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 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*).