Chapter 5: Two-species competition dynamics

In Chapter 4 we presented a number of models describing growth of one species of (cancer) cell. Because of the heterogeneous nature of cancers, it is important to develop tools to study the growth and interactions of more than one species of cells. While many types of interactions are possible among cancer cells, competition for resources or space is of central importance. Such dynamics can determine whether different cell clones can coexist or whether only one cell clone persists and the other one goes extinct. These dynamics are very related to the topic of interspecific competition in ecology, and the models explored here will be similar in nature. We start by exploring a specific, simple model that describes the competition for space among two species or clones of cancer cells. We subsequently generalize this analysis by considering axiomatic models of competition among two species of cells.