Skip to main content
Log in

Scheduling Viability Tests for Seeds in Long-Term Storage Based on a Bayesian Multi-Level Model

  • Published:
Journal of Agricultural, Biological, and Environmental Statistics Aims and scope Submit manuscript


Genebank managers conduct viability tests on stored seeds so they can replace lots that have viability near a critical threshold, such as 50 or 85 % germination. Currently, these tests are typically scheduled at uniform intervals; testing every 5 years is common. A manager needs to balance the cost of an additional test against the possibility of losing a seed lot due to late retesting. We developed a data-informed method to schedule viability tests for a collection of 2,833 maize seed lots with 3 to 7 completed viability tests per lot. Given these historical data reporting on seed viability at arbitrary times, we fit a hierarchical Bayesian seed-viability model with random seed lot specific coefficients. The posterior distribution of the predicted time to cross below a critical threshold was estimated for each seed lot. We recommend a predicted quantile as a retest time, chosen to balance the importance of catching quickly decaying lots against the cost of premature tests. The method can be used with any seed-viability model; we focused on two, the Avrami viability curve and a quadratic curve that accounts for seed after-ripening. After fitting both models, we found that the quadratic curve gave more plausible predictions than did the Avrami curve. Also, a receiver operating characteristic (ROC) curve analysis and a follow-up test demonstrated that a 0.05 quantile yields reasonable predictions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others


  • Berkson, J. (1953), “A Statistically Precise and Relatively Simple Method of Estimating the Bioassay with Quantal Response, Based on the Logistic Function,” Journal of the American Statistical Association, 48, 565–599.

    MATH  Google Scholar 

  • Bewley, J. D. (1997), “Seed Germination and Dormancy,” Plant Cell, 9, 1055–1066.

    Article  Google Scholar 

  • Chantre, G. R., Batlla, D., Sabbatini, M. R., and Orioli, G. (2009), “Germination Parameterization and Development of an After-Ripening Thermal-Time Model for Primary Dormancy Release of Lithospermum arvense Seeds,” Annals of Botany, 103, 1291–1301.

    Article  Google Scholar 

  • Ellis, R. H., and Roberts, E. H. (1980), “Improved Equations for the Prediction of Seed Longevity,” Annals of Botany, 45, 13–30.

    Google Scholar 

  • Finch-Savage, W. E., and Leubner-Metzger, G. (2006), “Seed Dormancy and the Control of Germination,” New Phytologist, 171, 501–523.

    Article  Google Scholar 

  • Gelman, A. (2006), “Prior Distributions for Variance Parameters in Hierarchical Models,” Bayesian Analysis, 1, 514–534.

    Google Scholar 

  • Gelman, A., and Hill, J. (2007), Data Analysis Using Regression and Multilevel/Hierarchical Models, New York: Cambridge University Press.

    Google Scholar 

  • Gelman, A., Carlin, J. B., Stern, H. S., and Rubin, D. B. (2004), Bayesian Data Analysis (2nd ed.), Boca Raton, FL: Chapman and Hall/CRC Press.

    MATH  Google Scholar 

  • Harrell, F. E. Jr. (2001), Regression Modeling Strategies With Applications to Linear Models, Logistic Regression, and Survival Analysis, New York: Springer.

    MATH  Google Scholar 

  • Hay, F. R., Mead A., Manger, K., and Wilson, F.J. (2003) “One-Step Analysis of Seed Storage Data and the Longevity of Arabidopsis thaliana Seeds,” Journal of Experimental Botany, 54, 993–1011.

    Article  Google Scholar 

  • Holdsworth, M. J., Bentsink, L., and Soppe, W. J. J. (2008), “Molecular Networks Regulating Arabidopsis Seed Maturation, After-Ripening, Dormancy and Germination,” New Phytologist, 179, 33–54.

    Article  Google Scholar 

  • ISTA (2009), International Rules for Seed Testing, Bassersdorf: International Seed Testing Association.

    Google Scholar 

  • Krzanowski, W. J., and Hand, D. J. (2009), ROC Curves for Continuous Data, Boca Raton, FL: Chapman and Hall/CRC Press.

    Book  MATH  Google Scholar 

  • Laird, N. M., and Ware, J. H. (1982), “Random-Effects Models for Longitudinal Data,” Biometrics, 38, 963–974.

