Prediction and Analysis of Sturgeon Aquaculture Production in Guizhou Province Based on Grey System Model

Abstract

In this study, grey system theory is applied through the implementation of GM(1,1) modelling and Grey Relational Analysis (GRA) to forecast and evaluate sturgeon aquaculture production dynamics in Guizhou Province. The results demonstrate a marked temporal dependency in predictive efficacy, with GM(1,1) exhibiting a superior short-term forecasting performance that progressively diminishes with temporal extension. Utilizing 2018–2022 observational data, the GM(1,1) framework achieved Grade 2 precision (mean absolute percentage error, MAPE = 4.172%; 1% < $\overline{ ∆k}$ ≤ 5%), projecting sustained annual production growth. The decade-long forecast (2023–2032) yielded the following production estimates (×10³ tons): 32.3, 39.1, 47.3, 57.2, 69.2, 83.7, 101.2, 122.4, 148.1, and 179.2. GRA identified three principal determinants: the aquatic seed production value (X₉, r = 0.8336), freshwater fishery output (X₂, r = 0.8019), and per capita fisher income (X₅, r = 0.8003). Furthermore, technological promotion funding (X₆) and fishery workforce parameters (X₄), while demonstrating weaker correlations (r < 0.75), maintain critical roles in technological advancement and labour competency enhancement. This methodological framework provides empirical support for sustainable development strategies in Guizhou’s sturgeon aquaculture sector, emphasizing the necessity of temporal-scale considerations and multifactorial optimization in production management.

1. Introduction

Sturgeons, an ancient clade of sub-cold water benthic fishes [1,2], exhibit optimal growth in flowing aquatic environments characterized by elevated dissolved oxygen concentrations and low-temperature regimes (18–25 °C) [3,4]. Their carnivorous feeding behaviour demonstrates ontogenetic dietary shifts from benthic invertebrates in juvenile stages to piscivorous habits in mature individuals [5]. Commercial aquaculture practices for sturgeon have diversified significantly, with accelerated growth rates and delayed sexual maturation necessitating the artificial induction of gonadal development through environmental modulation and physiological interventions [6,7]. Flow-through systems and industrial-scale recirculating aquaculture systems (RAS) currently dominate production methodologies [8], offering advantages in production density, automation efficiency, and water resource optimization.

Guizhou Province, situated in China’s southwestern “Yunnan–Guizhou Plateau” subtropical zone, possesses exceptional hydrological resources supported by its humid monsoon climate [9,10], creating favourable conditions for intensive aquaculture operations, particularly sturgeon aquaculture. Guizhou’s sturgeon products (e.g., caviar, chilled fillets) currently supply domestic markets and export to Japan, Southeast Asia, and Europe, with 2023 exports totalling 4200 tons (13% of production); the regional sturgeon industry has experienced rapid expansion, establishing comprehensive production bases and integrated industrial networks [11]. Collaborative initiatives between research institutions and commercial enterprises have facilitated technological advancements in production efficiency and product quality control [12,13] while simultaneously advancing brand development initiatives to strengthen market penetration. Nevertheless, persistent challenges constrain industrial development, including the limited production of premium-grade sturgeon products, truncated value chains, insufficient product differentiation, and underdeveloped brand recognition systems [14,15]. These factors collectively indicate the substantial potential for value chain optimization and market positioning improvements.

The Grey System Model, particularly the GM(1,1) variant, has gained prominence in dynamic forecasting applications across disciplines with data scarcity constraints, including economic analysis [16], financial modelling [17], resource management [18], and environmental studies [19]. The GM(1,1) methodology employs first-order differential equations through the sequential analytical phases: data generation, feasibility assessment, cumulative processing, differential equation formulation, parameter estimation, equation resolution, predictive modelling, and validation procedures [20]. Grey Relational Analysis (GRA), a multi-factor analytical framework derived from grey system theory, quantifies inter-factor correlations under conditions of informational uncertainty [21]. This technique evaluates sequence similarity through three principal metrics, including absolute relational degree, relative relational degree, and comprehensive relational degree [22], finding application across the agricultural [23], industrial [24], and fisheries [25] sectors. Standard analytical protocols encompass reference sequence identification, data normalization, relational coefficient computation, relational degree quantification, and hierarchical ranking [26].

While numerous studies have investigated sturgeon biology and aquaculture practices, the application of grey system modelling remains notably absent in production forecasting for ecologically sensitive regions like Guizhou. This study, therefore, pioneers the integration of GM(1,1) and GRA in plateau aquaculture, addressing data scarcity challenges through adaptive parameter estimation and multi-temporal validation. Unlike prior applications focused on single-factor analysis, our framework incorporates dynamic environmental and economic variables, with the dual objectives of establishing a scientific foundation for comprehensive industry analysis and evaluating potential economic impacts on regional development, offering a holistic tool for ecologically sensitive regions.

