The R* rule and energy flux in a plant-nutrient ecosystem

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 , where 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 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, , and not same as S_MinR*, for .