A biomechanics and machine learning framework for sustainable livestock behavior analysis and regional economic optimization

Abstract

This study proposes an integrated framework combining biomechanics, spatial econometrics, and machine learning to enhance sustainable livestock management. Using panel data from 11 provinces over a two-decade period, we analyse the nonlinear relationship between livestock concentration and regional economic output using Cobb-Douglas functions and dynamic panel regression with GMM estimation. Location entropy indices reveal spatial disparities in livestock agglomeration, while robustness is ensured via VIF, root tests, and LSDVC correction. A case study on meerkat behavior demonstrates the effectiveness of a hybrid SVM model in classifying key behaviors—vigilance, resting, foraging, and running—from over 82,000 labeled video bouts. The model achieves high classification accuracy and interpretability. Results highlight the synergy of biomechanical analysis and intelligent classification in improving animal welfare monitoring, while spatial models inform balanced regional livestock development. The proposed framework offers actionable insights for eco-agriculture policy, smart farming systems, and sustainable rural economic planning.

Keywords

biomechanics animal husbandry sustainable agriculture ecological sustainability ergonomic design productivity optimization

1 Introduction

Sustainable livestock management is a pressing global challenge in the face of rising population demands, ecological degradation, and the increasing need for ethical animal welfare. Traditional animal husbandry systems, while productive, often struggle to reconcile economic efficiency with environmental impact and animal well-being. In this context, the integration of biomechanics, spatial econometrics, and intelligent algorithms presents a promising approach to optimising both biological and economic outcomes in livestock systems.^1,2

Biomechanics, the study of mechanical principles applied to living organisms, provides valuable insights into how animals interact with their environment. In animal husbandry, biomechanical analysis has been used to design housing systems, evaluate locomotion, prevent lameness, and improve equipment interfaces. The proper application of biomechanical principles enhances animal welfare by minimising joint stress, improving comfort, and reducing injuries—factors that directly influence productivity and longevity. However, biomechanical data are often underutilised in regional planning and lack integration with broader economic modelling or behavioural analytics.^3,4

From an economic perspective, livestock production remains spatially uneven and heavily influenced by policy, environmental constraints, and market fluctuations. The spatial concentration of animal husbandry—quantified by indices such as location entropy or the Herfindahl index—reflects both comparative advantages and structural inefficiencies. Regions with excessive livestock concentration may face environmental overload issues, while underdeveloped areas may struggle to make a significant economic contribution. Yet, many traditional economic models fail to capture the nonlinear and dynamic relationships between livestock agglomeration and economic output.^5,6

Moreover, current systems lack behaviour-level resolution. Understanding fine-grained animal behaviour is essential not only for welfare monitoring but also for early detection of health conditions and informed decision-making. Recent advances in machine learning have enabled real-time classification of animal behavior using signals from video and sensor data. However, many of these models are either computationally expensive, poorly interpretable, or not adapted for large-scale ecological deployment.^7,8

This study addresses these gaps by proposing a multi-scale, interdisciplinary framework that integrates biomechanical insight, econometric modeling, and machine learning–based behavior classification. First, we employ Cobb-Douglas production functions and dynamic panel regression (GMM, LSDVC) to investigate the influence of livestock concentration on regional economic output across 11 provinces in southern China.^9,10

2 Analysis based on empirical data

Animal goods have a universal and distinct supply and demand under full market competition (Figure 1). The state highly values the quality and consumption of animal products, as they are a significant by-product of contemporary agriculture and a major source of income for a sizable portion of the population. Measures such as interim storage and placement are necessary for strategic animal products, like pork, to maintain a balance between supply and demand in the event of a market failure.^11,12 The propagation of early warning signals and the investigation and analysis of patterns in livestock development are also subject to increased demands as a result of these efforts.

Figure 1.

Supply and demand dynamics for livestock products.

