Ju Shu, DeAngelis Donald L
Department of Biology, University of Miami, P.O. Box 249118, Coral Gables, Florida 33125, USA.
J Theor Biol. 2009 Feb 7;256(3):326-32. doi: 10.1016/j.jtbi.2008.10.002. Epub 2008 Oct 15.
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*).
R规则预测，能够在最低水平的限制性资源R下以稳态生存的物种会排除所有其他物种。简单模型表明，这一概念不一定与洛特卡的猜想一致，即生态系统应朝着最大功率状态Max(G)演化，其中G是系统的功率或生物量生产速率。为了详细探讨这种关系，我们使用了一个已发表的植物 - 养分系统模型，其中植物可以在叶片、根系和木材之间采用各种能量分配策略S。我们发现，导致Min(N(pore*))（其中N(pore*)是我们模型中土壤孔隙水中的一种限制性养分，在蒂尔曼的符号中相当于R*）的分配策略S(MinR*)，与使根系能量通量最大化的策略S(MaxG_root)相同。然而，该分配策略与为植物系统产生最大功率或最大光合速率Max(G)的策略S(MaxG)不同。因此，我们得出结论，Min(N(pore*))和Max(G)不一定会在生态系统中同时出现。我们还研究了哪种策略S(fit)是最适合的；也就是说，在允许竞争时会排除任何其他策略。我们通过数学证明，策略S(fit)与S(MinR*)、S(MaxG)和S(MaxG_root)不同。我们还考虑了植物能够对系统的外部养分输入产生积极影响的可行情况。在这种情况下，使根系能量通量最大化的策略S(MaxG_root)与导致土壤孔隙水中可用养分最大浓度Max(N pore*)的策略S(MaxR*)相同，而与导致Min(N pore*)的S(MinR*)不同。
