The logistic (Verhulst) model for sigmoid microbial growth curves revisited
The logistic (Verhulst) model for sigmoid microbial growth curves revisited
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DOI：
10.1016/j.foodres.2007.01.012
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发表时间：
2007-01-01
影响因子：
8.1
通讯作者：
Normand, Mark D.
中科院分区：
文献类型：
--
作者：
Peleg, Micha;Corradini, Maria G.;Normand, Mark D.
logistic （Verhulst）增长模型及其当前的各种修改都基于等温瞬时增长率与瞬时种群规模和栖息地中仍然可用的资源比例成正比的概念。在半对数坐标上绘制的生长曲线表现出较长的滞后时间，原来的模型是不合适的。这个问题可以通过用对数生长比代替有机体数量作为方程中的自变量来消除。此外，实际增长率对人口瞬时规模和剩余资源的依赖可能具有不同于原始模型所要求的统一的比例因子。当这些都纳入到方程中，所得的广义模型可以解释几乎所有观察到的s型增长模式，等温和非等温，除了那些显示真正的峰值。已发表的各种细菌在不同培养基中的生长数据证明了这一点，包括一些表现出特别长的“滞后时间”的细菌。由于大多数s型等温增长曲线可以用只有三个可调参数的经验模型来描述，扩展模型就像其他修改版本的Verhulst方程一样，不遵守简约原则。然而，它的比例因子为观察到的一大类生长模式提供了初步的动力学解释，而不像一些现有模型那样援引生长参数之间的假设普遍关系。(c) 2007 Elsevier Ltd.版权所有。
The logistic (Verhulst) growth model and its various current modifications are all based on the notion that the isothermal momentary growth rate is proportional to the momentary population's size and the fraction of resources that are still available in the habitat. The model as originally formulated is inappropriate for growth curves that exhibit a long lag time when plotted on semi logarithmic coordinates. This problem can be eliminated by replacing the number of organisms as the independent variable in the equation by the logarithmic growth ratio. Moreover, the actual growth rate's dependence on the population's momentary size and residual resources might have scaling factors that are different from unity as the original model requires. When these are incorporated into the equation, the resulting generalized model can account for almost all observed sigmoid growth patterns, isothermal and non-isothermal, except for those that show a true peak. This is demonstrated with published growth data of various bacteria in different media, including some that exhibit a particularly long 'lag time'. Since most sigmoid isothermal growth curves can be described by empirical models that have only three adjustable parameters, the expanded model, like other modified versions of Verhulst's equation, does not abide by the principle of parsimony. However, its scaling factors provide a tentative kinetic explanation of a large class of observed growth patterns without invoking hypothetical universal relationships between growth parameters, as some current models do. (c) 2007 Elsevier Ltd. All rights reserved.