Compute the Peak value (\(PV\)) or Emergence Energy (\(EE\)) (Czabator 1962; Bonner 1967) and Germination value (\(GV\)) (Czabator 1962; Djavanshir and Pourbeik 1976; Brown and Mayer 1988) .
PeakValue(germ.counts, intervals, total.seeds, partial = TRUE)
GermValue(
germ.counts,
intervals,
total.seeds,
partial = TRUE,
method = c("czabator", "dp"),
from.onset = TRUE,
k = 10
)Germination counts at each time interval. Can be partial
or cumulative as specified in the argument partial.
The time intervals.
Total number of seeds.
logical. If TRUE, germ.counts is considered as
partial and if FALSE, it is considered as cumulative. Default is
TRUE.
The method for computing germination value. Either
"czabator" or "dp".
logical. If TRUE, duration is considered only from
the onset of germination. If FALSE, full duration of germination
test is considered. Default is TRUE.
Constant (See Details). Default is 10.
A list with the following components:
The germination value.
The data frame of calculations.
The end of test value (Only for method dp).
Peak value (\(PV\)) is the maximum quotient obtained by dividing successive cumulative germination values by the relevant incubation time (Czabator 1962) .
\[PV = \max\left ( \frac{G_{1}}{T_{1}},\frac{G_{2}}{T_{2}},\cdots \frac{G_{k}}{T_{k}} \right )\]
Where, \(T_{i}\) is the time from the start of the experiment to the \(i\)th interval, \(G_{i}\) is the cumulative germination percentage in the \(i\)th time interval, and \(k\) is the total number of time intervals.
It represents the mean daily germination of the most vigorous component of the seed lot, and is a mathematical expression of the break, or shoulder, of a typical sigmoid germination curve (Djavanshir and Pourbeik 1976) . It is the accumulated number of seeds germinated at the point on the germination curve at which the rate of germination starts to decrease. It is also described as Emergence energy (Bonner 1967) .
For daily germination counts, germination value (\(GV\)) is computed as
follows (Czabator 1962)
(Specified
by the argument method = "czabator").
\[GV = PV \times MDG\]
Where, \(PV\) is the peak value, and \(MDG\) is the mean daily germination percentage from the onset of germination.
Germination value (\(GV\)) can also be computed for other time intervals of successive germination counts, by replacing \(MDG\) with the mean germination percentage per unit time (\(\overline{GP}\)).
A new estimation of germination value was given by
Djavanshir and Pourbeik (1976)
as
follows (Specified by the argument method = "dp").
\[GV = \frac{\sum DGS}{N} \times GP \times c\]
Where, \(DGS\) is the daily germination speed computed by dividing cumulative germination percentage by the number of days since the onset of germination, \(N\) is the frequency or number of DGS calculated during the test, \(GP\) is the germination percentage expressed over 100, and \(c\) is a constant. The value of \(c\) is decided on the basis of average daily speed of germination (\(\frac{\sum DGS}{N}\)). If it is less than 10, then \(c\) value of 10 can be used and if it is more than 10, then value of 7 or 8 can be used for \(c\).
For both methods of computing \(GV\), only the duration from the onset
of germination is considered by default. Alternatively, modified \(GV\)
(\(GV_{mod}\)), where the entire duration from the beginning of the test
is considered can be obtained by using the argument from.onset = FALSE
(Brown and Mayer 1988)
.
Bonner FT (1967).
“Ideal sowing depth for sweetgum seed.”
Tree Planters' Notes, 18(1), 1--1.
Brown RF, Mayer DG (1988).
“Representing cumulative germination. 1. A critical analysis of single-value germination indices.”
Annals of Botany, 61(2), 117--125.
Czabator FJ (1962).
“Germination value: An index combining speed and completeness of pine seed germination.”
Forest Science, 8(4), 386--396.
Djavanshir K, Pourbeik H (1976).
“Germination value-A new formula.”
Silvae Genetica, 25(2), 79--83.
