Guidelines for standardising the application of discriminant analysis of principal components to genotype data

Abstract

Discriminant analysis of principal components (DAPC) has become a popular method for visualising population structure due to its simplicity, computational speed, and freedom from demographic assumptions. Despite the popularity of DAPC, there has been little discussion on best practise. In this work, I provide guidelines for standardising the use of DAPC in studies of population genetic structure. An often-overlooked fact is that DAPC generates a model describing the genetic differences among a set of populations defined by a researcher. I demonstrate that appropriate parameterisation of this model is critical for obtaining biologically meaningful results. I show that the number of leading PC axes used as predictors of among population differences, paxes, should not exceed the k - 1 biologically informative PC axes that are expected for k effective populations in a genotype dataset. This k - 1 criterion for paxes selection is more appropriate compared to the widely used proportional variance criterion, which often results in a choice of paxes >> k - 1. DAPC parameterised with no more than the leading k - 1 PC axes is: (1) more parsimonious; (2) captures maximal among-population variation on biologically relevant predictors; (3) less sensitive to unintended interpretations of population structure; and (4) more generally applicable to independent sample sets. Assessing model fit should be routine practise and can aid interpretation of population structure when implementing DAPC. Additionally, it is imperative that researchers clearly articulate their study goals, that is, testing a priori expectations versus studying de novo inferred populations. Distinguishing between these goals is important because it dictates whether a researchers results can be treated as a test of the hypothesis that significant genetic differences exist among populations. Defining populations a priori (before observing the genotype data) constitutes a true hypothesis test, but populations defined de novo (after observing the genotype data) cannot be used to test this hypothesis due to issues with circularity. The discussion and practical recommendations provided in this work provide the molecular ecology community a roadmap for applying DAPC to their genotype datasets.