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Modelling seed germination in response to continuous variables: use and limitations of probit analysis and alternative approaches

Published online by Cambridge University Press:  07 July 2014

Fiona R. Hay*
Affiliation:
T.T. Chang Genetic Resources Center, International Rice Research Institute, DAPO Box 7777, Metro, Manila, Philippines
Andrew Mead
Affiliation:
School of Life Sciences, Gibbet Hill Campus, The University of Warwick, CV4 7AL, UK
Mark Bloomberg
Affiliation:
School of Forestry, University of Canterbury, Christchurch 8140, New Zealand
*Corresponding
*Correspondence Fax: +63-2580-5699 E-mail: f.hay@irri.org

Abstract

Probit-based models relating a proportional response variable to a temporal explanatory variable, assuming that the times to response are normally distributed within the population, have been used in seed biology for describing the rate of loss of viability during seed ageing and the progress of germination over time in response to environmental signals (e.g. water, temperature). These models may be expressed as generalized linear models (GLMs) with a probit (cumulative normal distribution) link function, and, using GLM fitting procedures in current statistical software, parameters of these models are efficiently estimated while taking into account the binomial error distribution of the dependent variable. The fitted parameters can then be used to calculate the ‘traditional’ model parameters, such as the hydro- or hydrothermal time constant, the mean or median response of the seeds (e.g. mean time to death, median base water potential), and the standard deviation of the normal distribution of that response. Furthermore, through consideration of the deviance and residuals, performing model evaluation and modification can lead to improved understanding of the underlying physiological/ecological processes. However, fitting a binomial GLM is not appropriate for the cumulative count data often collected from germination studies, as successive observations are not independent, and time-to-event/survival analysis should be considered instead. This review discusses well-known probit-based models, providing advice on how to collect appropriate data and fit the models to those data, and gives an overview of alternative analysis approaches to improve understanding of the underlying mechanisms of seed dormancy and germination behaviour.

Type
Research Papers
Copyright
Copyright © Cambridge University Press 2014 

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References

Alvarado, V. and Bradford, K.J. (2005) Hydrothermal time analysis of seed dormancy in true (botanical) potato seeds. Seed Science Research 15, 7788.Google Scholar
Bazin, J., Batlla, D., Dussert, S., El-Maarouf-Bouteau, H. and Bailly, C. (2011) Role of relative humidity, temperature, and water status in dormancy alleviation of sunflower seeds during dry after-ripening. Journal of Experimental Botany 62, 627640.CrossRefGoogle ScholarPubMed
Bernal-Lugo, I. and Leopold, A.C. (1998) The dynamics of seed mortality. Journal of Experimental Botany 49, 14551461.Google Scholar
Bliss, C. (1935) The calculation of the dosage-mortality curve. Annals of Applied Biology 22, 134167.CrossRefGoogle Scholar
Bloomberg, M., Sedcole, J.R., Mason, E.G. and Buchan, G. (2009) Hydrothermal time germination models for radiate pine (Pinus radiata D. Don). Seed Science Research 19, 171182.CrossRefGoogle Scholar
Boddy, L.G., Bradford, K.J. and Fischer, A.J. (2012) Population-based threshold models describe weed germination and emergence patterns across varying temperature, moisture and oxygen conditions. Journal of Applied Ecology 49, 12251236.CrossRefGoogle Scholar
Bolker, B.M., Brooks, M.E., Clark, C.J., Geange, S.W., Poulsen, J.R., Stevens, H.H. and White, J.-S.S. (2009) Generalized linear mixed models: a practical guide for ecology and evolution. Trends in Ecology and Evolution 24, 127135.CrossRefGoogle ScholarPubMed
Bradford, K.J. (1990) A water relations analysis of seed germination rates. Plant Physiology 94, 840849.CrossRefGoogle ScholarPubMed
