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Methodological foundations of applying three-axis graphs in the analysis of agricultural production efficiency
The article considers the methodological principles of triaxial graphs using in the analysis of the agricultural production efficiency. It is substantiated that the methodology of triaxial graphs is based on the concept of barycentric coordinates, which are expedient to use for modeling systems with three components, where the sum of the particles is always equal to 100%, which limits the system to two degrees of freedom. It is emphasized that ternary diagrams are the world standard for soil texture classifying with the purpose of a well-founded cultivation strategy, make it possible to visualize the contribution of individual factors (number of spikelets, grain size) to the total grain yield and help to assess not the absolute content of N:P:K, but their mutual balance for precise adjustment of fertilization.
It is established that this methodological approach is expedient to use for assessing the balance between renewable (R), non-renewable (N) and purchased (F) resources, which allows to establish the dependence of modern systems on technological investments. It is argued that the use of graphs in the current environment is combined with machine learning (Random Forest) and satellite monitoring for real time yield forecasting.
The necessity of applying three-axis graphs as a modern tool of statistical analysis in agricultural economics has been established. It has been clarified that tabular data provides the basis for production calculating and financial indicators, but their analytical value is limited by the difficulties of visual comparison between heterogeneous data series. Statistical data of SRL «AgroVerde» for the period 2020– 2024, including gross yield, harvested area, cost of production, sales revenues, and profit, have been systematized. Calculations of return on sales, cost recovery, unit costs, and profit per hectare and per centner of wheat have been carried out.
The potential of three-axis graphical visualization, which enables the integrated representation of multi-level indicators (costs per hectare, unit production costs, profit per hectare, and profit per centner) in a single coordinate system, has been evaluated. It has been proven that the application of three-axis graphs allows to identify multidirectional trends — such as the growth of unit production costs accompanied by a simultaneous decline in profit per hectare. It has been substantiated that the use of trend equations in graphical interpretation increases the reliability of analysis and provides a quantitative confirmation of the dynamics of the studied indicators.
It has been emphasized that three-axis graphs should be considered not only as a means of statistical data visualization but also as a method of forecasting, contributing to the identification of development patterns in agricultural production and the formulation of scientifically grounded managerial decisions.
Keywords: three-axis graph, cost of production, profitability, profit, expenditures, agricultural economics, statistical analysis.
https://orcid.org/0000-0003-0015-90571. Tartanus, M.; Sas, D.; Borowski, B.; Malusà, E.; Kozak, M. (2025). Ternary vs. Right-Angled Plots in Agricultural Research: An Assessment of Data Representation Efficiency and User Perception. Appl. Sci. Vol. 15. DOI: https://doi.org/10.3390/app15189949
2. Interactive: how to use a ternary plot – Geology is the Way. Available at: https://geologyistheway.com/geo/how-to-use-a-ternary-plot/
3. Ternary Plot – Ingeniería Elemental. Available at: https://www.ingenieriaelemental.com/posts/en/ternary-plot
4. Soil fertility. Available at: https://uk.wikipedia.org/wiki/%D0%A0%D0%BE%D0%B4%D1%8E%D1%87%D1%96%D1%81%D1%82%D1%8C_%D2%91%D1%80%D1%83%D0%BD%D1%82%D1%83
5. Golba, J., Rozbicki, J., Gozdowski, D., Sas, D., Mądry, W., Piechociński, M., Kurzyńska, L., Studnicki, M., Derejko, A. (2013). Adjusting yield components under different levels of N applications in winter wheat. Int. J. Plant Prod. Vol. 7. Рр.139-150.
6. Thomas W. (1937). Foliar diagnosis: Principles and practice. Plant Physiol. Vol.12. 571 p. DOI: https://doi.org/10.1104/pp.12/3/571
7. Ternary Plots for Three-Variable Compositional Data – Dev3lop. Available at: https://dev3lop.com/ternary-plots-for-three-variable-compositional-data/
8. Cai, J W, Fu, X, Sun, X W, et al. (2008). Ternary diagram used in emergy accounting of regional agricultural economic systems. Acta Ecologica Sinica. Vol. 28(02). Pp. 710-719. Available at: https://www.researchgate.net/publication/282720880_Ternary_diagram_used_in_emergy_accounting_of_regional_agricultural_economic_systems
9. Liu, X, Zhu, Y, Zhang, B, Lu, H and Zhang, T. (2025). Patiotemporal evolution patterns and driving factors of agricultural ecological efficiency in the Yangtze River Economic Belt, China. Front. Sustain. Food Syst. Vol. 9. DOI: https://doi.org/10.3389/fsufs.2025.1618536
10. Yue, Shen, Haibo, Li. (2025). Carbon Emission Efficiency in China (2010-2025): Dual-Scale Analysis, Drivers, and Forecasts Across the Eight Comprehensive Economic Zones. Sustainability. Vol. 17(22). DOI: https://doi.org/10.3390/su172210007
11. Xie, Hualin, Yanwei, Znang, Yongrok, Choi. (2018). Measuring the Cultivated Land Use Efficiency of the Main Grain-Producing Areas in China under the Constraints of Carbon Emissions and Agricultural Nonpoint Source Pollution. Sustainability. Vol. 10(6):1932. DOI: https://doi.org/10.3390/su10061932
12. Xie, Z., Wu S., Liu, X., Shi, H., Hao, M., Zhao, W., Fu, X., Liu, Y. (2025). Land Consolidation Potential Assessment by Using the Production– Living–Ecological Space Framework in the Guanzhong Plain, China. Sustainability. Vol. 17. DOI: https://doi.org/10.3390/su17156887
13. Mark Musumba, Philip Grabowski, Cheryl Palm, Sieglinde Snapp. Introducing the sustainable intensification assessment framework. Available at: https://cgspace.cgiar.org/bitstreams/8b-744f4b-e45d-4e04-9a48f607d8c0de5e/download
14. Antonio Rodrıguez, Rosa Canals, and Maria-Teresa Sebastia. (2020). Рositive effects of legumes on soil organic carbon storage disappear at high legume proportion across a wide range of environmental conditions in grasslands in the Pyrenees. Preprints. DOI: https://doi.org/10.22541/au.158930956.66985695
15. Xinying Jiao, Jingtao Ma, Guoxiang Liu, Yancang Li, Chenggang Li. (2024). Spatial–temporal evolution and influencing factors of the eco-efficiency of cultivated land-use in the Beijing–Tianjin–Hebei region in the context of food security. Front. Sustain. Food Syst. Vol. 8. DOI: https://doi.org/10.3389/fsufs.2024.1462031
16. Zitian Gao, Danlu Guo, Dongryeol, Andrew W. Western. (2023). Training sample selection for robust multi-year within-season crop classification using machine learning. Computers and Electronics in Agriculture. Vol. 210(1). DOI: https://doi.org/10.1016/j.compag.2023.107927
17. Parmacli, D. M. (2006). The economic potential of land in agriculture: Monograph. Chişinău:ASEM.
18. Parmacli, D. M., & Babi, L. I. (2008). Agrarian economics: Textbook. Chişinău.
19. Parmacli, D. M., & Dudoglo, T. D. (2017). Graphical method in statistics: Educational and methodological guide. Comrat State University, Research Center «Progress».
20. Parmacli, D. M., Todorich, L. P., Dudoglo, T. D., Kuraxina, S. S., & Yanioglo, A. I. (2017). Land productivity in agriculture (Monograph, Ed. D. M. Parmacli). Comrat State University, Research Center «Progress». Comrat: Centrografic.
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