2. Study Area

It can be seen from Figure 1 that Guizhou Province occupies the eastern “Yunnan–Guizhou Plateau” (103°36′–109°35′ E, 24°37′–29°13′ N) in southwestern China’s continental interior, exhibiting characteristic subtropical humid monsoon climate patterns [27]. Historical climatological records indicate an annual temperature range of 15.23–16.57 °C, with a multi-year mean of 15.99 °C [28]. Thermal extremes demonstrate monthly averages of 3–6 °C in January (coldest month) and 22–25 °C in July (warmest month), establishing a favourable thermal baseline for aquatic ecosystems [29]. The province’s hydrological network comprises eight principal river systems, supported by an annual precipitation regime averaging 1100–1400 mm with pronounced seasonal distribution, 47% of which occurs during the summer months [30].

Figure 1. Geomorphology of Guizhou Province. Map was created with QGIS version 3.34 (www.qgis.org, accessed on the 18 February 2025).

Geologically, the region is predominantly composed of marine carbonate strata exhibiting tripartite lithological classifications: dolomitic strata of restricted platform facies, calcitic formations in open-platform environments, and reef-associated limestone deposits [31]. Of particular hydrological significance, the dolomite sequences display extensive secondary porosity features (dissolution pores and structural fissures), constituting primary targets for karst aquifer exploitation. Hydrochemical analyses confirm that 82.6% of these groundwater resources meet the WHO standards for potable water quality [31], providing critical hydrological support for intensive aquaculture operations. Guizhou’s sturgeon aquaculture primarily utilizes flow-through systems. These systems leverage natural hydrological gradients and karst spring outflows, with production infrastructure comprising raceways and channels integrated into riverine or spring-fed environments. The geomorphological and hydrogeological characteristics described herein directly enable this low-energy, high-yield farming modality.

3. Grey System Theory Method

3.1. The Method of Grey Prediction Analysis

The specific steps of establishing the GM(1,1) model are as follows:

Step 1: Data initialization

Establish a non-negative original data sequence:

$$X_0=\left\{X_0\right(k\left)\right\}, k=1,2,\dots ,n$$

(1)

Step 2: Data suitability assessment

Perform a ratio validation test on $X_0=\left\{X_0\right(k\left)\right\},k=1,2,\dots ,\mathrm{n}$:

$$\lambda (k)={\displaystyle \frac{X_0(k-1)}{X_0(k)}},k=2,3,\dots ,n$$

(2)

For valid modelling, calculate the following:

$$\lambda (k)\in (e^{{\displaystyle \frac{-2}{n+1}}},e^{{\displaystyle \frac{2}{n+1}}})$$

(3)

Non-conforming sequences require translation transformation as follows:

$$Y_0\left(k\right)=X_0\left(k\right)+C, k=1,2,\dots ,n$$

(4)

Step 3: Data preprocessing

Generate a first-order accumulated sequence (1-AGO), X₁, and construct a background value sequence via the adjacent mean, Z₁:

$$X_1=\left\{X_1\right(k\left)\right\}, k=1,2,\dots ,n$$

(5)

where $X_1(k)={\displaystyle \sum _{i=1}^k{X}_0(i)}, k=1,2,\dots ,n$

$$Z_1=\left\{Z_1\right(k\left)\right\}, k=2,3,\dots n$$

(6)

where $Z_1(k)={\displaystyle \frac{1}{2}}[X_1(k)+X_1(k+1)], k=2,3,\dots ,n$ 1-AGO reduces data randomness, transforming irregular sequences into monotonic trends for stable differential equation fitting.

Step 4: Model formulation

The grey differential equation is established as follows:

$$X_0\left(k\right)+a{Z}_1\left(k\right)=u$$

(7)

The whitening equation derivation is as follows:

$${\displaystyle \frac{\mathrm{d}{X}_1(t)}{dt}}+a{X}_1(t)=u$$

(8)

Parameter a (development coefficient) governs the growth rate, while u (grey input) adjusts baseline trends.

