Plants adapt to continual changes in environmental conditions throughout their life spans. High-throughput phenotyping methods have been developed to noninvasively monitor the physiological responses to abiotic/biotic stresses on a scale spanning a long time, covering most of the vegetative and reproductive stages. However, some of the physiological events comprise almost immediate and very fast responses towards the changing environment which might be overlooked in long-term observations. Additionally, there are certain technical difficulties and restrictions in analyzing phenotyping data, especially when dealing with repeated measurements. In this study, a method for comparing means at different time points using generalized linear mixed models combined with classical time series models is presented. As an example, we use multiple chlorophyll time series measurements from different genotypes. The use of additional time series models as random effects is essential as the residuals of the initial mixed model may contain autocorrelations that bias the result. The nature of mixed models offers a viable solution as these can incorporate time series models for residuals as random effects. The results from analyzing chlorophyll content time series show that the autocorrelation is successfully eliminated from the residuals and incorporated into the final model. This allows the use of statistical inference.

Department of Electrical and Computer Engineering Democritus University of Thrace 67100 Xanthi Greece

Functional Genomics and Proteomics of Plants CEITEC Central European Institute of Technology and National Centre for Biotechnology Research Faculty of Science Kamenice 5 62500 Brno Czech Republic

Photon Systems Instruments 66424 Drásov Czech Republic

Plant Sciences Core Facility CEITEC Central European Institute of Technology Masaryk University Kamenice 5 62500 Brno Czech Republic

See more in PubMed

Box G.E.P., Jenkins G.M., Reinsel G.C., Ljung G.M. Time Series Analysis: Forecasting and Control. John Wiley & Sons; Hoboken, NJ, USA: 2015. pp. 21–46.

Kaiser E., Morales A., Harbinson J., Kromdijk J., Heuvelink E., Marcelis L.F.M. Dynamic Photosynthesis in Different Environmental Conditions. J. Exp. Bot. 2015;66:2415–2426. doi: 10.1093/jxb/eru406. PubMed DOI

Kaiser E., Morales A., Harbinson J. Fluctuating Light Takes Crop Photosynthesis on a Rollercoaster Ride. Plant Physiol. 2018;76:977–989. doi: 10.1104/pp.17.01250. PubMed DOI PMC

Kaiser E., Galvis V.C., Armbruster U. Efficient Photosynthesis in Dynamic Light Environments: A Chloroplast’s Perspective. Biochem. J. 2019;476:2725–2741. doi: 10.1042/BCJ20190134. PubMed DOI PMC

Morales A., Kaiser E. Photosynthetic acclimation to fluctuating irradiance in plants. Front. Plant Sci. 2020;11:268. doi: 10.3389/fpls.2020.00268. PubMed DOI PMC

Way D.A., Pearcy R.W. Sunflecks in Trees and Forests: From Photosynthetic Physiology to Global Change Biology. Tree Physiol. 2012;32:1066–1081. doi: 10.1093/treephys/tps064. PubMed DOI

Peak D., Mott K.A. A New, Vapour-Phase Mechanism for Stomatal Responses to Humidity and Temperature. Plant Cell Environ. 2011;34:162–178. doi: 10.1111/j.1365-3040.2010.02234.x. PubMed DOI

Stitt M., Lunn J., Usadel B. Arabidopsis and Primary Photosynthetic Metabolism—More than the Icing on the Cake. Plant J. 2010;61:1067–1091. doi: 10.1111/j.1365-313X.2010.04142.x. PubMed DOI

Taylor S., Terry N. Limiting Factors in Photosynthesis: V. Photochemical Energy Supply Colimits Photosynthesis at Low Values of Intercellular CO2 Concentration. Limiting Factors in Photosynthesis: V. Photochemical Energy Supply Colimits Photosynthesis at Low Values of Intercellular CO2 Concentration. Plant Physiol. 1984;75:82–86. doi: 10.1104/pp.75.1.82. PubMed DOI PMC

