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Fitting net photosynthetic light-response curves with Microsoft Excel — a critical look at the models

An Erratum to this article was published on 01 September 2014


In this study, we presented the most commonly employed net photosynthetic light-response curves (P N/I curves) fitted by the Solver function of Microsoft Excel. Excel is attractive not only due to its wide availability as a part of the Microsoft Office suite but also due to the increased level of familiarity of undergraduate students with this tool as opposed to other statistical packages. In this study, we explored the use of Excel as a didactic tool which was built upon a previously published paper presenting an Excel Solver tool for calculation of a net photosynthetic/chloroplastic CO2-response curve. Using the Excel spreadsheets accompanying this paper, researchers and students can quickly and easily choose the best fitted P N/I curve, selecting it by the minimal value of the sum of the squares of the errors. We also criticized the misuse of the asymptotic estimate of the maximum gross photosynthetic rate, the light saturation point estimated at a specific percentile of maximum net photosynthetic rate, and the quantum yield at zero photosynthetic photon flux density and we proposed the replacement of these variables by others more directly linked to plant ecophysiology.

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average relative errors

C c :

chloroplast CO2 concentration

C i :

intercellular CO2 concentration

I :

photosynthetic photon flux density

I comp :

light compensation point

I max :

light saturation point beyond which there is no significant change in P N

I sat :

light saturation point

I sat(n) :

light saturation point at a specific percentile (n) of P Nmax

I sat(85) :

light saturation point for P N + R D equal to 85% of P Nmax

I sat(90) :

light saturation point for P N + R D equal to 90% of P Nmax

I sat(95) :

light saturation point for P N + R D equal to 95% of P Nmax

I (50) :

light saturation point for P N + R D equal to 50% of P Nmax

k :

adjusting factor

P g :

gross photosynthetic rate

P gmax :

maximum gross photosynthetic rate

P N :

net photosynthetic rate

P N(Imax) :

maximum net photosynthetic rate obtained at I = I max

P Nmax :

maximum net photosynthetic rate

R D :

dark respiration

R 2 :

coefficient of determination


sum of the absolute errors


sum of the squares of the errors

V max :

enzyme maximum velocity


adjusting factor


adjusting factor


convexity factor


quantum yield

ϕ(I) :

quantum yield at a particular value of I

\(\varphi _{(I_{comp} )} \) :

quantum yield at I = I comp

\(\varphi _{(I_{comp} - I_{200} )} \) :

quantum yield at the range between I comp and I = 200 μmol(photon) m−2 s−1

\(\varphi _{(I_0 )} \) :

quantum yield at I = 0 μmol(photon) m−2 s−1

\(\varphi _{(I_0 - I_{comp} )} \) :

quantum yield at the range between I = 0 μmol(photon) m−2 s−1 and I comp

ϕmax :

theoretical maximum quantum yield

χ2 :

Chi-square test


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Correspondence to F. de A. Lobo.

Additional information

Acknowledgments: This study was supported by grants from the Instituto Nacional de Ciência e Tecnologia em Áreas Úmidas (INAU), Programa Institutos Nacionais de Ciência e Tecnologia (CNPq/MCT), and from Fundação de Amparo à Pesquisa do Estado de Mato Grosso (FAPEMAT) and scholarships from Conselho Nacional de Desenvolvimento Cientifico e Tecnológico (CNPq). We would like to thank Dr. Clóvis Nobre de Miranda for allowing us to conduct the research on his farm and for giving us the facilities to work there.

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Lobo, F., de Barros, M.P., Dalmagro, H.J. et al. Fitting net photosynthetic light-response curves with Microsoft Excel — a critical look at the models. Photosynthetica 51, 445–456 (2013).

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Additional key words

  • curve fitting
  • iteration
  • nonlinear regression
  • P N/I curve
  • Solver function