2005, 2(2): 381-418. doi: 10.3934/mbe.2005.2.381

The Ecology and Evolutionary Biology of Cancer: A Review of Mathematical Models of Necrosis and Tumor Cell Diversity


Department of Life Sciences, Scottsdale Community College, 9000 E. Chaparral Rd., Scottsdale, AZ 85256, United States

Received  January 2005 Revised  March 2005 Published  March 2005

Recent evidence elucidating the relationship between parenchyma cells and otherwise ''healthy'' cells in malignant neoplasms is forcing cancer biologists to expand beyond the genome-centered, ''one-renegade-cell'' theory of cancer. As it becomes more and more clear that malignant transformation is context dependent, the usefulness of an evolutionary ecology-based theory of malignant neoplasia becomes increasingly clear. This review attempts to synthesize various theoretical structures built by mathematical oncologists into potential explanations of necrosis and cellular diversity, including both total cell diversity within a tumor and cellular pleomorphism within the parenchyma. The role of natural selection in necrosis and pleomorphism is also examined. The major hypotheses suggested as explanations of these phenomena are outlined in the conclusions section of this review. In every case, mathematical oncologists have built potentially valuable models that yield insight into the causes of necrosis, cell diversity and nearly every other aspect of malignancy; most make predictions ultimately testable in the lab or clinic. Unfortunately, these advances have gone largely unexploited by the empirical community. Possible reasons why are considered.
Citation: John D. Nagy. The Ecology and Evolutionary Biology of Cancer: A Review of Mathematical Models of Necrosis and Tumor Cell Diversity. Mathematical Biosciences & Engineering, 2005, 2 (2) : 381-418. doi: 10.3934/mbe.2005.2.381

Avner Friedman. A hierarchy of cancer models and their mathematical challenges. Discrete and Continuous Dynamical Systems - B, 2004, 4 (1) : 147-159. doi: 10.3934/dcdsb.2004.4.147


Urszula Ledzewicz, Heinz Schättler. On the role of pharmacometrics in mathematical models for cancer treatments. Discrete and Continuous Dynamical Systems - B, 2021, 26 (1) : 483-499. doi: 10.3934/dcdsb.2020213


Jiaxu Li, James D. Johnson. Mathematical models of subcutaneous injection of insulin analogues: A mini-review. Discrete and Continuous Dynamical Systems - B, 2009, 12 (2) : 401-414. doi: 10.3934/dcdsb.2009.12.401


Irina Kareva, Faina Berezovkaya, Georgy Karev. Mixed strategies and natural selection in resource allocation. Mathematical Biosciences & Engineering, 2013, 10 (5&6) : 1561-1586. doi: 10.3934/mbe.2013.10.1561


Tao Li, Suresh P. Sethi. A review of dynamic Stackelberg game models. Discrete and Continuous Dynamical Systems - B, 2017, 22 (1) : 125-159. doi: 10.3934/dcdsb.2017007


Isabelle Gallagher. A mathematical review of the analysis of the betaplane model and equatorial waves. Discrete and Continuous Dynamical Systems - S, 2008, 1 (3) : 461-480. doi: 10.3934/dcdss.2008.1.461


Yuanyuan Huang, Yiping Hao, Min Wang, Wen Zhou, Zhijun Wu. Optimality and stability of symmetric evolutionary games with applications in genetic selection. Mathematical Biosciences & Engineering, 2015, 12 (3) : 503-523. doi: 10.3934/mbe.2015.12.503


Francesca Verrilli, Hamed Kebriaei, Luigi Glielmo, Martin Corless, Carmen Del Vecchio. Effects of selection and mutation on epidemiology of X-linked genetic diseases. Mathematical Biosciences & Engineering, 2017, 14 (3) : 755-775. doi: 10.3934/mbe.2017042


Cicely K. Macnamara, Mark A. J. Chaplain. Spatio-temporal models of synthetic genetic oscillators. Mathematical Biosciences & Engineering, 2017, 14 (1) : 249-262. doi: 10.3934/mbe.2017016


Zhouchen Lin. A review on low-rank models in data analysis. Big Data & Information Analytics, 2016, 1 (2&3) : 139-161. doi: 10.3934/bdia.2016001


Yangjin Kim, Avner Friedman, Eugene Kashdan, Urszula Ledzewicz, Chae-Ok Yun. Application of ecological and mathematical theory to cancer: New challenges. Mathematical Biosciences & Engineering, 2015, 12 (6) : i-iv. doi: 10.3934/mbe.2015.12.6i


M.A.J Chaplain, G. Lolas. Mathematical modelling of cancer invasion of tissue: dynamic heterogeneity. Networks and Heterogeneous Media, 2006, 1 (3) : 399-439. doi: 10.3934/nhm.2006.1.399


Hsiu-Chuan Wei. Mathematical and numerical analysis of a mathematical model of mixed immunotherapy and chemotherapy of cancer. Discrete and Continuous Dynamical Systems - B, 2016, 21 (4) : 1279-1295. doi: 10.3934/dcdsb.2016.21.1279


Georgios I. Papayiannis. Robust policy selection and harvest risk quantification for natural resources management under model uncertainty. Journal of Dynamics and Games, 2022, 9 (2) : 203-217. doi: 10.3934/jdg.2022004


Kaitlin Riegel. Frustration in mathematical problem-solving: A systematic review of research. STEM Education, 2021, 1 (3) : 157-169. doi: 10.3934/steme.2021012


Natalia L. Komarova. Spatial stochastic models of cancer: Fitness, migration, invasion. Mathematical Biosciences & Engineering, 2013, 10 (3) : 761-775. doi: 10.3934/mbe.2013.10.761


Louis-Pierre Chaintron, Antoine Diez. Propagation of chaos: A review of models, methods and applications. Ⅱ. Applications. Kinetic and Related Models, , () : -. doi: 10.3934/krm.2022018


Reinhard Bürger. A survey of migration-selection models in population genetics. Discrete and Continuous Dynamical Systems - B, 2014, 19 (4) : 883-959. doi: 10.3934/dcdsb.2014.19.883


Pierre-Emmanuel Jabin. Small populations corrections for selection-mutation models. Networks and Heterogeneous Media, 2012, 7 (4) : 805-836. doi: 10.3934/nhm.2012.7.805


Xueting Cui, Xiaoling Sun, Dan Sha. An empirical study on discrete optimization models for portfolio selection. Journal of Industrial and Management Optimization, 2009, 5 (1) : 33-46. doi: 10.3934/jimo.2009.5.33

2018 Impact Factor: 1.313


  • PDF downloads (126)
  • HTML views (0)
  • Cited by (61)

Other articles
by authors

[Back to Top]