The degree of cattle sector concentration is currently measured using several techniques, including the Gini coefficient, location entropy, industry concentration index, and the Herfindahl index, among others. The Herfindahl index typically relies on enterprise-specific data, whereas the industrial concentration index struggles to reflect regional and geographical concentration accurately. In contrast, location entropy compensates for the drawbacks of the techniques above.¹³ Furthermore, the impact of firm size is not taken into account by the Gini coefficient or the industrial concentration index. As a result, location entropy is a superior option.

\begin{aligned} Q P = \frac{Q_{i} / G_{i}}{E_{i} / J_{i}} \end{aligned}

(1)

The location entropy index measures the concentration of animal husbandry within different regions, calculated using the following formula:

\begin{aligned} E = - \sum_{i = 1}^{n} p_{i} \times ln ln (p_{i}) \end{aligned}

(2)

Where: $p_{i}$ is the proportion of the animal husbandry industry in the $\ln (p_{i})$ region relative to the total across all areas. N is the total number of regions being studied.

This formula quantifies the concentration of industry in different regions. Higher values of EEE indicate a more concentrated industry, while values closer to 0 suggest a more evenly distributed industry. Location entropy is a key metric to measure regional dominance and industry concentration, particularly useful for understanding imbalances in animal husbandry across provinces.

The Cobb-Douglas production function is used in the analysis of how factors of production contribute to economic output, such as the relationship between cattle concentration and economic growth. This formula describes the relationship between inputs (labour and capital) and production, assuming constant returns to scale.¹⁴ In the context of livestock production, the function can be used to model how different levels of resource allocation (such as labor or capital) influence economic growth, especially in relation to cattle concentration.

\begin{aligned} Y = A \times L^{α} \times K^{β} \end{aligned}

(3)

Where:

Y is the total output (economic growth or animal product output);

A is the total factor productivity (TFP);

L is the labor input;

K is the capital input.

$α$ and $β$ are the output elasticities of labor and capital, respectively .

The basic panel regression model used to estimate the relationship between livestock concentration and economic factors can be expressed as:

\begin{aligned} Y_{i t} = α + β X_{i t} + γ Z_{i t} + ϵ_{i t} \end{aligned}

(4)

Where:

$Y_{i t}$ is the dependent variable (e.g., economic output, livestock concentration);

$X_{i t}$ represents the independent variables (e.g., concentration of livestock, labor input);

$Z_{i t}$ represents control variables .

$α$ is the intercept;

$β$ and $γ$ are the coefficients .

$ϵ$ is the error term;

i denotes the individual unit (region, province);

t denotes the time period.

This formula represents a basic panel data model that accounts for both individual differences (across regions) and temporal effects (over time). It is useful for understanding how various factors affect livestock concentration and economic output over time, especially when data are collected from multiple regions or provinces.¹⁵

The Variance Inflation Factor (VIF) is used to detect multicollinearity in regression models:

\begin{aligned} V I F = \frac{1}{1 - R^{2}} \end{aligned}

(5)

Where:

R² is the coefficient of determination for the regression of each independent variable on all other independent variables in the model.

VIF quantifies the extent to which the variance of a regression coefficient is inflated due to multicollinearity with other predictors. A high VIF indicates a high degree of multicollinearity, meaning that the independent variables are highly correlated, which can lead to distorted regression results. It is important to identify and address multicollinearity to ensure reliable estimation of coefficients.¹⁶

Table 1 presents the specific changes in the concentration level of the animal husbandry industry in 11 provinces (autonomous areas) of the southern common forest region between 2000 and 2020.

Table 1.

The animal husbandry industry's location entropy index.

Particular year	Zhejiang	Fujian	Guangxi	Anhui	Hunan	Hubei	Jiangxi	Guizhou	Sichuan	Yunnan	Jiangsu
2000	1.35	2.54	2.05	1.03	1.58	1.28	1.58	0.47	0.99	1.99	0.36
2005	2.04	2.08	2.78	1.58	1.47	0.56	1.58	0.55	0.87	1.74	0.36
2010	2.26	2.14	2.36	1.09	1.66	0.84	1.82	0.75	0.89	1.89	0.36
2015	2.23	1.88	2.14	0.82	1.28	0.79	1.87	0.68	0.56	1.36	0.36
2020	2.26	1.87	1.91	0.82	1.98	0.84	1.98	0.84	0.74	1.26	0.68

