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Title: Scheduling viability tests for seeds in long-term storage based on a Bayesian Multi-Level Model

item TRAPP II, ALLAN - Iowa State University
item DIXON, PHILIP - Iowa State University
item Widrlechner, Mark
item Kovach, David

Submitted to: Journal of Agricultural, Biological, and Environmental Statistics
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 1/21/2012
Publication Date: 4/3/2012
Citation: Trapp II, A., Dixon, P., Widrlechner, M.P., Kovach, D.A. 2012. Scheduling viability tests for seeds in long-term storage based on a Bayesian Multi-Level Model. Journal of Agricultural, Biological, and Environmental Statistics. 17(2):192-208. Available online at

Interpretive Summary: How frequently should seed samples held in long-term storage be tested? Ideally, it would be frequently enough to detect when seed germination is about to drop below a critical threshold, but not so often that it quickly depletes the seeds or incurs unnecessary testing costs. We developed a statistical method to predict when the germinability of corn samples will reach a pre-specified, critical threshold. It uses historical test data (germination percentage at known seed ages) for many related samples with 3 or more germination observations per sample. It produces a predicted distribution of seed age when a sample will reach a critical threshold. The recommended time to next test is based on a quantile of the predicted distribution, chosen to balance testing costs against the cost of possible sample loss. The method was developed and tested by using data on 2833 corn samples that have been stored at the USDA-ARS North Central Regional Plant Introduction Station in Ames, Iowa. We also assessed model performance by comparing its predictions to newly generated germination data. Our method assumes that seed deterioration follows a quadratic curve with random coefficients, but it can be easily adapted to other seed deterioration curves and other crops with historical germination data. The choice of a quantile for predictions is based on a Receiver-Operating-Characteristic curve, a method widely used for signal detection in engineering and medical research. Our model should be valuable for seed conservation at genebanks and can increase the overall efficiency of germination testing.

Technical Abstract: 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.