x <- c(0, 0, 34, 40, 21, 10, 4, 5, 3, 5, 8, 7, 7, 6, 6, 4, 0, 2, 0, 2)
y <- c(0, 0, 34, 74, 95, 105, 109, 114, 117, 122, 130, 137, 144, 150,
156, 160, 160, 162, 162, 164)
int <- 1:length(x)
total.seeds = 200
# From partial germination counts
#----------------------------------------------------------------------------
PeakValue(germ.counts = x, intervals = int, total.seeds = 200)
#> [1] 9.5
GermValue(germ.counts = x, intervals = int, total.seeds = 200,
method = "czabator")
#> $`Germination Value`
#> [1] 38.95
#>
#> [[2]]
#> germ.counts intervals Cumulative.germ.counts Cumulative.germ.percent
#> 3 34 3 34 17.0
#> 4 40 4 74 37.0
#> 5 21 5 95 47.5
#> 6 10 6 105 52.5
#> 7 4 7 109 54.5
#> 8 5 8 114 57.0
#> 9 3 9 117 58.5
#> 10 5 10 122 61.0
#> 11 8 11 130 65.0
#> 12 7 12 137 68.5
#> 13 7 13 144 72.0
#> 14 6 14 150 75.0
#> 15 6 15 156 78.0
#> 16 4 16 160 80.0
#> 17 0 17 160 80.0
#> 18 2 18 162 81.0
#> 19 0 19 162 81.0
#> 20 2 20 164 82.0
#> DGS
#> 3 5.666667
#> 4 9.250000
#> 5 9.500000
#> 6 8.750000
#> 7 7.785714
#> 8 7.125000
#> 9 6.500000
#> 10 6.100000
#> 11 5.909091
#> 12 5.708333
#> 13 5.538462
#> 14 5.357143
#> 15 5.200000
#> 16 5.000000
#> 17 4.705882
#> 18 4.500000
#> 19 4.263158
#> 20 4.100000
#>
GermValue(germ.counts = x, intervals = int, total.seeds = 200,
method = "dp", k = 10)
#> $`Germination Value`
#> [1] 53.36595
#>
#> [[2]]
#> germ.counts intervals Cumulative.germ.counts Cumulative.germ.percent
#> 3 34 3 34 17.0
#> 4 40 4 74 37.0
#> 5 21 5 95 47.5
#> 6 10 6 105 52.5
#> 7 4 7 109 54.5
#> 8 5 8 114 57.0
#> 9 3 9 117 58.5
#> 10 5 10 122 61.0
#> 11 8 11 130 65.0
#> 12 7 12 137 68.5
#> 13 7 13 144 72.0
#> 14 6 14 150 75.0
#> 15 6 15 156 78.0
#> 16 4 16 160 80.0
#> 17 0 17 160 80.0
#> 18 2 18 162 81.0
#> 19 0 19 162 81.0
#> 20 2 20 164 82.0
#> DGS SumDGSbyN GV
#> 3 5.666667 5.666667 9.633333
#> 4 9.250000 7.458333 27.595833
#> 5 9.500000 8.138889 38.659722
#> 6 8.750000 8.291667 43.531250
#> 7 7.785714 8.190476 44.638095
#> 8 7.125000 8.012897 45.673512
#> 9 6.500000 7.796769 45.611097
#> 10 6.100000 7.584673 46.266503
#> 11 5.909091 7.398497 48.090230
#> 12 5.708333 7.229481 49.521942
#> 13 5.538462 7.075752 50.945411
#> 14 5.357143 6.932534 51.994006
#> 15 5.200000 6.799262 53.034246
#> 16 5.000000 6.670744 53.365948
#> 17 4.705882 6.539753 52.318022
#> 18 4.500000 6.412268 51.939373
#> 19 4.263158 6.285850 50.915385
#> 20 4.100000 6.164414 50.548194
#>
#> $testend
#> [1] 16
#>
GermValue(germ.counts = x, intervals = int, total.seeds = 200,
method = "czabator", from.onset = FALSE)
#> $`Germination Value`
#> [1] 38.95
#>
#> [[2]]
#> germ.counts intervals Cumulative.germ.counts Cumulative.germ.percent
#> 1 0 1 0 0.0
#> 2 0 2 0 0.0
#> 3 34 3 34 17.0
#> 4 40 4 74 37.0
#> 5 21 5 95 47.5
#> 6 10 6 105 52.5
#> 7 4 7 109 54.5
#> 8 5 8 114 57.0
#> 9 3 9 117 58.5
#> 10 5 10 122 61.0
#> 11 8 11 130 65.0
#> 12 7 12 137 68.5
#> 13 7 13 144 72.0
#> 14 6 14 150 75.0
#> 15 6 15 156 78.0
#> 16 4 16 160 80.0
#> 17 0 17 160 80.0
#> 18 2 18 162 81.0
#> 19 0 19 162 81.0
#> 20 2 20 164 82.0
#> DGS
#> 1 0.000000
#> 2 0.000000