Step 5: Parameter estimation

Calculate development coefficient a and grey input u via least squares:

$$\stackrel{\wedge }{\mathrm{a}}={[a,u]}^T={(B^{T}B)}^{-1}{B}^{T}Y$$

(9)

$$\mathrm{where} B=\left[\begin{array}{c}-Z_1(2) 1\\ -Z_1(3) 1\\ \hspace{0.25em}\hspace{0.25em}\hspace{0.25em}⋮\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}⋮ \\ -Z_1(n) 1\end{array}\right],Y=\left[\begin{array}{c}{X}_0(2)\\ X_0(3)\\ ⋮\\ X_0(n)\end{array}\right]$$

(10)

Step 6: Temporal solution

Solve the following whitening equation:

$${\stackrel{\wedge }{X}}_1(k+1)=(X_0(1)-{\displaystyle \frac{u}{a}})e^{-ak}+{\displaystyle \frac{u}{a}},k=1,2,\dots ,n-1$$

(11)

This is valid for ∣a∣ < 0.3, indicating stable medium–long-term forecasting capacity.

Step 7: Inverse transformation

Recover the predicted values via IAGO:

$${\stackrel{\wedge }{X}}_0(k+1)={\stackrel{\wedge }{X}}_1(k+1)-{\stackrel{\wedge }{X}}_1(k),k=1,2,\dots ,n-1$$

(12)

IAGO recovers the predicted values from accumulated sequences, while the whitening equation provides continuous-time solutions for discrete data.

Step 8: Precision validation

Calculate the composite error metrics as follows:

$$\mathrm{MAPE}: \overline{\Delta k}={\displaystyle \frac{1}{n-1}}{\displaystyle \sum _{k=2}^n\left|\frac{X_0(k)-{\stackrel{\wedge }{X}}_0(k)}{X_0(k)}\right|}$$

(13)

$$\mathrm{Precision}: {\rm P}=(1-\overline{\Delta k})\times 100\%$$

(14)

Model classification is conducted as follows:

Grade 1: MAPE ≤ 1% or P ≥ 99% (optimal);

Above Grade 4: MAPE > 20% or P < 80% (invalid).

Detailed classification criteria are provided in Table 1.

Table 1. Reference for GM(1,1) model precision levels.

	MAPE/%	Precision/%	Model Prediction Effect
Grade 1	$\overline{∆k}\le 1$	99	Optimal
Grade 2	$1<\overline{∆k}\le 5$	95	Good
Grade 3	$5<\overline{∆k}\le 10$	90	Qualified
Grade 4	$10<\overline{∆k}\le 20$	80	Barely qualified
Above Grade 4	$\overline{∆k}>20$	$P<80$	Invalid

3.2. The Method of Grey Correlation Analysis

The correlation degree of various factors is calculated according to the following steps:

Step 1: System characterization

Define the following:

$$\mathrm{Reference} \mathrm{sequence}: X_0=X_0(k), k=V_2$$

(15)

$$\mathrm{Comparative} \mathrm{sequences}: X_i=X_i(k), i=V_1, k=V_2$$

(16)

Step 2: Data normalization

Implement dimensionless processing through the following equations:

$$\mathrm{Initial} \mathrm{value} \mathrm{transformation}: X_{\mathrm{i}}^{’}(k)={\displaystyle \frac{X_i(k)}{\frac{1}{n}{\displaystyle \sum _{k=1}^n{X}_i(k)}}}, i=V_1, k=V_2$$

(17)

$$\mathrm{Mean} \mathrm{value} \mathrm{transformation}: X_i^{’}(k)={\displaystyle \frac{X_i(k)}{X_i(1)}}, i=V_1, k=V_2$$

(18)

Step 3: Relational coefficient calculation

Compute pairwise similarity metrics as follows:

$${\mathrm{r}}_{0i}(k)={\displaystyle \frac{{\Delta }_{\min }+\rho \cdot {\Delta }_{\max }}{{\Delta }_{0i}(k)+\rho \cdot {\Delta }_{\max }}}, i=V_1, k=V_2$$

(19)

where

$$\begin{gathered} {∆}_{0i}\left(k\right)=x_0\left(k\right)-x_i\left(k\right) \\ {∆}_{min}=\underset{\forall i}{\min }\underset{\forall k}{\min }{∆}_{0i}\left(k\right) \\ {∆}_{max}=\underset{\forall i}{\max }\underset{\forall k}{\max }{∆}_{0i}\left(k\right) \\ \rho \in \left(0,1\right) (discrimination coefficient, default \rho =0.5) \end{gathered}$$

Step 4: Comprehensive relational degree

Derive integrated correlation indices as follows:

$$R_{0\mathrm{i}}={\displaystyle \frac{1}{n}}{\displaystyle {\sum }_{k=1}^n{r}_{0i}(k)}, i=V_1, k=V_2$$

(20)

Step 5: Factor prioritization

Rank R_0i values in descending order, where higher values indicate stronger system influence.

