Analysis of genetic marker-phenotype relationships by jack-knifed partial least squares regression (PLSR)

Summary

The utility of a relatively new multivariate method, bi-linear modelling by cross-validated partial least squares regression (PLSR), was investigated in the analysis of QTL. The distinguishing feature of PLSR is to reveal reliable covariance structures in data of different types with regard to the same set objects. Two matrices X (here: genetic markers) and Y (here: phenotypes) are interactively decomposed into latent variables (PLS components, or PCs) in a way which facilitates statistically reliable and graphically interpretable model building. Natural collinearities between input variables are utilized actively to stabilise the modelling, instead of being treated as a statistical problem. The importance of cross-validation/jack-knifing as an intuitively appealing way to avoidoverfitting, is emphasized. Two datasets from chromosomalmapping studies of different complexity were chosen for illustration (QTL for tomato yield and for oat heading date). Results from PLSR analysis were compared to published results and to results using the package PLABQTL in these data sets. Inall cases PLSR gave at least similar explained validation variances as the reported studies. An attractive feature is that PLSR allows the analysis of several traits/replicates in one analysis, and the direct visual identification of individuals with desirable marker genotypes. It is suggested that PLSRmaybe useful in structural and functional genomics and in markerassisted selection, particularly in cases with limited number of objects.