Prediction of Yield And Vegetative Growth in Apple Using Mathematical Modeling Methods

Year 2023, Volume: 9 Issue: 4, 201 - 210, 31.12.2023

Hamit Armağan , Ersin Atay

Abstract

In this study, the aim is to predict the yield and vegetative growth of apple trees over the economic lifespan of an orchard (15 years) based on mathematical models with high determination coefficients applied to data from the first 7 years following orchard establishment. Trees of the 'Golden Reinders' apple variety grafted on M.9 rootstock were used in the study conducted under the conditions of the “Göller Yöresi”. A total of 15 trees were selected following orchard establishment, and their yield and trunk diameter values were determined over 7 years. Regression models for yield and vegetative growth were constructed using the data collected with the assistance of the Matlab program. The results were comparatively evaluated, and the power regression model emerged as prominent in determining the year-tree trunk diameter relationship, while the Fourier regression model took precedence in establishing the tree trunk diameter-yield relationship. It was concluded that answering the question of how yield and vegetative growth evolve throughout the economic lifespan of apple orchards can only be achieved through such modeling approaches.

Keywords

machine learning, Malus x domestica, regression, crop load

Matematiksel Modelleme Yöntemleri İle Elmada Verim ve Vejetatif Gelişimin Tahmin Edilmesi

Abstract

Bu çalışmada elma ağaçlarında yüksek belirleme katsayısına sahip matematiksel modellemelerle bahçe tesisini takip eden ilk 7 yıl verisine dayalı olarak bahçenin ekonomik ömrünü (15 yıl) kapsayacak şekilde verim ve vejetatif gelişimin tahmin edilmesi amaçlanmıştır. Göller Yöresi şartlarında yürütülen çalışmada M.9 anaçlı ‘Golden Reinders’ elma çeşidine ait ağaçlar kullanılmıştır. Bahçe tesisini takiben toplamda 15 ağaç belirlenmiş ve 7 yıl boyunca aynı ağaçların verim ve gövde çapı değerleri belirlenmiştir. Matlab programı yardımıyla toplanan verilere dayalı verim ve vejetatif gelişim regresyon modellemeleri yapılmıştır. Sonuçlar karşılaştırmalı olarak değerlendirilmiş ve yıl-ağaç gövde çapı ilişkisinin belirlenmesinde kuvvet regresyon modeli, ağaç gövde çapı-verim ilişkisinin belirlenmesinde ise fourier regresyon modeli ön plana çıkmıştır. Elma bahçelerinin ekonomik ömrü boyunca verim ve vejetatif gelişim nasıl bir seyir izler sorusunun cevabının ancak bu tarz modellemeler yardımıyla cevaplanabileceği sonucuna varılmıştır.

