneity of the color gradient intuitively shows the distribution pattern of krill resources, the positional shift of high-density areas, and the dynamic changes between different years.

[0023] Example 3, as Figures 1 to 16As shown, based on Examples 1 and 2, this invention provides a prediction of krill resource distribution around the South Shetland Islands: 1. Krill density data are based on four acoustic surveys conducted by Chinese Antarctic krill fishing vessels in the waters surrounding the South Shetland Islands between 2013 and 2018, conducted in December 2013, March 2015, January 2016, and February 2018, respectively. Environmental data include seabed depth, slope, distance from shelf break, sea surface temperature, bottom temperature, sea surface salinity, sea surface height, mixed layer thickness, current velocity, distance from sea ice edge, and chlorophyll a concentration. Data processing involved converting all projections to the EPSG:6932 coordinate system and resampling them to four spatial resolutions of 5km, 10km, 15km, and 20km for comparative experiments.

[0024] 2. The Pearson correlation coefficient matrix of 11 environmental variables was calculated. The results showed that, under the four spatial resolutions, the correlation coefficients between sea surface height and seabed depth were between -0.81 and -0.82, the correlation coefficients between sea surface height and distance from the shelf break were between 0.79 and 0.82, and the correlation coefficient between seabed depth and distance from the shelf break was -0.93. According to the screening rules, sea surface height and seabed depth were removed, and the remaining 9 variables were retained.

[0025] 3. Select four algorithms—GAM, RF, ANN, and XGBoost—to construct sub-models: GAM uses the Tweedie error distribution; RF settings: ntree=1000, mtry=3; ANN is set to size=10, decay=0.01, and maxit=500; XGBoost settings: nrounds=500, eta=0.01, max_depth=5, objective="reg:tweedie".

[0026] 4. Evaluate the performance of each sub-model and select GAM, RF, and XGBoost models for ensemble model construction: At a resolution of 5km, the ensemble model prediction is 0.145×GAM+0.507×RF+0.348×XGBoost; At a resolution of 10km, the ensemble model prediction is 0.146×GAM+0.462×RF+0.392×XGBoost; At a resolution of 15km, the ensemble model prediction is 0.127×GAM+0.442×RF+0.431×XGBoost; At a resolution of 20km, the ensemble model prediction is 0.147×GAM+0.398×RF+0.455×XGBoost.

[0027] Under 10-fold cross-validation, GAM exhibits unique resolution response characteristics, with its error decreasing and interpretability increasing as spatial resolution coarsens. The extreme gradient boosting model performs second best at 5km, 10km, and 15km resolutions, but shows a significant performance decline at 20km resolution. ANN consistently performs the worst at all resolutions, with its predictive ability continuously decreasing as resolution coarsens, revealing the inherent limitations of this model in modeling small-sample ecological data. The ensemble model demonstrates competitive predictive performance at all spatial resolutions, with its accuracy consistently ranking between the best and second best single models. Compared to single models, the ensemble model has lower variance in its predictions, indicating stronger robustness and lower uncertainty.

[0028] 5. For example Figure 3 The ranking of variable importance shows that the relative importance derived by GAM varies with spatial resolution, while ANN exhibits instability in the relative importance of variables, and the algorithm remains relatively stable. RF identifies distance from sea ice edge, sea surface temperature, mixed layer depth, and seabed temperature as relatively important variables. XGBoost, on the other hand, highlights the importance of distance from sea ice edge, mixed layer depth, seabed temperature, and distance from shelf break. For the ensemble model, the variable importance reflects the combined results of each algorithm. Distance from sea ice edge is the most important and stable variable across all resolutions, followed by mixed layer depth and sea surface temperature; this pattern is highly consistent with the results of RF and XGBoost, further confirming the dominant role of these environmental factors in influencing krill resource distribution.

