PREMISE: Seed germination over time is characterized by a sigmoid curve, called a germination curve, in which the percentage (or absolute number) of seeds that have completed germination is plotted against time. A number of individual coefficients have been developed to characterize this germination curve. However, as germination is considered to be a qualitative developmental response of an individual seed that occurs at one time point, but individual seeds within a given treatment respond at different time points, it has proven difficult to develop a single index that satisfactorily incorporates both percentage and rate. The aim of this paper is to develop a new coefficient, the continuous germination index (CGI), which quantifies seed germination as a continuous process, and to compare the CGI with other commonly used indexes. METHODS: To create the new index, the germination curves were smoothed using nondecreasing splines and the CGI was derived as the area under the resulting spline. For the comparison of the CGI with other common indexes, a regression model with functional response was developed. RESULTS: Using both an experimentally obtained wild pea (Pisum sativum subsp. elatius) seed data set and a hypothetical data set, we showed that the CGI is able to characterize the germination process better than most other indices. The CGI captures the local behavior of the germination curves particularly well. DISCUSSION: The CGI can be used advantageously for the characterization of the germination process. Moreover, B-spline coefficients extracted by its construction can be employed for the further statistical processing of germination curves using functional data analysis methods.

Department of Botany Palacký University Faculty of Science Šlechtitelů 27 Olomouc 783 71 Czech Republic

Department of Mathematical Analysis and Applications of Mathematics Palacký University Faculty of Science 17 Listopadu 12 Olomouc 771 46 Czech Republic

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Baskin, C. C. , and Baskin J. M.. 2014. Seeds: Ecology, biogeography, and evolution of dormancy and germination. Academic Press, San Diego, California, USA.

Benech Arnold, R. L. , Fenner M., and Edwards P.. 1991. Changes in germinability, ABA content and ABA embryonic sensitivity in developing seeds of Sorghum bicolor (L.) Moench. induced by water stress during grain filling. New Phytologist 118(2): 339–347. PubMed

Bewley, J. D. , Bradford K. J., Hilhorst H. W. M., and Nonogaki H.. 2013. Seeds: Physiology of development, germination and dormancy, 3rd ed Springer, New York, New York, USA.

Bradford, K. J. 2002. Applications of hydrothermal time to quantifying and modeling seed germination and dormancy. Weed Science 50(2): 248–260.

Brown, R. , and Mayer D.. 1988a. Representing cumulative germination. 1. A critical analysis of single‐value germination indices. Annals of Botany 61: 117–125.

Brown, R. , and Mayer D.. 1988b. Representing cumulative germination. 2. The use of Weibull and other empirically derived curves. Annals of Botany 61: 127–138.

Burghardt, L. T. , Edwards B. R., and Donohue K.. 2015. Multiple paths to similar germination behavior in Arabidopsis thaliana . New Phytologist 209(3): 1301–1312. PubMed

Czabator, F. 1962. Germination value: An index combining speed and completeness of pine seed germination. Forest Science 8: 386–396.

De Boor, C. 1978. A practical guide to splines, vol. 27. Springer‐Verlag, New York, New York, USA.

Dierckx, P. 1993. Curve and surface fitting with splines. Oxford University Press, Oxford, United Kingdom.

El‐Kassaby, Y. , Moss I., Kolotelo D., and Stoehr M.. 2008. Seed germination: Mathematical representation and parameters extraction. Forest Science 54(2): 220–227.

Fenner, M. , and Thompson K.. 2005. The ecology of seeds. Cambridge University Press, Cambridge, United Kingdom.

Hay, F. , Mead A., and Bloomberg M.. 2014. Modelling seed germination in response to continuous variables: Use and limitations of probit analysis and alternative approaches. Seed Science Research 24(3): 165–186.

Hradilová, I. , Duchoslav M., Brus J., Pechanec V., Hýbl M., Kopecký P., Smržová L., et al. 2019. Variation in wild pea (Pisum sativum subsp. elatius) seed dormancy and its relationship to the environment and seed coat traits. PeerJ 7: e6263. PubMed PMC

Jones, K. W. , and Sanders D.. 1987. The influence of soaking pepper seed in water or potassium salt solutions on germination at three temperatures. Journal of Seed Technology 11(1): 97–102.

Kader, M. 2005. A comparison of seed germination calculation formulae and the associated interpretation of resulting data. Journal & Proceedings of the Royal Society of New South Wales 138: 65–75.

Lawson, C. L. , and Hanson R. J.. 1995. Solving least squares problems, vol. 15. SIAM, Philadelphia, Pennsylvania, USA.

Machalová, J. 2002a. Optimal interpolating and optimal smoothing spline. Journal of Electrical Engineering 53: 79–82.

Machalová, J. 2002b. Optimal interpolatory splines using B‐spline representation. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium, Mathematica 41(1): 105–118.

Machalová, J. , Hron K., and Monti G. S.. 2016. Preprocessing of centred logratio transformed density functions using smoothing splines. Journal of Applied Statistics 43(8): 1419–1435.

McNair, J. , Sunkara A., and Frobish D.. 2012. How to analyse seed germination data using statistical time‐to‐event analysis: Non‐parametric and semi‐parametric methods. Seed Science Research 22(2): 77–95.

Orchard, T. 1977. Estimating the parameters of plant seedling emergence. Seed Science and Technology 5(1): 61–69.

Probert, R. J. 2000. The role of temperature in the regulation of seed dormancy and germination In Fenner M. [ed.], Seeds: The ecology of regeneration in plant communities, 2nd ed., 261–292, CABI, Wallingford, Oxfordshire, United Kingdom.

Ramsay, J. O. , and Silverman B. W.. 2005. Functional data analysis In Ramsay J. O. and Silverman B. W.eds.], Encyclopedia of statistics in behavioral science, 2nd ed. Springer, New York, New York, USA.

Ranal, M. A. , and de Santana D. G.. 2006. How and why to measure the germination process? Brazilian Journal of Botany 29(1): 1–11.

R Core Development Team . 2019. R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria: Website https://www.R‐project.org/ [accessed 16 May 2020].

Soltani, E. , Ghaderi‐Far F., Baskin C. C., and Baskin J. M.. 2015. Problems with using mean germination time to calculate rate of seed germination. Australian Journal of Botany 63(8): 631–635.

Talská, R. , Menafoglio A., Machalová J., Hron K., and Fišerová E.. 2018. Compositional regression with functional response. Computational Statistics & Data Analysis 123: 66–85.

Weitbrecht, K. , Müller K., and Leubner‐Metzger G.. 2011. First off the mark: Early seed germination. Journal of Experimental Botany 62(10): 3289–3309. PubMed

Yuan, W. , Flowers J., Sahraie D., Ehrenreich I., and Purugganan M.. 2016. Extreme QTL mapping of germination speed in Arabidopsis thaliana . Molecular Ecology 25: 4177–4196. PubMed

Physical Dormancy Release in Medicago truncatula Seeds Is Related to Environmental Variations