  Unstable dynamics characterizes the evolution of most solid tumors. Because
of an increased failure of maintaining genome integrity, a cumulative increase
in the levels of gene mutation and loss is observed. Previous work suggests
that instability thresholds to cancer progression exist, defining phase
transition phenomena separating tumor-winning scenarios from tumor extinction
or coexistence phases. Here we present an integral equation approach to the
quasispecies dynamics of unstable cancer. The model exhibits two main phases,
characterized by either the success or failure of cancer tissue. Moreover, the
model predicts that tumor failure can be due to either a reduced selective
advantage over healthy cells or excessive instability. We also derive an
approximate, analytical solution that predicts the front speed of aggressive
tumor populations on the instability space.
