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Iterative chemostat: A modelling framework linking biosynthesis to nutrient cycling on ecological and evolutionary time scales

Bryan College of Health Sciences, Bryan Medical Center, Lincoln NE 68506

Special Issues: Resource Explicit Population Models

In the classical chemostat, the output of the system has no effect on its input. This contrasts with many ecological systems, where the output at the end of a growing season affects nutrient inputs for subsequent seasons. Here, an iterative-continuous modelling framework is introduced that retains the structure of classical ecological models within each iteration but accounts for nutrient feedbacks between iterations. As an example, the framework is applied to the classical chemostat model, where nutrient outputs affect the supply ratio at each iteration. Furthermore, the biotic parameters in the model, including organismal demands for nitrogen (N) and phosphorus (P), are linked to core biogenic processes—protein and rRNA synthesis. This biosynthesis is further deconstructed into 11 biological constants and rates, most of which are deeply shared among all organisms. By linking the fundamental macromolecular machinery to the cycling of nutrients on the ecosystem scale, the framework enables to rigorously formulate qualitative and quantitative questions about the evolution of nutrient ratios and the existence of stoichiometric attractors, such as the puzzling persistence of the Redfield N:P ratio of 16 in the ocean. While the framework presented here is theoretical, it readily permits setting up empirical experiments for testing its predictions.
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Keywords chemostat; Redfield ratio; nitrogen; plankton; nutrient cycling; mathematical model; nucleotide; amino acid; ribosome; RNA polymerase

Citation: Irakli Loladze. Iterative chemostat: A modelling framework linking biosynthesis to nutrient cycling on ecological and evolutionary time scales. Mathematical Biosciences and Engineering, 2019, 16(2): 990-1004. doi: 10.3934/mbe.2019046


  • 1. T. H. Chrzanowski and J. P. Grover, Element content of Pseudomonas fluorescens varies with growth rate and temperature: a replicated chemostat study addressing ecological stoichiometry, Limnol. Oceanogr., 53 (2008), 1242–1251.
  • 2. C. T. Codeço and J. P. Grover, Competition along a spatial gradient of resource supply: a microbial experimental model, Am. Nat., 157 (2001), 300–315.
  • 3. S. J. Daines, J. R. Clark and T. M. Lenton, Multiple environmental controls on phytoplankton growth strategies determine adaptive responses of the N : P ratio, Ecol. Lett., 17 (2014), 414–425.
  • 4. P. De Leenheer and H. Smith, Feedback control for chemostat models, J. Math. Biol., 46 (2003), 48–70.
  • 5. O. Diekmann, A beginners guide to adaptive dynamics, Summer School on Mathematical Biology, (2004), 63–100.
  • 6. P. G. Falkowski and C. S. Davis, Natural proportions, Nature, 431 (2004), 131.
  • 7. S. A. Geritz, G. Mesze and J. A. Metz, Evolutionarily singular strategies and the adaptive growth and branching of the evolutionary tree, Evol. ecol., 12 (1998), 35-57.
  • 8. J. Grosse, A. Burson, M. Stomp, J. Huisman and H. T. S. Boschker, From ecological stoichiometry to biochemical composition: Variation in N and P supply alters key biosynthetic rates in marine phytoplankton, Front. Microbiol., 8 (2017), 1–11.
  • 9. H. Guo and L. Chen, Periodic solution of a chemostat model with Monod growth rate and impulsive state feedback control, J. Theor. Biol., 260 (2009), 502–509.
  • 10. C. A. Klausmeier, Successional state dynamics: a novel approach to modeling nonequilibrium foodweb dynamics, J. Theor. Biol., 262 (2010), 584–595.
  • 11. C. A. Klausmeier, E. Litchman, T. Daufresne and S. A. Levin, Optimal nitrogen-to-phosphorus stoichiometry of phytoplankton, Nature, 429 (2004), 171–174.
  • 12. I. Loladze and J. J. Elser, The origins of the Redfield nitrogen to phosphorus ratio are in a homoeostatic protein to rRNA ratio, Ecol. lett., 14 (2011), 244–250.
  • 13. S. J. Pirt and W. M. Kurowski, An extension of the theory of the chemostat with feedback of organisms. Its experimental realization with a yeast culture, J. Gen. Microbiol., 63 (1970), 357–366.
  • 14. A. C. Redfield, On the proportions of organic derivatives in sea water and their relations to the composition of plankton, James Johnstone Memorial Volume, Univ. Liverpool, (1934) 176–192.
  • 15. S. Rinaldi and M. Scheffer, Geometric analysis of ecological models with slow and fast processes, Ecosystems, 3 (2000), 507–521.
  • 16. H. L. Smith and P. Waltman, The Theory of the Chemostat: Dynamics of Microbial Competition, Cambridge university press, 1995.
  • 17. R. W. Sterner and J. J. Elser, Ecological Stoichiometry: the Biology of Elements from Molecules to the Biosphere, Princeton University Press, 2002.
  • 18. T. Tyrrell, The relative influences of nitrogen and phosphorus on oceanic primary production, Nature, 400 (1999), 525–531.
  • 19. T. S. Weber and C. Deutsch, Ocean nutrient ratios governed by plankton biogeography, Nature, 467 (2010), 550–554.


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