Abstract
The height of rice plants is not only an important component of the crop canopy structure but also a crucial pathway for increasing crop yield. In this study, we used a logistic regression model to fit the plant height data of rice varieties cultivated in Taiwan over years and interpret the parameters from the perspective of crop growth. The logistic model has five critical points which allows for the inference of various growth stages: absolute acceleration point (AAP, completion of seedling establishment), maximum acceleration point (MAP, tillering initiation), inflection point (IP, effective tillering), maximum deceleration point (MDP, panicle initiation), and asymptotic deceleration point (ADP, heading). We found that the autumn cropping season reached the point of maximum growth rate earlier (AAP: 5; MAP: 11; IP: 19; MDP: 28; ADP: 34 days) than the spring cropping season, with noticeable advancements in the critical points of IP, MDP, and ADP. According to the model parameters, the period between AAP and ADP is the main growth stage of rice plant height, with the maximum growth rate of autumn crops exceeding that of spring crops. The results showed that there was no significant difference between the early and recent varieties in terms of the time to reach the maximum growth rate and its slope for both cropping seasons. The model can be applied to rice cultivation management to schedule the timing of fertilizer application and irrigation.
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Data is provided within the supplementary information file.
References
Hsieh, C. Y., Fang, S. L., Wu, Y. F., Chu, Y. C. & Kuo, B. J. Using sigmoid growth curves to establish growth models of tomato and eggplant stems suitable for grafting in subtropical countries. Horticulturae 7, 537 (2021).
Chang, T., Yin, H. & Xin, M. Distribution characteristics of photosynthetically active radiation in rice canopy and its relationship with leaf area index. Chin. J. Agrometeorol. 31, 251–254 (2010).
Chen, R. K. & Chen, C. L. Effects of nitrogen fertilization rates on the culm development of rice. Res. Bull. Tainan DARES. 66, 24–38 (2015).
Jones, H. G. & Rotenberg, E. Energy, radiation and temperature regulation in plants. In Encyclopedia of Life Science. 1–8 (Wiley, 2001).
Xie, L., Xu, Z. J. & Lin, E. D. Utilization and interception of light on rice population during filling stage. Chin. J. Agrometeorol. 26, 207–209 (2005).
Wang, J. S., Chu, S. C. & Chang, S. C. Rice health management technology applied to improve rice quality. Miaoli Agric. Newsl. 78, 1–5 (2017).
Verhulst, P. F. A note on population growth. Corresp Math. Phys. 10, 113–121 (1838).
Karn, E., De Leon, T., Espino, L. & Al-Khatib, K. Brim-DeForest, W. Effects of competition from California weedy rice (Oryza sativa f. spontanea) biotypes on a cultivated rice variety. Weed Technol. 34, 666–674 (2020).
Korkmaz, M., Volkan, O. D. A. & Basustaoglu, E. O. A study over determination of asymptotic deceleration and absolute acceleration points in logistic growth model. Turkish J. Math. 10, 33–37 (2018).
Fang, S. L. et al. Using sigmoid growth models to simulate greenhouse tomato growth and development. Horticulturae 8, 1021 (2022).
Lin, F. H. Achievements and prospects of rice variety improvement in Taiwan. Spec. Publ TARI. 9, 47–69 (1996).
Chen, H., Wu, Y. C., Teng, C. Y. & Li, C. H. A century-long monitoring of rice plant height during growth period in central Taiwan. Sci. data. 12, 740 (2025).
Hsieh, C. Y., Chen, H., Wu, Y. C., Teng, C. Y. & Li, C. H. Study of the rice yield variations under water saving scenarios using DSSAT crop model. PLoS One. 20, e0329509 (2025).
Chi, K. S., Tsai, C. H. & Huang, C. S. Growth behavior and grain production of three rice varieties exhibiting different plant types in Taipei. J. Taiwan. Agric. Res. 23, 166–117 (1974).
Hseu, C. S. & Song, S. A new variety of rice-Taikeng 9. Taichung Agric. Newsl. 5, 5–6 (1993).
