Cancer as a moving target: understanding the composition and rebound growth kinetics of recurrent tumors.

We introduce a stochastic branching process model of diversity in recurrent tumors whose growth is driven by drug resistance. Here, an initially declining population can escape certain extinction via the production of mutants whose fitness is drawn at random from a mutational fitness landscape. Using a combination of analytical and computational techniques, we study the rebound growth kinetics and composition of the relapsed tumor. We find that the diversity of relapsed tumors is strongly affected by the shape of the mutational fitness distribution. Interestingly, the model exhibits a qualitative shift in behavior depending on the balance between mutation rate and initial population size. In high mutation settings, recurrence timing is a strong predictor of the diversity of the relapsed tumor, whereas in the low mutation rate regime, recurrence timing is a good predictor of tumor aggressiveness. Analysis reveals that in the high mutation regime, stochasticity in recurrence timing is driven by the random survival of small resistant populations rather than variability in production of resistance from the sensitive population, whereas the opposite is true in the low mutation rate setting. These conclusions contribute to an evolutionary understanding of the suitability of tumor size and time of recurrence as prognostic and predictive factors in cancer.