Genome-wide association studies and QTL mapping for traits deviating from normal distribution

Quantitative traits are the targets for genome-wide association studies (GWAS) and quantitative trait locus (QTL) mapping. After adjusting for systematic effects, these traits are assumed to be normally distributed so that typical linear models and linear mixed models (LMMs) can be used to detect markers associated with QTLs. Many traits in crops, animals and humans, however, do not follow the assumed normal distribution and many of them are not even continuously distributed. We developed statistical models and software packages to map QTLs and perform association studies for such non-normal traits under the generalized linear mixed model (GLMM) framework. We developed a pseudo response (PSR) method to estimate the polygenic variance by generating a pseudo-response variable that is treated as a conventional quantitative trait. We then scanned the genome for markers associated with the PSR variable in the usual LMM. The new method is called the pseudo response generalized linear mixed model (PSR-GLMM). We illustrated the method with the purple color trait of rice (binary trait) and a set of simulated non-normal traits. We then applied the method to four datasets: a binary trait from an Arabidopsis population, a binomial trait from a pig population, a Poisson trait from the same pig population and an ordinal trait from a dog population. A software package has been developed in R to perform GWAS and QTL mapping for binary, binomial, Poisson, and ordinal traits (PSR-GLMM/R), including normally distributed traits as a special case. The R package can also be applied to perform GLMM analysis for a general purpose beyond QTL mapping and GWAS.