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A Flexible Sigmoid Function of Determinate Growth

Gompertz函数 乙状窦函数 逻辑函数 威布尔分布 数学 功能(生物学) 增长率 应用数学 数学分析 统计 生物 计算机科学 几何学 人工神经网络 进化生物学 机器学习
作者
Xinyou Yin
出处
期刊:Annals of Botany [Oxford University Press]
卷期号:91 (3): 361-371 被引量:690
标识
DOI:10.1093/aob/mcg029
摘要

A new empirical equation for the sigmoid pattern of determinate growth, ‘the beta growth function’, is presented. It calculates weight (w) in dependence of time, using the following three parameters: tm, the time at which the maximum growth rate is obtained; te, the time at the end of growth; and wmax, the maximal value for w, which is achieved at te. The beta growth function was compared with four classical (logistic, Richards, Gompertz and Weibull) growth equations, and two expolinear equations. All equations described successfully the sigmoid dynamics of seed filling, plant growth and crop biomass production. However, differences were found in estimating wmax. Features of the beta function are: (1) like the Richards equation it is flexible in describing various asymmetrical sigmoid patterns (its symmetrical form is a cubic polynomial); (2) like the logistic and the Gompertz equations its parameters are numerically stable in statistical estimation; (3) like the Weibull function it predicts zero mass at time zero, but its extension to deal with various initial conditions can be easily obtained; (4) relative to the truncated expolinear equation it provides more reasonable estimates of final quantity and duration of a growth process. In addition, the new function predicts a zero growth rate at both the start and end of a precisely defined growth period. Therefore, it is unique for dealing with determinate growth, and is more suitable than other functions for embedding in process‐based crop simulation models to describe the dynamics of organs as sinks to absorb assimilates. Because its parameters correspond to growth traits of interest to crop scientists, the beta growth function is suitable for characterization of environmental and genotypic influences on growth processes. However, it is not suitable for estimating maximum relative growth rate to characterize early growth that is expected to be close to exponential.
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