Natural selection among tumor cell clones is thought to produce hallmark properties of malignancy. Efforts to understand evolution of one such hallmark—the angiogenic switch—has suggested that selection for angiogenesis can “run away” and generate a hypertumor, a form of evolutionary suicide by extreme vascular hypo- or hyperplasia. This phenomenon is predicted by models of tumor angiogenesis studied with the techniques of adaptive dynamics. These techniques also predict that selection drives tumor proliferative potential towards an evolutionarily stable strategy (ESS) that is also convergence-stable. However, adaptive dynamics are predicated on two key assumptions: (i) no more than two distinct clones or evolutionary strategies can exist in the tumor at any given time; and (ii) mutations cause small phenotypic changes. Here we show, using a stochastic simulation, that relaxation of these assumptions has no effect on the predictions of adaptive dynamics in this case. In particular, selection drives proliferative potential towards, and angiogenic potential away from, their respective ESSs. However, these simulations also show that tumor behavior is highly contingent on mutational history, particularly for angiogenesis. Individual tumors frequently grow to lethal size before the evolutionary endpoint is approached. In fact, most tumor dynamics are predicted to be in the evolutionarily transient regime throughout their natural history, so that clinically, the ESS is often largely irrelevant. In addition, we show that clonal diversity as measured by the Shannon Information Index correlates with the speed of approach to the evolutionary endpoint. This observation dovetails with results showing that clonal diversity in Barrett's esophagus predicts progression to malignancy.