Keywords

makine öğrenmesi, Malus x domestica, regresyon, ürün yükü

References

• [1] T. Ayoub Shaikh, T. Rasool, and F. Rasheed Lone, “Towards leveraging the role of machine learning and artificial intelligence in precision agriculture and smart farming,” Comput. Electron. Agric., vol. 198, p. 107119, Jul. 2022, doi: 10.1016/J.COMPAG.2022.107119.
• [2] M. Pathan, N. Patel, H. Yagnik, and M. Shah, “Artificial cognition for applications in smart agriculture: A comprehensive review,” Artif. Intell. Agric., vol. 4, pp. 81–95, Jan. 2020, doi: 10.1016/J.AIIA.2020.06.001.
• [3] K. G. Liakos, P. Busato, D. Moshou, S. Pearson, and D. Bochtis, “Machine Learning in Agriculture: A Review,” Sensors 2018, Vol. 18, Page 2674, vol. 18, no. 8, p. 2674, Aug. 2018, doi: 10.3390/S18082674.
• [4] T. U. Rehman, M. S. Mahmud, Y. K. Chang, J. Jin, and J. Shin, “Current and future applications of statistical machine learning algorithms for agricultural machine vision systems,” Comput. Electron. Agric., vol. 156, pp. 585–605, Jan. 2019, doi: 10.1016/J.COMPAG.2018.12.006.
• [5] I. Keramatlou, M. Sharifani, H. Sabouri, M. Alizadeh, and B. Kamkar, “A simple linear model for leaf area estimation in Persian walnut (Juglansregia L.),” Sci. Hortic. (Amsterdam)., vol. 184, pp. 36–39, Mar. 2015, doi: 10.1016/j.scienta.2014.12.017.
• [6] P. Freund, R. J. and Wilson, W. J., Sa, Regression analysis: Statistical Modeling of a response variable (2nd ed). California, USA, Elsevier.
• [7] A. Kamilaris and F. X. Prenafeta-Boldú, “Deep learning in agriculture: A survey,” Comput. Electron. Agric., vol. 147, pp. 70–90, Apr. 2018, doi: 10.1016/J.COMPAG.2018.02.016.
• [8] S. Chen et al., “Rapid estimation of leaf nitrogen content in apple-trees based on canopy hyperspectral reflectance using multivariate methods,” Infrared Phys. Technol., vol. 111, p. 103542, Dec. 2020, doi: 10.1016/J.INFRARED.2020.103542.
• [9] J. K. Basak et al., “Regression Analysis to Estimate Morphology Parameters of Pepper Plant in a Controlled Greenhouse System,” J. Biosyst. Eng., vol. 44, no. 2, pp. 57–68, Jun. 2019, doi: 10.1007/S42853-019-00014-0/FIGURES/11.
• [10] I. Boldina and P. G. Beninger, “Strengthening statistical usage in marine ecology: linear regression,” J. Exp. Mar. Bio. Ecol., vol. 474, pp. 81–91, Jan. 2016, doi: 10.1016/j.jembe.2015.09.010.
• [11] V. Strijov and G. W. Weber, “Nonlinear regression model generation using hyperparameter optimization,” Comput. Math. with Appl., vol. 60, no. 4, pp. 981–988, Aug. 2010, doi: 10.1016/J.CAMWA.2010.03.021.
• [12] N. Panigrahi and B. S. Das, “Evaluation of regression algorithms for estimating leaf area index and canopy water content from water stressed rice canopy reflectance,” Inf. Process. Agric., vol. 8, no. 2, pp. 284–298, 2021, doi: 10.1016/j.inpa.2020.06.002.
• [13] X. Ye, S. Abe, and S. Zhang, “Estimation and mapping of nitrogen content in apple trees at leaf and canopy levels using hyperspectral imaging,” Precis. Agric., vol. 21, no. 1, pp. 198–225, Feb. 2020, doi: 10.1007/S11119-019-09661-X/FIGURES/15.
• [14] H. Armağan, “Color Based Segmentation with k-Means Clustering Algorithm and Numerical Analysis of the Effect of Color Spaces on Image Quantities.,” El-Cezeri, vol. 9, no. 4, pp. 1506–1517, Dec. 2022, doi: 10.31202/ECJSE.1141148.
• [15] H. Armağan, E. Atay, X. Crété, P.-E. Lauri, M. Ersoy, and O. Oral, “Deep Learning-Based Prediction Model of Fruit Growth Dynamics in Apple,” In Smart Applications with Advanced Machine Learning and Human-Centred Problem Design, Cham: Springer International Publishing, 2023, pp. 367–373.
• [16] M. Altalak, M. A. Uddin, A. Alajmi, and A. Rizg, “Smart Agriculture Applications Using Deep Learning Technologies: A Survey,” Appl. Sci., vol. 12, no. 12, Jun. 2022, doi: 10.3390/app12125919.
• [17] J. G. A. Barbedo, “Detection of nutrition deficiencies in plants using proximal images and machine learning: A review,” Comput. Electron. Agric., vol. 162, pp. 482–492, Jul. 2019, doi: 10.1016/J.COMPAG.2019.04.035.
• [18] M. S. Suchithra and M. L. Pai, “Improving the prediction accuracy of soil nutrient classification by optimizing extreme learning machine parameters,” Inf. Process. Agric., vol. 7, no. 1, pp. 72–82, Mar. 2020, doi: 10.1016/J.INPA.2019.05.003.
• [19] E. Atay, X. Crété, D. Loubet, and P. E. Lauri, “Diurnal and Seasonal Growth Responses of Apple Trees to Water-Deficit Stress,” Erwerbs-Obstbau, vol. 65, pp. 1–6, 2022, doi: 10.1007/s10341-022-00689-4.
• [20] S. Huang, X. Fan, L. Sun, Y. Shen, and X. Suo, “Research on Classification Method of Maize Seed Defect Based on Machine Vision,” J. Sensors, vol. 2019, 2019, doi: 10.1155/2019/2716975.
• [21] “TÜİK,2023.” [Online]. Available: https://data.tuik.gov.tr/Kategori/GetKategori?p=Tarim-111 [Accessed Nov. 26, 2023].
• [22] “FAOSTAT.” [Online]. Available: https://www.fao.org/faostat/en/#data [Accessed Nov. 26, 2023].
• [23] E. Atay, B. Hucbourg, A. Drevet, and P. É. Lauri, “Effects of preharvest deficit irrigation treatments in combination with reduced nitrogen fertilization on orchard performance of nectarine with emphasis on postharvest diseases and pruning weights,” Acta Sci. Pol. Hortorum Cultus, vol. 18, no. 1, pp. 207–217, 2019, doi: 10.24326/asphc.2019.1.21.
• [24] E. Atay and F. Koyuncu, “Branch induction via prolepsis in apple nursery trees,” Acta Hortic., vol. 1139, pp. 439–444, 2016, doi: 10.17660/ActaHortic.2016.1139.76.