Quantile function modeling with application to salinity tolerance analysis of plant data

BACKGROUND: In plant science, the study of salinity tolerance is crucial to improving plant growth and productivity under saline conditions. Since quantile regression is a more robust, comprehensive and flexible method of statistical analysis than the commonly used mean regression methods, we applied a set of quantile analysis methods to barley field data. We use univariate and bivariate quantile analysis methods to study the effect of plant traits on yield and salinity tolerance at different quantiles. RESULTS: We evaluate the performance of barley accessions under fresh and saline water using quantile regression with covariates such as flowering time, ear number per plant, and grain number per ear. We identify the traits affecting the accessions with high yields, such as late flowering time has a negative impact on yield. Salinity tolerance indices evaluate plant performance under saline conditions relative to control conditions, so we identify the traits affecting the accessions with high values of indices using quantile regression. It was observed that an increase in ear number per plant and grain number per ear in saline conditions increases the salinity tolerance of plants. In the case of grain number per ear, the rate of increase being higher for plants with high yield than plants with average yield. Bivariate quantile analysis methods were used to link the salinity tolerance index with plant traits, and it was observed that the index remains stable for earlier flowering times but declines as the flowering time decreases. CONCLUSIONS: This analysis has revealed new dimensions of plant responses to salinity that could be relevant to salinity tolerance. Use of univariate quantile analyses for quantifying yield under both conditions facilitates the identification of traits affecting salinity tolerance and is more informative than mean regression. The bivariate quantile analyses allow linking plant traits to salinity tolerance index directly by predicting the joint distribution of yield and it also allows a nonlinear relationship between the yield and plant traits.