Modelling Plant Growth Based on Gompertz, Logistic Curve, Extreme Gradient Boosting and Light Gradient Boosting Models Using High Dimensional Image Derived Maize (Zea mays L.) Phenomic Data

Peter Gachoki¹, Moses Muraya² and Gladys Njoroge^1,

¹Department of Physical Sciences, Chuka University, P.O Box 109-60400, Chuka, Kenya

²Department of Plant Sciences, Chuka University, P.O Box 109-60400, Chuka, Kenya

Cite this paper

Peter Gachoki, Moses Muraya and Gladys Njoroge. Modelling Plant Growth Based on Gompertz, Logistic Curve, Extreme Gradient Boosting and Light Gradient Boosting Models Using High Dimensional Image Derived Maize (Zea mays L.) Phenomic Data. American Journal of Applied Mathematics and Statistics. 2022; 10(2):52-64. doi: 10.12691/AJAMS-10-2-3

Abstract

Modelling of plant growth is vital for hypotheses testing and carrying out virtual plant growth and development experiments, which may otherwise take a long time under field conditions. Modelling of plant growth has been aggravated by new phenotyping platforms that generate high dimensional data non-destructively over the entire growth time of a plant using a set of camera system. Such platforms generate high-throughput phenomic data, which is complex and constitute many features collected at multiple growth points for the same plant. However, the classical models are limited in that they can only model a single feature at a time. The objective of this study was to apply dynamic plant growth models that could be used to dissect complex relationships between plant growth and development using several modelling strategies. These included sigmoid, light GBM and XGBoost models. The image derived phenomic data was obtained from the Leibniz Institute of Plant Genetics and Crop Plant Research Gatersleben, Germany. The models were fitted using R statistical software and compared based on RMSE, R-squared, AIC and BIC performance metrics. The results showed that the XGBoost (RMSE = 2.1641) and Light GBM (RMSE = 2.7776) performed better than the Gompertz (RMSE = 3.8378) and the logistic function (RMSE = 3.8378) models in modelling maize plant growth. The XGBoost model (RMSE = 2.1641) showed better performance than Light GBM model (RMSE = 2.7776) in modelling maize plant growth. The Gompertz model using plant volume had AIC and BIC values for 139738.3 and 139763.4, respectively. The Gompertz model for plant side area had AIC and BIC values for 98436.15 and 98461.31, respectively. The logistic function model for plant volume had AIC and BIC values for 139749.2 and 139774.4, respectively. The logistic function model for plant side area had AIC and BIC values for 98415.95 and 98441.11, respectively. The Gompertz model and logistic function models showed almost the same performance in modelling maize plant growth. The non-parametric models, the XGBoost and light GBM, were found to perform better than the classical models (Gompertz and logistic functions) in modelling maize plant growth. Therefore, the study recommends the use of XGBoost as a generic model to fit high dimensional and complex phenotypic data in modelling plant growth and prediction of plant biomass yield at different growth points.