    Article  MATH  Google Scholar 

  • Leubner-Metzger, G. (2003), “Functions and Regulation of β-1, 3-Glucanases During Seed Germination, Dormancy Release and After-Ripening,” Seed Science Research, 13, 17–34.

    Article  Google Scholar 

  • Lunn, D. J., Thomas, A., Best, N., and Spiegelhalter, D. (2000), “WinBUGS—A Bayesian Modelling Framework: Concepts, Structure, and Extensibility,” Statistics and Computing, 10, 325–337.

    Article  Google Scholar 

  • Mead, A., and Gray, D. (1999), “Prediction of Seed Longevity: A Modification of the Shape of the Ellis and Roberts Seed Survival Curves,” Seed Science Research, 9, 63–73.

    Google Scholar 

  • Nagel, M., and Börner, A. (2010), “The Longevity of Crop Seeds Stored Under Ambient Conditions,” Seed Science Research, 20, 1–12.

    Article  Google Scholar 

  • Sharrock, S., Anishetty, N. M., and Fowler, C. (1998), “Discussion Paper on the Global Regeneration Need: Evidence Collected from Country Reports Prepared for the International Technical Conference on Plant Genetic Resources,” in Regeneration of Seed Crops and Their Wild Relatives, eds. J. Engels and R. R. Rao, Rome: International Plant Genetic Resources Institute, pp. 86–104.

    Google Scholar 

  • Silverman, B. W. (1986), Density Estimation for Statistics and Data Analysis, London: Chapman and Hall.

    MATH  Google Scholar 

  • Singer, J. D., and Willett, J. B. (2003), Applied Longitudinal Data Analysis, New York: Oxford University Press.

    Book  Google Scholar 

  • Sivakumar, V., Anandalakshmi, R., Warrier, R. R., Tigabu, M., Odén, P. C., Vijayachandran, S. N., Geetha, S., and Singh, B. G. (2006), “Effects of Presowing Treatments, Desiccation and Storage Conditions on Germination of Strychnos nux-vomica Seeds, a Valuable Medicinal Plant,” New Forests, 32, 121–131.

    Article  Google Scholar 

  • Steadman, K. J., Crawford, A. D., and Gallagher, R. S. (2003), “Dormancy Release in Lolium rigidum Seeds is a Function of Thermal After-Ripening Time and Seed Water Content,” Functional Plant Biology, 30, 345–352.

    Article  Google Scholar 

  • Tang, S., TeKrony, D. M., Egli, D. B., and Cornelius, P. L. (2000), An Alternative Model to Predict Corn Seed Deterioration During Storage,” Crop Science, 40, 463–470.

    Article  Google Scholar 

  • USDA-ARS (2010a), “Germplasm Enhancement of Maize,” available online at:. (last accessed: October 20, 2010).

  • — (2010b), “USDA-ARS Station Facts and Purpose for Ames Plant Introduction Station,” available online at: (last accessed: October 20, 2010).

  • Walters, C., Wheeler, L. M., and Grotenhuis, J. M. (2005), “Longevity of Seeds Stored in a Genebank: Species Characteristics,” Seed Science Research, 15, 1–20.

    Article  Google Scholar 

  • Wang, R., Bai, Y., and Tanino, K. (2004), “Effect of Seed Size and Sub-zero Imbibition-Temperature on the Thermal Time Model of Winterfat (Eurotia lanata (Pursh.) Moq.),” Environmental and Experimental Botany, 51, 183–197.

    Article  Google Scholar 

  • Widrlechner, M. P. (2007), “While They Were Asleep: Do Seeds After-Ripen in Cold Storage? Experiences with Calendula,” Combined Proceedings International Plant Propagators’ Society, 56, 377–382.

    Google Scholar 

  • Williams, R. J., Hirsh, A. G., Meryman, H. T., and Takahashi, T. A. (1993), “The High-Order Kinetics of Cytolysis in Stressed Red-Cells,” Journal of Thermal Analysis, 40, 857–862.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Allan Trapp II.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Trapp, A., Dixon, P., Widrlechner, M.P. et al. Scheduling Viability Tests for Seeds in Long-Term Storage Based on a Bayesian Multi-Level Model. JABES 17, 192–208 (2012).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

Key Words