#> 3 5.666667
#> 4 9.250000
#> 5 9.500000
#> 6 8.750000
#> 7 7.785714
#> 8 7.125000
#> 9 6.500000
#> 10 6.100000
#> 11 5.909091
#> 12 5.708333
#> 13 5.538462
#> 14 5.357143
#> 15 5.200000
#> 16 5.000000
#> 17 4.705882
#> 18 4.500000
#> 19 4.263158
#> 20 4.100000
#>
GermValue(germ.counts = x, intervals = int, total.seeds = 200,
method = "dp", k = 10, from.onset = FALSE)
#> $`Germination Value`
#> [1] 46.6952
#>
#> [[2]]
#> germ.counts intervals Cumulative.germ.counts Cumulative.germ.percent
#> 1 0 1 0 0.0
#> 2 0 2 0 0.0
#> 3 34 3 34 17.0
#> 4 40 4 74 37.0
#> 5 21 5 95 47.5
#> 6 10 6 105 52.5
#> 7 4 7 109 54.5
#> 8 5 8 114 57.0
#> 9 3 9 117 58.5
#> 10 5 10 122 61.0
#> 11 8 11 130 65.0
#> 12 7 12 137 68.5
#> 13 7 13 144 72.0
#> 14 6 14 150 75.0
#> 15 6 15 156 78.0
#> 16 4 16 160 80.0
#> 17 0 17 160 80.0
#> 18 2 18 162 81.0
#> 19 0 19 162 81.0
#> 20 2 20 164 82.0
#> DGS SumDGSbyN GV
#> 1 0.000000 0.000000 0.000000
#> 2 0.000000 0.000000 0.000000
#> 3 5.666667 1.888889 3.211111
#> 4 9.250000 3.729167 13.797917
#> 5 9.500000 4.883333 23.195833
#> 6 8.750000 5.527778 29.020833
#> 7 7.785714 5.850340 31.884354
#> 8 7.125000 6.009673 34.255134
#> 9 6.500000 6.064153 35.475298
#> 10 6.100000 6.067738 37.013202
#> 11 5.909091 6.053316 39.346552
#> 12 5.708333 6.024567 41.268285
#> 13 5.538462 5.987174 43.107655
#> 14 5.357143 5.942172 44.566291
#> 15 5.200000 5.892694 45.963013
#> 16 5.000000 5.836901 46.695205
#> 17 4.705882 5.770370 46.162961
#> 18 4.500000 5.699794 46.168331
#> 19 4.263158 5.624182 45.555871
#> 20 4.100000 5.547972 45.493374
#>
#> $testend
#> [1] 16
#>
# From cumulative germination counts
#----------------------------------------------------------------------------
PeakValue(germ.counts = y, interval = int, total.seeds = 200,
partial = FALSE)
#> [1] 9.5
GermValue(germ.counts = y, intervals = int, total.seeds = 200,
partial = FALSE, method = "czabator")
#> $`Germination Value`
#> [1] 38.95
#>
#> [[2]]
#> germ.counts intervals Cumulative.germ.counts Cumulative.germ.percent
#> 3 34 3 34 17.0
#> 4 40 4 74 37.0
#> 5 21 5 95 47.5
#> 6 10 6 105 52.5
#> 7 4 7 109 54.5
#> 8 5 8 114 57.0
#> 9 3 9 117 58.5
#> 10 5 10 122 61.0
#> 11 8 11 130 65.0
#> 12 7 12 137 68.5
#> 13 7 13 144 72.0
#> 14 6 14 150 75.0
#> 15 6 15 156 78.0
#> 16 4 16 160 80.0
#> 17 0 17 160 80.0
#> 18 2 18 162 81.0
#> 19 0 19 162 81.0
#> 20 2 20 164 82.0
#> DGS
#> 3 5.666667
#> 4 9.250000
#> 5 9.500000
#> 6 8.750000
#> 7 7.785714
#> 8 7.125000
#> 9 6.500000
#> 10 6.100000
#> 11 5.909091
#> 12 5.708333
#> 13 5.538462
#> 14 5.357143
#> 15 5.200000
#> 16 5.000000
#> 17 4.705882
#> 18 4.500000
#> 19 4.263158
#> 20 4.100000
#>
GermValue(germ.counts = y, intervals = int, total.seeds = 200,
partial = FALSE, method = "dp", k = 10)
#> $`Germination Value`
#> [1] 53.36595
#>
#> [[2]]
#> germ.counts intervals Cumulative.germ.counts Cumulative.germ.percent
#> 3 34 3 34 17.0
#> 4 40 4 74 37.0
#> 5 21 5 95 47.5
#> 6 10 6 105 52.5
#> 7 4 7 109 54.5
#> 8 5 8 114 57.0
#> 9 3 9 117 58.5
#> 10 5 10 122 61.0
#> 11 8 11 130 65.0
#> 12 7 12 137 68.5