Bailey S., Walters R.G., Jansson S., Horton P. Acclimation of Arabidopsis thaliana to the Light Environment: The Existence of Separate Low Light and High Light Responses. Planta. 2001;213:794–801. doi: 10.1007/s004250100556. PubMed DOI

Anderson J.M., Chow W.S., Park Y.I. The Grand Design of Photosynthesis: Acclimation of the Photosynthetic Apparatus to Environmental Cues. Photosynth. Res. 1995;46:129–139. doi: 10.1007/BF00020423. PubMed DOI

Nelson N., Ben-Shem A. The Complex Architecture of Oxygenic Photosynthesis. Nat. Rev. Mol. Cell Biol. 2004;5:971–982. doi: 10.1038/nrm1525. PubMed DOI

Mir R.R., Reynolds M., Pinto F., Khan M.A., Bhat M.A. High-Throughput Phenotyping for Crop Improvement in the Genomics Era. Plant Sci. 2019;282:60–72. doi: 10.1016/j.plantsci.2019.01.007. PubMed DOI

Pérez-Bueno M.L., Pineda M., Barón M. Phenotyping Plant Responses to Biotic Stress by Chlorophyll Fluorescence Imaging. Front. Plant Sci. 2019;10:1135. doi: 10.3389/fpls.2019.01135. PubMed DOI PMC

Humplík J.F., Dostál J., Ugena L., Spíchal L., de Diego N., Vencálek O., Fürst T. Bayesian Approach for Analysis of Time-to-Event Data in Plant Biology. Plant Methods. 2020;16:14. doi: 10.1186/s13007-020-0554-1. PubMed DOI PMC

Flood P.J., Kruijer W., Schnabel S.K., Schoor R., Jalink H., Snel J.F.H., Harbinson J., Aarts M.G.M. Phenomics for Photosynthesis, Growth and Reflectance in Arabidopsis thaliana Reveals Circadian and Long-Term Fluctuations in Heritability. Plant Methods. 2016;12:1–14. doi: 10.1186/s13007-016-0113-y. PubMed DOI PMC

Hedeker D.R., Gibbons R.D. Longitudinal Data Analysis. John Wiley and Sons; Hoboken, NJ, USA: 2006. pp. 47–79.

Tanaka R., Kobayashi K., Masuda T. Tetrapyrrole Metabolism in Arabidopsis thaliana. Arab. Book. 2011;9:e0145. doi: 10.1199/tab.0145. PubMed DOI PMC

Reinbothe S., Reinbothe C., Apel K., Lebedev N. Evolution of Chlorophyll Biosynthesis—The Challenge to Survive Photooxidation. Cell. 1996;86:703–705. doi: 10.1016/S0092-8674(00)80144-0. PubMed DOI

McCulloch C.E., Neuhaus J.M. Generalized Linear Mixed Models. In: Armitage P., Colton T., editors. Encyclopedia of Biostatistics. 2nd ed. Volume 2. John Wiley and Sons; Hoboken, NJ, USA: 2005. pp. 2085–2089.

Clauw P., Coppens F., de Beuf K., Dhondt S., van Daele T., Maleux K., Storme V., Clement L., Gonzalez N., Inzé D. Leaf Responses to Mild Drought Stress in Natural Variants of Arabidopsis. Plant Physiol. 2015;167:800–816. PubMed PMC

Corbeil R.R., Searle S.R. Restricted Maximum Likelihood (REML) Estimation of Variance Components in the Mixed Model. Technometrics. 1976;18:31–38. doi: 10.2307/1267913. DOI

Hunger M., Döring A., Holle R. Longitudinal Beta Regression Models for Analyzing Health-Related Quality of Life Scores over Time. BMC Med. Res. Methodol. 2012;12:144. doi: 10.1186/1471-2288-12-144. PubMed DOI PMC

Draper N.R., Smith H. Applied Regression Analysis. John Wiley and Sons; Hoboken, NJ, USA: 1998. pp. 299–326.