Keywords

Phenomic data, XGBoost, Light GBM, Gompertz model and logistic function model

Copyright

This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References

[1]	Fourcaud, T., Zhang, X., Stokes, A., Lambers, H., & Körner, C. (2008). Plant growth modelling and applications: the increasing importance of plant architecture in growth models. Annals of Botany, 101(8), 1053-1063.
[2]	Vos, J., Evers, J. B., Buck-Sorlin, G. H., Andrieu, B., Chelle, M., & De Visser, P. H. (2009). Functional–structural plant modelling: a new versatile tool in crop science. Journal of experimental Botany, 61(8), 2101-2115.
[3]	Rahaman, M., Chen, D., Gillani, Z., Klukas, C., & Chen, M. (2015). Advanced phenotyping and phenotype data analysis for the study of plant growth and development. Frontiers in plant science, 6, 619.
[4]	Dold, Christian. (2018). Climate Change Impacts on Corn Phenology and Productivity. 10.5772/intechopen.76933.
[5]	Chen, D., Neumann, K., Friedel, S., Kilian, B., Chen, M., Altmann, T., & Klukas, C. (2014). Dissecting the phenotypic components of crop plant growth and drought responses based on high-throughput image analysis. The Plant Cell, 26(12), 4636-4655.
[6]	Klukas, C., Chen, D., & Pape, J. M. (2014). Integrated analysis platform: an open-source information system for high-throughput plant phenotyping. Plant physiology, 165(2), 506-518.
[7]	Junker A, Muraya MM, Weigelt-Fischer K, Arana-Ceballos F, Klukas C, Melchinger AE, Meyer RC, Riewe D, Altmann T (2015) Optimizing experimental procedures for quantitative evaluation of crop plant performance in high throughput phenotyping systems. Frontiers in Plant Sciences. 5(770): 1-21.
[8]	Muraya MM, Chu J, Zhao Y, Junker A, Klukas C, Reif JC, Altmann T (2017) Genetic variation of growth dynamics in maize (Zea mays L.) revealed through automated non-invasive phenotyping. The Plant Journal, 89: 366-380.
[9]	Boyd, D., & Crawford, K. (2011,). Six provocations for big data. In A decade in internet time: Symposium on the dynamics of the internet and society.
[10]	Unnisabegum, A., Hussain, M., & Shaik, M. (2019). Data Mining Techniques for Big Data, Vol. 6, Special Issue. 10.13140/RG.2.2.25408.07686.
[11]	Blum, A., Hopcroft, J., & Kannan, R. (2020). Foundations of data science. Cambridge University Press.
[12]	Neumann, K., Klukas, C., Friedel, S., Rischbeck, P., Chen, D., Entzian, A., & Kilian, B. (2015). Dissecting spatiotemporal biomass accumulation in barley under different water regimes using high-throughput image analysis. Plant, cell & environment, 38(10), 1980-1996.
[13]	Karadavut, U., Palta, C., Kokten, K., & Bakoglu, A. (2010). Comparative study on somen on-linear growth models describing leaf growth of maize. Int. J.Agric. Biol. 12, 227-230.
[14]	Golzarian, M. R., Frick, R. A., Rajendran, K., Berger, B., Roy, S., Tester, M., & Lun, D. S. (2011). Accurate inference of shoot biomass from high-throughput images of cereal plants. Plant methods, 7(1), 1-11.
[15]	Flombaum, P., & Sala, O. E. (2007). A non-destructive and rapid method to estimate biomass and aboveground net primary production in arid environments. Journal of Arid Environments, 69(2), 352-358.
[16]	Rani, Sushma & Anurag, & Rao, Srinivas. (2019). Study and Analysis of Noise Effect on Big Data Analytics. 8. 5841-5850.
[17]	Xu, Y., Qiu, Y., & Schnable, J. C. (2018). Functional modeling of plant growth dynamics. The Plant Phenome Journal, 1(1), 1-10.
[18]	Bratsas, C., Koupidis, K., Salanova, J. M., Giannakopoulos, K., Kaloudis, A., & Aifadopoulou, G. (2020). A Comparison of Machine Learning Methods for the Prediction of Traffic Speed in Urban Places. Sustainability, 12(1), 142.
