Bulletin of Mathematical Biology

, Volume 66, Issue 4, pp 663–687

Competition and natural selection in a mathematical model of cancer

  • John D. Nagy

DOI: 10.1016/j.bulm.2003.10.001

Cite this article as:
Nagy, J.D. Bull. Math. Biol. (2004) 66: 663. doi:10.1016/j.bulm.2003.10.001


A malignant tumor is a dynamic amalgamation of various cell phenotypes, both cancerous (parenchyma) and healthy (stroma). These diverse cells compete over resources as well as cooperate to maintain tumor viability. Therefore, tumors are both an ecological community and an integrated tissue. An understanding of how natural selection operates in this unique ecological context should expose unappreciated vulnerabilities shared by all cancers. In this study I address natural selection’s role in tumor evolution by developing and exploring a mathematical model of a heterogenous primary neoplasm. The model is a system of nonlinear ordinary differential equations tracking the mass of up to two different parenchyma cell types, the mass of vascular endothelial cells from which new tumor blood vessels are built and the total length of tumor microvessels. Results predict the possibility of a hypertumor—a focus of aggressively reproducing parenchyma cells that invade and destroy part or all of the tumor, perhaps before it becomes a clinical entity. If this phenomenon occurs, then we should see examples of tumors that develop an aggressive histology but are paradoxically prone to extinction. Neuroblastoma, a common childhood cancer, may sometimes fit this pattern. In addition, this model suggests that parenchyma cell diversity can be maintained by a tissue-like integration of cells specialized to provide different services.

Copyright information

© Society for Mathematical Biology 2004

Authors and Affiliations

  • John D. Nagy
    • 1
  1. 1.Department of BiologyScottsdale Community CollegeScottsdaleUSA