[0029] 6. For example Figure 4 , Figure 5 and Figure 6 The partial dependence plot shows that GAM generated the smoothest and most interpretable response curve, indicating that krill density is negatively correlated with sea surface temperature and positively correlated with distance from the sea ice edge. Figure 4 ); RF maintained a stable response pattern across different resolution ranges, but its predicted values ​​increased with increasing spatial resolution, and the algorithm's response curve exhibited a complex nonlinear pattern ( Figure 5 ANNs generate unstable and unpredictable biased patterns at different resolutions, with response curves varying drastically across different resolutions, frequent sign inversions and non-monotonic patterns, and a lack of ecological rationality. Figure 6 XGBoost generated the most stable and ecologically significant partial dependency curves across all resolutions; for example... Figure 7As shown, the response curve exhibits a smooth nonlinear pattern, and the curve shape and predicted values ​​remain consistent across different resolution ranges. Figure 7 The partial dependency curve generated by the ensemble model achieves a balanced trade-off between the smooth, interpretable patterns of the generalized additive model and the complex data-driven responses of random forests and extreme gradient boosting; compared to the single-tree model, this curve exhibits a smoother transition while capturing more nuanced response features than GAM, thus combining the statistical robustness of average ensemble with ecological realism. Figure 8 ).

[0030] 7. Based on the ensemble model, the distribution of krill resources around the South Shetland Islands at different spatial resolutions was predicted. The results are as follows: Figure 9-16 As shown, the spatial distribution of krill resources is visually displayed using color gradients (red represents high values, blue represents low values). The distribution of krill resources exhibits significant spatial heterogeneity, with high-density areas mainly concentrated in specific sea areas such as the northern side of the South Shetland Islands, the area around Elephant Island, and the Bransfield Channel, while low-density areas are widely distributed in other areas. Regarding the impact of spatial resolution, high-resolution models (e.g., 5km) can more finely depict the local details of krill distribution. High-density areas show continuous distribution characteristics, reflecting the aggregation of krill in local sea areas; while low-resolution models (e.g., 5km)... Due to data aggregation effects, the 20km model smooths out the differences in krill resource distribution, with high-density areas mainly appearing as independent point distributions, resulting in a simpler overall spatial pattern. Comparing the same resolution prediction maps from January 2016 and February 2018, there are significant changes in the spatial distribution pattern of krill resources. In February 2018, the distribution of krill north of 61°S decreased significantly, and the overall krill density in the study area also decreased. This dynamic change across years may reflect the impact of changes in marine environmental conditions on krill distribution, demonstrating the spatiotemporal dynamic characteristics of krill resource distribution.

[0031] The above are merely specific embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. The scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for predicting the distribution of Antarctic krill resources based on multi-algorithm ensemble, characterized in that, Includes the following steps: Step 1: Obtain krill acoustic survey density data and multi-source environmental variable data. Perform coordinate projection transformation, missing value processing and grid aggregation on the data to construct a modeling dataset and perform logarithmic transformation to mitigate the bias of zero-inflation features on model training. Step 2: Calculate the Pearson correlation coefficient and variance inflation factor among the environmental variables. Combined with the correlation ranking of krill density, construct a correlation-collinearity dual screening criterion to adaptively remove redundant variables and retain key ecological driving factors. That is, remove highly collinear variables and retain variables that are more strongly correlated with krill density. Step 3: Construct single sub-models for six heterogeneous algorithms, namely GAM, RF, ANN, XGBoost, MARS and SVM, respectively, to capture the multi-mode nonlinear relationship between krill density and marine environment, and suppress the prediction fluctuations of single algorithms in heterogeneous sea areas. Step 4: Use K-fold cross-validation to calculate the mean absolute error, root mean square error and coefficient of determination of each sub-model. Based on performance ranking, select usable sub-models and eliminate unstable sub-models that lack ecological rationality. Step 5: Using a dual weighting strategy based on RMSE and R², the combined weights of the available sub-models are calculated based on the cross-validation results, and a weight smoothing factor is introduced to suppress the interference of low-performance sub-models. The weighted fusion is then used to obtain the integrated prediction value. Step 6: Based on multi-algorithm integration and dynamic weighted fusion technology, output the model performance comparison results, environmental variable importance ranking, partial dependency response curve, and krill resource density spatial distribution map.

