Predicting the Time of 50% Seed Viability in Maize

A Decision Rule for Testing Seed Viability

Allan Trapp II, Iowa State UniversityPhilip Dixon, Iowa State UniversityMark Widrlechner, USDA-ARS NCRPISDavid Kovach, USDA-ARS NCRPISIntroductionViability testing at the NCRPIS has generally been on a fixed schedule (5 to 10-year intervals)Testing is labor intensive and depletes seedsAre such close testing intervals needed for all accessions?Can intervals be customized by seedlot?

Purpose of StudyCreate a decision rule for seedlot-specific viability testing for maizeUsing Bayesian methods, fit a quadratic random coefficients model to the dataCalculate time of critical viability (50%) from t50 posterior distributionSchedule tests based on the lower 5% quantile of the posterior distribution Validate the decision rule Retrospective analysisNew tests

Data DescriptionAnalyzed 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

Testing Events 34567Seed Lots118051991416852Why Quadratic Model?

These are collective data for the four cohorts of seedlots that were produced in a given year and have been tested five times in the same cycle. Seed age (in years) is on the X-axis, and normal germination (as a proportion) is on the Y-axis. Not an expected pattern of viability change for maize. Would be expected to be more appropriate for species that are known to afterripen in storage.These are the four largest cohorts of seedlots that had at least five tests all run in the same years. Age of seeds on X axis and proportion of normal germ on Y axis.Traditional Viability Curves vs. Quadratic CurvesQuadratic can fit data wellCaptures rates of declineAccounts for after-ripeningAllows for different initial germination values

Plot of Seed Lot Regression Lines

Tests of 5 individual seedlots over time you can see some odd things here a projected value >1 (in blue) and an upward curving sample (in purple).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 unreliableSolution?Problems with Plots:Fitting a three-parameter model to no more than seven observations.Cases exist where you cannot estimate uncertaintyConvex shape of curves is questionable (purple example)Predictions are not reliableSolution?Quadratic Random Coefficients ModelQuadratic Random Coefficients ModelCalculates the general case (fixed effects curve) based on all data pointsThen uses posterior distributions of the BLUPs and MCMC methods Creating shrinkage plots for individual seedlotsThus allowing each seedlot fit to be adjusted by data from the broader universe of seedlots

Use Markov Chain Monte Carlo to derive the posterior distributions of the beta vectors of each seed lot. These vectors are equivalent to the BLUPs (Best Linear Unbiased Predictors) of a Frequentist approach.10Fixed Effect Plot (All 2833 Accessions)Seed age (yr.)Germination

germ = 0.92606 + .006156*seed age - .000397*seed age^2.

Shrinkage PlotEach individual seedlot is compared to the fixed-effect plot and is modified in relation to the overall dataset, more so for curves based on only 3 data points, less so for curves based on more values.12Calculating t50 (time to decline to 50% viability)ti,50 estimates based on iterate of posterior distribution

Apply the quadratic equation

depends on estimated concavity, apex, and initial germination

Distribution of Median ti,50ti,50 calculated by solving the quadratic model2152 lots about 20 to 80 years But 372 lots with ti,50 > 150 yearsAnd 1 lot with ti,50 = 0 years

2833 values calculated, 336 as high as infinity, peak is between 30 and 40 yearsProblems with median t50 valuesWant a more conservative seed-age estimate of 50% germinationEstimates greater than 150 years impracticalLooking for lower credible bound estimatesPosterior distribution of ti,50 is knownUse a lower quantile of the posterior distribution as a decision rule

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

Using the lower 5% quantile, we now have only 21 seed lots where the estimated t50 is infinity. Suggests that for most maize seedlots, if one had 0, 5, and 10 year data then one could typically run the fourth test somewhere between years 20 and 40.16Assessing the 5% Quantile Cut-Offfrom a Frequentist ApproachAnalyzed 135 seedlots where the germination fell below 50% on the last viability testAnalyzed 2531 seedlots where the germination was above 50% on the last viability testSelected 125 seedlots to test in 2009, based on bootstrap t50 values, in five time strataExamined both false-positive and false-negative ratesFrom this point forward, our two assessments were based on the Frequentist approach, a computationally less efficient method to generate distibutions of t50s. In this approach, we did not have access to the actual distributions of the t50s, so we used 1000 bootstrapped data sets to estimate t50 distribution.17Results of AssessmentAnalyzed 135 seedlots where the germination fell below 50% on the last viability testOn average, predicted year to test was one year before time that