Bradford, K.J. (1995) Water relations in seed germination. pp. 351396 in Kigel, J.; Galili, G. (Eds) Seed development and germination. New York, Marcel Dekker.Google Scholar
Bradford, K.J. (2002) Applications of hydrothermal time to quantifying and modeling seed germination and dormancy. Weed Science 50, 248260.CrossRefGoogle Scholar
Bradford, K.J. (2005) Threshold models applied to seed germination ecology. New Phytologist 165, 338341.CrossRefGoogle ScholarPubMed
Bradford, K.J. and Somasco, O.A. (1994) Water relations of lettuce seed thermoinhibition. I. Priming and endosperm effects on base water potential. Seed Science Research 4, 110.CrossRefGoogle Scholar
Bradford, K.J. and Still, D.W. (2004) Applications of hydrotime analysis in seed testing. Seed Technology 26, 7585.Google Scholar
Bradford, K.J., Tarquis, A.M. and Duran, J.M. (1993) A population-based threshold model describing the relationship between germination rates and seed deterioration. Journal of Experimental Botany 44, 12251234.CrossRefGoogle Scholar
Bradford, K.J., Benech-Arnold, R.L., Côme, D. and Corbineau, F. (2008) Quantifying the sensitivity of barley seed germination to oxygen, abscisic acid, and gibberellin using a population-based threshold model. Journal of Experimental Botany 59, 335347.CrossRefGoogle ScholarPubMed
Brain, P. and Butler, R.C. (1988) Cumulative count data. GenStat Newsletter 22, 3847.Google Scholar
Butler, L.H., Hay, F.R., Ellis, R.H., Smith, R.D. and Murray, T.B. (2009) Priming and re-drying improve the survival of mature seeds of Digitalis purpurea during storage. Annals of Botany 103, 12611270.CrossRefGoogle ScholarPubMed
Campbell, R.K. and Sorensen, F.C. (1979) A new basis for characterizing germination. Journal of Seed Technology 4, 2434.Google Scholar
Chantre, G.R., Batlla, D., Sabbatini, M.R. and Orioli, G. (2009) Germination parameterization and development of an after-ripening thermal-time model for primary dormancy release of Lithospermum arvense seeds. Annals of Botany 103, 12911301.CrossRefGoogle ScholarPubMed
Chejara, V.K., Kristiansen, P., Whalley, R.D.B., Sindel, B.M. and Nadolny, C. (2008) Factors affecting germination of Coolatai Grass (Hyparrhenia hirta). Weed Science 56, 543548.CrossRefGoogle Scholar
Covell, S., Ellis, R.H., Roberts, E.H. and Summerfield, R.H. (1986) The influence of temperature on seed germination rate in grain legumes. I. A comparison of chickpea, lentil, soybean and cowpea at constant temperatures. Journal of Experimental Botany 37, 705715.CrossRefGoogle Scholar
Cox, D.R. and Oakes, D. (1984) Analysis of survival data. Boca Raton, Chapman & Hall/CRC.Google Scholar
Crauford, P.Q., Ellis, R.H., Summerfield, R.J. and Menin, L. (1996) Development in cowpea (Vigna unguiculata). I. The influence of temperature on seed germination and seedling emergence. Experimental Agriculture 32, 112.CrossRefGoogle Scholar
Crawford, A.D., Hay, F.R., Plummer, J.A., Probert, R.J. and Steadman, K.J. (2013) One-step fitting of seed viability constants for two Australian plant species, Eucalyptus erythrocorys (Myrtaceae) and Xanthorrhoea preissii (Xanthorrhoeacea). Australian Journal of Botany 61, 110.CrossRefGoogle Scholar
Dahal, P. and Bradford, K.J. (1990) Effects of priming and endosperm integrity on seed germination rates of tomato genotypes. II. Germination at reduced water potential. Journal of Experimental Botany 41, 14411453.CrossRefGoogle Scholar
Dahal, P. and Bradford, K.J. (1994) Hydrothermal time analysis of tomato seed germination at suboptimal temperature and reduced water potential. Seed Science Research 4, 7180.CrossRefGoogle Scholar
Dahal, P., Bradford, K.J. and Jones, R.A. (1990) Effects of priming and endosperm integrity on seed germination rates of tomato genotypes. I. Germination at suboptimal temperatures. Journal of Experimental Botany 41, 14311439.CrossRefGoogle Scholar
Dahal, P., Bradford, K.J. and Haigh, A.M. (1993) The concept of hydrothermal time in seed germination and priming. pp. 10091014 in Côme, D.; Corbineau, F. (Eds) Fourth international workshop on seeds: basic and applied aspects of seed biology, vol. 3. Paris, Association pour la Formation Professionnelle de l'Interprofession Semences.Google Scholar