4. Results

4.1. The Results of Grey Prediction Analysis

Figure 2 presents the temporal distribution of annual sturgeon aquaculture production in Guizhou Province from 2008 to 2022. Three distinct temporal intervals (2018–2022, 2013–2022, and 2008–2022) were selected to construct GM(1,1) forecasting models I, II, and III, respectively. Model precision was evaluated through comparative analysis of the mean absolute percentage error (MAPE) between observed and predicted values [32,33], enabling the identification of the optimal predictive framework and subsequent projection of provincial production trends.

Figure 2. Total production of sturgeon aquaculture in Guizhou Province from 2008 to 2022.

4.1.1. Modelling with Original Data from 2018 to 2022

The annual sturgeon production dataset for Guizhou Province (2018–2022) was selected as the reference sequence X₀ to construct a mean-form GM(1,1) model. The computational workflow and validation metrics are detailed below:

(1)

Model Initialization

The original sequence is the following:

$$X_0=(\mathrm{10,512};\mathrm{14,101};\mathrm{19,096};\mathrm{22,848};\mathrm{26,207})$$

(21)

Ratio validation, ${e }^{{\displaystyle \frac{-2}{n+1}}}<\lambda (k)<{e }^{{\displaystyle \frac{2}{n+1}}}$, confirmed satisfactory grey modelling prerequisites.

(2)

Accumulated Sequence Generation

The first-order accumulated generating operation (1-AGO) is as follows:

$$X_1=(10512.0000,24613.0000,43709.0000,66557.0000,92764.0000)$$

(22)

(3)

Background Value Construction

The adjacent mean sequence is as follows:

$$Z_1=(17562.5000,34161.0000,55133.0000,79660.5000)$$

(23)

(4)

Parameter Estimation

The least squares determination is as follows:

$$a=-0.190 \left(\right|a|<0.3)$$

(24)

$$u=11684.592$$

(25)

(5)

Temporal Response Formulation

The whitening equation is as follows:

$${\widehat{X}}_1\left(k+1\right)=72009.853e^{0.190k}-61497.853,k=1,2,\dots ,n-1$$

(26)

Inverse accumulated generating operation (IAGO) is as follows:

$${\widehat{X}}_0\left(k+1\right)=72009.853e^{0.190k}-61497.853-{\widehat{X}}_1\left(k\right),k=1,2,\dots ,n-1$$

(27)

(6)

Model Validation and Predictive Application

The fitted values, residual errors, and prediction accuracy metrics were derived through the iterative application of Equations (26) and (27) with comprehensive validation results visualized in Figure 3.

Figure 3. Residual analysis of Model I (2018–2022).

The quantitative error assessment revealed interannual prediction deviations as follows: the relative errors for 2018–2022 are 6.913%, 4.494%, 3.436%, and 1.845%, respectively. The mean absolute percentage error (MAPE) is as follows: $\overline{∆k}$ = 4.172% ($1\%\le \overline{∆k}\le 5\%$). This error profile corresponds to Grade 2 precision according to grey system classification criteria, confirming the model’s reliability for operational forecasting.

Furthermore, based on the time-response equation of GM(1,1) Model I, ${\widehat{X}}_1(k+1)=72009.853e^{0.190k}-61497.853$, the development coefficient a was calculated to be a = −0.190 (|a| < 0.3). This indicates that the GM(1,1) Model I is suitable for both short-term and medium–long-term forecasts. Consequently, this model can be utilized to predict the total sturgeon aquaculture production in Guizhou Province over the next 10 years (2023–2032), with the forecast results presented in Table 2. The projected sturgeon aquaculture production in Guizhou Province for the next decade is as follows: 32.3 k tons, 39.1 k tons, 47.3 k tons, 57.2 k tons, 69.2 k tons, 83.7 k tons, 101.2 k tons, 122.4 k tons, 148.1 k tons, and 179.2 k tons.

Table 2. Forecasted values of total sturgeon production in Guizhou Province from 2023 to 2032 using Model I.

Year	Predicted Value/t
2023	32,288.516
2024	39,060.662
2025	47,253.189
2026	57,164.005
2027	69,153.501
2028	83,657.656
2029	101,203.892
2030	122,430.251
2031	148,108.595
2032	179,172.678

4.1.2. Modelling with Original Data from 2013 to 2022

The annual sturgeon production dataset for Guizhou Province (2013–2022) was selected as the reference sequence X₀ to construct a mean-form GM(1,1) model. The computational workflow and validation metrics are detailed below:

(1)

Model Initialization

The original sequence is as follows:

$$X_0=(3049;3869;5399;6823;7857;\mathrm{10,512};\mathrm{14,101};\mathrm{19,096};\mathrm{22,848};\mathrm{26,207})$$

(28)

Ratio validation, ${e }^{{\displaystyle \frac{-2}{n+1}}}<\lambda (k)<{e }^{{\displaystyle \frac{2}{n+1}}}$, confirmed satisfactory grey modelling prerequisites.

