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Background  There is a plethora of methods for genome-wide association studies. However, only a few of them may be classified as multi-trait and multi-locus, i.e. consider the influence of multiple genetic variants to several correlated phenotypes.    Results  We propose a multi-trait multi-locus model which employs structural equation modeling (SEM) to describe complex associations between SNPs and traits -  m ulti- t rait  m ulti- l ocus  SEM  (mtmlSEM). The structure of our model makes it possible to discriminate pleiotropic and single-trait SNPs of direct and indirect effect. We also propose an automatic procedure to construct the model using factor analysis and the maximum likelihood method. For estimating a large number of parameters in the model, we performed Bayesian inference and implemented Gibbs sampling. An important feature of the model is that it correctly copes with non-normally distributed variables, such as some traits and variants.    Conclusions  We applied the model to Vavilov’s collection of 404 chickpea ( Cicer arietinum L.)  accessions with 20-fold cross-validation. We analyzed 16 phenotypic traits which we organized into five groups and found around 230 SNPs associated with traits, 60 of which were of pleiotropic effect. The model demonstrated high accuracy in predicting trait values.

Multi-trait multi-locus SEM model discriminates SNPs of different effects