Demir, I., Kenanoglu, B.B., Mavi, K., Celikkol, T., Hay, F. and Sariyildiz, Z. (2009) Derivation of constants (K E, CW) for the viability equation for pepper seeds and the subsequent test of its applicability. HortScience 44, 16791682.Google Scholar
Demir, I., Kenanoglu, B.B., Hay, F.R., Mavi, K. and Celikko, T. (2011) Determination of seed moisture constants (K E, CW) for the viability equation for watermelon, melon, and cucumber seeds. Seed Science and Technology 39, 527532.CrossRefGoogle Scholar
Dickie, J.B., Ellis, R.H., Kraak, H.L., Ryder, K. and Tompsett, P.B. (1990) Temperature and seed storage longevity. Annals of Botany 65, 197204.CrossRefGoogle Scholar
Dumur, D., Pilbeam, C.J. and Craigon, J. (1990) Use of the Weibull function to calculate cardinal temperatures in faba bean. Journal of Experimental Botany 41, 14231430.CrossRefGoogle Scholar
El-Kassaby, Y.A., Moss, I., Kolotelo, D. and Stoehr, M. (2008) Seed germination: mathematical representation and parameters extraction. Forest Science 54, 220227.Google Scholar
Ellis, R.H. and Hong, T.D. (2007) Quantitative response of the longevity of seed of twelve crops to temperature and moisture content in hermetic storage. Seed Science and Technology 35, 432444.CrossRefGoogle Scholar
Ellis, R.H. and Roberts, E.H. (1980a) Improved equations for the prediction of seed longevity. Annals of Botany 45, 1330.CrossRefGoogle Scholar
Ellis, R.H. and Roberts, E.H. (1980b) Influence of temperature and moisture on seed viability period in barley (Hordeum distichum L.). Annals of Botany 45, 3137.CrossRefGoogle Scholar
Ellis, R.H., Hong, T.D. and Roberts, E.H. (1983) Safe procedures for the removal of rice seed dormancy. Seed Science and Technology 11, 77112.Google Scholar
Ellis, R.H., Covell, S., Roberts, E.H. and Summerfield, R.J. (1986) The influence of temperature on seed germination rate in grain legumes. II. Intraspecific variation in chickpea (Cicer arietinum L.) at constant temperatures. Journal of Experimental Botany 37, 15031515.CrossRefGoogle Scholar
Ellis, R.H., Simon, G. and Covell, S. (1987) The influence of temperature on seed germination rate in grain legumes. III. A comparison of five faba bean genotypes at constant temperatures using a new screening method. Journal of Experimental Botany 38, 10331043.CrossRefGoogle Scholar
Finney, D.J. (1971) Probit analysis. Cambridge, Cambridge University Press.Google Scholar
Garcia-Huidobro, J., Monteith, J.L. and Squire, G.R. (1982) Time, temperature and germination of pearl millet (Pennizetum typhoides S. & H.). I. Constant temperature. Journal of Experimental Botany 33, 288296.CrossRefGoogle Scholar
Gianinetti, A. and Cohn, M.A. (2007) Seed dormancy in red rice. XII: Population-based analysis of dry-afterripening with a hydrotime model. Seed Science Research 17, 253271.CrossRefGoogle Scholar
Gołaszewska, J. and Bochenek, A. (2008) A computational procedure for a hydrotime concept of seed germination. Biometrical Letters 45, 5567.Google Scholar
Graziani, A. and Steinmaus, S.J. (2009) Hydrothermal and thermal time models for the invasive grass, Arundo donax . Aquatic Botany 90, 7884.CrossRefGoogle Scholar
Gummerson, R.J. (1986) The effect of constant temperatures and osmotic potentials n the germination of sugar beet. Journal of Experimental Botany 37, 729741.CrossRefGoogle Scholar
Hardegree, S.P. (2006) Predicting germination response to temperature. I. Cardinal-temperature models and subpopulation-specific regression. Annals of Botany 97, 11151125.CrossRefGoogle ScholarPubMed
Hay, F.R., Mead, A., Manger, K. and Wilson, F.J. (2003) One-step analysis of seed storage data and the longevity of Arabidopsis thaliana seeds. Journal of Experimental Botany 54, 9931011.CrossRefGoogle ScholarPubMed
Hay, F., Klin, J. and Probert, R. (2006) Can a post-harvest ripening treatment extend the longevity of Rhododendron L. seeds? Scientia Horticulturae 111, 8083.CrossRefGoogle Scholar
