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.
Similar content being viewed by others
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
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.
Baly, E.C.C.: The kinetics of photosynthesis. — Proc. R. Soc. Lond. B 117: 218–239, 1935.
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.
Campbell, G.S., Norman, J.M.: An Introduction to Environmental Biophysics. 2nd Ed. Springer-Verlag, New York 1998.
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.
Christie, D.: Resampling with Excel. — Teach. Stat. 26: 9–13, 2004.
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.
Donovan, T.M., Welden, C.W.: Spreadsheet Exercises in Ecology and Evolution. Sinauer Associates, Sunderland 2002.
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.
Falkowski, P.G., Raven, J.A.: Aquatic Photosynthesis. Princeton University Press, Princenton 2007.
Gallegos, C.L., Platt, T.: Photosynthesis measurements on natural populations of phytoplankton: numerical analysis. — Can. Bull. Fish. Aquat. Sci. 210: 103–112, 1981.
Govindjee, Beatty, J.T., Gest, H., Allen, J.F.: Discoveries in Photosynthesis. Springer, Dordrecht 2005.
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.
Hunt, R., Causton, D.R., Shipley, B., Askew, A.P.: A modern tool for classical growth analysis. — Ann. Bot. 90: 485–488, 2002.
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.
Jassby, A.D., Platt, T.: Mathematical formulation of the relationship between photosynthesis and light for phytoplankton. — Limnol. Oceanogr. 21: 540–547, 1976.
Jones, H.B., Archer, N., Rotenberg, E., Casa, R.: Radiation measurement for plant ecophysiology. — J. Exp. Bot. 54: 879–889, 2003.
Jones, M.B.: Photosynthetic responses of C3 and C4 wetland species in a tropical swamp. — J. Ecol. 76: 253–262, 1988.
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.
Kok, B.: On the interrelation of respiration and photosynthesis in green plants. — Biochim. Biophys. Acta 3: 625–631, 1949.
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.
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.
LI-COR Bioscience: Using the LI-6400 Version 5. LI-COR Bioscience, Inc., Lincoln, NE, USA 2004.
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.
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.
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.
Luo, Y., Hui, D., Cheng, W. et al.: Canopy quantum yield in a mesocosm study. — Agric. For. Meteorol. 100: 35–48, 2000.
Nobel, P.S.: Physicochemical and Environmental Plant Physiology. Elsevier, Amsterdam 2009.
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.
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.
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.
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.
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.
Ratkowsky, D.A.: Nonlinear Regression Modeling — A Unified Practical Approach. Marcel Dekker, New York 1983.
Ratkowsky, D.A.: Handbook of Nonlinear Regression Models. Marcel Dekker, New York 1990.
Seber, G.A.F., Wild, C.J.: Nonlinear Regression. Wiley-Interscience, Hoboken 2003.
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.
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.
Smith, E.L.: Photosynthesis in relation to light and carbon dioxide. — PNAS 22: 504–511, 1936.
Stanhill, G., Fuchs, M.: The relative flux density of photosynthetically active radiation. — J. Appl. Ecol. 14: 317–322, 1977.
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.
Webb, W.L., Newton, M., Starr, D.: Carbon dioxide exchange of Alnus rubra: a mathematical model. — Oecologia 17: 281–291, 1974.
Wertin, T.M., Teskey, R.O.: Close coupling of whole-plant respiration to net photosynthesis and carbohydrates. — Tree Physiol. 28: 1831–1840, 2008.
Ye, Z.-P.: A new model for relationship between irradiance and the rate of photosynthesis in Oryza sativa. — Photosynthetica 45: 637–640, 2007.
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.
Author information
Authors and Affiliations
Corresponding author
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
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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11099-013-0045-y