Skip to main content

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

Abstract

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.

This is a preview of subscription content, access via your institution.

Abbreviations

ARE:

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

SAE:

sum of the absolute errors

SSE:

sum of the squares of the errors

V max :

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 = 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

References

  1. Abe, M., Yokota, K., Kurashima, A., Maegawa, M.: High water temperature tolerance in photosynthetic activity of Zostera japonica Ascherson and Graebner seedlings from Ago Bay, Mio Prefecture, central Japan. — Fish. Sci. 75: 1117–1123, 2009.

    Article  CAS  Google Scholar 

  2. Baly, E.C.C.: The kinetics of photosynthesis. — Proc. R. Soc. Lond. B 117: 218–239, 1935.

    Article  CAS  Google Scholar 

  3. Brown, A.M.: A step-by-step guide to non-linear regression analysis of experimental data using a Microsoft Excel spreadsheet. — Comput. Methods Programs Biomed. 65: 191–200, 2001.

    PubMed  Article  CAS  Google Scholar 

  4. Campbell, G.S., Norman, J.M.: An Introduction to Environmental Biophysics. 2nd Ed. Springer-Verlag, New York 1998.

    Book  Google Scholar 

  5. Chen, L., Tam, N.F.Y., Huang, J. et al.: Comparison of ecophysiological characteristics between introduced and indigenous mangrove species in China. — Est. Coast Shelf Sci. 79: 644–652, 2008.

    Article  Google Scholar 

  6. Christie, D.: Resampling with Excel. — Teach. Stat. 26: 9–13, 2004.

    Article  Google Scholar 

  7. Devacht, S., Lootens, P., Roldán-Ruiz, I. et al.: Influence of low temperatures on the growth and photosynthetic activity of industrial chicory, Cichorium intybus L. partim. — Photosynthetica 47: 372–380, 2009.

    Article  CAS  Google Scholar 

  8. Donovan, T.M., Welden, C.W.: Spreadsheet Exercises in Ecology and Evolution. Sinauer Associates, Sunderland 2002.

    Google Scholar 

  9. Dubois, J.-J.B., Fiscus, E.L., Booker, F.L. et al.: Optimizing the statistical estimation of the parameters of the Farquhar-Von Caemmerer-Berry model of photosynthesis. — New Phytol. 176: 402–414, 2007.

    PubMed  Article  Google Scholar 

  10. Falkowski, P.G., Raven, J.A.: Aquatic Photosynthesis. Princeton University Press, Princenton 2007.

    Google Scholar 

  11. Gallegos, C.L., Platt, T.: Photosynthesis measurements on natural populations of phytoplankton: numerical analysis. — Can. Bull. Fish. Aquat. Sci. 210: 103–112, 1981.

    Google Scholar 

  12. Govindjee, Beatty, J.T., Gest, H., Allen, J.F.: Discoveries in Photosynthesis. Springer, Dordrecht 2005.

    Book  Google Scholar 

  13. Harley, P.C., Baldocchi, D.D.: Scaling carbon dioxide and water vapor exchange from leaf to canopy in a deciduous forest. I. Leaf model and parametrization. — Plant Cell Environ. 18: 1146–1156, 1995.

    Article  Google Scholar 

  14. Hunt, R., Causton, D.R., Shipley, B., Askew, A.P.: A modern tool for classical growth analysis. — Ann. Bot. 90: 485–488, 2002.

    PubMed  Article  CAS  Google Scholar 

  15. Jacovides, C.P., Tymvios, F.S., Asimakopoulos, D.N. et al.: Global photosynthetically active radiation and its relationship with global solar radiation in the Eastern Mediterranean basin. — Theor. Appl. Climatol. 74: 227–233, 2003.

    Article  Google Scholar 

  16. Jassby, A.D., Platt, T.: Mathematical formulation of the relationship between photosynthesis and light for phytoplankton. — Limnol. Oceanogr. 21: 540–547, 1976.

    Article  CAS  Google Scholar 

  17. Jones, H.B., Archer, N., Rotenberg, E., Casa, R.: Radiation measurement for plant ecophysiology. — J. Exp. Bot. 54: 879–889, 2003.

    PubMed  Article  CAS  Google Scholar 

  18. Jones, M.B.: Photosynthetic responses of C3 and C4 wetland species in a tropical swamp. — J. Ecol. 76: 253–262, 1988.

    Article  Google Scholar 

  19. Kaipiainen, E.L.: Parameters of photosynthesis light curve in Salix dasyclados and their changes during the growth season. — Russ. J. Plant Physiol. 56: 445–453, 2009.

    Article  CAS  Google Scholar 

  20. Kok, B.: On the interrelation of respiration and photosynthesis in green plants. — Biochim. Biophys. Acta 3: 625–631, 1949.

    Article  CAS  Google Scholar 

  21. Kumar, K.V., Sivanesan, S.: Isotherm parameters for basic dyes onto activated carbon: comparison of linear and non-linear method. — J. Hazard. Mater. 129: 147–150, 2006.

    PubMed  Article  CAS  Google Scholar 

  22. Lambers, H., Chapin III, F.S., Pons, T.L.: Response of photosynthesis to light. — In: Lambers, H., Chapin III, F.S., Pons, T.L. (eds.): Plant Physiological Ecology. Pp. 26–47. Springer, New York 2008.

