Hostname: page-component-7857688df4-7f72j Total loading time: 0 Render date: 2025-11-19T07:54:22.467Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  07 February 2012

James N. McNair ,
Anusha Sunkara  and
Daniel Frobish
James N. McNair*
Affiliation:
Annis Water Resources Institute, Grand Valley State University, 740 West Shoreline Drive, Muskegon, Michigan 49441, USA
Anusha Sunkara
Affiliation:
Department of Statistics, Grand Valley State University, Allendale, Michigan 49401, USA
Daniel Frobish
Affiliation:
Department of Statistics, Grand Valley State University, Allendale, Michigan 49401, USA
*
*Correspondence Fax: 00-1-616-331-3864 Email: mcnairja@gvsu.edu
Get access Rights & Permissions [Opens in a new window]

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.

Keywords

failure-time analysisfrailtyKaplan–Meier estimatorlife-table estimatorlog-rank testreliability analysissurvival analysis

Information

Type
Review Papers
Information
Seed Science Research , Volume 22 , Issue 2 , June 2012 , pp. 77 - 95
Copyright
Copyright © Cambridge University Press 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Andersen, P.K., Borgan, Ø., Gill, R.D. and Keiding, N. (1993) Statistical models based on counting processes. New York, Springer-Verlag.CrossRefGoogle Scholar
Baskin, C.C. and Baskin, J.M. (2001) Seeds: Ecology, biogeography, and evolution of dormancy and germination. New York, Academic Press.Google Scholar
Baskin, J.M. and Baskin, C.C. (1983) Germination ecology of Veronica arvensis. Journal of Ecology 71, 57–68.CrossRefGoogle Scholar
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.Google Scholar
Böhmer, P.E. (1912) Theorie der unabhängigen Wahrscheinlichkeiten. pp. 327–343 in Reports, Memoirs, and Proceedings of the Seventh International Congress of Actuaries, September 1912, Amsterdam, vol. 2.Google Scholar
Bonner, F.T. and Dell, T.R. (1976) The Weibull function: a new method of comparing seed vigor. Journal of Seed Technology 1, 96–103.Google Scholar
Bram, M.R. and McNair, J.N. (2004) Seed germinability and its seasonal onset in three populations of Japanese knotweed. Weed Science 52, 759–767.CrossRefGoogle Scholar
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, 581–591.CrossRefGoogle Scholar
Brown, R.F. and Mayer, D.G. (1988a) Representing cumulative germination. 1. A critical analysis of single-value germination indices. Annals of Botany 61, 117–125.CrossRefGoogle Scholar
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, 127–138.CrossRefGoogle Scholar
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, 156–158.CrossRefGoogle Scholar
Cox, D.R. and Oakes, D. (1984) Analysis of survival data. New York, Chapman and Hall.Google Scholar
Czabator, F.J. (1962) Germination value: an index combining speed and completeness of pine seed germination. Forest Science 8, 386–396.Google Scholar
Draper, N.R. and Smith, H. (1998) Applied regression analysis (3rd edition). New York, John Wiley and Sons.CrossRefGoogle Scholar
Elandt-Johnson, R.C. and Johnson, N.L. (1980) Survival models and data analysis. New York, John Wiley and Sons.Google Scholar
Farmer, R.R. (1997) Seed ecophysiology of temperate and boreal zone forest trees. Delray Beach, Florida, St. Lucie Press.Google Scholar
Fox, G.A. (1990) Perennation and the persistence of annual life histories. American Naturalist 135, 829–840.CrossRefGoogle Scholar
Fox, G.A. (2001) Failure-time analysis. pp. 235–266 in Scheiner, S.M.; Gurevich, J. (Eds) Design and analysis of ecological experiments (2nd edition). New York, Oxford University Press.CrossRefGoogle Scholar
Goodchild, N.A. and Walker, M.G. (1971) A method of measuring seed germination in physiological studies. Annals of Botany 35, 615–621.CrossRefGoogle Scholar
Gunjača, J. and Šarčević, H. (2000) Survival analysis of the wheat germination data. pp. 307–310 in 22nd International Conference on Information Technology Interfaces ITI 2000, June 2000, Pula, Croatia.Google Scholar
ISTA (International Seed Testing Association) (1985) International rules for seed testing. Seed Science and Technology 13, 307–513.Google Scholar
Janssen, J.G.M. (1973) A method of recording germination curves. Annals of Botany 37, 705–708.CrossRefGoogle Scholar
Kaplan, E.L. and Meier, P. (1958) Nonparametric estimation from incomplete observations. Journal of the American Statistical Association 53, 457–481.CrossRefGoogle Scholar
Klein, J.P. and Moeschberger, M.L. (2003) Survival analysis: techniques for censored and truncated data (2nd edition). New York, Springer-Verlag.CrossRefGoogle Scholar
Kutner, M.H., Nachtsheim, C.J., Neter, J. and Li, W. (2004) Applied linear statistical models. New York, McGraw-Hill.Google Scholar
Lawless, J.F. (2003) Statistical models and methods for lifetime data. New York, John Wiley and Sons.Google Scholar
Lee, E.T. and Wang, J.W. (2003) Statistical methods for survival analysis (3rd edition). New York, John Wiley and Sons.CrossRefGoogle Scholar
Maguire, J.D. (1962) Speed of germination – aid in selection and evaluation for seedling emergence and vigor. Crop Science 2, 176–177.CrossRefGoogle Scholar
Maller, R.A. and Zhou, X. (1996) Survival analysis with long-term survivors. New York, John Wiley and Sons.Google Scholar
Montgomery, D.C., Peck, E.A. and Vining, G.G. (2001) Introduction to linear regression analysis (3rd edition). New York, John Wiley and Sons.Google Scholar
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, 187–198.CrossRefGoogle Scholar
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).Google Scholar
Ranal, M.A. and Santana, D.G. (2006) How and why to measure the germination process. Revista Brasileira de Botânica 29, 1–11.Google Scholar
Ryan, T.P. (1997) Modern regression methods. New York, John Wiley and Sons.Google Scholar
SAS Institute Inc. (2004) SAS OnlineDoc® 9.1.3. Cary, North Carolina, SAS Institute Inc.Google Scholar
Scott, S.J. and Jones, R.A. (1982) Low temperature seed germination of Lycopersicon species evaluated by survival analysis. Euphytica 31, 869–883.CrossRefGoogle Scholar
Scott, S.J., Jones, R.A. and Williams, W.A. (1984) Review of data analysis for seed germination. Crop Science 24, 1192–1199.CrossRefGoogle Scholar
Therneau, T.M. and Grambsch, P.M. (2000) Modeling survival data: extending the Cox model. New York, Springer-Verlag.CrossRefGoogle Scholar
Timson, J. (1965) A new method of recording germination data. Nature 207, 216–217.CrossRefGoogle Scholar
Tipton, J.L. (1984) Evauation of three growth curve models for germination data analysis. Journal of the American Society of Horticultural Science 109, 451–454.Google Scholar
Supplementary material: PDF

McNair et al. supplementary material

Supplementary data

Download McNair et al. supplementary material(PDF)
PDF 307.4 KB