Photosynthetica

, 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. Lobo
  • M. P. de Barros
  • H. J. Dalmagro
  • Â. C. Dalmolin
  • W. E. Pereira
  • É. C. de Souza
  • G. L. Vourlitis
  • C. E. Rodríguez Ortíz
Article

Abstract

In this study, we presented the most commonly employed net photosynthetic light-response curves (PN/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 PN/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 

Abbreviations

ARE

average relative errors

Cc

chloroplast CO2 concentration

Ci

intercellular CO2 concentration

I

photosynthetic photon flux density

Icomp

light compensation point

Imax

light saturation point beyond which there is no significant change in PN

Isat

light saturation point

Isat(n)

light saturation point at a specific percentile (n) of PNmax

Isat(85)

light saturation point for PN + RD equal to 85% of PNmax

Isat(90)

light saturation point for PN + RD equal to 90% of PNmax

Isat(95)

light saturation point for PN + RD equal to 95% of PNmax

I(50)

light saturation point for PN + RD equal to 50% of PNmax

k

adjusting factor

Pg

gross photosynthetic rate

Pgmax

maximum gross photosynthetic rate

PN

net photosynthetic rate

PN(Imax)

maximum net photosynthetic rate obtained at I = Imax

PNmax

maximum net photosynthetic rate

RD

dark respiration

R2

coefficient of determination

SAE

sum of the absolute errors

SSE

sum of the squares of the errors

Vmax

enzyme maximum velocity

β

adjusting factor

γ

adjusting factor

θ

convexity factor

ϕ

quantum yield

ϕ(I)

quantum yield at a particular value of I

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

quantum yield at I = Icomp

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

quantum yield at the range between Icomp 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 Icomp

ϕmax

theoretical maximum quantum yield

χ2

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
  • 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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