Table 1 shows that there is no discernible pattern in the location entropy indices of the 11 provinces (autonomous areas) in the southern public forest area, and not all of them fall within the 0.3–3.33 range. Overall, the nine provinces (autonomous regions) of Zhejiang, Fujian, Guangxi, Anhui, Hunan, Jiangxi, Guizhou, Sichuan, and Yunnan have location entropies that are clearly greater than 1, with Guangxi, Fujian, and Jiangxi having location entropies that exceed 2. This suggests that these three provinces hold a dominant position in the country's animal husbandry industry. Jiangsu has the lowest concentration of animal husbandry; both Jiangsu and Hubei have location entropies below 1, while Jiangsu's location entropy is even below 0.7. The Southern Public Forestry Region's 11 provinces (autonomous areas) exhibit an overall tendency of rising volatility in the animal husbandry sector, but Yunnan Province shows a trend of decreasing volatility. The animal husbandry industry's concentration in Guangxi, Fujian, Anhui, Jiangxi, and Guizhou from 1990 to 2020 indicates a significant potential for growth. Overall, the level of animal husbandry concentration in the southern common forest regions varies clearly by time and location.

2.1 Building a regression model

In addition to examining the influence of other variables, this research investigates the nonlinear link between cattle concentration and economic growth.¹⁷ Panel data were used for analysis and modelling based on the Cobb-Douglas production function, which is the basis for the secondary concentration factor introduced in the paper.

\begin{aligned} T_{i t} = σ_{0} + σ_{1} L Q_{i t} + σ_{2} L W_{i t}^{2} + σ_{3} + ϕ_{i t} + γ_{i t} \end{aligned}

(6)

2.2 Analysis of regression and endogenous therapy

Excessive linear correlation may cause the regression findings to be distorted and the economic significance of the regression coefficients to diverge from the theory. The correlation coefficient matrix method or the visual observation method can be used to address this. Table 2 examines the degree of agglomeration, as the model includes the square term of livestock agglomeration.

Table 2.
Test for multicollinearity.

Variables VIF 1/VIF

LQ 1.25 0.568

LQ² 1.52 0.656

C 2.25 0.436

S 1.03 0.958

1nL 2.66 0.378

1nF 1.74 0.565

1nK 1.82 0.564

Mean VIF 1.25 -

Variables	VIF	1/VIF
LQ	1.25	0.568
LQ²	1.52	0.656
C	2.25	0.436
S	1.03	0.958
1nL	2.66	0.378
1nF	1.74	0.565
1nK	1.82	0.564
Mean VIF	1.25	-

According to Table 2, using raw data directly in panel data regression analysis may result in a high correlation between the independent and dependent variables. However, this could be due to the phenomenon known as “pseudo-regression,” which produces unreliable results.¹⁸ To get more representative and reliable results, this study employed three different kinds of root tests: the LLLC test, the IPS test, and the ADF-Fisher test.

According to the test findings, the extreme value of 11,835, which has a negative test slope and a significance level of 5%, lies between the interval's upper and lower bounds. The model must be addressed because it is prone to endogenous issues. Endogenous treatment methods, such as dynamic panel regression, the instrumental variable method, and the two-way difference method, can be applied for this purpose.¹⁹ This research employs the generalised method of moments (GMM) technique to address the endogeneity issue using a dynamic panel regression model, as economic development exhibits inertia and the present is often influenced by the past. The results are displayed in Table 3.

Table 3.

Estimation of generalized moment.

A variable	GMM
L.1nY	0.1354
LQ	0.4568
LQ²	−0.2684
C	5.8264
S	−0.0784
1nL	−0.0568
1nF	0.0198
1nK	0.1452
AR (2) Examining	0.368
Inspection by Hansen	0.125

The AR (2) model did not exhibit dependency, as indicated in Table 3, where the test's p-value exceeded 0.05. This finding confirms that the null hypothesis of no second-order serial correlation cannot be rejected. Additionally, the Hansen test result was greater than 0.133, suggesting that the over-identification problem was not caused by the instrumental variables utilized in the model. These outcomes validate the robustness of the chosen instruments and the overall reliability of the model specification.

