Keywords
first germination time
continuous-time Markov chains
germinación de semillas
tiempo de la primera germinación
cadenas de Markov a tiempo continuo
How to Cite
Abstract
Assuming that the germination process of a seed passes through several stages (or states), including a state of non-germination, we model this phenomenon by means of a continuous-time Markov chain. The distribution of the germination time and the average of the first germination is obtained. In particular, when the duration of the process at each stage is on average the same we see that the proposed model adjusts rather well some experimental data.
References
G.J. Barry, R.J. Cawood, R.G. Flood, Curve fitting of germination data using the Richards function, Plant, Cell and Environment, 11(1988), no. 3, 183–188. Doi: 10.1111/j.1365-3040.1988.tb01135.x
A. Bould, B.K. Abrol, A model for seed germination curves, Seed Sci and Tech, 9(1981), no. 2, 601–611.
H. Challa, Prediction of production: requisite of an integrated approach, Acta Hortic. 229(1988), 133–141. Doi: 10.17660/ActaHortic.1988.229.11
A.A. Goloff Jr., F.A. Bazzaz, A germination model for natural seed population, J. Theor. Biol. 52(1975), no. 2, 259–283. Doi: 10.1016/0022-5193(75)90001-6
M.K. Gupta, P. Chandra, D.V.K. Samuel, B. Singh, A. Singh, M.K. Garg, Modeling of tomato seedling growth in greenhouse, Agric. Res. 1(2012), 362–369. Doi: 10.1007/s40003-012-0035-5
Y. Hara, Estimating the temperature dependence of germination time by assuming multiple rate-determining steps, Plant. Prod. Sci. 8(2005), no. 4, 361–367. Doi: 10.1626/pps.8.361
H.O. Harley, The modified Gauss-Newton method for the fitting of nonlinear regresion function by least squares, Technometric 3(1961), no. 2, 269–280. Doi: 10.2307/1266117
P.G. Hoel, S.C. Port, C.J. Stone, Introduction to Stochastic Processes, Houghton Mifflin, Boston, 1972.
F.H. Hsu, C.J. Nelson, W.S. Chow, A mathematical model to utilize the logistic function in germination and seedling growth, J. Expl. Bot. 351(1984), no. 11, 1629–1640. doi: 10.1093/jxb/35.11.1629
J.G.M. Janssen, A method of recording germination curves, Ann. Bot. 37(1973), no. 4, 705–708. doi: 10.1093/oxfordjournals.aob.a084738
J.R. Norris, Markov Chains, Cambridge University Press, 1997. doi: 10.1017/CBO9780511810633
J.H.M. Thornley, Germination of seeds and spores, Annals of Botany 41(1977), no. 6, 1363–1365. doi: 10.1093/oxfordjournals.aob.a085425
M. Torres, G. Frutos, Logistic function analysis of germination behaviour of age fennel seeds, Enviromental and Experimental Botany, 30(1990), no. 3, 383–390. doi: 10.1016/0098-8472(90)90051-5
S. Tseng, J.P. Hsu, A stochastic analysis of seed germination, Botanic Bulletin of the Academia Sinica 30(1989), 201–205.