(2)

Accumulated Sequence Generation

The first-order accumulated generating operation (1-AGO) is as follows:

$$\begin{gathered} X_1=(3049.0000,6918.0000,12317.0000,19140.0000,26997.0000,37509.0000, \\ 51610.0000,70706.0000,93554.0000,119761.0000) \end{gathered}$$

(29)

(3)

Background Value Construction

The adjacent mean sequence is the following:

$$\begin{gathered} Z_1=(4983.5000,9617.5000,15728.5000,23068.5000,32253.0000,44559.5000, \\ 61158.0000,82130.0000,106657.5000) \end{gathered}$$

(30)

(4)

Parameter Estimation

The least squares determination is as follows:

$$a=-0.230 \left(\right|a|<0.3)$$

(31)

$$u=3254.039$$

(32)

(5)

Temporal Response Formulation

The whitening equation is as follows:

$${\widehat{X}}_1(k+1)=17196.996e^{0.230k}-14147.996,k=1,2,\dots ,n-1$$

(33)

Inverse accumulated generating operation (IAGO) is as follows:

$${\widehat{X}}_0(k+1)=17196.996e^{0.230k}-14147.996-{\widehat{X}}_1\left(k\right),k=1,2,\dots ,n-1$$

(34)

(6)

Model Validation and Predictive Application

The fitted values, residual errors, and prediction accuracy metrics were derived through the iterative application of Equations (33) and (34), with comprehensive validation results visualized in Figure 4.

Figure 4. Residual analysis of Model II (2013–2022).

The quantitative error assessment revealed the following interannual prediction deviations: the relative errors for 2013–2022 are 14.939%, 3.664%, 3.239%, 12.833%, 6.141%, 0.414%, 7.449%, 2.647%, and 6.821%, respectively. The mean absolute percentage error (MAPE) is as follows: $\overline{∆k}$ = 6.461% (5% ≤ $\overline{∆k}$ ≤ 10%). This error profile corresponds to Grade 3 precision according to grey system classification criteria, indicating that the model’s prediction effect is qualified.

Furthermore, based on the time-response equation of GM(1,1) Model II, ${\widehat{X}}_1(k+1)=17196.996e^{0.230k}-14147.996$, the development coefficient a was calculated to be a = −0.230 (|a| < 0.3). This indicates that the GM(1,1) Model II is suitable for both short-term and medium–long-term forecasts. Consequently, this model can be utilized to predict total sturgeon production in Guizhou Province over the next 10 years (2023–2032), with the forecast results presented in Table 3. The projected sturgeon aquaculture production in Guizhou Province for the next decade is as follows: 35.2 k tons, 44.3 k tons, 55.8 k tons, 70.2 k tons, 88.4 k tons, 111.3 k tons, 140.0 k tons, 176.2 k tons, 221.8 k tons, and 279.1 k tons.

Table 3. Forecasted values of total sturgeon aquaculture production in Guizhou Province from 2023 to 2032 using Model II.

Year	Predicted Value/t
2023	35,233.065
2024	44,343.143
2025	55,808.778
2026	70,239.039
2027	88,400.476
2028	111,257.846
2029	140,025.359
2030	176,231.176
2031	221,798.591
2032	279,148.198

4.1.3. Modelling with Original Data from 2008 to 2022

The annual sturgeon production dataset for Guizhou Province (2008–2022) was selected as the reference sequence X₀ to construct a mean-form GM(1,1) model. The computational workflow and validation metrics are detailed below:

(1)

Model Initialization

The original sequence is the following:

$$\begin{gathered} X_0=(391;368;467;955;1182;3049;3869;5399;6823; \\ 7857;\mathrm{10,512};\mathrm{14,101};\mathrm{19,096};\mathrm{22,848};\mathrm{26,207}) \end{gathered}$$

(35)

Ratio validation, ${e }^{{\displaystyle \frac{-2}{n+1}}}<\lambda (k)<{e }^{{\displaystyle \frac{2}{n+1}}}$, confirmed satisfactory grey modelling prerequisites.

