人类群体遗传空间结构的"克立格"模型

通过将“克立格”技术应用于人类群体遗传学领域，构建了人类群体遗传空间结构的“克立格”模型，并论述了其原理和计算方法。以HLA-A基因座为例，应用“克立格”模型，定量分析了中国人群HLA-A基因座的空间遗传异质性；对HLA-A基因频率的空间数据矩阵进行了主成分分析，进而定义了人类群体遗传结构的综合遗传测度(SPC)，绘制了综合遗传测度和主成分(PC)的“克立格”地图，分析了其群体遗传空间结构特性。与其他空间插值或平滑方法相比，人类群体遗传空间结构的“克立格”模型具有明显优点：1)“克立格”估计以空间遗传变异函数模型为基础，在绘制空间遗传结构地图之前，可利用变异函数模型定量分析所研究基因座(或多基因座)的空间遗传异质性；2)“克立格”插值方法是真正意义上的无偏估计模型，它利用待估区域周围的已知群体遗传调查点数据，并充分考虑调查点的空间影响范围，给出待估区域的最优估计值；3)“克立格”模型允许估计插值误差，这种插值误差既可用于评价空间估计效果，又可通过绘制误差地图指导在误差过高的地点增加新的群体遗传调查样本点，以优化估计效果。然而，人类群体遗传空间结构的“克立格”模型也存在一定缺点：1)若不能用任何理论遗传变异函数模型拟合观察遗传变异函数值，则不能建立“克立格”模型；2)若理论遗传变异函数的拟合优度很低，则据此建立的“克立格”模型的估计标准差在整个空间范围内会很大，此时“克立格”模型不适用于估计群体遗传空间结构。出现上述两种情形时，应选用不考虑空间相关性的空间随机插值方法绘制群体遗传结构地图，如基因绘图软件中的Cavalli-Sforza方法，反向距离加权法和条样函数插值法等。

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.