Also, biplots are used occasionally for another kind of genomics data, gene expression data, whether or not the word “biplot” is mentioned. The standard term for a figure showing both is a “biplot.” The contrasting term used here for showing only rows or only columns is a “monoplot.” And our generic term for either a monoplot or a biplot is a “graph.” Biplots were first introduced by Gabriel and have become the norm in countless applications of PCA, including ecology and agriculture. PCA is applicable to a two-way factorial design, that is, a data matrix, and it provides a dual analysis of both the rows and the columns of a matrix. In order to understand contemporary practices and to identify optimal practices, this article explores three topics: two kinds of PCA graphs, three SNP codings, and six PCA variants.įirst, we consider two kinds of PCA graphs. Effective PCA of SNP data is worthwhile because of numerous vital applications that span microbes, plants, animals, and humans. Fortunately, this opportunity comes at a small cost: Changing from one kind of graph to another, or from one SNP coding to another, or from one data transformation to another, as needed in order to optimize PCA analysis, is a simple matter requiring negligible change in procedure, effort, and computation. Greater understanding of the consequences of these three choices opens an opportunity for researchers to make informed and optimal choices, and thereby to gain even more biological insight and practical value from their SNP data. These three choices impact which kinds of structure and patterns in SNP data can be displayed and discovered in PCA graphs.Ĭurrent practices-as documented by a literature survey of 125 representative articles that apply PCA to SNP data-suffice to justify the well-deserved popularity and abundant success of PCA for elucidating population structure ( S1 Table). They are indicated in this article’s title: the kind of graph produced, the way that SNP reads (A, C, G, or T) are coded numerically, and the transformation applied to the data prior to PCA analysis. Rather, three methodological choices are implicated necessarily in each and every PCA analysis and graph of SNP data.

PCA is not a single method that is always done exactly the same way. This article focuses on the one research purpose identified in its title, elucidating population structure-although its discussion and citations make evident the broader relevance of the results and principles presented here. These PCA analyses serve a multitude of research purposes, including increasing biological understanding, accelerating crop breeding, and improving human medicine. Single nucleotide polymorphism (SNP) data is common in the genetics and genomics literature, and principal components analysis (PCA) is one of the statistical analyses applied most frequently to SNP data. The ultimate benefit from informed and optimal choices of PCA graph, SNP coding, and PCA variant, is expected to be discovery of more biology, and thereby acceleration of medical, agricultural, and other vital applications. We also document contemporary practices by a literature survey of 125 representative articles that apply PCA to SNP data, find that virtually none implement our recommendations. Our main three recommendations are simple and easily implemented: Use PCA biplots, SNP coding 1 for the rare allele and 0 for the common allele, and double-centered PCA (or AMMI1 if main effects are also of interest). PCA is not a single method that is always done the same way, but rather requires three choices which we explore as a three-way factorial: two kinds of PCA graphs by three SNP codings by six PCA variants. Accordingly, PCA graphs are frequently used to provide a low-dimensional visualization in order to display and discover patterns in SNP data from humans, animals, plants, and microbes-especially to elucidate population structure. SNP datasets are high-dimensional, often with thousands to millions of SNPs and hundreds to thousands of samples or individuals.

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