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The \(R^*\) rule and energy flux in a plant-nutrient ecosystem. (English) Zbl 1400.92578

Summary: 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 \(Min(N_{pore}^*)\).

MSC:

92D40 Ecology
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