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

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 * ) .