Fig. 4

Effect of fossil sample size on model support and parameter estimates. Random subsampling of the fossil data shows that model support (Akaike weight) for EB becomes overwhelming with just 7 sampled fossils (extinct taxa), but the relative support of other models only stabilizes at some point between 40 and 47 sampled fossils (left side). In contrast, the model parameter estimates (right side) do not seem to approach an asymptote as more fossils are added, except the adaptive optimum (θ₁) of the OU model and, to a lesser extent, the rate of exponential decay (β) of the EB model. Note that we introduced a small horizontal displacement in the points in order to visually separate the various model series; the analyses were performed with the fossil sample sizes labelled on the horizontal scale, with no intermediate values. Also, the Brownian diffusion rate (σ²) is shown log-transformed in order to better accommodate the large range of values. The lines connect the medians between sample size categories; θ₀ is the reconstructed number of branchiostegals at the root of the tree. The white noise is not shown here because it is strongly rejected by our results (see Table 1)