A Decision Rule for Testing Seed Viability

1. A Decision Rule for Testing Seed Viability Allan Trapp II, Iowa State University Philip Dixon, Iowa State University Mark Widrlechner, USDA-ARS NCRPIS David Kovach, USDA-ARS NCRPIS

2. Introduction • Viability testing at the NCRPIS has generally been on a fixed schedule (5 to 10-year intervals) • Testing is labor intensive and depletes seeds • Are such close testing intervals needed for all accessions? • Can intervals be customized by seedlot?

3. Purpose of Study • Create a decision rule for seedlot-specific viability testing for maize • Using Bayesian methods, fit a quadratic random coefficients model to the data • Calculate time of critical viability (50%) from t50 posterior distribution • Schedule tests based on the lower 5% quantile of the posterior distribution • Validate the decision rule • Retrospective analysis • New tests

4. Data Description • Analyzed 2,833 NCRPIS maize seedlots (all Ames increases) • All lots had at least 3 viability tests • Time between any two successive tests was typically 5 to 7 years • All seed stored under similar conditions • Viability tests performed on 200 seeds

5. Why Quadratic Model?

6. Traditional Viability Curves vs. Quadratic Curves • Quadratic can fit data well • Captures rates of decline • Accounts for after-ripening • Allows for different initial germination values

7. Plot of Seed Lot Regression Lines

8. Problems with Plots: • Fitting a three-parameter model to no more than seven observations. • Cases exist where you cannot estimate uncertainty (only 3 points) • Convex shape of curves is questionable (purple example) • Predictions may be unreliable • Solution?

9. Problems with Plots: • Fitting a three-parameter model to no more than seven observations. • Cases exist where you cannot estimate uncertainty • Convex shape of curves is questionable (purple example) • Predictions are not reliable • Solution? • Quadratic Random Coefficients Model

10. Quadratic Random Coefficients Model • Calculates the general case (fixed effects curve) based on all data points • Then uses posterior distributions of the BLUP’s and MCMC methods • Creating “shrinkage plots” for individual seedlots • Thus allowing each seedlot “fit” to be adjusted by data from the broader universe of seedlots

11. Fixed Effect Plot (All 2833 Accessions) Germination Seed age (yr.)

12. Shrinkage Plot

13. Calculating t50 (time to decline to 50% viability) • ti,50estimates based on iterate of β posterior distribution • Apply the quadratic equation • ± depends on estimated concavity, apex, and initial germination

14. Distribution of Median ti,50 ti,50calculated by “solving” the quadratic model 2152 lots about 20 to 80 years But 372 lots with ti,50 > 150 years And 1 lot with ti,50 = 0 years

15. Problems with median t50 values • Want a more conservative seed-age estimate of 50% germination • Estimates greater than 150 years impractical • Looking for lower credible bound estimates • Posterior distribution of ti,50 is known • Use a lower quantile of the posterior distribution as a decision rule

16. Comparing Earliest 5% Quantile from the Posterior Distribution to the Raw t50

17. Assessing the 5% Quantile Cut-Offfrom a Frequentist Approach • Analyzed 135 seedlots where the germination fell below 50% on the last viability test • Analyzed 2531 seedlots where the germination was above 50% on the last viability test • Selected 125 seedlots to test in 2009, based on bootstrap t50 values, in five time strata • Examined both false-positive and false-negative rates

18. Results of Assessment • Analyzed 135 seedlots where the germination fell below 50% on the last viability test • On average, predicted year to test was one year before time that <50% test was recorded, but there was a 40% false negative rate • Analyzed 2531 seedlots where the germination was above 50% on the last viability test • Excellent results, 0.3% false positive rate

19. A Second Assessment • Selected 125 seedlots to test in 2009, based on bootstrap t50 values, in five time strata • All but one of the seedlots with new values <50% were predicted by the model • Accurately identified seedlots with high viability levels

20. The Next Steps… • Examining subsets of the large maize dataset (endosperm type, inbred vs. population, etc.) • Examining other species with large datasets • Will look at protocols for initial germination testing that generate the most useful data for future prediction • Can generalize to different viability values (not just 50%) • Testing quantiles other than 5% • Software development