Les modeles sigmoides en biologie vegetale
Les modeles sigmoides en biologie vegetale
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植物生物学中的乙状结肠模型
DOI：
10.1007/bf00114175
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发表时间：
1991
影响因子：
1.3
通讯作者：
G. Cusset
中科院分区：
文献类型：
--
作者：
G. Cusset
ResumeRevue des fontements Conceptuels de modeles très souvent雇员。摘要观察到的生物生长曲线通常呈 S 形。通常的做法是使用 Verhulst 逻辑曲线或 Gompertz 曲线来拟合此类数据。本文批判性地考虑了这些描述性模型背后的概念基础。Logistic 模型由 Verhulst 开发，以适应人口不可能无限期增长的常识观察。基于化学动力学（单分子反应的自催化）的考虑，理查森提出了使用相同方程来描述个体生长的理由，但由于他错误地推导了基本方程而受到严厉批评（Snell，1929）。过于简单是错误的（Priestley & Pearsall，1922）。 Von Bertalanffy (1957) 随后基于这样的假设进行了论证：作为第一个近似，可以假设分解代谢和合成代谢的速率分别与体重和体重功率 (< 1) 成正比。 Gauuse (1934) 在人口背景下重新推导了 Verhulst 方程，假设人均增长率与最大可能人口规模和已积累人口规模之间的差异（解释为“仍然空置的地方”的数量）成正比。这一观点受到尼克尔森（Nicholson，1933）、米尔恩（Milne，1962）、史密斯（Smith，1954）和鲁比诺夫（Rubinov，1973）的激烈挑战。事实上，“空位”的含义从未完全明确。最后，Lotka (1925) 设计了第三种主要方法，只需在二次项后截断自主生长微分定律的零附近的泰勒展开式。戴维森 (Davidson) (1928) 将公开描述人类死亡率的基于经验的 Gompertz 模型应用于生物体的生长。格雷（Gray，1929）密切相关的模型也仅具有纯粹的现象学基础。 Makany (1991) 最近提出了一种理论解释。作者介绍了以下生物系统：一个取之不尽用之不竭的发生器，它产生本质上惰性的，即不可破坏和不可复制的元素，这些元素容纳在一个可以计数的空间中。这是一个占用的概率问题，可以使用瓮模型。所获得的离散分布的渐近定律是Gompertz 定律。Richards (1959) 和Nelder (1961) 的综合增长函数更加灵活，它基于纯粹的数学概括。没有其他理论方法可以解释它们。这些模型的概念基础及其适用性在乘法或增生增长的情况下进行了讨论（Richards，1969）。在实践中，建议在乘法增长的情况下使用 Von Bertalanffy 模型，在增生增长的情况下使用 Makany 模型，并在这两种情况下使用逻辑函数，但仅作为二次项的近似值和经验数据的纯粹描述性公式。因此没有提及自催化理论或“空位”。
ResumeRevue des fondements conceptuels de modèles sigmoïdes très souvent employés. Examen de leur applicabilité aux modes de croissance multiplicatif et accrétionnaire.AbstractObserved biological growth curves generally are sigmoid in appearance. It is common practice to fit such data with either a Verhulst logistic or a Gompertz curve. This paper critically considers the conceptual bases underlying these descriptive models.The logistic model was developed by Verhulst to accommodate the common sense observation that populations cannot keep growing indefinitely. A justification for using the same equation to describe the growth of individuals, based on considerations from chemical kinetics (autocatalysis of a monomolecular reaction), was put forward by Richardson, but met with heavy criticism as a result of his erroneous derivation of the basic equation (Snell, 1929). It errs on the side of over-simplicity (Priestley & Pearsall, 1922). Von Bertalanffy (1957) subsequently based a justification on the assumption that, as a first approximation, the rates of catabolism and anabolism may be assumed to be proportional to weight and power (< 1) of weight respectively. Gause (1934) rederived the Verhulst equation in a population context by assuming the per capita growth rate to be proportional to the difference, interpreted as the number of “still vacant places”, between the maximal possible and the already accumulated population sizes. This point of view was fiercely challenged by Nicholson (1933), Milne (1962), Smith (1954) and Rubinov (1973). And indeed, what is meant by “vacant places” has never become entirely clear. Finally Lotka (1925) devised a third leading approach by just truncating a Taylor expansion around zero of the differential law for autonomous growth after the second degree term.The empirically based Gompertz model avowedly describing human mortality was applied to the growth of organisms by Davidson (1928). The closely related model by Gray (1929) also has a pure phenomenological basis only. A theoretical interpretation has recently been propounded by Makany (1991). This author introduces the following biological system: an inexhaustible generator which produces essentially inert, i.e. non-destructible and non-reproducing elements, which accommodate in a space where they can be counted. It is a probabilistic problem of occupancy and an urn model can be used. The asymptotic law of the obtained discrete distribution is a Gompertz one.The comprehensive growth functions, more flexible, of Richards (1959) and Nelder (1961) are based on sheer mathematical generalizations. There is no other theoretical way to explain them.The conceptual bases of these models and their applicability are discussed in cases of multiplicative or accretionary growth (Richards, 1969). In practice it is advisable to use the Von Bertalanffy model in case of a multiplicative growth, the Makany model in accretionary growth and the logistic function in both cases, but only as an approximation at the second degree term and as a purely descriptive formula of empirical data. Thus without any reference to an autocatalytic theory or “vacant places”.