Erratum to: 'Reference-free inference of tumor phylogenies from single-cell sequencing data'.

Unfortunately, the original version of this article [1] contained an error. Figures 2, 4 and 5 were incorrect and the captions for Figs. 4 and 5 were incorrect. Below are the correct figures and captions:

Fig. 2

Histogram of k-mer relative abundances. Both 20- and 25-mer relative abundance densities appear log-laplacian. These data included 20- and 25-mers found in all tumor cells. a Histogram of 20-mer relative abundances in log10 scale. b Histogram of 25-mer relative abundances in log10 scale

Fig. 4

20-mer bootstrap consensus neighbor-joining tree built from T10 primary breast tumor cells (prefix C), T16 primary (prefix P) and metastatic data (prefix M). Distinct groupings of cells are labeled as clusters

Fig. 5

20-mer bootstrap consensus neighbor-joining tree built from T16 primary (prefix P) and metastatic data (prefix M). Distinct groupings of cells are labeled as clusters