Wu, Y. L. Rice lodging resistance breeding. J. Agric. Assn Taiwan. 62, 63–67 (1968).
Passos, J. R. D. S., Pinho, S. Z. D., Carvalho, L. R. D. & Mischan, M. M. Critical points in logistic growth curves and treatment comparisons. Sci. Agric. 69, 308–312 (2012).
Fahad, S. et al. & Khan M. A. Rice responses and tolerance to high temperature. In Advances in Rice Research for Abiotic Stress Tolerance. 201–224 (Woodhead, 2019).
Hsu, T. C. Cultivate Paddy Rice Seedling Approach (Taitung DARES, 2008).
Vergara, B. S., Jackson, B. & De Datta, S. K. IRRI,. Deep water rice and its response to deep water stress. In Climate and Rice. 301–319 (1976).
Lur, H. S. Physiological development and healthy management in rice. Spec. Publ TARI. 111, 17–32 (2004).
Lu, C. T., Jwo, W. S., Lu, H. Y., Wei, M. L. & Lin, W. S. Using accumulated temperature and information and communication technology to improve rice field management efficiency. Spec. Publ TDARES. 119, 1–7 (2013).
Wu, Y. P., Liao, D. J. & Chou, S. Y. Cultivation and management technology of high-quality rice. Tech. Serv. Q. Bull. TARI. 31, 15–20 (2020).
Wu, T. Y., Tsai, J. H. & Chang, S. C. Rational fertilization techniques for rice in Miaoli region. Special Publication TDARES. 100, 27–30 (2010).
Chan, L. F., Yang, C. H., Jwo, W. S. & Lu, S. Y. Help the rice to see the pulse and look at the complexion. Tech. Serv. Q. Bull. TARI. 14, 7–12 (2003).
Yang, J. L., Cheng, C. C. & Hseu, C. S. Cultivation and management techniques for producing high-quality rice. Tech. Trans. TDARES. 193, 3–10 (2015).
Ting, W. Y. Evaluation of growth stages for rice variety Taitung 30 at Taitung area. Res. Bull. Taitung DARES. 21, 17–26 (2011).
Álvarez-Herrera, J. G., Pinzón-Gómez, L. P. & Vélez, J. E. Growth and production of rice (Oryza Sativa L.) under different fertilization plans with silicon. Ing. Investig. 37, 7–15 (2017).
Chen, H., Wu, Y. C., Cheng, C. C. & Teng, C. Y. Effect of climate-change induced water-deficit stress on long-term rice yield. Plos One. 18, e0284290 (2023a).
Chen, H., Wu, Y. C. & Teng, C. Y. Temporal variation of the relationships between rice yield and climate variables since 1925. PeerJ 11, e16045 (2023b).
Chen, H., Wu, Y. C., Teng, C. Y. & Li, C. H. Effect of climate warming on rice spikelet fertility in central Taiwan. J. Agri For. 72, 1–11 (2025).
Elzhov, T. V. et al. A. S. S. Package ‘minpack. lm’. Title R Interface Levenberg-Marquardt Nonlinear Least-Sq (Algorithm Found MINPACK Plus Support Bounds, 2016).
R Core Team. R: A Language and Environment for Statistical Computing. https://www.R-project.org/ (R Foundation for Statistical Computing, 2021).
Acknowledgements
The authors wish to thank Dr. Jia-Ling Yang and other researchers in Taichung District Agricultural Research and Extension Station, Ministry of Agriculture, Taiwan who assisted in the field investigation and data collection.
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C.Y.H. designed and conducted the analyses, and wrote the first draft of the manuscript. H.C. designed and conducted the analyses, supervised the project, and wrote and revised the manuscript. Y.C.W., C.Y.T., and C.H.L. collected the data.
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Hsieh, CY., Chen, H., Wu, YC. et al. Using critical points of logistic model to describe the growth of rice plant height in Taiwan.
Sci Rep (2026). https://doi.org/10.1038/s41598-026-41295-8
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DOI: https://doi.org/10.1038/s41598-026-41295-8
Keywords
- Crop model
- Historical data
- Logistic model
- Plant height
- Rice
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