Skip to main content
×
×
Home

How to analyse seed germination data using statistical time-to-event analysis: non-parametric and semi-parametric methods

  • James N. McNair (a1), Anusha Sunkara (a2) and Daniel Frobish (a2)
Abstract

Seed germination experiments are conducted in a wide variety of biological disciplines. Numerous methods of analysing the resulting data have been proposed, most of which fall into three classes: intuition-based germination indexes, classical non-linear regression analysis and time-to-event analysis (also known as survival analysis, failure-time analysis and reliability analysis). This paper briefly reviews all three of these classes, and argues that time-to-event analysis has important advantages over the other methods but has been underutilized to date. It also reviews in detail the types of time-to-event analysis that are most useful in analysing seed germination data with standard statistical software. These include non-parametric methods (life-table and Kaplan–Meier estimators, and various methods for comparing two or more groups of seeds) and semi-parametric methods (Cox proportional hazards model, which permits inclusion of categorical and quantitative covariates, and fixed and random effects). Each method is illustrated by applying it to a set of real germination data. Sample code for conducting these analyses with two standard statistical programs is also provided in the supplementary material available online (at http://journals.cambridge.org/). The methods of time-to-event analysis reviewed here can be applied to many other types of biological data, such as seedling emergence times, flowering times, development times for eggs or embryos, and organism lifetimes.

Copyright
Corresponding author
*Correspondence Fax: 00-1-616-331-3864 Email: mcnairja@gvsu.edu
References
Hide All
Andersen, P.K., Borgan, Ø., Gill, R.D. and Keiding, N. (1993) Statistical models based on counting processes. New York, Springer-Verlag.
Baskin, C.C. and Baskin, J.M. (2001) Seeds: Ecology, biogeography, and evolution of dormancy and germination. New York, Academic Press.
Baskin, J.M. and Baskin, C.C. (1983) Germination ecology of Veronica arvensis. Journal of Ecology 71, 5768.
Belsley, D.A., Kuh, E. and Welsch, R.E. (2004) Regression diagnostics: Indentifying influential data and sources of collinearity. New York, John Wiley and Sons.
Böhmer, P.E. (1912) Theorie der unabhängigen Wahrscheinlichkeiten. pp. 327343 in Reports, Memoirs, and Proceedings of the Seventh International Congress of Actuaries, September 1912, Amsterdam, vol. 2.
Bonner, F.T. and Dell, T.R. (1976) The Weibull function: a new method of comparing seed vigor. Journal of Seed Technology 1, 96103.
Bram, M.R. and McNair, J.N. (2004) Seed germinability and its seasonal onset in three populations of Japanese knotweed. Weed Science 52, 759767.
Brown, R.F. (1987) Germination of Aristida armata under constant and alternating temperatures and its analysis with the cumulative Weibull distribution as a model. Australian Journal of Botany 35, 581591.
Brown, R.F. and Mayer, D.G. (1988a) Representing cumulative germination. 1. A critical analysis of single-value germination indices. Annals of Botany 61, 117125.
Brown, R.F. and Mayer, D.G. (1988b) Representing cumulative germination. 1. The use of Weibull and other empirically derived curves. Annals of Botany 61, 127138.
Carneiro, J.W.P. (1994) Determinação do número de sementes para avaliar o desempenho germinativo de sementes de capim braquiária (Brachiaria brizantha cv. Marandú). Revista Brasileira de Sementes 16, 156158.
Cox, D.R. and Oakes, D. (1984) Analysis of survival data. New York, Chapman and Hall.
Czabator, F.J. (1962) Germination value: an index combining speed and completeness of pine seed germination. Forest Science 8, 386396.
Draper, N.R. and Smith, H. (1998) Applied regression analysis (3rd edition). New York, John Wiley and Sons.
Elandt-Johnson, R.C. and Johnson, N.L. (1980) Survival models and data analysis. New York, John Wiley and Sons.
Farmer, R.R. (1997) Seed ecophysiology of temperate and boreal zone forest trees. Delray Beach, Florida, St. Lucie Press.
Fox, G.A. (1990) Perennation and the persistence of annual life histories. American Naturalist 135, 829840.
Fox, G.A. (2001) Failure-time analysis. pp. 235266 in Scheiner, S.M.; Gurevich, J. (Eds) Design and analysis of ecological experiments (2nd edition). New York, Oxford University Press.
Goodchild, N.A. and Walker, M.G. (1971) A method of measuring seed germination in physiological studies. Annals of Botany 35, 615621.
Gunjača, J. and Šarčević, H. (2000) Survival analysis of the wheat germination data. pp. 307310 in 22nd International Conference on Information Technology Interfaces ITI 2000, June 2000, Pula, Croatia.
ISTA (International Seed Testing Association) (1985) International rules for seed testing. Seed Science and Technology 13, 307513.
Janssen, J.G.M. (1973) A method of recording germination curves. Annals of Botany 37, 705708.
Kaplan, E.L. and Meier, P. (1958) Nonparametric estimation from incomplete observations. Journal of the American Statistical Association 53, 457481.
Klein, J.P. and Moeschberger, M.L. (2003) Survival analysis: techniques for censored and truncated data (2nd edition). New York, Springer-Verlag.
Kutner, M.H., Nachtsheim, C.J., Neter, J. and Li, W. (2004) Applied linear statistical models. New York, McGraw-Hill.
Lawless, J.F. (2003) Statistical models and methods for lifetime data. New York, John Wiley and Sons.
Lee, E.T. and Wang, J.W. (2003) Statistical methods for survival analysis (3rd edition). New York, John Wiley and Sons.
Maguire, J.D. (1962) Speed of germination – aid in selection and evaluation for seedling emergence and vigor. Crop Science 2, 176177.
Maller, R.A. and Zhou, X. (1996) Survival analysis with long-term survivors. New York, John Wiley and Sons.
Montgomery, D.C., Peck, E.A. and Vining, G.G. (2001) Introduction to linear regression analysis (3rd edition). New York, John Wiley and Sons.
Onofri, A., Gresta, F. and Tei, F. (2010) A new method for the analysis of germination and emergence data of weed species. Weed Research 50, 187198.
R Development Core Team (2009) R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. Available at http://www.R-project.org (accessed 30 December 2011).
Ranal, M.A. and Santana, D.G. (2006) How and why to measure the germination process. Revista Brasileira de Botânica 29, 111.
Ryan, T.P. (1997) Modern regression methods. New York, John Wiley and Sons.
SAS Institute Inc. (2004) SAS OnlineDoc® 9.1.3. Cary, North Carolina, SAS Institute Inc.
Scott, S.J. and Jones, R.A. (1982) Low temperature seed germination of Lycopersicon species evaluated by survival analysis. Euphytica 31, 869883.
Scott, S.J., Jones, R.A. and Williams, W.A. (1984) Review of data analysis for seed germination. Crop Science 24, 11921199.
Therneau, T.M. and Grambsch, P.M. (2000) Modeling survival data: extending the Cox model. New York, Springer-Verlag.
Timson, J. (1965) A new method of recording germination data. Nature 207, 216217.
Tipton, J.L. (1984) Evauation of three growth curve models for germination data analysis. Journal of the American Society of Horticultural Science 109, 451454.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Seed Science Research
  • ISSN: 0960-2585
  • EISSN: 1475-2735
  • URL: /core/journals/seed-science-research
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Keywords

Type Description Title
PDF
Supplementary materials

McNair et al. supplementary material
Supplementary data

 PDF (307 KB)
307 KB

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed