### Abstract

The R* rule predicts that the species that can survive in steady state at the lowest level of limiting resource, R*, excludes all other species. Simple models indicate that this concept is not necessarily consistent with Lotka's conjecture that an ecological system should evolve towards a state of maximum power, Max(G), where G is the power, or rate of biomass production of the system. To explore the relationship in detail, we used a published model of a plant-nutrient system in which a plant can use various strategies, S, of allocation of energy between foliage, roots, and wood. We found that the allocation strategy, S_{MinR*}, that leads to Min (N_{pore}^{*}), where N_{pore} ^{*} is a limiting nutrient in soil pore water in our model (and equivalent to R* in Tilman's notation), is the same as the strategy, S_{MaxG-root}, for which energy flux to roots is maximized. However, that allocation strategy is different from the strategy, S_{MaxG}, that produces maximum power, or maximum photosynthetic rate, for the plant system, Max(G). Hence, we conclude that Min (N_{pore}^{*}) and Max(G) should not necessarily co-occur in an ecological system. We also examined which strategy, S_{fit}, was fittest; that is, eliminated any other strategies, when allowed to compete. The strategy S_{fit} differed from S_{MinR*}, S_{MaxG}, and S_{MaxG-root}, which we demonstrated mathematically. We also considered the feasible situation in which a plant is able to positively influence external nutrient input to the system. Under such conditions, the strategy, S_{MaxG-root}, that maximizes energy flux to roots was the same as the strategy, S_{MaxR*}, that leads to maximum concentration of available nutrient in soil pore water, Max (N_{pore}^{*}), and not same as S_{MinR*}, for Min (N_{pore}^{ *}).

Original language | English (US) |
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Pages (from-to) | 326-332 |

Number of pages | 7 |

Journal | Journal of theoretical biology |

Volume | 256 |

Issue number | 3 |

DOIs | |

State | Published - Feb 7 2009 |

### Keywords

- Limiting nutrient
- Maximum power principle
- Nutrient cycling
- Optimal energy allocation
- Plant competition

### ASJC Scopus subject areas

- Medicine(all)
- Immunology and Microbiology(all)
- Biochemistry, Genetics and Molecular Biology(all)
- Agricultural and Biological Sciences(all)
- Modeling and Simulation
- Statistics and Probability
- Applied Mathematics

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## Cite this

*Journal of theoretical biology*,

*256*(3), 326-332. https://doi.org/10.1016/j.jtbi.2008.10.002