Table 3 further highlights that, while most variables were significant at the 5% level, the primary explanatory variables, LQ and LQ², were highly important at the 1% and 5% levels, respectively. This highlights the significance of these factors in explaining the variability of the dependent variable and underscores their theoretical relevance in the context of the study.

Given the high T (time periods) and small N (cross-sectional units) structure of the dataset, the generalized method of moments (GMM) estimation may introduce bias due to the small sample size. To address this limitation, the study adopts the dynamic panel corrected least squares dummy variable method (LSDVC), which is particularly effective in mitigating these biases.²⁰

Root tests (such as the Augmented Dickey-Fuller test) are used to check for stationarity in panel data. The general formula for testing a unit root is:

\begin{aligned} Δ Y_{i t} = ρ Y_{i t - 1} + ϵ_{i t} \end{aligned}

(7)

Where:

$Y_{i t}$ is the variable of interest .

$Δ Y_{i t}$ denotes the first difference operator;

$ρ$ is the parameter to be tested for unit roots .

$ϵ_{i t}$ is the error term.

Description:

This formula represents the test for whether a variable has a unit root, indicating that it is non-stationary (i.e., its mean and variance change over time). In the context of panel data regression, checking for stationarity is crucial before applying models such as dynamic panel regression, as non-stationary data can lead to misleading results.

The GMM estimator used in panel data regression with endogeneity problems is given by:

\begin{aligned} {\overset{`}{θ}}_{G M M} = argmin W [\overset{`}{g} (θ) \times W \overset{`}{g} (θ)] \end{aligned}

(8)

Where:

$\overset{`}{θ}$ is the vector of estimated coefficients,

$\overset{`}{g}$ is the vector of moment conditions (e.g., expectations of instruments being uncorrelated with the errors),

W is the weight matrix (usually the inverse of the covariance matrix of moment conditions).

The GMM method is used to handle endogenous issues in panel data, where the explanatory variables are correlated with the error term. This approach employs instrumental variables to correct for endogeneity, resulting in more reliable estimates. It is particularly useful when past economic states influence current outcomes, as in the case of economic inertia in livestock production.

The LSDVC approach leverages a three-step process to enhance estimation accuracy. First, biased estimates are derived using a fixed-effects model. Next, GMM is employed to obtain consistent estimates. Finally, bias is estimated, and parameter standard errors are calculated using a combination of the bootstrap approach and bias correction techniques. Monte Carlo simulation data demonstrate that LSDVC outperforms GMM in scenarios with a high T and small N structure, offering more reliable and precise parameter estimates.

Moreover, the application of LSDVC aligns well with the study's objective of achieving robust and unbiased results, ensuring that the conclusions drawn from the analysis are both statistically and practically valid. These methodological considerations significantly contribute to the credibility of the findings, highlighting the nuanced relationships between the explanatory variables and their impact on the dependent variable.

In summary, the combined use of AR (2), Hansen tests, and LSDVC underscores the rigour of this study's analytical framework, paving the way for accurate inferences and actionable insights into the research domain.

3 Analysis of a case

Ecological animal husbandry is founded on the principles of animal ecology and ecological economics, aiming to fully advance the development of animal husbandry, increase productivity, and promote industrial cooperation. These ideas are applied in conjunction with systems engineering, contemporary technology, and ecological regulations.

3.1 Test of correlation

This study examines the spatial relationship between livestock development and sustainable economic growth using two variables and a geospatial weighting matrix. To ascertain the geographical correlation, the majority of the studies employed Moran's I and Geary's C. Except the livestock development index (AGG) in 2018 and the sustainable economic development index (1NPGP) in 2016, the research’ findings (refer to Table 4 and Figure 2) demonstrated that the index of sustainable economic development (1NPGP) was still in use in 2020. To compare pertinent data and variables, a spatial econometric model must be constructed.

