Graphs in phylogenetic comparative analysis: Anscombe’s quartet revisited

1. In 1973 the statistician Francis Anscombe used a clever set of bivariate datasets (now known as Anscombe’s quartet) to illustrate the importance of graphing data as a component of statistical analyses. In his example, each of the four datasets yielded identical regression coefficients and model fits, and yet when visualized revealed strikingly different patterns of covariation between x and y. 2. Phylogenetic comparative methods are statistical methods too, yet visualizing the data and phylogeny in a sensible way that would permit us to detect unexpected patterns or unanticipated deviations from model assumptions is not a routine component of phylogenetic comparative analyses. 3. Here, we use a quartet of phylogenetic datasets to illustrate that the same estimated parameters and model fits can be obtained from data that were generated using markedly different procedures – including pure Brownian motion evolution and randomly selected data uncorrelated with the tree. Just as in the ca...