[19]	Kong, Y., & Yu, T. (2018). A deep neural network model using random forest to extract feature representation for gene expression data classification. Scientific reports, 8(1), 1-9.
[20]	Putra, F. H. R., Larkin, D., Khanagha, S., & Panza, K. (2019). Paper to be presented at DRUID19 Copenhagen Business School, Copenhagen, Denmark June 19-21, 2019.
[21]	Zhang, Y. F., Fitch, P., & Thorburn, P. J. (2020). Predicting the Trend of Dissolved Oxygen Based on the kPCA-RNN Model. Water, 12(2), 585.
[22]	Greenland, S., Senn, S. J., Rothman, K. J., Carlin, J. B., Poole, C., Goodman, S. N., & Altman, D. G. (2016). Statistical tests, P values, confidence intervals, and power: a guide to misinterpretations. European journal of epidemiology, 31(4), 337-350.
[23]	Shahani, N. M., Zheng, X., Liu, C., Hassan, F. U., & Li, P. (2021). Developing an XGBoost Regression Model for Predicting Young’s Modulus of Intact Sedimentary Rocks for the Stability of Surface and Subsurface Structures. Front. Earth Sci, 9, 761990.
[24]	Teleken, J. T., Galvão, A. C., & Robazza, W. D. S. (2017). Comparing non-linear mathematical models to describe growth of different animals. Acta Scientiarum. Animal Sciences, 39, 73-81.
[25]	Sprouffske, K., & Wagner, A. (2016). Growth curver: an R package for obtaining interpretable metrics from microbial growth curves. BMC bioinformatics, 17(1), 172.
[26]	Gachoki, Peter, Moses Muraya, and Gladys Njoroge. "Features Selection in Statistical Classification of High Dimensional Image Derived Maize (Zea Mays L.) Phenomic Data." American Journal of Applied Mathematics and Statistics 10, no. 2 (2022): 44-51.
[27]	Bermingham, J. R. (2003). On exponential growth and mathematical purity: a reply to Bartlett. Population and Environment, 25(1), 71-73.
[28]	Sepaskhah, A. R., Fahandezh-Saadi, S., & Zand-Parsa, S. (2011). Logistic model application for prediction of maize yield under water and nitrogen management. Agricultural Water Management, 99(1), 51-57.
[29]	Xiangxiang, W., Quanjiu, W., Jun, F., Lijun, S., & Xinlei, S. (2014). Logistic model analysis of winter wheat growth on China's Loess Plateau. Canadian Journal of Plant Science, 94(8), 1471-1479.
[30]	Osman, A. I. A., Ahmed, A. N., Chow, M. F., Huang, Y. F., & El-Shafie, A. (2021). Extreme gradient boosting (Xgboost) model to predict the groundwater levels in Selangor Malaysia. Ain Shams Engineering Journal, 12(2), 1545-1556.
[31]	Huang, J. C., Tsai, Y. C., Wu, P. Y., Lien, Y. H., Chien, C. Y., Kuo, C. F., ... & Kuo, C. H. (2020). Predictive modeling of blood pressure during hemodialysis: A comparison of linear model, random forest, support vector regression, XGBoost, LASSO regression and ensemble method. Computer methods and programs in biomedicine, 195, 105536.
[32]	Kopitar, L., Kocbek, P., Cilar, L., Sheikh, A., & Stiglic, G. (2020). Early detection of type 2 diabetes mellitus using machine learning-based prediction models. Scientific reports, 10(1), 1-12.
[33]	Liang, Y., Wu, J., Wang, W., Cao, Y., Zhong, B., Chen, Z., & Li, Z. (2019, August). Product marketing prediction based on XGboost and LightGBM algorithm. In Proceedings of the 2nd International Conference on Artificial Intelligence and Pattern Recognition (pp. 150-153).
[34]	Pu, Q., Li, Y., Zhang, H., Yao, H., Zhang, B., Hou, B., & Zhao, L. (2019). Screen efficiency comparisons of decision tree and neural network algorithms in machine learning assisted drug design. Science China Chemistry, 62(4), 506-514.
[35]	Abdulhafedh, A. (2017). Incorporating the multinomial logistic regression in vehicle crash severity modeling: A detailed overview. Journal of Transportation Technologies, 7(03), 279.
