Estimation of parameters of a biochemically based model of photosynthesis using a genetic algorithm

Abstract

Photosynthesis response to carbon dioxide concentration can provide data on a number of important parameters related to leaf physiology. The genetic algorithm (GA), which is a robust stochastic evolutionary computational algorithm inspired by both natural selection and natural genetics, is proposed to simultaneously estimate the parameters [including maximum carboxylation rate allowed by ribulose 1·5-bisphosphate carboxylase/oxygenase (Rubisco) carboxylation rate (Vcmax), potential lightsaturated electron transport rate (Jmax), triose-phosphate utilization (TPU), leaf dark respiration in the light (Rd) and mesophyll conductance (gm)] of the photosynthesis models presented by Farquhar, von Caemmerer and Berry, and Ethier and Livingston. The results show that by properly constraining the parameter bounds the GA-based estimate methods can effectively and efficiently obtain globally (or, at least near globally) optimal solutions, which are as good as or better than those obtained by non-linear curve fitting methods used in previous studies. More complicated problems such as taking the gm variation response to CO2 into account can be easily formulated and solved by using GA. The influence of the crossover probability (Pc), mutation probability (Pm), population size and generation on the performance of GA was also investigated.

Parameterization of a coupled CO<sub>2</sub> and H<sub>2</sub>O gas exchange model at the leaf scale of <i>Populus euphratica</i>

“…For example, in very rare circumstances, data include samples of two segments (A c and A j ), but wide bounds result in an A/C i set for which one of the two functions (e.g. A j ) happens to provide a better fit than two functions combined, despite the underlying presence of two phases (Su et al, 2009). In this circumstance, we say the GA method obtained biologically implausible estimates for the parameters of the FvCB model.…”

Surfing the Hyperbola Equations of the Steady-State Farquhar–von Caemmerer–Berry C3 Leaf Photosynthesis Model: What Can a Theoretical Analysis of Their Oblique Asymptotes and Transition Points Tell Us?

“…When the A/C i rate curves of the FvCB model are analysed under steady-state conditions and the photorespiratory and respiratory CO 2 release is also assumed to take place at the site of the Rubisco carboxylation, the quadratic equations for A c , A j and A p (see "Appendix 1", Eqs. A8-A10) can be fitted following different approaches, where g m is taken as a constant parameter (Duursma 2015; Gu et al 2010;Sharkey 2016;Su et al 2009). Some of the nonlinear fitting methods require starting from initial guessed parameters and letting the fit improve with successive iterations, while others constrain the C i values at which the transition point between c and j occurs.…”

“…The above fitting methods also take up that the A/C i rate curves reach asymptotic values for A at supraoptimal CO 2 concentration, when there is experimental evidence for the inhibition of the net CO 2 assimilation rate by CO 2 itself at high concentrations (Woo and Wong 1983). Also, some of these fitting methods make use of approximate estimations for J max and T p -where T p stands for the rate of phosphate release in triose phosphate utilisation-when C c approaches infinity in an A/C c rate curve (Su et al 2009) or they reasonably assume that the order of the three limitation states along the C i axis is the same as along the C c axis (Gu et al 2010). Dynamic models of photosynthesis are also suitable to analyse the leaf CO 2 assimilation response under fluctuating environmental stimuli such as sunlight irradiance, atmospheric CO 2 concentration or stomatal response to light (Bellasio 2019;Morales et al 2018;Noe and Giersch 2004); however, they add complexity to the analysis or they have not been developed completely to date.…”

“…The simplicity of the quadratic equations for A c , A j and A p still makes the steadystate FvCB model very useful in fitting approaches to estimate biochemical parameters from leaf photosynthesis (Duursma 2015; Gu et al 2010;Sharkey 2016;Su et al 2009). After nearly 40 years of research on the FvCB model, its quadratic equations still hide mathematical features of interest to establish when this model becomes short or when an extended FvCB model would be more suitable for the estimation of the biochemical parameters.…”

Functional Enrichment of Utopian Distribution of Plant Life-Forms

“…Life-forms are often seen in differing proportions or spectra; plants show chaotic patterns of evolution in terms of their individual growth processes and numbers [18][19][20]. Life-form differences are often associated with variable gradients in topographical and climatic conditions [21,22].…”