, Volume 51, Issue 3, pp 445–456 | Cite as

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

  • F. de A. LoboEmail author
  • M. P. de Barros
  • H. J. Dalmagro
  • Â. C. Dalmolin
  • W. E. Pereira
  • É. C. de Souza
  • G. L. Vourlitis
  • C. E. Rodríguez Ortíz


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.

Additional key words

curve fitting iteration nonlinear regression PN/I curve Solver function 



average relative errors


chloroplast CO2 concentration


intercellular CO2 concentration


photosynthetic photon flux density


light compensation point


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


light saturation point


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


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


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


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


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


adjusting factor


gross photosynthetic rate


maximum gross photosynthetic rate


net photosynthetic rate


maximum net photosynthetic rate obtained at I = I max


maximum net photosynthetic rate


dark respiration


coefficient of determination


sum of the absolute errors


sum of the squares of the errors


enzyme maximum velocity


adjusting factor


adjusting factor


convexity factor


quantum yield


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


theoretical maximum quantum yield


Chi-square test


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Supplementary material

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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • F. de A. Lobo
    • 1
    Email author
  • M. P. de Barros
    • 2
  • H. J. Dalmagro
    • 2
  • Â. C. Dalmolin
    • 2
  • W. E. Pereira
    • 3
  • É. C. de Souza
    • 4
  • G. L. Vourlitis
    • 5
  • C. E. Rodríguez Ortíz
    • 6
  1. 1.Departamento de Solos e Engenharia RuralFAMEV/UFMTCuiabá-MTBrasil
  2. 2.Programa de Pós-Graduação em Física AmbientalIF/UFMTCuiabá-MTBrasil
  3. 3.Departamento de Ciências Fundamentais e SociaisCCA/UFPBAreia-PBBrasil
  4. 4.Departamento de EstatísticaICET/UFMTCuiabá-MTBrasil
  5. 5.Department of Biological ScienceCSUSMSan Marcos-CAUSA
  6. 6.Departamento de Botânica e EcologiaIB/UFMTCuiabá-MTBrasil

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