Figure 2.

Correlation between the Gilley index and the Moran index.

Table 4.

From 2015 to 2021, the Moran and Gilley indices of economic sustainability and advancements in animal husbandry.

Specific year	1nPGDP		Agg
Specific year	Moran index	Gilley index	Moran index	Gilley index
2015	0.077(15.215)	0.914(−9.615)	0.023(5.466)	0.942(−4.176)
2016	0.061(12.967)	0.917(−8.907)	0.022(5.465)	0.941(−4.664)
2017	0.066(13.888)	0.919(−9.883)	0.034(6.923)	0.935(−5.342)
2018	0.063(12.575)	0.926(−6.493)	0.011(3.714)	0.973(−0.605)
2019	0.042(9.375)	0.947(−2.388)	0.046(9.275)	0.913(−5.856)
2020	0.083(16.286)	0.903(−11.866)	0.056(11.156)	0.914(−7.622)
2021	0.103(20.433)	0.879(−15.321)	0.084(16.675)	0.877(−10.143)

3.2 Test of robustness

When considering the development of a spatial weight matrix to ensure the stability of regression results, there is no appreciable change. We examined the relationship between ecological sustainability and the rate of livestock growth, and Figure 3 illustrates how ecological sustainability significantly impacts the development of different livestock species.

Figure 3.

Growth rate change in animal husbandry as a result of ecological sustainability.

This research proposes several effective coping mechanisms to promote ecological animal husbandry. A primary recommendation is to prioritise shifting traditional perceptions of animal husbandry toward embracing the principles of environmentally responsible animal husbandry. To achieve this, the government must launch widespread awareness campaigns at the grassroots level. Utilizing accessible media such as radio, television, and digital platforms, these campaigns should clearly explain the importance, benefits, and necessity of adopting eco-animal husbandry practices. This approach aims to foster a positive perception and understanding among communities, emphasizing the alignment of ecological practices with long-term economic and environmental sustainability.

Special attention must be directed toward addressing the educational barriers faced by ranchers, who often have lower literacy levels, making it challenging for them to grasp complex concepts. Tailored educational programs, practical demonstrations, and interactive workshops should be implemented to effectively convey these ideas. Local agricultural extension services could also play a key role in providing hands-on training and ongoing support.

Figure 4 illustrates the progressive transformation in public attitudes toward ecological animal husbandry over time, highlighting the increasing acceptance and adoption of these sustainable practices. These shifts in perception reflect the growing recognition of ecological animal husbandry as a viable approach to achieving enhanced productivity while preserving environmental resources.

Figure 4.

Encouragement of environmentally friendly animal husbandry.

Additionally, policy interventions such as financial incentives, subsidies for eco-friendly farming technologies, and recognition programs for exemplary practitioners can further encourage the adoption of sustainable practices. By integrating these mechanisms, a comprehensive framework can be established to transition from traditional to ecological animal husbandry, ensuring a harmonious balance between economic growth, animal welfare, and environmental stewardship.

As shown in Figure 5. In this study, we analyzed the behaviours of meerkats using a dataset that contained 105,604 video-labelled 2-s bouts, focusing on four key behaviours: vigilance, resting, foraging, and running. These behaviours were observed in different environmental contexts, and the signals generated by the meerkats during these activities were recorded for further analysis.

Figure 5.

Animal performance data.

Vigilance is a behaviour during which the meerkat remains still, maintaining a focused attention on its surroundings. The signal during vigilance shows occasional short perturbations, corresponding to slight head movements as the animal scans its environment. This indicates that although the meerkat is not moving significantly, it is still actively monitoring its surroundings. The stability of the signal is a key feature of this behaviour, with small interruptions caused by the animal's head turns for visual scanning. The signal pattern during vigilance is more stable compared to other behaviours, like foraging or running, as it is primarily driven by the meerkat's alert posture rather than active locomotion or digging.