2. The method for predicting the distribution of Antarctic krill resources based on multi-algorithm integration as described in claim 1, characterized in that: Step 1 specifically includes: Acoustic data in three frequency bands (38, 70, and 120 kHz) were collected using fish finders on board Antarctic krill fishing vessels. Based on the acoustic survey and assessment method recommended by SC-CAMLR, krill resource density data were calculated and output with 1 nautical mile as the basic integral range unit. Simultaneously acquire eleven-dimensional multi-source environmental variable data, including seabed depth, slope, distance from shelf break, sea surface temperature, seabed temperature, sea surface salinity, sea surface height, mixed layer depth, current velocity, distance from sea ice edge, and chlorophyll a concentration, and establish a multimodal feature set across four categories of environmental factors: topography, physical oceanography, sea ice, and organisms. All data were uniformly projected to the Antarctic Equal Area Projected Coordinate System EPSG:6932, missing value imputation and grid aggregation were completed, and a logarithmic transformation with the natural constant e as the base was performed on the krill density to balance the influence of zero observations and non-zero observations in model training.

3. The method for predicting the distribution of Antarctic krill resources based on multi-algorithm integration according to claim 1, characterized in that: Step 2 specifically includes: Calculate the Pearson correlation coefficient between any two environmental variables. When the absolute value of the correlation coefficient is greater than 0.7, it is considered highly collinear. Calculate the correlation coefficient between the two highly collinear variables and the krill density after logarithmic transformation. Determine which variables to retain based on the strength of the association with the response variable. The variance inflation factor was calculated for the environmental variables retained after Pearson screening. A variance inflation factor of less than 10 was used as the threshold for the absence of significant collinearity, and redundant variables exceeding the threshold were removed. Based on the results of Pearson correlation ranking and variance inflation factor test, a dual screening criterion of correlation and collinearity is constructed. While retaining the variables most closely related to the ecological driving force of krill density, information redundancy caused by the inherent coupling relationship between environmental variables is adaptively eliminated.

4. The method for predicting the distribution of Antarctic krill resources based on multi-algorithm integration according to claim 3, characterized in that: Step 2 also includes: Calculate the Pearson correlation coefficient between each environmental variable and the krill density after logarithmic transformation. Construct a ranking table of the ecological association strength of candidate predictors based on the absolute value of the correlation coefficient, and prioritize environmental driving factors that have a statistically significant association with the distribution of krill resources. Construct a correlation coefficient matrix among environmental variables. For highly collinear variable pairs with an absolute correlation coefficient greater than 0.7, sort them according to the established ecological association strength, and remove the pair with a weaker correlation to krill density from each pair of highly collinear variables. The variance inflation factor is calculated iteratively for the remaining set of variables. In each iteration, the variable with the largest variance inflation factor is removed, and the calculation is repeated before entering the next iteration, until the variance inflation factor of all remaining variables is less than 10.

5. The method for predicting the distribution of Antarctic krill resources based on multi-algorithm integration according to claim 1, characterized in that: Step 3 specifically includes: We constructed single sub-models of six heterogeneous algorithms with different underlying mathematical principles: GAM, RF, ANN, XGBoost, MARS, and SVM. We utilized the structural dissimilarity between the algorithms to maximize the diverse response patterns between captured krill density and environmental factors. Each sub-model employs a differentiated parameter configuration optimized for zero-inflation continuous data. This includes GAM binding to the Tweedie error distribution to adapt to the peak-heavy-tailed distribution characteristics of krill density, RF using a self-governing aggregation mechanism to reduce the overfitting risk of a single decision tree, and ANN limiting the number of neurons in a single hidden layer to establish a balance between underfitting and overfitting. XGBoost employs a tree-by-tree iterative fitting strategy for residuals and binds them to the Tweedie objective function. MARS achieves piecewise linear fitting through automatic basis function selection and pruning mechanisms. SVM constructs a flat hyperplane regression function under the constraint of an insensitive loss function.

