Simon Tavaré introduced Approximate Bayesian Computation (ABC) for simulating posterior distributions where computing the likelihood is intractable. In 2010, Tavaré and Andrea Sottoriva extended ABC to complex models from cancer biology. On the other hand, Hisashi Ohtsuki, Martin Nowak and colleagues have introduced evolutionary graph theory, the study of evolutionary dynamics on graphs, and have proved results about time to fixation (i.e., for one subpopulation to take over the graph) in several settings. We will recapitulate these results and also characterize the nontrivial spatial distributions that arise and are observed during clinical timescales. We will use measures of spatial/spatiotemporal statistics of point processes arising from a variety of fields as summary statistics for ABC, to see if we can use them to distinguish regimes of interest in the parameter space corresponding to different hypotheses (e.g., cooperation, competition, and neutral coexistence of different subpopulations occupying the graph). We will apply the resulting new statistical tests to images of heterogeneous tumors, informing the course of therapy. Time permitting, we will touch on the connection with our work on the theory of graphical games. This research is in progress.