Correction to: Tree-Based Unrooted Phylogenetic Networks

1 Correction to: Bull Math Biol (2018) 80:404–416 https://doi.org/10.1007/s11538-017-0381-3

The level-5 example of a network presented in Fig. 4 of Francis et al. (2018) is tree-based even though it states in the caption and in the text that this is not the case. This is because it contains the spanning tree with leaf-set $\{x,y\}$ given by the path $x, a, v_1, v_2, e, f, g, h, b, c, d, y$. The example should be replaced by the network in Fig. 1, which is level-5 and not tree-based. The network in Fig. 1 is not tree-based since any spanning tree with leaf-set $\{x,y\}$ must contain the edges $\{x,a\}$ and $\{d,y\}$ as well as one of the paths $b,h,h^{\prime },c$ or $b,h^{\prime },h,c$ and one of the paths $f,g,g^{\prime },e$ or $f,g^{\prime },g,e$. It follows that the spanning tree then must also contain the edges $\{a,b\}$, $\{c,d\}$, $\{a,f\}$, and $\{e,d\}$, which is impossible. We thank Remie Janssen and Yukihiro Murakami for bringing this issue and replacement example to our attention.

Fig. 1

A level-5 network that is not tree-based

Since drafting this erratum, other authors have independently pointed out the same error and made a more comprehensive corresponding fix (Fischer et al. 2018).