Bulletin of Mathematical Biology

, Volume 80, Issue 1, pp 151–174 | Cite as

From Experiment to Theory: What Can We Learn from Growth Curves?

  • Irina Kareva
  • Georgy Karev
Original Article


Finding an appropriate functional form to describe population growth based on key properties of a described system allows making justified predictions about future population development. This information can be of vital importance in all areas of research, ranging from cell growth to global demography. Here, we use this connection between theory and observation to pose the following question: what can we infer about intrinsic properties of a population (i.e., degree of heterogeneity, or dependence on external resources) based on which growth function best fits its growth dynamics? We investigate several nonstandard classes of multi-phase growth curves that capture different stages of population growth; these models include hyperbolic–exponential, exponential–linear, exponential–linear–saturation growth patterns. The constructed models account explicitly for the process of natural selection within inhomogeneous populations. Based on the underlying hypotheses for each of the models, we identify whether the population that it best fits by a particular curve is more likely to be homogeneous or heterogeneous, grow in a density-dependent or frequency-dependent manner, and whether it depends on external resources during any or all stages of its development. We apply these predictions to cancer cell growth and demographic data obtained from the literature. Our theory, if confirmed, can provide an additional biomarker and a predictive tool to complement experimental research.


Population heterogeneity Density-dependent model Frequency-dependent model Tumor growth Prospective and retrospective analysis Multi-phase growth 



The authors would like to thank Dr. Senthil Kabilan for his invaluable help with parameter fitting, the anonymous reviewer and Dr. Micha Peleg for their thoughtful and valuable comments and suggestions. This research was partially supported by the Intramural Research Program of the NCBI, NIH (to GK).

Compliance with Ethical Standards

Conflict of interest

The authors declare no conflict of interest.

Supplementary material

11538_2017_347_MOESM1_ESM.xlsx (13 kb)
Supplementary material 1 (xlsx 13 KB)
11538_2017_347_MOESM2_ESM.pdf (106 kb)
Supplementary material 2 (pdf 106 KB)


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Copyright information

© Society for Mathematical Biology 2017

Authors and Affiliations

  1. 1.Mathematical and Computational Sciences Center, School of Human Evolution and Social ChangeArizona State UniversityTempeUSA
  2. 2.EMD Serono, Merck KGaABillericaUSA
  3. 3.National Center for Biotechnology InformationNational Institutes of HealthBethesdaUSA

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