Fig. 4

Factors that contribute to non-uniqueness. a The number of solutions increased with increasing number n of mutations, but decreased with increasing number m of bulk samples. b Every solution of an PPM instance F is a spanning arborescence in the ancestry graph \(G_F\). The number of spanning arborescences in \(G_F\) also increased with increasing n and decreased with increasing m. c The decrease in the number of solutions and spanning arborescences with increasing m is explained by the branching coefficient of \(\gamma (G_F)\), which is the fraction of distinct pairs of mutations that occur on distinct branches in \(G_F\). The fraction of such pairs increased with increasing m. d The median edge recall of the inferred trees T increased with increasing m