Survival of the Fastest

The chapter opens with the addition of a “carrying capacity” term to the predator–prey model of the previous chapter. We then compare two populations with differing growth rates under such a model, finding that the faster-growing population will eventually replace the slower-growing one, an observation that we relate to the idea of Darwinian selection. Next some of the gaps in this view of Darwinian evolution are considered, causing us to postpone treatment of parts of evolutionary theory to later chapters. We then note that this chapter’s model of interacting populations is applicable to cell lineages competing in a cancerous tumor. We consider an example problem of the appearance of drug resistance in a slowly growing tumor. With a simple drug treatment regime, the resistant cells completely replace the susceptible ones, resulting in a tumor that cannot be treated with the drug. However, if we assume that the resistance to the drug is costly, we find that periodic application of the drug allows us to keep the tumor in check due to the reduced reproductive ability of the resistant cells seen in the absence of the drug.