The use of Gompertz models in growth analyses, and new Gompertz-model approach: An addition to the Unified-Richards family.
The use of Gompertz models in growth analyses, and new Gompertz-model approach: An addition to the Unified-Richards family.
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DOI：
10.1371/journal.pone.0178691
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发表时间：
2017
期刊：
影响因子：
3.7
通讯作者：
Tjørve E
中科院分区：
文献类型：
--
作者：
Tjørve KMC;Tjørve E
Gompertz模型是众所周知的，并广泛应用于生物学的许多方面。它经常被用来描述动物和植物的生长，以及细菌和癌细胞的数量或体积。许多参数化和重新参数化的不同用途被发现在文献中，其中Gompertz-Laird是一个更常用的。在这里，我们回顾，介绍，并讨论了许多重新参数化和Gompertz模型的一些参数化，我们分为Ti（I型）和W 0（II型）的形式。在W 0形式中，起始点参数（表示出生或阴影值（W 0））取代了拐点时间参数（Ti）。我们还提出了新的“统一”的版本（U-版本）的传统的Ti -形式和简化的W 0-形式。其中，增长率常数代表相对增长率，而不仅仅是一个未指定的增长系数。我们还提出了U-版本的增长率参数返回绝对增长率（而不是相对）。新的U-Gompertz模型是统一理查兹（U-理查兹）模型的特例，因此属于U-模型的理查兹族。作为U型模型，它们具有一组参数，这些参数在系列中的模型之间是可比的，没有转换方程。这些改进很简单，可能看起来微不足道，但对那些研究有机体生长的人来说非常重要，因为两种新的U-Gompertz形式可以方便快捷地获得描述Gompertz模型形状的大多数生长类型所需的所有形状参数。
The Gompertz model is well known and widely used in many aspects of biology. It has been frequently used to describe the growth of animals and plants, as well as the number or volume of bacteria and cancer cells. Numerous parametrisations and re-parametrisations of varying usefulness are found in the literature, whereof the Gompertz-Laird is one of the more commonly used. Here, we review, present, and discuss the many re-parametrisations and some parameterisations of the Gompertz model, which we divide into Ti (type I)- and W0 (type II)-forms. In the W0-form a starting-point parameter, meaning birth or hatching value (W0), replaces the inflection-time parameter (Ti). We also propose new “unified” versions (U-versions) of both the traditional Ti -form and a simplified W0-form. In these, the growth-rate constant represents the relative growth rate instead of merely an unspecified growth coefficient. We also present U-versions where the growth-rate parameters return absolute growth rate (instead of relative). The new U-Gompertz models are special cases of the Unified-Richards (U-Richards) model and thus belong to the Richards family of U-models. As U-models, they have a set of parameters, which are comparable across models in the family, without conversion equations. The improvements are simple, and may seem trivial, but are of great importance to those who study organismal growth, as the two new U-Gompertz forms give easy and fast access to all shape parameters needed for describing most types of growth following the shape of the Gompertz model.