van den Berg H A
Department of Theoretical Biology, Vrije Universiteit Amsterdam, The Netherlands.
Math Biosci. 1998 Apr;149(1):1-22. doi: 10.1016/s0025-5564(97)10019-0.
Liebig's law of the Minimum is reformulated in terms of biomass composition dynamics. The doctrine of the single limiting nutrient is shown to be invalid generally. The nutritional status of a unicellular organism is expressed in terms of state variables; one which represents the subsistence composition and a number of reserve surplus type variables. It is proposed that the property of being limiting should be defined in terms of the reserve surplus variables. On the basis of this definition, it can be decided whether a nutrient, or combination of nutrients, is limiting, both in transient and steady states. The concept of multiple limitation is shown to have two distinct meanings on these definitions. A non-interactive minimum model, based on a 'hard' minimum operator, is introduced. Smooth interactive models may be formulated which have this minimum model as a limiting case. One such model is described. Numerical simulations show how the behaviour of this smooth model can approximate that of the minimum model: apparently hard non-linearities can arise in the smooth model, through time-scale separation.
利比希最小因子定律依据生物量组成动态进行了重新阐述。单一限制营养素学说总体上被证明是无效的。单细胞生物的营养状况通过状态变量来表示；一个代表生存组成，还有若干储备过剩型变量。建议根据储备过剩变量来定义限制属性。基于这一定义，可以确定一种营养素或营养素组合在瞬态和稳态下是否具有限制作用。在这些定义下，多重限制概念有两种不同含义。引入了一个基于“硬”最小算子的非交互式最小模型。可以构建以该最小模型为极限情况的平滑交互式模型。描述了其中一个这样的模型。数值模拟展示了这种平滑模型的行为如何近似最小模型：通过时间尺度分离，平滑模型中可能会出现看似硬的非线性。