#> 13 7 13 144 72.0
#> 14 6 14 150 75.0
#> 15 6 15 156 78.0
#> 16 4 16 160 80.0
#> 17 0 17 160 80.0
#> 18 2 18 162 81.0
#> 19 0 19 162 81.0
#> 20 2 20 164 82.0
#> DGS SumDGSbyN GV
#> 3 5.666667 5.666667 9.633333
#> 4 9.250000 7.458333 27.595833
#> 5 9.500000 8.138889 38.659722
#> 6 8.750000 8.291667 43.531250
#> 7 7.785714 8.190476 44.638095
#> 8 7.125000 8.012897 45.673512
#> 9 6.500000 7.796769 45.611097
#> 10 6.100000 7.584673 46.266503
#> 11 5.909091 7.398497 48.090230
#> 12 5.708333 7.229481 49.521942
#> 13 5.538462 7.075752 50.945411
#> 14 5.357143 6.932534 51.994006
#> 15 5.200000 6.799262 53.034246
#> 16 5.000000 6.670744 53.365948
#> 17 4.705882 6.539753 52.318022
#> 18 4.500000 6.412268 51.939373
#> 19 4.263158 6.285850 50.915385
#> 20 4.100000 6.164414 50.548194
#>
#> $testend
#> [1] 16
#>
GermValue(germ.counts = y, intervals = int, total.seeds = 200,
partial = FALSE, method = "czabator", from.onset = FALSE)
#> $`Germination Value`
#> [1] 38.95
#>
#> [[2]]
#> germ.counts intervals Cumulative.germ.counts Cumulative.germ.percent
#> 1 0 1 0 0.0
#> 2 0 2 0 0.0
#> 3 34 3 34 17.0
#> 4 40 4 74 37.0
#> 5 21 5 95 47.5
#> 6 10 6 105 52.5
#> 7 4 7 109 54.5
#> 8 5 8 114 57.0
#> 9 3 9 117 58.5
#> 10 5 10 122 61.0
#> 11 8 11 130 65.0
#> 12 7 12 137 68.5
#> 13 7 13 144 72.0
#> 14 6 14 150 75.0
#> 15 6 15 156 78.0
#> 16 4 16 160 80.0
#> 17 0 17 160 80.0
#> 18 2 18 162 81.0
#> 19 0 19 162 81.0
#> 20 2 20 164 82.0
#> DGS
#> 1 0.000000
#> 2 0.000000
#> 3 5.666667
#> 4 9.250000
#> 5 9.500000
#> 6 8.750000
#> 7 7.785714
#> 8 7.125000
#> 9 6.500000
#> 10 6.100000
#> 11 5.909091
#> 12 5.708333
#> 13 5.538462
#> 14 5.357143
#> 15 5.200000
#> 16 5.000000
#> 17 4.705882
#> 18 4.500000
#> 19 4.263158
#> 20 4.100000
#>
GermValue(germ.counts = y, intervals = int, total.seeds = 200,
partial = FALSE, method = "dp", k = 10, from.onset = FALSE)
#> $`Germination Value`
#> [1] 46.6952
#>
#> [[2]]
#> germ.counts intervals Cumulative.germ.counts Cumulative.germ.percent
#> 1 0 1 0 0.0
#> 2 0 2 0 0.0
#> 3 34 3 34 17.0
#> 4 40 4 74 37.0
#> 5 21 5 95 47.5
#> 6 10 6 105 52.5
#> 7 4 7 109 54.5
#> 8 5 8 114 57.0
#> 9 3 9 117 58.5
#> 10 5 10 122 61.0
#> 11 8 11 130 65.0
#> 12 7 12 137 68.5
#> 13 7 13 144 72.0
#> 14 6 14 150 75.0
#> 15 6 15 156 78.0
#> 16 4 16 160 80.0
#> 17 0 17 160 80.0
#> 18 2 18 162 81.0
#> 19 0 19 162 81.0
#> 20 2 20 164 82.0
#> DGS SumDGSbyN GV
#> 1 0.000000 0.000000 0.000000
#> 2 0.000000 0.000000 0.000000
#> 3 5.666667 1.888889 3.211111
#> 4 9.250000 3.729167 13.797917
#> 5 9.500000 4.883333 23.195833
#> 6 8.750000 5.527778 29.020833
#> 7 7.785714 5.850340 31.884354
#> 8 7.125000 6.009673 34.255134
#> 9 6.500000 6.064153 35.475298
#> 10 6.100000 6.067738 37.013202
#> 11 5.909091 6.053316 39.346552
#> 12 5.708333 6.024567 41.268285
#> 13 5.538462 5.987174 43.107655
#> 14 5.357143 5.942172 44.566291
#> 15 5.200000 5.892694 45.963013
#> 16 5.000000 5.836901 46.695205
#> 17 4.705882 5.770370 46.162961
#> 18 4.500000 5.699794 46.168331
#> 19 4.263158 5.624182 45.555871
#> 20 4.100000 5.547972 45.493374
#>
#> $testend
#> [1] 16
#>