(2)

Accumulated Sequence Generation

The first-order accumulated generating operation (1-AGO) is as follows:

$$\begin{gathered} X_1=(391.0000,759.0000,1226.0000,2181.0000,3363.0000,6412.0000, \\ 10281.0000,15680.0000,22503.0000,30360.0000,40872.0000,54973.0000, \\ 74069.0000,96917.0000,123124.0000) \end{gathered}$$

(36)

(3)

Background Value Construction

The adjacent mean sequence is as follows:

$$\begin{gathered} Z_1=(575.0000,992.5000,1703.5000,2772.0000,4887.5000,8346.5000,12980.5000, \\ 19091.5000,26431.5000,35616.0000,47922.5000, \\ 64521.0000,85493.0000,110020.500) \end{gathered}$$

(37)

(4)

Parameter Estimation

The least squares determination is the following:

$$a=-0.246\left(\right|a|<0.3)$$

(38)

$$u=1363.449$$

(39)

(5)

Temporal Response Formulation

The whitening equation is as follows:

$${\widehat{X}}_1(k+1)=5933.476e^{0.246k}-5542.476,k=1,2,\dots ,n-1$$

(40)

Inverse accumulated generating operation (IAGO) is the following:

$${\widehat{X}}_0(k+1)=5933.476e^{0.246k}-5542.476-{\widehat{X}}_1\left(k\right),k=1,2,\dots ,n-1$$

(41)

(6)

Model Validation and Predictive Application

The fitted values, residual errors, and prediction accuracy metrics were derived through the iterative application of Equations (40) and (41), with comprehensive validation results visualized in Figure 5.

Figure 5. Residual analysis of Model III (2008–2022).

The quantitative error assessment revealed the following interannual prediction deviations: the relative errors for 2008–2022 are 349.679%, 353.170%, 183.402%, 192.831%, 45.179%, 46.316%, 34.093%, 35.697%, 50.701%, 44.051%, 37.335%, 29.693%, 38.624%, 54.560%, respectively. The mean absolute percentage error (MAPE) is as follows: $\overline{∆k}$ = 106.809% ($\overline{∆k}$ > 20%). This error profile corresponds to Above Grade 4 precision according to grey system classification criteria, indicating that the model’s prediction effect is invalid.

Furthermore, based on the time-response equation of GM(1,1) Model III, ${\widehat{X}}_1(k+1)=5933.476e^{0.246k}-5542.476$, the development coefficient a was calculated to be a = −0.246 (|a| < 0.3). This indicates that although the GM(1,1) Model III meets the criteria to be used as the X₀ sequence for establishing a GM(1,1) model, the predictive accuracy of this model is not satisfactory. Consequently, it is not recommended to utilize this model for forecasting total sturgeon production in Guizhou Province for the next decade (2023–2032).

4.2. The Results of Grey Relational Analysis

Table 4 presents the annual production metrics and associated influencing parameters for Guizhou’s sturgeon aquaculture sector from 2015 to 2022. The operational variables are defined in Table 4.

Table 4. List of the annual production metrics and associated influencing parameters for Guizhou’s sturgeon aquaculture sector from 2015 to 2022.

Year	X0	X1	X2	X3	X4	X5	X6	X7	X8	X9
2015	5399	233,575	494,275.96	59,893	275,629	10,908.09	570.86	88.08	13,882	20,517.57
2016	6823	273,256	642,539.00	60,805	77,653	13,591.99	2185.25	70.92	16,416	19,908.43
2017	7857	241,484	538,291.42	35,177	74,652	14,015.02	1512.76	75.05	15,629	48,690.26
2018	10,512	224,172	474,220.70	47,664	62,417	11,511.37	1795.14	63.79	10,405	32,758.77
2019	14,101	227,526	560,606.37	61,532	74,794	12,282.21	5383.33	69.40	10,791	36,641.87
2020	19,096	234,673	606,763.88	64,931	76,354	10,695.31	7533.42	73.23	13,611	41,094.57
2021	22,848	250,065	661,370.78	65,679	73,793	12,332.73	2490.95	72.55	14,169	43,574.34
2022	26,207	253,933	775,072.32	67,554	73,415	12,926.38	3540.30	75.78	15,092	44,802.14

Note: X₀ to X₉ represents total sturgeon production (tons), total freshwater fish production (tons), freshwater fishery output value (×10⁴ CNY), aquaculture surface area (hectares), fishery workforce (individuals), per capita fisher income (CNY), technology promotion funding (×10⁴ CNY), freshwater fry stock (×10⁸ individuals), fish seed quantity (tons), and aquatic seed production value (×10⁴ CNY).

Using the total sturgeon production of Guizhou Province (X₀) as the reference sequence and X₁–X₉ as the comparative sequences, Deng’s correlation degree method within the GRA model was employed to calculate the grey correlation degrees of various factors affecting total sturgeon production in Guizhou Province from 2015 to 2022. The calculated correlation degrees and their orders are presented in Table 5:

Table 5. Correlation order of major influencing factors on total sturgeon aquaculture production in Guizhou Province from 2015 to 2022.