Wolfinger R.D. Heterogeneous Variance-Covariance Structures for Repeated Measures. J. Agric. Biol. Environ. Stat. 1996;1:205–230. doi: 10.2307/1400366. DOI

Lütkepohl H., Xu F. The Role of the Log Transformation in Forecasting Economic Variables. Empir. Econ. 2012;42:619–638. doi: 10.1007/s00181-010-0440-1. DOI

Brooks M.E., Kristensen K., van Benthem K.J., Magnusson A., Berg C.W., Nielsen A., Skaug H.J., Maechler M., Bolker B.M. glmmTMB Balances Speed and Flexibility among Packages for Zero-Inflated Generalized Linear Mixed Modeling. R J. 2017;9:378–400. doi: 10.32614/RJ-2017-066. DOI

Hyndman R.J., Khandakar Y. Automatic Time Series Forecasting: The Forecast Package for R. J. Stat. Softw. 2008;27:1–22. doi: 10.18637/jss.v027.i03. DOI

Hyndman R., Athanasopoulos G., Bergmeir C., Caceres G., Chhay L., O’Hara-Wild M., Petropoulos F., Razbash S., Wang E., Yasmeen F., et al. Forecasting Functions for Time Series and Linear Models. [(accessed on 20 November 2020)];2019 Available online: https://cran.r-project.org/web/packages/forecast/forecast.pdf.

R Core Team . R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing; Vienna, Austria: 2014. [(accessed on 20 November 2020)]. Available online: http://www.R-project.org/

Rstudio T. RStudio: Integrated Development for R. RStudio, PBC; Boston, MA, USA: 2020. DOI

Hyndman R.J., Athanasopoulos G. Forecasting: Principles and Practice. 2nd ed. OTexts; Melbourne, Australia: 2018. [(accessed on 20 November 2020)]. Available online: OTexts.com/fpp2.

Lee S., Lee D.K. What Is the Proper Way to Apply the Multiple Comparison Test? Korean J. Anesthesiol. 2018;71:353. doi: 10.4097/kja.d.18.00242. PubMed DOI PMC

Fitzmaurice G., Laird N., Ware J. Applied Longitudinal Analysis. 2nd ed. John Wiley & Sons; Hoboken, NJ, USA: 2011. pp. 76–86.

Crowder M.J., Hand D.J. Analysis of Repeated Measures. 2nd ed. CRC Press; Boca Raton, FL, USA: 2017. pp. 5–11.

Sun D., Zhu Y., Xu H., He Y., Cen H. Time-Series Chlorophyll Fluorescence Imaging Reveals Dynamic Photosynthetic Fingerprints of sos Mutants to Drought Stress. Sensors. 2019;19:2649. PubMed PMC

Banks J.M. Chlorophyll Fluorescence as a Tool to Identify Drought Stress in Acer Genotypes. Environ. Exp. Bot. 2018;155:118–127. doi: 10.1016/j.envexpbot.2018.06.022. DOI

Liu X., Li Y., Zhong S. Interplay between Light and Plant Hormones in the Control of Arabidopsis Seedling Chlorophyll Biosynthesis. Front. Plant Sci. 2017;8:1433. doi: 10.3389/fpls.2017.01433. PubMed DOI PMC

Zhong S., Shi H., Xue C., Wei N., Guo H., Deng X.W. Ethylene-Orchestrated Circuitry Coordinates a Seedling’s Response to Soil Cover and Etiolated Growth. Proc. Natl. Acad. Sci. USA. 2014;111:3913–3920. doi: 10.1073/pnas.1402491111. PubMed DOI PMC

Hau B. Mathematical Functions to Describe Disease Progress Curves of Double Sigmoid Pattern. Phytopathology. 1993;83:928–932.

Neher D.A., Campbell C.L. Underestimation of Disease Progress Rates with the Logistic, Monomolecular, and Gompertz Models When Maximum Disease Intensity Is Less Than 100 Percent. Phytopathology. 1992;82:811–814.

iReenCAM: automated imaging system for kinetic analysis of photosynthetic pigment biosynthesis at high spatiotemporal resolution during early deetiolation