Von Bertalanffy's growth equation should not be used to model age and size at maturity
Von Bertalanffy's growth equation should not be used to model age and size at maturity
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DOI：
10.1086/285995
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发表时间：
1997-02-01
影响因子：
2.9
通讯作者：
Taylor, PD
中科院分区：
文献类型：
--
作者：
Day, T;Taylor, PD
生活史进化的研究在融合理论预测和经验观察方面取得了相当大的成功（罗夫1992; Stearns 1992）。通常，相对简单的模型会产生非常准确的预测。一个特别令人感兴趣的领域是对成熟年龄的研究（Kozlowski 1992; Bernardo 1993;其中的参考文献）。已经提出了几个模型来解释不同物种成熟时年龄的变化，每个模型通常采用一套不同的关于死亡率、生长、繁殖力和适当的适应性度量的假设。结果往往对这些成分的选择很敏感;因此，重要的是要知道什么时候简单的配方就足够了。在这里，我们关注其中一个组成部分：增长函数。在第一部分中，我们提出了一般的建模框架共同的大多数上述研究，并考虑如何选择一个合适的增长方程。我们建议，生长轨迹应指定两个独立的方程：一个早产儿方程，其中基本上没有剩余的能量是专门用于再生产和成熟后方程，其中所有（确定性增长）或一些（不确定性增长）的剩余能量是专门用于再生产。如果没有这样的规范，在成熟时年龄和大小的演变模型中可能会出现逻辑上的不一致。我们认为，冯Bertalanffy（VB）方程是滥用在不确定和确定的成熟度增长模型。在不确定增长下，通常不采用成熟前和成熟后增长曲线的单独说明。在确定的增长下，这样一个单独的规格，VB方程往往不能提供一个适当的描述prema。
The study of life-history evolution has enjoyed considerable success in melding theoretical prediction with empirical observation (Roff 1992; Stearns 1992). Often relatively simple models yield remarkably accurate predictions. One area of particular interest has been the study of age at maturity(Kozlowski 1992; Bernardo 1993; references therein). Several models have been proposed to explain variation in age at maturity across species, and each usually employs a different set of assumptions regarding mortality rates, growth, fecundity, and the appropriate measure of fitness. Results are often sensitive to the choice of these components; therefore, it is important to know when simple formulations are adequate. Here we focus on one of these components: the growth function. In the first section, we present the general modeling framework common to most of the aforementioned studies and consider how to choose an appropriate growth equation. We suggest that the growth trajectory should be specified by two separate equations: a prematurity equation in which essentially no surplus energy is devoted to reproduction and a postmaturity equation in which all (determinate growth) or some (indeterminate growth) surplus energy is devoted to reproduction. Logical inconsistencies can arise in models of the evolution of age and size at maturity when such a specification is not made. We believe that the von Bertalanffy(VB) equation is misused in both indeterminate and determinate growth models of maturity. Under indeterminate growth, a separate specification of pre-and postmaturity growth curves is usually not employed. Under determinate growth, in which such a separate specification is made, the VB equation often fails to provide an appropriate description of prema-