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The Application of Functional Analysis of Variance in Assessing Germination in Seed Research
Farshid Ghaderi-Far , Majid Azimmohseni , Sima Sheikhveisi
Department of Statistics, Golestan University, Gorgan, Iran. , m.azimmohseni@gu.ac.ir
Abstract:   (64 Views)

Objective: This study introduces functional analysis of variance as a method for comparing germination trends under different treatments over a given time interval. This approach not only enables the comparison of treatments over the entire time period but also allows for treatment comparisons at each specific moment in time. Moreover, it identifies critical time points at which the maximum significant difference between treatments occurs, which can serve as novel germination indices.
Method: In this study, real experimental data from four germination studies were analyzed: (1) the effect of temperature on Nigella sativa germination, (2) the effect of salinity stress on Zea mays seed germination, (3) the comparison of germination among different Triticum astivum cultivars, and (4) the effect of water stress on Brassica napus germination. Using spline functions, germination data from these experiments were modeled as a function of time. The results of functional analysis were then used to compare treatments in terms of both germination percentage and germination time across the four experiments.
Results: The results of the functional analysis demonstrated its high efficiency in detecting significant or non-significant differences between treatments throughout the germination period. Furthermore, this method enabled comparisons of germination percentages at any given time point, as well as comparisons of germination times at various germination percentiles, providing detailed insights into the nature of differences among treatments. This approach also facilitated the introduction of new germination indices applicable to different seed types.
Conclusions: Overall, the results of this study indicate that the stepwise functional analysis method introduced here is an effective and precise tool for comparing treatments in germination data. This approach not only enhances treatment comparisons but also provides detailed insights into the nature of differences between treatments. Moreover, it overcomes the limitations associated with using conventional germination indices for treatment comparisons.