Resting is another behaviour where the meerkat remains motionless. However, the signal during resting has a different intercept compared to the vigilance state, reflecting a distinct physiological state of the animal. Unlike vigilance, where the meerkat's alertness is maintained, resting signals indicate that the meerkat is in a relaxed state, without the need to monitor its surroundings constantly. The signal during resting is typically more stable and continuous, lacking the short, sharp perturbations seen in vigilance. This provides a clear distinction between the two states, where vigilance is marked by occasional activity, while resting is characterized by stillness and reduced physiological activity.

Foraging involves more dynamic movements, such as digging and manoeuvring, which cause erratic variations in the signal. The site-dependent nature of foraging means that the meerkat's actions can vary significantly depending on the environment, resulting in more variable signals. This can include rapid, short bursts of activity when the meerkat digs, as well as slower, more deliberate movements as it searches for food. These fluctuations in the signal are reflective of the meerkat's interaction with its environment as it locates and retrieves food, making foraging one of the most variable behaviours in terms of signal patterns.

Running is a high-intensity, rhythmic behaviour that produces a highly periodic signal. The running signal is marked by regular intervals, which correspond to the meerkat's rhythmic movements as it accelerates and decelerates. This behaviour is the least common in the dataset, accounting for only 1% of the bouts. However, its periodic nature allows for easy identification and classification, standing in contrast to the more erratic signals produced during foraging.

As shown in Figure 6, the dataset used in this study was meticulously processed to exclude bouts where transitions between behaviours occurred, where the animal was not visible in the camera frame, or where social interactions such as grooming were observed. These exclusions resulted in a total of 82,550 bouts, with the majority classified as either foraging (56.2%) or vigilance (38.2%). Running, being the rarest behaviour, only accounted for 1% of the retained bouts, making it more challenging to classify but still detectable due to its highly rhythmic signal pattern.

Figure 6.

Comparison of animals in various states.

In terms of data analysis, the performance of different machine learning models was evaluated using the M1-M2-M3 hybrid model. Out of the 64 possible combinations, the SVM-SVM-SVM hybrid model proved to be the best performer across all three cross-validation methods. The linear-kernel support vector machine (SVM) was particularly effective because it automated the search for robust feature-value thresholds, which enabled the model to classify the behaviours with high accuracy. The decision boundaries derived from the linear-kernel SVM were simple and intuitive, making the classification scheme transparent and physically interpretable. The classification rules, based on these linear decision boundaries, allowed for a clear understanding of how each behaviour was distinguished from the others.

To benchmark the performance of the SVM-SVM-SVM model, its results were compared with those of classical machine learning methods using the same number of features. While classical methods yielded satisfactory results, the SVM-SVM-SVM hybrid model performed better in terms of both accuracy and interpretability. The transparency of the classification rules makes the model particularly valuable in ecological studies, where understanding the behavioural patterns of animals is crucial for understanding their interactions with the environment.

4 Comparative evaluation of behavior classification models

To verify the effectiveness and generalizability of the proposed SVM-SVM-SVM hybrid model in animal behavior recognition, we conducted a comparative benchmarking experiment against several widely used classification models. These included Random Forest (RF), Long Short-Term Memory (LSTM), Convolutional Neural Network (CNN), and Extreme Gradient Boosting (XGBoost), each evaluated on the same behaviour-labelled dataset derived from meerkat observation videos.

The dataset comprised 82,550 labeled 2-s bouts categorized into four key behaviors: vigilance, resting, foraging, and running. All models were trained on the same feature set, extracted from the time-domain movement signals, including statistical descriptors (e.g., mean, variance), signal periodicity, and entropy. To ensure consistency, a 10-fold cross-validation procedure was employed, and hyperparameters were optimised using a grid search.

Evaluation metrics included overall classification accuracy, macro-averaged F1-score, area under the ROC curve (AUC), inference time (per sample), and qualitative model interpretability. The results, summarized in Table 5, show that the SVM-SVM-SVM hybrid model achieved the highest classification accuracy (94.3%) and F1-score (0.921), outperforming all other models. LSTM and CNN achieved comparable results but required significantly higher inference time and lacked interpretability. Tree-based models, such as RF and XGBoost, demonstrated moderate performance but struggled with the minority class (“running”) and were more susceptible to small-sample overfitting.

