Modeling Stalk and Root Lodging as a Heterogeneous Zero-Inflated Process.

Zero-inflated data (ZID) arise when observations are generated from a mixture of some known statistical distribution and a null distribution. In biological data, this occurs when conditions needed for the expression of a phenotype are not met for all observations. Stalk and Root lodging (RL and SL) are two important factors in the commercial viability of maize hybrids and are typically measured as counts of the number of lodged plants in a given plot. The phenotypic distributions of these traits show a high proportion of zeros, suggesting the traits may follow a heterogeneous zero-inflated Poisson distribution (ZIP). To test this theory, a heterogeneous Bayesian ZIP model was applied to several SL and RL datasets. The 95% high density posterior intervals showed significant and heterogeneous mixing proportions of the null and Poisson distributions, indicating SL and RL do follow a heterogeneous zero-inflated process. To evaluate the impact of modeling assumptions on the predictions of genetic merit when data are distributed as ZIP, a simulation study was conducted. Data were simulated using both Poisson (D1) and ZIP (D2) distributions, and analyzed using models assuming Poisson (M1) and ZIP (M2) distributions. For D1 there was no difference in the predictive accuracy of M1 and M2; however, M2 showed significantly more accurate predictions of genetic merit for D2, suggesting zero-inflated models may improve accuracy of SL and RL analysis.