Hay, F.R., Smith, R.D., Ellis, R.H. and Butler, L.H. (2010) Developmental changes in the germinability, desiccation tolerance, hardseededness, and longevity of individual seeds of Trifolium ambiguum . Annals of Botany 105, 10351052.CrossRefGoogle ScholarPubMed
Hundertmark, M., Buitink, J., Leprince, O. and Hincha, D.K. (2011) The reduction of seed-specific dehydrins reduces seed longevity in Arabidopsis thaliana . Seed Science Research 21, 165173.CrossRefGoogle Scholar
Hunter, E.A., Glasbey, C.A. and Naylor, R.E.L. (1984) The analysis of data from germination tests. Journal of Agricultural Science 102, 207213.CrossRefGoogle Scholar
ISTA (2013) International rules for seed testing edition 2013. Bassersdorf, Switzerland, International Seed Testing Association.Google Scholar
Janssen, J.G.M. (1973) A method for recording germination curves. Annals of Botany 37, 705708.CrossRefGoogle Scholar
Kaplan, E.L. and Meier, P. (1958) Nonparametric estimation from incomplete observations. Journal of the American Statistical Association 53, 457481.CrossRefGoogle Scholar
Kebreab, E. and Murdoch, A.J. (1999a) A quantitative model for loss of primary dormancy and induction of secondary dormancy in imbibed seeds of Orobanche spp. Journal of Experimental Botany 50, 211219.CrossRefGoogle Scholar
Kebreab, E. and Murdoch, A.J. (1999b) Modelling the effects of water stress and temperature on germination rate of Orobanche aegyptiaca seeds. Journal of Experimental Botany 50, 655664.CrossRefGoogle Scholar
Lee, Y., Nelder, J.A. and Pawitan, Y. (2006) Generalized linear models with random effects: unified analysis via H-likelihood. Boca Raton, Chapman & Hall/CRC.CrossRefGoogle Scholar
Manso, R., Fortin, M., Calama, R. and Pardos, M. (2013) Modelling seed germination in forest tree species through survival analysis. The Pinus pinea L. case study. Forest Ecology and Management 289, 515524.CrossRefGoogle Scholar
McCullagh, P. and Nelder, J.A. (1989) Generalized linear models (2nd edition). Florida, Chapman & Hall/CRC.CrossRefGoogle Scholar
McNair, J.N., Sunkara, A. and Frobish, D. (2012) How to analyse seed germination data using statistical time-to-event analysis: non-parametric and semi-parametric methods. Seed Science Research 22, 7795.CrossRefGoogle Scholar
Mead, A. and Gray, D. (1999) Prediction of seed longevity: a modification of the shape of the Ellis and Roberts seed survival curves. Seed Science Research 9, 6373.CrossRefGoogle Scholar
Mesgaran, M.B., Mashhadi, H.R., Alizadeh, H., Hunt, J., Young, K.R. and Cousens, R.D. (2013) Importance of distribution function selection for hydrothermal time models of seed germination. Weed Research 53, 89101.CrossRefGoogle Scholar
Naylor, R.E.L. (2007) Using segmented regression to analyse the response of germination to temperature. Seed Science and Technology 35, 539549.CrossRefGoogle Scholar
Ni, B.-R. and Bradford, K.J. (1992) Quantitative models characterizing seed germination responses to abscisic acid and osmoticum. Plant Physiology 98, 10571068.CrossRefGoogle ScholarPubMed
Ni, B.-R. and Bradford, K.J. (1993) Germination and dormancy of abscisic acid- and gibberellin-deficient mutant tomato (Lycopersicon esculentum) seeds. Sensitivity of germination to abscisic acid, gibberellin, and water potential. Plant Physiology 101, 607617.CrossRefGoogle ScholarPubMed
O'Neill, M.E., Thomson, P., Jacobs, B.C., Brain, P., Butler, R.C., Turner, H. and Mitakda, B. (2004) Fitting and comparing seed germination models with a focus on the inverse normal distribution. Australian and New Zealand Journal of Statistics 46, 349366.CrossRefGoogle Scholar
Onofri, A., Gresta, F. and Tei, F. (2010) A new method for the analysis of germination and emergence data of weed species. Weed Research 50, 187198.CrossRefGoogle Scholar
Payne, R.W., Harding, S.A., Murray, D.A., Soutar, D.M., Baird, D.B., Glaser, A.I., Welham, S.J., Gilmour, A.R., Thompson, R. and Webster, R. (2011) GenStat release 14 reference manual, part 2, directives. Hemel Hempstead, UK, VSN International.Google Scholar
