Bulletin of Mathematical Biology

, Volume 77, Issue 2, pp 319–338

Resource Consumption, Sustainability, and Cancer

  • Irina Kareva
  • Benjamin Morin
  • Carlos Castillo-Chavez
Review Article

DOI: 10.1007/s11538-014-9983-1

Cite this article as:
Kareva, I., Morin, B. & Castillo-Chavez, C. Bull Math Biol (2015) 77: 319. doi:10.1007/s11538-014-9983-1


Preserving a system’s viability in the presence of diversity erosion is critical if the goal is to sustainably support biodiversity. Reduction in population heterogeneity, whether inter- or intraspecies, may increase population fragility, either decreasing its ability to adapt effectively to environmental changes or facilitating the survival and success of ordinarily rare phenotypes. The latter may result in over-representation of individuals who may participate in resource utilization patterns that can lead to over-exploitation, exhaustion, and, ultimately, collapse of both the resource and the population that depends on it. Here, we aim to identify regimes that can signal whether a consumer–resource system is capable of supporting viable degrees of heterogeneity. The framework used here is an expansion of a previously introduced consumer–resource type system of a population of individuals classified by their resource consumption. Application of the Reduction Theorem to the system enables us to evaluate the health of the system through tracking both the mean value of the parameter of resource (over)consumption, and the population variance, as both change over time. The article concludes with a discussion that highlights applicability of the proposed system to investigation of systems that are affected by particularly devastating overly adapted populations, namely cancerous cells. Potential intervention approaches for system management are discussed in the context of cancer therapies.


Cancer Heterogeneity Evolution of resistance Host-parasite Resource-consumer Sustainability 

Copyright information

© Society for Mathematical Biology 2014

Authors and Affiliations

  • Irina Kareva
    • 1
    • 2
  • Benjamin Morin
    • 1
    • 3
  • Carlos Castillo-Chavez
    • 1
    • 4
  1. 1.Mathematical, Computational Modeling Sciences CenterArizona State UniversityTempeUSA
  2. 2.Newman-Lakka Institute for Personalized Cancer CareFloating Hospital for Children, Tufts Medical CenterBostonUSA
  3. 3.Global Institute of SustainabilityArizona State UniversityTempeUSA
  4. 4.School of Human Evolution and Social ChangesArizona State UniversityTempeUSA

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