6. The method for predicting the distribution of Antarctic krill resources based on multi-algorithm integration according to claim 1, characterized in that: Step 4 specifically includes: We employ a K-fold cross-validation strategy, dividing the entire dataset into K subsets. Each time, we use K-1 subsets as the training set and the remaining subset as the test set, repeating this process K times to complete the full data round-robin evaluation. The mean absolute error, root mean square error, and coefficient of determination of each sub-model in cross-validation are calculated together. The root mean square error imposes a nonlinear penalty on high-bias predictions to highlight the risk of extreme errors, and the coefficient of determination is used to measure the share of the model in explaining the spatial variation of krill density. Based on the comprehensive ranking results of the three indicators, the sub-models that rank in the top three in terms of root mean square error and coefficient of determination and whose partial dependence curves maintain sign consistency when spatial resolution changes are prioritized for retention. The excluded algorithms are defined as interference models and removed from the ensemble pool.

7. The method for predicting the distribution of Antarctic krill resources based on multi-algorithm integration according to claim 6, characterized in that: Step 4 also includes: Calculate the cross-fold standard deviation of the root mean square error of each sub-model in K-fold cross-validation, and use the numerical value of this standard deviation to measure the model’s prediction sensitivity to different data subsets, and identify unstable algorithms with abnormally high error in specific spatial partitions or environmental gradient intervals. Ecological rationality assessment is conducted based on the morphological consistency of the partial dependence response curve under multiple spatial resolutions. Sub-models that exhibit positive and negative sign reversal, non-monotonic violent oscillations, or ecological paradox patterns in response curves at different resolutions are excluded, ensuring that the marginal effects output by the selected models conform to known prior knowledge of krill ecology. A quantitative admission threshold is established where the mean root mean square error does not exceed the median of the entire model set and the cross-fold standard deviation is lower than the set mean. This threshold is combined with the ecological smoothness of the response curve to form a dual filtering barrier.

8. The method for predicting the distribution of Antarctic krill resources based on multi-algorithm integration according to claim 1, characterized in that: Step 5 specifically includes: Based on the root mean square error of each available sub-model in cross-validation, an error inverse weighting strategy is adopted to ensure that the sub-model with the smaller prediction error receives a higher contribution ratio in the ensemble fusion, while the model with the larger error is automatically suppressed. Based on the determination coefficients of each available sub-model, the explanatory power normalization weighting method is used to assign fusion weights to the sub-models that characterize the complex relationship between krill density and environmental variables. The RMSE weights and R² weights are adaptively harmonicized and normalized, enabling the sub-models with both high accuracy and strong interpretability to play a leading role in the integration, thus forming a comprehensive weight allocation mechanism that takes into account both statistical error and the authenticity of ecological response.

9. The method for predicting the distribution of Antarctic krill resources based on multi-algorithm integration according to claim 8, characterized in that: Step 5 further includes: In the process of calculating the comprehensive weight, a nonlinear weight smoothing factor is introduced to adaptively compress and suppress the original weights of the low-performance sub-models, thereby reducing the interference contribution of inferior models in the integration process. A weighted summation strategy under the dual constraints of accuracy and interpretation is adopted to fuse the prediction outputs of each sub-model, so that the integrated prediction value achieves optimal fusion based on the dynamic adjustment of the contribution of each sub-model; The weight combination parameters are independently optimized for different spatial resolution scenarios, enabling the ensemble model to adaptively adjust the fusion ratio of each sub-model according to the resolution change.

10. The method for predicting the distribution of Antarctic krill resources based on multi-algorithm integration according to claim 1, characterized in that: Step 6 specifically includes: A permutation importance assessment method based on root mean square error is adopted. The performance degradation of the ensemble model is calculated by randomly shuffling each environmental variable, and the normalized ranking of environmental variable importance is output. We generated partial dependence response curves between key ecological driving factors and krill resource density, and revealed the nonlinear response law and threshold effect of krill density to dominant environmental factors in a smooth and interpretable visualization. The study area is discretized into a multi-resolution regular grid system. Environmental variables of each grid cell are extracted and combined into an integrated model to generate a raster layer of krill resource density spatial distribution under different spatial resolutions and different survey time phases. The spatial pattern is visualized using an ecological color scale.

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