Representing cumulative germination.: 2. The use of the weibull function and other empirically derived curves

Annals of Botany

Volumn 61, Issue 2, 1988, Pages 127-138

  Brown, R F ^a   Mayer, D G ^a  

^a DEPARTMENT OF AGRICULTURE AND FISHERIES   (Australia)

Author keywords

Cumulative germination; Gompertz function; Logistic (autocatalytic) function; Mitscherlich (monomolecular) function; Modelling; Morgan Mercer Flodin function; Richards function; Simulation; Weibull function

Indexed keywords

EID: 38249030395     PISSN: 03057364     EISSN: None     Source Type: Journal    
DOI: 10.1093/oxfordjournals.aob.a087535     Document Type: Article

References (34)

1. Akaike, H., 1970. Statistical predictor identification. Annals of the Institute of Statistics and Mathematics 22, 203-17.
2. Berrettoni, J. N., 1964, Practical applications of the Weibull distribution. Industrial Quality Control 21, 71-9.
3. Bierhuizen, J. F., Wagenvoort, W. A. and Nilwik, H., 1978. Analysis of the relationship between temperature and germination of sweet pepper. Acta Horticulturae 83, 195-9.
4. Bould, A. and Abrol, B. K., 1981. A model for seed germination curves. Seed Science and Technology 9, 601-11.
5. Brown, R. F., 1987. Germination of Aristida armata under constant and alternating temperatures and its analysis with the cumulative Weibull distribution as a model. Australian Journal of Botany 35, 581-91.
6. Akaike, H., and Mayer, D. G., 1986. Problems in applying Thomley’s model of germination. Annals of Botany 57, 49-53.
7. Akaike, H., 1988. Representing cumulative germination. 1. A critical analysis of single-value germination indices. Annals of Botany 61, 117-25.
8. Campbell, R. F. and Sorensen, F. C., 1979. A new basis for characterising germination. Journal of Seed Technology 4, 24-34.
9. Dubey, S. D., 1967. Normal and Weibull distributions. Naval Research Logistics Quarterly 14, 69-79.
10. Akaike, H., 1968. A compound Weibull distribution. Naval Research Logistics Quarterly 15, 179-88.
11. Elias, C. O. and Causton, D. R., 1976. Studies on data variability and the use of polynomials to describe plant growth. New Phytologist 77, 421-30.
12. Freeman, T. G., 1984. Selecting the best model to fit data. Proceedings of the Sixth Biennial Conference of the Simulation Society of Australia, 13-15 August 1984, University of Adelaide, South Australia, pp. 145-7.
13. Goodchild, N. A. and Walker, M. G., 1971. A method of measuring seed germination in physiological studies. Annals of Botany 35, 615-21.
14. Hsu, F. H., Nelson, C. J. and Chow, W. S., 1984. A mathematical model to utilise the logistic function in germination and seedling growth. Journal of Experimental Botany 35, 1629-40.
15. Hunt, R., 1979. Plant growth analysis: the rationale behind the use of the fitted mathematical function. Annals of Botany 43, 245-9.
16. Janssen, J. G. M., 1973. A method of recording germination curves. Annals of Botany 37, 705-8.
17. Johnson, N. L. and Kotz, S., 1970. Distributions in Statistics: Continuous Univariate Distributions, vol. 1, pp. 250-271. Wiley, New York.
18. Landsberg, J. J., 1977. Some useful equations for biological studies. Experimental Agriculture 13, 273-86.
19. Lapp, M. S. and Skoropad, W. P., 1976. A mathematical model of conidial germination and appressorial formation for Colletotrichum graminicola. Canadian Journal of Botany 54, 2239-42.
20. Leslie, J. K., 1965. Factors affecting grass establishment on the black earths of Queensland. Proceedings of the IXth International Grassland Congress 1, 245-9.
21. Akaike, H., 1970. Studies of latent periods and their distribu-tions for germinating seed populations of rhodes grass (Chloris gayana Kunth.) and Makarikari grass (Panicum coloratum L. var. makarikariense) with particular reference to temperature responses. Ph.D. thesis, University of Queensland.
22. Morgan, P. H., Mercer, L. P. and Flodin, N. W. (1975). General model for nutritional responses of higher organisms. Proceedings of the National Academy of Sciences, USA 72, 4327-4331.
23. Patel, J. K., Kapadia, C. H. and Owen, D. B., 1976. Handbook of Statistical Distributions, 302 pp. Dekker, New York.
24. Plait, A., 1962. The Weibull distribution -with tables. Industrial Quality Control 19, 17-26.
25. Ratkowsky, D. A., 1983. Non-linear Regression Modelling: a Unified Practical Approach, 276 pp. Dekker, New York.
26. Rawlings, J. O. and Cure, W. W., 1985. The Weibull function as a dose-response model to describe ozone effects on crop yields. Crop Science 25, 807-814.
27. Richards, F. J., 1959. A flexible growth function for empirical use. Journal of Experimental Botany 10, 290-300.
28. Richter, D. D. and Switzer, G. L., 1982. A technique for determining quantitative expressions of dormancy in seeds. Annals of Botany 50, 459-63.
29. Schimpf, D. J., Flint, S. D. and Palmblad, I. G., 1977. Representation of germination curves with the logistic function. Annals of Botany 41, 1357-60.
30. Scott, S. J., Jones, R. A. and Williams, W. A., 1984. Review of data analysis methods for seed germination. Crop Science 24, 1192-9.
31. Thornley, J. H. M., 1977. Germination of seeds and spores. Annals of Botany 41, 1363-5.
32. Tucker, H. and Wright, L. N., 1965. Estimating rapidity of germination. Crop Science 5, 398-9.
33. Venus, J. C. and Causton, D. R., 1979. Plant growth analysis: the use of the Richards functions as an alternative to polynomial exponentials. Annals of Botany 43, 623-32.
34. Weibull, W., 1951. A statistical distribution function of wide applicability. Journal of Applied Mechanics 18, 293-7.