[36]	Rivas, E. M., Gil de Prado, E., Wrent, P., de Silóniz, M. I., Barreiro, P., Correa, E. C., & Peinado, J. M. (2014). A simple mathematical model that describes the growth of the area and the number of total and viable cells in yeast colonies. Letters in applied microbiology, 59(6), 594-603.
[37]	Martins, K. V., Dourado-Neto, D., Reichardt, K., Favarin, J. L., Sartori, F. F., Felisberto, G., & Mello, S. C. (2017). Maize dry matter production and macronutrient extraction model as a new approach for fertilizer rate estimation. Anais da Academia Brasileira de Ciências, 89, 705-716.
[38]	Connor, D. J., Loomis, R. S., & Cassman, K. G. (2011). Crop ecology: productivity and management in agricultural systems. Cambridge University Press.
[39]	Xie, W. Y., Pan, N. X., Zeng, H. R., Yan, H. C., Wang, X. Q., & Gao, C. Q. (2020). Comparison of nonlinear models to describe the feather growth and development curve in yellow-feathered chickens. Animal, 14(5), 1005-1013.
[40]	Wardhani, W. S., & Kusumastuti, P. (2014). Describing the height growth of corn using Logistic and Gompertz model. AGRIVITA, Journal of Agricultural Science, 35(3), 237-241.
[41]	Ismail, Z., Khamis, A., & Jaafar, M. Y. (2003). Fitting nonlinear Gompertz curve to tobacco growth data. Pakistan Journal of Agronomy, 2(4), 223-236.
[42]	Tessmer, O.L., Jiao, Y., Cruz, J.A., Kramer, D.M., & Chen, J. (2013). Functional approach to high-through put plant growth analysis. BMCSyst.Biol. 7 (Suppl.6): S17.
[43]	Moustakas, N. K., Akoumianakis, K. A., & Passam, H. C. (2011). Patterns of dry biomass accumulation and nutrient uptake by okra ('abelmoschus esculentus'(L.) Moench.) Under different rates of nitrogen application. Australian Journal of Crop Science, 5(8), 993-1000.
[44]	Noor, R. R., Saefuddin, A., & Talib, C. (2012). Comparison on accuracy of Logistic, Gompertz and Von Bertalanffy models in predicting growth of new born calf until first mating of Holstein Friesian heifers. Journal of Indonesian Tropical Animal Agriculture, 37(3), 151-160.
[45]	Sariyel, V., Aygun, A., & Keskin, I. (2017). Comparison of growth curve models in partridge. Poultry Science, 96(6), 1635-1640.
[46]	Levy, J., Mussack, D., Brunner, M., Keller, U., Cardoso-Leite, P., & Fischbach, A. (2020). Contrasting classical and machine learning approaches in the estimation of value-added scores in large-scale educational data. Frontiers in psychology, 2190.
[47]	Hansen, B. D., Tamouk, J., Tidmarsh, C. A., Johansen, R., Moeslund, T. B., & Jensen, D. G. (2020, July). Prediction of the Methane Production in Biogas Plants Using a Combined Gompertz and Machine Learning Model. In International Conference on Computational Science and Its Applications (pp. 734-745). Springer, Cham.
[48]	Ravnik, J., Jovanovac, J., Trupej, A., Vištica, N., & Hriberšek, M. (2021). A sigmoid regression and artificial neural network models for day-ahead natural gas usage forecasting. Cleaner and Responsible Consumption, 3, 100040.
[49]	AlDaoud, E. (2019). Comparison between XGBoost, LightGBM and CatBoost using a home credit dataset. International Journal of Computer and Information Engineering, 13(1), 6-10.
[50]	Ke, G., Meng, Q., Finley, T., Wang, T., Chen, W., Ma, W., & Liu, T. Y. (2017). Lightgbm: A highly efficient gradient boosting decision tree. Advances in neural information processing systems, 30.
[51]	Alshari, Haithm & Saleh, Yahya & Odabas, Alper. (2021). Comparison of Gradient Boosting Decision Tree Algorithms for CPU Performance. Erciyes Tip Dergisi. 157-168.
[52]	Marques, Armando & Prates, Pedro & Pereira, André & Oliveira, M. & Fernandes, José & Ribeiro, Bernardete. (2020). Performance Comparison of Parametric and Non- Parametric Regression Models for Uncertainty Analysis of Sheet Metal Forming Processes. Metals.