    Chapter  Google Scholar 

  23. LI-COR Bioscience: Using the LI-6400 Version 5. LI-COR Bioscience, Inc., Lincoln, NE, USA 2004.

    Google Scholar 

  24. Lloyd, J., Grace, C., Miranda, A.C. et al.: A simple calibrated model of Amazon rainforest productivity based on leaf biochemical properties. — Plant Cell. Environ. 18: 1129–1145, 1995.

    Article  Google Scholar 

  25. Long, S.P., Hällgren, J.-E.: Measurement of CO2 assimilation by plants in the field and the laboratory. — In: Hall, D.O., Scurlock, J.M.O., Bolhàr-Nordenkampf, H.R. et al. (eds.): Photosynthesis and Production in a Changing Environment. A Field and Laboratory Manual. Pp. 129–167. Chapman and Hall, London 1993.

    Chapter  Google Scholar 

  26. Lootens, P., Van Waes, J., Carlier, L.: Effect of a short photoinhibition stress on photosynthesis, chlorophyll a fluorescence and pigment contents of different maize cultivars. Can a rapid and objective stress indicator be found? — Photosynthetica 42: 187–192, 2004.

    Article  CAS  Google Scholar 

  27. Luo, Y., Hui, D., Cheng, W. et al.: Canopy quantum yield in a mesocosm study. — Agric. For. Meteorol. 100: 35–48, 2000.

    Article  Google Scholar 

  28. Nobel, P.S.: Physicochemical and Environmental Plant Physiology. Elsevier, Amsterdam 2009.

    Google Scholar 

  29. Nobel, P.S.: Achievable productivities of certain CAM plants: basis for high values compared with C3 and C4 plants. — New Phytol. 119: 183–205, 1991.

    Article  CAS  Google Scholar 

  30. Ögren, E.: Convexity of the photosynthetic light-response curve in relation to intensity and direction of light during growth. — Plant Physiol. 101: 1013–1019, 1993.

    PubMed  Google Scholar 

  31. Prado, C.H.B.A., de Moraes, J.P.A.P.V., de Mattos, E.A.: Gas exchange and leaf water status in potted plants of Copaifera langsdorffii. 1. Responses to water stress. — Photosynthetica 30: 207–213, 1994.

    CAS  Google Scholar 

  32. Prado, C.H.B.A., de Moraes, J.P.A.P.V.: Photosynthetic capacity and specific leaf mass in twenty woody species of cerrado vegetation under field conditions. — Photosynthetica 33: 103–112, 1997.

    Article  Google Scholar 

  33. Prioul, J.L., Chartier, P.: Partitioning of transfer and carboxylation components of intracellular resistance to photosynthetic CO2 fixation: A critical analysis of the methods used. — Ann. Bot. 41: 789–800, 1977.

    Google Scholar 

  34. Ratkowsky, D.A.: Nonlinear Regression Modeling — A Unified Practical Approach. Marcel Dekker, New York 1983.

    Google Scholar 

  35. Ratkowsky, D.A.: Handbook of Nonlinear Regression Models. Marcel Dekker, New York 1990.

    Google Scholar 

  36. Seber, G.A.F., Wild, C.J.: Nonlinear Regression. Wiley-Interscience, Hoboken 2003.

    Google Scholar 

  37. Sharkey, T.D., Bernacchi, C.J., Farquhar, G.D., Singsaas, E.L.: In Practice: Fitting photosynthetic carbon dioxide response curves for C3 leaves. — Plant Cell Environ. 30: 1035–1040, 2007.

    PubMed  Article  CAS  Google Scholar 

  38. Singsaas, E.L., Ort, D.R., DeLucia, E.H.: Variation in measured values of photosynthetic quantum yield in ecophysiological studies. — Oecologia 128: 15–23, 2001.

    Article  Google Scholar 

  39. Smith, E.L.: Photosynthesis in relation to light and carbon dioxide. — PNAS 22: 504–511, 1936.

    PubMed  Article  CAS  Google Scholar 

  40. Stanhill, G., Fuchs, M.: The relative flux density of photosynthetically active radiation. — J. Appl. Ecol. 14: 317–322, 1977.

    Article  Google Scholar 

  41. Vervuren, P.J.A., Beurskens, M.H.H., Blom, C.W.P.M.: Light acclimation, CO2 response and long-term capacity of underwater photosynthesis in three terrestrial plant species. — Plant Cell Environ. 22: 959–968, 1999.

    Article  Google Scholar 

  42. Webb, W.L., Newton, M., Starr, D.: Carbon dioxide exchange of Alnus rubra: a mathematical model. — Oecologia 17: 281–291, 1974.

    Article  Google Scholar 

  43. Wertin, T.M., Teskey, R.O.: Close coupling of whole-plant respiration to net photosynthesis and carbohydrates. — Tree Physiol. 28: 1831–1840, 2008.

    PubMed  Article  CAS  Google Scholar 

  44. Ye, Z.-P.: A new model for relationship between irradiance and the rate of photosynthesis in Oryza sativa. — Photosynthetica 45: 637–640, 2007.

    Article  CAS  Google Scholar 

  45. Zeinalov, Y.: Mechanisms of photosynthetic oxygen evolution and fundamental hypotheses of photosynthesis. — In: Pessarakli, M. (ed.): Handbook of Photosynthesis. Pp. 3–19. Taylor and Francis, Boca Ratón 2005.

    Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

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.

An erratum to this article is available at http://dx.doi.org/10.1007/s11099-014-0045-6.

Electronic supplementary material

Rights and permissions

Reprints and Permissions

About this article

Cite this article

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). https://doi.org/10.1007/s11099-013-0045-y

Download citation

Additional key words

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