A general method for parameter estimation in light-response models.

Lei Chen,Cang Hui,Xiaofei Cheng,Zhong-Bin Li,Bai-Lian Li,Pei-Jian Shi

doi:10.1038/srep27905

Abstract

Selecting appropriate initial values is critical for parameter estimation in nonlinear photosynthetic light response models. Failed convergence often occurs due to wrongly selected initial values when using currently available methods, especially the kind of local optimization. There are no reliable methods that can resolve the conundrum of selecting appropriate initial values. After comparing the performance of the Levenberg–Marquardt algorithm and other three algorithms for global optimization, we develop a general method for parameter estimation in four photosynthetic light response models, based on the use of Differential Evolution (DE). The new method was shown to successfully provide good fits (R2 > 0.98) and robust parameter estimates for 42 datasets collected for 21 plant species under the same initial values. It suggests that the DE algorithm can efficiently resolve the issue of hyper initial-value sensitivity when using local optimization methods. Therefore, the DE method can be applied to fit the light-response curves of various species without considering the initial values.

Highlights

Where P (I) is the net photosynthetic rate, I the irradiance, a the initial quantum efficiency, Amax the net light saturated photosynthetic rate, and Rd the dark respiration rate
The nonrectangular model is more flexible for its additional curvature parameter (θ); when θ = 0, it becomes the rectangular model[5,22]
The estimates of θ for the photosynthetic datasets of Brassica rapa var. chinensis (L.) Kitam., Camellia sinensis (L.) Kuntze and Impatiens balsamina L. were all close to zero, the other three parameters of the nonrectangular model were equal to those estimated from the rectangular model (Supplementary Tables S1 and S2)

Summary

Introduction

Where P (I) is the net photosynthetic rate, I the irradiance, a the initial quantum efficiency, Amax the net light saturated photosynthetic rate, and Rd the dark respiration rate. Selecting appropriate initial values is crucial for fitting these nonlinear models and estimating their parameters. For biologically meaningful parameters, using the estimates directly from experiments would be a first try for assigning the initial values. The built-in functionality to fit nonlinear models in these software packages normally implement algorithms of local optimization for regression and parameter estimation, such as the Gauss-Newton, Levenberg-Marquardt and Nelder-Mead algorithms. To develop effective methods for resolving the problem of assigning appropriate initial values when using these nonlinear models, we need to go beyond local optimization. Recent comparisons have suggested that the Differential Evolution (DE) algorithm performs better than other global optimization methods such as the genetic algorithm and simulated annealing[18,19]. The application of global optimization algorithms to parameter estimation in photosynthetic light-response models is lacking

Objectives

Methods

Results