Pierce, D.A. and Schafer, D.W. (1986) Residuals in generalized linear models. Journal of the American Statistical Association 81, 977986.CrossRefGoogle Scholar
Pritchard, H.W. and Dickie, J.B. (2003) Predicting seed longevity: the use and abuse of seed viability equations. pp. 653721 in Smith, R.D.; Dickie, J.B.; Linington, S.H.; Pritchard, H.W.; Probert, R.J. (Eds) Seed conservation: turning science into practice. Kew, UK, Royal Botanic Gardens Kew.Google Scholar
Probert, R.J., Daws, M.I. and Hay, F.R. (2009) Ecological correlates of ex situ seed longevity: a comparative study on 195 species. Annals of Botany 104, 5769.CrossRefGoogle ScholarPubMed
Ritz, C., Pipper, C.B. and Streibig, J.C. (2013) Analysis of germination data from agricultural experiments. European Journal of Agronomy 45, 16.CrossRefGoogle Scholar
Roberts, E.H. (1960) The viability of cereal seed in relation to temperature and moisture. Annals of Botany 24, 1231.CrossRefGoogle Scholar
Roman, E.S., Thomas, A.G., Murphy, S.D. and Swanton, C.J. (1999) Modeling germination and seedling elongation of common lambsquarters (Chenopodium album). Weed Science 47, 149155.Google Scholar
Rowse, H.R. and Finch-Savage, W.E. (2003) Hydrothermal threshold models can describe the germination response of carrot (Daucus carota) and onion (Allium cepa) seed populations across both sub- and supra-optimal temperatures. New Phytologist 158, 101108.CrossRefGoogle Scholar
Scott, S.J. and Jones, R.A. (1985) Cold tolerance in tomato. I. Seed germination and early seedling growth of Lycopersicon esculentum . Physiologia Plantarum 65, 487492.CrossRefGoogle Scholar
Scott, S.J., Jones, R.A. and Williams, W.A. (1984) Review of data analysis methods for seed germination. Crop Science 24, 11921199.CrossRefGoogle Scholar
Shafii, B. and Price, W.J. (2001) Estimation of cardinal temperatures in germination data analysis. Journal of Agricultural Biological and Environmental Statistics 6, 356366.CrossRefGoogle Scholar
Sokal, R.R. and Rohlf, F.J. (2012) Biometry: the principles and practices of statistics in biological research. New York, W.H. Freeman & Company.Google Scholar
Thomas, P.B., Morris, E.C., Auld, T.D. and Haigh, A.M. (2010) The interaction of temperature, water availability and fire cues regulates seed germination in a fire-prone landscape. Oecologia 162, 293302.CrossRefGoogle Scholar
Walters, C. (1998) Understanding the mechanisms and kinetics of seed aging. Seed Science Research 8, 223244.CrossRefGoogle Scholar
Walters, C., Wheeler, L.M. and Grotenhuis, J.M. (2005) Longevity of seeds stored in a genebank: species characteristics. Seed Science Research 15, 120.CrossRefGoogle Scholar
Watt, M.S., Xu, V. and Bloomberg, M. (2010) Development of a hydrothermal time seed germination model which uses the Weibull distribution to describe base water potential. Ecological Modelling 221, 12671272.CrossRefGoogle Scholar
Watt, M.S., Bloomberg, M. and Finch-Savage, W.E. (2011) Development of a hydrothermal time model that accurately characterizes how thermoinhibition regulates seed germination. Plant, Cell and Environment 34, 870876.CrossRefGoogle Scholar
Wood, I.P. and Hay, F.R. (2010) Priming increases the longevity and changes the water sorption properties of Rhododendron griersonianum seeds. Seed Science and Technology 38, 683692.CrossRefGoogle Scholar
Zambrano-Navea, C., Bastida, F. and Gonzalez-Andujar, J.L. (2013) A hydrothermal seedling emergence model for Conyza bonariensis . Weed Research 53, 213220.CrossRefGoogle Scholar
Zewdie, M. and Ellis, R.H. (1991) Comparisons of seed longevity between tef and niger in similar storage conditions. Seed Science and Technology 19, 303307.Google Scholar
Zhang, H., McGill, C.R., Irving, L.J., Kemp, P.D. and Zhou, D. (2013) A modified thermal time model to predict germination rate of ryegrass and tall fescue at constant temperatures. Crop Science 53, 240249.CrossRefGoogle Scholar
Zuk-Gołaszewska, K., Bochenek, A. and Gołaszewski, J. (2007) Effect of scarification on seed germination of red clover in hydrotime model terms. Seed Science and Technology 35, 326336.CrossRefGoogle Scholar
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