What is meant by “genes at the trunk of the evolutionary tree”?
I think the article is using a phylogenetic tree to explain the stages of how the tumor has evolved.

According to Nature.com >>


  All trees have a shared 'trunk', which represents the complement of
  mutations shared by all malignant cells within the cancer.


Or simplified by Britannica.com >>


  Phylogenetic tree, also called Dendrogram, a diagram showing the
  evolutionary interrelations of a group of organisms derived from a
  common ancestral form. The ancestor is in the tree “trunk”; organisms
  that have arisen from it are placed at the ends of tree “branches.”


For a visual representation, this is a phylogenetic tree for evolution of breast cancer >>



Image Source: Phylogenetic Cancer Trees