Targeted therapies provide an exciting new approach to combat human cancer. The immediate effect is a dramatic reduction in disease burden, but in most cases, the tumor returns as a consequence of resistance. Various mechanisms for the evolution of resistance have been implicated, including mutation of target genes and activation of other drivers. There is increasing evidence that the reason for failure of many targeted treatments is a small preexisting subpopulation of resistant cells; however, little is known about the genetic composition of this resistant subpopulation. Using the novel approach of ordering the resistant subclones according to their time of appearance, here we describe the full spectrum of resistance mutations present in a metastatic lesion. We calculate the expected and median number of cells in each resistant subclone. Surprisingly, the ratio of the medians of successive resistant clones is independent of any parameter in our model; for example, the median of the second clone divided by the median of the first is ffiffiffi 2 p − 1. We find that most radiographically detectable lesions harbor at least 10 resistant subclones. Our predictions are in agreement with clinical data on the relative sizes of resistant subclones obtained from liquid biopsies of colorectal cancer patients treated with epidermal growth factor receptor (EGFR) blockade. Our theory quantifies the genetic heterogeneity of resistance that exists before treatment and provides information to design treatment strategies that aim to control resistance.cancer | drug resistance | heterogeneity | mathematical biology A cquired resistance to treatment is a major impediment to successful eradication of cancer. Patients presenting with early-stage cancers can often be cured surgically, but patients with metastatic disease must be treated with systemic therapies (1). Traditional treatments such as chemotherapy and radiation that exploit the enhanced sensitivity of cancer cells to DNA damage have serious side effects and, although curative in some cases, often fail due to intrinsic or resistance acquired during treatment. Targeted therapies, a new class of drugs, inhibit specific molecules implicated in tumor development and are typically less harmful to normal cells compared with chemotherapy and radiation (2-5). In the case of many targeted treatments, patients initially have a dramatic response (6, 7), only to be followed by a regrowth of most of their lesions several months later (8-10). Acquired resistance is often a consequence of genetic alterations (usually point mutations) in the drug target itself or in other genes (10)(11)(12)(13)(14).Recently, mathematical modeling and clinical data were used to show that acquired resistance to an epidermal growth factor receptor (EGFR) inhibitor panitumumab in metastatic colorectal cancer patients is a fait accompli, because typical detectable metastatic lesions are expected to contain hundreds of cells resistant to the drug before the start of treatment (10). These cells would then expand ...