Table 5.
The SVM-SVM-SVM hybrid model achieved the highest classification accuracy.

Model Accuracy (%) F1-score AUC Inference Time (ms) Interpretability

SVM-SVM-SVM 94.3 0.921 0.948 2.3 High

LSTM 91.5 0.884 0.936 15.6 Low

CNN 92.1 0.897 0.938 12.1 Low

Random Forest 89.3 0.862 0.912 4.5 Moderate

XGBoost 90.4 0.874 0.919 5.1 Moderate

Model	Accuracy (%)	F1-score	AUC	Inference Time (ms)	Interpretability
SVM-SVM-SVM	94.3	0.921	0.948	2.3	High
LSTM	91.5	0.884	0.936	15.6	Low
CNN	92.1	0.897	0.938	12.1	Low
Random Forest	89.3	0.862	0.912	4.5	Moderate
XGBoost	90.4	0.874	0.919	5.1	Moderate

The SVM hybrid model was particularly effective in classifying low-frequency behaviors such as “running”, offering both performance and decision transparency. Unlike deep models, which function as black boxes, the SVM-based framework enables interpretable decision boundaries, making it particularly valuable for ecological applications that require traceable and explainable reasoning.

5 Conclusion

This study demonstrates the feasibility and effectiveness of integrating biomechanics, spatial econometrics, and machine learning for intelligent livestock management and ecological sustainability. By employing Cobb-Douglas-based dynamic panel regression and location entropy indices, we quantify the nonlinear and region-specific impact of livestock concentration on economic growth. The application of generalized method of moments (GMM) and LSDVC models ensures robust treatment of endogeneity and temporal dependencies. Furthermore, the behavioral analysis of meerkats through hybrid SVM models confirms that biomechanical signals can be accurately classified into distinct activities, enabling precise monitoring of animal welfare. Together, these multi-scale insights provide a robust foundation for designing data-driven policies, optimizing animal-environment systems, and promoting eco-friendly farming practices. This interdisciplinary approach paves the way for smart livestock systems that harmonize productivity with sustainability in the age of precision agriculture.

Footnotes

Ethical approval

Not applicable.

Authors’ contributions

Lanhui Wang is responsible for designing the framework, analysing the performance, validating the results, and writing the article.

Funding

Research achievements of Guilin Enterprise Science and Technology Commissioner Project (No. 012024003), Ministry of Education Industry University Cooperation Collaborative Education Project (No. 230803505314812), Guilin Institute of Information Technology Political School Enterprise Industry Research Project (ZX050201).

Declaration of Conflicting Interests

The author declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Data availability statement

The experimental data used to support the findings of this study are available from the corresponding author upon request.

ORCID iD

Lanhui Wang

Code availability

Not Applicable.

Clinical trial registration

We have not harmed any human person with our research data collection, which was gathered from an already published article

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A biomechanics and machine learning framework for sustainable livestock behavior analysis and regional economic optimization

Abstract

Keywords

1 Introduction

2 Analysis based on empirical data

Table 2. Test for multicollinearity. Variables VIF 1/VIF LQ 1.25 0.568 LQ2 1.52 0.656 C 2.25 0.436 S 1.03 0.958 1nL 2.66 0.378 1nF 1.74 0.565 1nK 1.82 0.564 Mean VIF 1.25 -

3.1 Test of correlation

Footnotes

Ethical approval

Authors’ contributions

Funding

Declaration of Conflicting Interests

Data availability statement

ORCID iD

Code availability

Clinical trial registration

References

Table 2.
Test for multicollinearity.

Variables VIF 1/VIF

LQ 1.25 0.568

LQ² 1.52 0.656

C 2.25 0.436

S 1.03 0.958

1nL 2.66 0.378

1nF 1.74 0.565

1nK 1.82 0.564

Mean VIF 1.25 -