Highlights

  • Functional analysis was applied to compare treatments in germination percentage data.
  • The method enabled treatment comparisons in terms of germination percentage at each moment in time, as well as comparisons of germination times at various percentiles.
  • Critical germination times and percentiles at which the maximum differences between treatments occur were introduced as novel germination indices.
Keywords: Functional analysis, Germination index, Monte Carlo, Permutation method, Spline function
Full-Text [PDF 678 kb]   (20 Downloads)    
Type of Study: Research | Subject: General
Received: 2025/04/10 | Revised: 2025/07/3 | Accepted: 2025/07/12
References
1. Agbangba, C. E., Aide, E. S., Honfo, H., & Kakai, R. G. (2024). On the use of post-hoc tests in environmental and biological sciences: A critical review. Heliyon, 10(3), e25312. [DOI:10.1016/j.heliyon.2024.e25312] [PMID] []
2. Alimagham, S. M., Ghaderi-Far, F., & Rabbani, M. R. (2013). Germination data analysis by using the four-parameter Hill model. Seed Research, 3(2), 86-94. [In Persian]
3. Andersen, R. (2009). Nonparametric methods for modeling nonlinearity in regression analysis. Annual Review of Sociology, 35(1), 67-85. [DOI:10.1146/annurev.soc.34.040507.134631]
4. Azimmohseni, M., Ghaderi-Far, F., Khalafi, M., Sadeghipour, H. R., & Ghezel, M. (2022). Comparison of time to the event and nonlinear regression models in the analysis of germination data. Iranian Journal of Seed Research, 9(1), 75-92. [In Persian] [DOI:10.52547/yujs.9.1.75]
5. Colbach, N., & Durr, C. (2003). Effects of seed production and storage conditions on black grass (Alopecurus myosuroides) germination and shoot elongation. Weed Science, 51(5), 708-718. [DOI:10.1614/P2002-051]
6. Colin, N., Habit, E., Manosalva, A., Maceda-Veiga, A., & Górski, K. (2022). Taxonomic and functional responses of species-poor riverine fish assemblages to the interplay of human-induced stressors. Water, 14(3), 355. [DOI:10.3390/w14030355]
7. Cuevas, A., Febrero, M., & Fraiman, R. (2010). An ANOVA test for functional data. Computational Statistics & Data Analysis, 47(1), 111-122. [DOI:10.1016/j.csda.2003.10.021]
8. Delaigle, A., & Hall, P. (2013). Classification using censored functional data. Journal of the American Statistical Association, 108(504), 1269-1283. [DOI:10.1080/01621459.2013.824893]
9. Frois Caldeira, J., Gupta, R., Suleman, M. T., & Torrent, H. S. (2021). Forecasting the term structure of interest rates of the BRICS: Evidence from a nonparametric functional data analysis. Emerging Markets Finance and Trade, 57(15), 4312-4329. [DOI:10.1080/1540496X.2020.1808458]
10. Gan, Y., Stobbe, E. H., & Njue, C. (1996). Evaluation of selected nonlinear regression models in quantifying seedling emergence rate of spring wheat. Crop Science, 36(1), 165-168. [DOI:10.2135/cropsci1996.0011183X003600010030x]
11. Gertheiss, J., Rügamer, D., Liew, B. X., & Greven, S. (2024). Functional data analysis: An introduction and recent developments. Biometrical Journal, 66(7), 353-371. [DOI:10.1002/bimj.202300363] [PMID]
12. Ghaderi-Far, F., & Gorzin, M. (2019). Applied research in seed technology. Gorgan University of Agricultural Science and Natural Resources. [In Persian]
13. Ghaderi-Far, F., Azimmohseni, M., & Bagheri, H. (2024). Evaluation of the generalized linear model to the germination percentage data and its comparison with the square root transformation. Iranian Journal of Seed Research, 10(2), 37-48. [In Persian] [DOI:10.61186/yujs.10.2.37]
14. Gianinetti, A. (2020). Basic features of the analysis of germination data with generalized linear mixed models. Data, 5(1), 6. [DOI:10.3390/data5010006]
15. Gonzalez‐Andujar, J. L., Francisco‐Fernandez, M., Cao, R., Reyes, M., Urbano, J. M., Forcella, F., & Bastida, F. (2016). A comparative study between nonlinear regression and nonparametric approaches for modelling Phalaris paradoxa seedling emergence. Weed Research, 56(5), 367-376. [DOI:10.1111/wre.12216]
16. Górecki, T., & Smaga, Ł. (2015). A comparison of tests for the one-way ANOVA problem for functional data. Computational Statistics, 30(4), 987-1010. [DOI:10.1007/s00180-015-0555-0]
17. Haj Seyedhadi, M. R., & Gonzalez-Andujar, J. L. (2009). Comparison of fitting weed seedling emergence models with nonlinear regression and genetic algorithm. Computers and Electronics in Agriculture, 65(1), 19-25. [DOI:10.1016/j.compag.2008.07.006]
18. Joosen, R. V. L., Kodde, J., Willems, L. A. J., Ligterink, W., Van der Plas, H. W., & Hilhorst, H. W. M. (2010). Germinator: A software package for high-throughput scoring and curve fitting of Arabidopsis seed germination. The Plant Journal, 62(1), 148-159. [DOI:10.1111/j.1365-313X.2010.04136.x] [PMID]
19. Khamadi, N., Nabipor, M., Roshanfekr, H., & Rahnama, A. (2016). Effect of sowing date and seed priming on emergence and yield and yield components of three bread wheat cultivars (Triticum aestivum L.). Applied Field Crops Research, 29(1), 119-125. [In Persian] [DOI:10.22092/aj.2016.109570]
20. Kneip, A., & Liebl, D. (2020). On the optimal reconstruction of partially observed functional data. The Annals of Statistics, 48(3), 1692-1717. [DOI:10.1214/19-AOS1856]
21. Leng, X., & Müller, H. G. (2006). Classification using functional data analysis for temporal gene expression data. Bioinformatics, 22(1), 68-76. [DOI:10.1093/bioinformatics/bti742] [PMID]
22. Loddo, D., Ghaderi-Far, F., Rastegar, Z., & Masin, R. (2018). Base temperatures for germination of selected weed species in Iran. Plant Protection Science, 54(1), 60-66. [DOI:10.17221/158/2016-PPS]
23. Lu, M., Hua, J., Yu, Z., & Xu, Y. (2024). Towards transient connectivity of river networks during rainfall events: Insight from hydrological observation and functional data analysis. Journal of Hydrology, 637, 131146. [DOI:10.1016/j.jhydrol.2024.131146]
24. Mamani, G. Q., Duarte, M. L., Almeida, L. S. D., & Martins Filho, S. (2024). Non-parametric survival analysis in seed germination of forest species. Journal of Seed Science, 46, e202446036. [DOI:10.1590/2317-1545v46288345]
25. Matsui, H., & Mochida, K. (2024). Functional data analysis-based yield modeling in year-round crop cultivation. Horticulture Research, 11(7), uhae144. [DOI:10.1093/hr/uhae144] [PMID] []
26. Mrkvicka, T., Myllymäki, M., Jilik, M., & Hahn, U. (2020). A one-way ANOVA test for functional data with graphical interpretation. Kybernetika, 56(3), 432-458. [DOI:10.14736/kyb-2020-3-0432]
27. Porali, F., Ghaderi-Far, F., Soltani, A., & Palevani, M. H. (2019). Comparison of different models for determining time up to 50% maximum germination: A case study of cottonseeds (Gossypium hirsutum). Iranian Journal of Seed Research, 5(2), 1-13. [In Persian] [DOI:10.29252/yujs.5.2.1]
28. Ramsay, J. O., & Silverman, B. W. (2005). Functional linear models for functional responses. In: Functional Data Analysis. Springer Series in Statistics. Springer, New York, NY. [DOI:10.1007/0-387-22751-2_16]
29. Romano, A., & Stevanato, P. (2020). Germination data analysis by time-to-event approaches. Plants, 9(5), 617. [DOI:10.3390/plants9050617] [PMID] []
30. Samieadel, S., Eshghizadeh, H. R., Zahedi, M., & Majidi, M. M. (2024). The interaction of planting date and irrigation regime effects on the yield and water use efficiency of Milk Thistle (Silybum marianum) ecotypes. Iranian Journal of Field Crop Science, 55(1), 105-121. [In Persian] [DOI:10.22059/ijfcs.2023.361558.655015]
31. Smaga, Ł. (2020). A note on repeated measures analysis for functional data. AStA Advances in Statistical Analysis, 104(1), 117-139. [DOI:10.1007/s10182-019-00352-6]
32. Talská, R., Machalová, J., Smýkal, P., & Hron, K. (2020). A comparison of seed germination coefficients using functional regression. Applications in Plant Sciences, 8(8), e11366. [DOI:10.1002/aps3.11366] [PMID] []
33. Tjørve, K. M. C., & Tjørve, E. (2017). A proposed family of Unified models for sigmoidal growth. Ecological Modeling, 359, 117-127. [DOI:10.1016/j.ecolmodel.2017.05.008]
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