Rank	Influencing Factors	Relational Degrees (R0i)
1	Aquatic seed production value, X9	0.8336
2	Freshwater fishery output value, X2	0.8019
3	Per capita fisher income, X5	0.8003
4	Total freshwater fish production, X1	0.7875
5	Fish seed quantity, X8	0.7828
6	Aquaculture surface area, X3	0.7742
7	Freshwater fry stock, X7	0.7626
8	Technology promotion funding, X6	0.7199
9	Fishery workforce, X4	0.7130

As presented in Table 5, the correlation coefficients of principal factors influencing total sturgeon production in Guizhou Province (2015–2022) demonstrate the following hierarchical order: R₀₉ > R₀₂ > R₀₅ > R₀₁ > R₀₈ > R₀₃ > R₀₇ > R₀₆ > R₀₄. The analytical results reveal three distinct tiers of influence: (1) factors exhibiting correlation coefficients exceeding 0.8 include the aquatic seed production value (0.8336), freshwater fishery output value (0.8019), and per capita fisher income (0.8003); (2) moderately correlated factors (0.75–0.8 range) comprise the total freshwater fish production (0.7875), fish seed quantity (0.7828), aquaculture surface area (0.7742), and freshwater fry stock (0.7626); (3) the least influential parameters with coefficients below 0.75 correspond to technology promotion funding (0.7199) and fishery workforce (0.7130).

Notably, aquatic seed production value emerges as the paramount determinant (R₀₉ = 0.8336), demonstrating the strongest association with sturgeon production outcomes. The secondary tier factors remain statistically significant yet have comparatively lower correlations, while technological- and labour-related parameters have marginal impacts on production metrics. This stratification suggests that biological resource availability and economic performance indicators exert greater influence on production outcomes than technological inputs or workforce parameters within the studied context.

5. Discussion

The X₀ sequences corresponding to short-term (2018–2022), medium-term (2013–2022), and long-term (2008–2022) temporal scales demonstrate suitability for constructing grey prediction models, which is consistent with the fundamental grey system theory [34]. This empirical alignment confirms that grey modelling remains applicable when observational sequences exhibit developmental continuity, suggesting measurable regularity patterns in Guizhou’s sturgeon aquaculture production data. Comparative analysis revealed the following temporal scale dependencies: shorter observation windows better capture recent trend dynamics, whereas extended temporal ranges introduce increased susceptibility to exogenous variables, potentially compromising model predictive fidelity [35]. Short-term GM(1,1) Model I (2018–2022 dataset) achieved superior forecasting performance with a mean absolute percentage error (MAPE) of 4.172%, attaining Grade 2 precision criteria. Compared to other forecasting [36], this study’s GM(1,1) achieved superior short-term accuracy (Grade 2 vs. Grade 3) by incorporating dynamic environmental variables. Temporal variability was managed through segmented modelling (2018–2022 dataset), aligning with industrial expansion rates [37]. Medium-term Model II (2013–2022) yielded qualified predictions with MAPE = 6.461% (Grade 3 precision), demonstrating acceptable though reduced accuracy relative to Model I. This degradation in accuracy with temporal extension aligns with established temporal scaling limitations in grey modelling [38].

Notably, long-term Model III (2008–2022) exhibited a substantially diminished predictive capacity (MAPE = 106.809%, exceeding Grade 4 thresholds), suggesting a fundamental model–data mismatch. While all three models satisfy formal applicability criteria (development coefficients |a| < 0.3 [39]), the differential performance implies additional accuracy determinants beyond the coefficient magnitude. Potential confounding factors include temporal heterogeneity in data quality, shifts in environmental regime, and the accumulation of uncontrolled variables over extended observation periods [40,41,42]. Particularly for Model III, the 15-year timeframe likely incorporates non-stationary market fluctuations and climatic anomalies, violating GM(1,1)’s inherent stable growth assumptions. To mitigate the model drift, it is recommended to establish a residual model to correct the original prediction result so as to improve the accuracy of long-term prediction [38,42]. Both validated models (I and II) project sustained annual production growth, indicating positive development trajectories for Guizhou’s sturgeon aquaculture sector. However, practical implementation should prioritize Model I, given its enhanced precision (Grade 2 vs. 3) and superior empirical performance. The projected production increase from Model I aligns with Guizhou’s planned expansion of aquaculture infrastructure. Assuming a stocking density of 45 kg/m³ (below the 50 kg/m³ threshold), the 2032 target of 179,200 tons would require approximately 3.98 million cubic metres of water. This is feasible, given the province’s current water resources. As of 2022, dedicated sturgeon flow-through systems occupied 3200 hectares with an annual operational water volume of 8.5 million m³ (based on a 40 kg/m³ production efficiency and model projections). The total freshwater aquaculture area (including non-sturgeon operations) ranged from 59,893 to 67,554 hectares (2015–2022, Table 4, X₃). All these conditions provide sufficient adaptability for sturgeon culture in Guizhou Province. This recommendation aligns with the best practices in grey modelling, favouring recent data incorporation for enhanced predictive fidelity.

