The "Kriging" model of spatial genetic structure in human population genetics.

This paper presents the application of Kriging technique in the field of human population genetics for quantifying the spatial genetic heterogeneity of HLA-A locus in the area of China,and for mapping its spatial genetic structure using the measurement of synthetic genetic structure (SPC) and the principal components (PC). Both principles of the method and the basic equations are given. The Kriging model has several advantages over other interpolation and smoothing methods. Firstly, it relies on the structure of the spatial genetic semivariogram model, which can be used to quantify the spatial genetic heterogeneity of the locus (loci) before mapping its spatial genetic structure. Secondly, it is virtually unbiased in the interpolation situation,where the location to be estimated is surrounded by data on all sides and is influenced within the range of these data. Thirdly, it allows of estimative error of interpolation, which can be used to appraise the predicting effect for the spatial estimation,and the error maps can be used to decide where to introduce new sampling population genetic data. However, the "Kriging" model also has some disadvantages. Firstly,when the theoretical spatial genetic semivariogram can not be fitted by any models, the "Kriging" model can not be set up. Secondly, if the Kriging model was built by a poor spatial genetic semivariogram,the Kriging estimation standard deviation is remarkably high in the whole area, hence the Kriging model can not be suitable to estimating the distribution of spatial genetic structure. In these situations,the interpolation algorithm, whose assumption is spatial random rather than spatial autocorrelation,such as the Cavalli-Sforza method in Genography, inverse distance-weighted methods, splines, should be used to estimate or map the distribution of spatial genetic structure.