Non-linear transformation of enzyme-linked immunosorbent assay (ELISA) measurements allows usage of linear models for data analysis.

BACKGROUND: In research questions such as in resistance breeding against the Beet necrotic yellow vein virus it is of interest to compare the virus concentrations of samples from different groups. The enzyme-linked immunosorbent assay (ELISA) counts as the standard tool to measure virus concentrations. Simple methods for data analysis such as analysis of variance (ANOVA), however, are impaired due to non-normality of the resulting optical density (OD) values as well as unequal variances in different groups. METHODS: To understand the relationship between the OD values from an ELISA test and the virus concentration per sample, we used a large serial dilution and modelled its non-linear form using a five parameter logistic regression model. Furthermore, we examined if the quality of the model can be increased if one or several of the model parameters are defined beforehand. Subsequently, we used the inverse of the best model to estimate the virus concentration for every measured OD value. RESULTS: We show that the transformed data are essentially normally distributed but provide unequal variances per group. Thus, we propose a generalised least squares model which allows for unequal variances of the groups to analyse the transformed data. CONCLUSIONS: ANOVA requires normally distributed data as well as equal variances. Both requirements are not met with raw OD values from an ELISA test. A transformation with an inverse logistic function, however, gives the possibility to use linear models for data analysis of virus concentrations. We conclude that this method can be applied in every trial where virus concentrations of samples from different groups are to be compared via OD values from an ELISA test. To encourage researchers to use this method in their studies, we provide an R script for data transformation as well as the data from our trial.

Prediction of Maize Phenotypic Traits With Genomic and Environmental Predictors Using Gradient Boosting Frameworks.

The development of crop varieties with stable performance in future environmental conditions represents a critical challenge in the context of climate change. Environmental data collected at the field level, such as soil and climatic information, can be relevant to improve predictive ability in genomic prediction models by describing more precisely genotype-by-environment interactions, which represent a key component of the phenotypic response for complex crop agronomic traits. Modern predictive modeling approaches can efficiently handle various data types and are able to capture complex nonlinear relationships in large datasets. In particular, machine learning techniques have gained substantial interest in recent years. Here we examined the predictive ability of machine learning-based models for two phenotypic traits in maize using data collected by the Maize Genomes to Fields (G2F) Initiative. The data we analyzed consisted of multi-environment trials (METs) dispersed across the United States and Canada from 2014 to 2017. An assortment of soil- and weather-related variables was derived and used in prediction models alongside genotypic data. Linear random effects models were compared to a linear regularized regression method (elastic net) and to two nonlinear gradient boosting methods based on decision tree algorithms (XGBoost, LightGBM). These models were evaluated under four prediction problems: (1) tested and new genotypes in a new year; (2) only unobserved genotypes in a new year; (3) tested and new genotypes in a new site; (4) only unobserved genotypes in a new site. Accuracy in forecasting grain yield performance of new genotypes in a new year was improved by up to 20% over the baseline model by including environmental predictors with gradient boosting methods. For plant height, an enhancement of predictive ability could neither be observed by using machine learning-based methods nor by using detailed environmental information. An investigation of key environmental factors using gradient boosting frameworks also revealed that temperature at flowering stage, frequency and amount of water received during the vegetative and grain filling stage, and soil organic matter content appeared as important predictors for grain yield in our panel of environments.

Genome-wide prediction methods for detecting genetic effects of donor chromosome segments in introgression populations.

BACKGROUND: Introgression populations are used to make the genetic variation of unadapted germplasm or wild relatives of crops available for plant breeding. They consist of introgression lines that carry small chromosome segments from an exotic donor in the genetic background of an elite line. The goal of our study was to investigate the detection of favorable donor chromosome segments in introgression lines with statistical methods developed for genome-wide prediction. RESULTS: Computer simulations showed that genome-wide prediction employing heteroscedastic marker variances had a greater power and a lower false positive rate compared with homoscedastic marker variances when the phenotypic difference between the donor and recipient lines was controlled by few genes. The simulations helped to interpret the analyses of glycosinolate and linolenic acid content in a rapeseed introgression population and plant height in a rye introgression population. These analyses support the superiority of genome-wide prediction approaches that use heteroscedastic marker variances. CONCLUSIONS: We conclude that genome-wide prediction methods in combination with permutation tests can be employed for analysis of introgression populations. They are particularly useful when introgression lines carry several donor segments or when the donor segments of different introgression lines are overlapping.

Identification of quantitative trait loci in rye introgression lines carrying multiple donor chromosome segments.

Introgression libraries can be used to make favorable genetic variation of exotic donor genotypes available in the genetic background of elite breeding material. Our objective was to employ a combination of the Dunnett test and a linear model analysis to identify favorable donor alleles in introgression lines (ILs) that carry long or multiple donor chromosome segments (DCS). We reanalyzed a dataset of two rye introgression libraries that consisted of ILs carrying on average about four donor segments. After identifying ILs that had a significantly better per se or testcross performance than the recipient line with the Dunnett test, the linear model analysis was in most instances able to clearly identify the donor regions that were responsible for the superior performance. The precise localization of the favorable DCS allowed a detailed analysis of pleiotropic effects and the study of the consistency of effects for per se and testcross performance. We conclude that in many cases the linear model analysis allows the assignment of donor effects to individual DCS even for ILs with long or multiple donor segments. This may considerably increase the efficiency of producing sub-ILs, because only such segments need to be isolated that are known to have a significant effect on the phenotype.

Distinct genetic architectures for male and female inflorescence traits of maize.

We compared the genetic architecture of thirteen maize morphological traits in a large population of recombinant inbred lines. Four traits from the male inflorescence (tassel) and three traits from the female inflorescence (ear) were measured and studied using linkage and genome-wide association analyses and compared to three flowering and three leaf traits previously studied in the same population. Inflorescence loci have larger effects than flowering and leaf loci, and ear effects are larger than tassel effects. Ear trait models also have lower predictive ability than tassel, flowering, or leaf trait models. Pleiotropic loci were identified that control elongation of ear and tassel, consistent with their common developmental origin. For these pleiotropic loci, the ear effects are larger than tassel effects even though the same causal polymorphisms are likely involved. This implies that the observed differences in genetic architecture are not due to distinct features of the underlying polymorphisms. Our results support the hypothesis that genetic architecture is a function of trait stability over evolutionary time, since the traits that changed most during the relatively recent domestication of maize have the largest effects.