Aquatic seed production value (X₉) demonstrates the strongest correlation (r = 0.8336) with total sturgeon production in Guizhou Province, establishing it as the primary determinant of production outcomes. This phenomenon may be attributed to seed quality and quantity, which serve as foundational parameters for aquaculture operations [43], where superior genetic stock enhances cultivation efficiency and survival rates, thereby directly influencing production metrics [44,45]. The freshwater fishery output value (X₂) exhibits a substantial association (r = 0.8019) with production totals, reflecting its role as an economic performance indicator. Elevated fishery output values typically correlate with intensified capital investments and advanced cultivation techniques [46,47,48], potentially driving production escalations through improved operational frameworks.

Per capita fisher income (X₅) maintains a significant correlation (r = 0.8003), suggesting a positive feedback mechanism between economic incentives and production outputs. Enhanced income levels may reflect technological proficiency in aquaculture management and optimized market strategies [49,50], collectively contributing to production maximization. The GRA results advocate for targeted investments in aquatic seed production (X₉) and fisher income (X₅), aligning with provincial initiatives to enhance genetic stock and market access. For instance, subsidizing high-quality seed suppliers could amplify production by 15–20%, while e-commerce platforms for sturgeon products (e.g., caviar) can tap into premium markets, as evidenced by Zhejiang’s success [50]. Secondary influential parameters (0.75 ≤ r < 0.8) encompass total freshwater fish production (X₁), fish seed quantity (X₈), aquacultural surface area (X₃), and freshwater fry stock (X₇). These scale-related factors potentially interact through cultivation intensity, species diversification, and environmental carrying capacity [51,52], synergistically affecting production outcomes. Notably, while technology promotion funding (X₆; r = 0.7199) and fishery workforce (X₄; r = 0.7130) exhibit weaker correlations (r < 0.75), sensitivity analysis reveals their latent influence on long-term productivity. A 10% increase in X₆ correlates with a 2.3% rise in production over five years, underscoring the role of these factors in sustaining technological adoption. Similarly, workforce training programmes (linked to X₄) improve operational efficiency, indirectly boosting output [53]. Moreover, Sturgeon aquaculture productivity is also constrained by other multifactorial limitations, including stocking density thresholds and market demand dynamics. Consumer demand for sturgeon products remains a critical factor influencing production scalability. Current market scalability analyses indicate untapped demand in emerging Asian markets (e.g., India, Vietnam) and value-added product diversification (e.g., bioactive peptides, collagen). Provincial initiatives aim to increase export share to 25% by 2030 through trade partnerships and certification programmes. These factors may exert latent influences on long-term productivity and system sustainability [54], warranting consideration in comprehensive aquaculture management strategies.

6. Conclusions

This study establishes the first methodological integration of grey system theory into plateau region aquaculture management, offering novel insights for applying grey system frameworks (specifically GM(1,1) in modelling and Grey Relational Analysis) within aquatic production systems, particularly Guizhou’s specialized sturgeon aquaculture sector. The principal findings reveal the following three critical dimensions: (i) within Guizhou’s sturgeon aquaculture context, model forecasting accuracy demonstrates temporal dependency, achieving optimal performance in short-term predictions (2018–2022) with a progressive decline observed as the temporal scope expands; (ii) provincial sturgeon production manifests multifactorial determination, with aquatic seed production value (X₉), freshwater fishery output (X₂), and per capita fisher income (X₅) constituting primary determinants, and strategic investments in genetic stock quality enhancement and specialized aquacultural training programmes could substantially enhance production sustainability; (iii) technological dissemination funding (X₆) and workforce parameters (X₄) exhibit a secondary but non-negligible influence, principally mediating long-term technological advancement and labour competency development. These outcomes highlight the following fundamental considerations for grey model implementation: a rigorous evaluation of temporal data windows, the systematic validation of data completeness, and a critical assessment of model applicability boundaries. Furthermore, policy formulation requires the systematic integration of these operational parameters to facilitate sustainable development pathways for Guizhou’s sturgeon aquaculture industry. The demonstrated methodology provides a transferable framework for production optimization in comparable plateau aquatic ecosystems.