Compute the following metrics:
FirstGermTimeTime of first germination or Germination time lag (\(t_{0}\)) (Edwards 1932; Czabator 1962; Goloff and Bazzaz 1975; Labouriau 1983; Ranal 1999; Quintanilla et al. 2000) .
LastGermTimeTime of last germination (\(t_{g}\)) (Edwards 1932; Labouriau 1983; Ranal and de Santana 2006) .
TimeSpreadGermTime spread of germination (Al-Mudaris 1998; Kader 2005) or Germination distribution (Schrader and Graves 2000) .
PeakGermTimePeak time of germination or Modal time of germination (\(t_{peak}\)) (Ranal and de Santana 2006) .
FirstGermTime(germ.counts, intervals, partial = TRUE)
LastGermTime(germ.counts, intervals, partial = TRUE)
PeakGermTime(germ.counts, intervals, partial = TRUE)
TimeSpreadGerm(germ.counts, intervals, partial = TRUE)Germination counts at each time interval. Can be partial
or cumulative as specified in the argument partial.
The time intervals.
logical. If TRUE, germ.counts is considered as
partial and if FALSE, it is considered as cumulative. Default is
TRUE.
For FirstGermTime, the time of first germination value in the
same unit of time as specified in the argument intervals.
For LastGermTime, the time of last germination value in the same
unit of time as specified in the argument intervals.
For TimeSpreadGerm, the time spread of germination value in the same
unit of time as specified in the argument intervals.
For PeakGermTime, the time(s) of peak germination value(s) as a
numeric vector in the same unit of time as specified in the argument
intervals.
Time of first germination indicates time of germination of the faster seeds in a seedlot.
Lower value of time of first germination indicates faster initiation of germination and lower value of time of last germination indicates faster termination of germination.
\[t_{0} = \min \lbrace T_{i} : N_{i} \neq 0 \rbrace\]
\[t_{g} = \max \lbrace T_{i} : N_{i} \neq 0 \rbrace\]
Where, \(T_{i}\) is the time from the start of the experiment to the \(i\)th interval and \(N_{i}\) is the number of seeds germinated in the \(i\)th time interval (not the accumulated number, but the number corresponding to the \(i\)th interval).
Time spread of germination (\(t_{g}-t_{0}\)) indicates difference between faster and slower germinating members of a sample.
Peak time of germination is the time in which highest frequency of germinated seeds are observed. Multiple peak times of germination are possible and if detected are indicated by a warning message.
\[t_{peak} = \lbrace T_{i} : N_{i} = N_{max} \rbrace\]
Where, \(N_{max}\) is the maximum number of seeds germinated per interval.
Al-Mudaris MA (1998).
“Notes on various parameters recording the speed of seed germination.”
Der Tropenlandwirt - Journal of Agriculture in the Tropics and Subtropics, 99(2), 147--154.
Czabator FJ (1962).
“Germination value: An index combining speed and completeness of pine seed germination.”
Forest Science, 8(4), 386--396.
Edwards TI (1932).
“Temperature relations of seed germination.”
The Quarterly Review of Biology, 7(4), 428--443.
Goloff AA, Bazzaz FA (1975).
“A germination model for natural seed populations.”
Journal of Theoretical Biology, 52(2), 259--283.
Kader MA (2005).
“A comparison of seed germination calculation formulae and the associated interpretation of resulting data.”
Journal and Proceedings of the Royal Society of New South Wales, 138, 65--75.
Labouriau LG (1983).
A Germinacao Das Sementes.
Organizacao dos Estados Americanos. Programa Regional de Desenvolvimento Cientifico e Tecnologico. Serie de Biologia. Monografia 24.
Quintanilla LG, Pajaron S, Pangua E, Amigo J (2000).
“Effect of temperature on germination in northernmost populations of Culcita macrocarpa and Woodwardia radicans.”
Plant Biology, 2(6), 612--617.
Ranal MA (1999).
“Effects of temperature on spore germination in some fern species from semideciduous mesophytic forest.”
American Fern Journal, 89(2), 149.
Ranal MA, de Santana DG (2006).
“How and why to measure the germination process?”
Brazilian Journal of Botany, 29(1), 1--11.
Schrader JA, Graves WR (2000).
“Seed germination and seedling growth of Alnus maritima from its three disjunct populations.”
Journal of the American Society for Horticultural Science, 125(1), 128--134.
x <- c(0, 0, 0, 0, 4, 17, 10, 7, 1, 0, 1, 0, 0, 0)
y <- c(0, 0, 0, 0, 4, 21, 31, 38, 39, 39, 40, 40, 40, 40)
z <- c(0, 0, 0, 0, 11, 11, 9, 7, 1, 0, 1, 0, 0, 0)
int <- 1:length(x)
# From partial germination counts
#----------------------------------------------------------------------------
FirstGermTime(germ.counts = x, intervals = int)
#> [1] 5
LastGermTime(germ.counts = x, intervals = int)
#> [1] 11
TimeSpreadGerm(germ.counts = x, intervals = int)
#> [1] 6
PeakGermTime(germ.counts = x, intervals = int)
#> [1] 6
# For multiple peak germination times
PeakGermTime(germ.counts = z, intervals = int)
#> Warning: Multiple peak germination times exist.
#> [1] 5 6
# From cumulative germination counts
#----------------------------------------------------------------------------
FirstGermTime(germ.counts = y, intervals = int, partial = FALSE)
#> [1] 5
LastGermTime(germ.counts = y, intervals = int, partial = FALSE)
#> [1] 11
TimeSpreadGerm(germ.counts = y, intervals = int, partial = FALSE)
#> [1] 6
PeakGermTime(germ.counts = y, intervals = int, partial = FALSE)
#> [1] 6
# For multiple peak germination time
PeakGermTime(germ.counts = cumsum(z), intervals = int, partial = FALSE)
#> Warning: Multiple peak germination times exist.
#> [1] 5 6