Compute the following metrics:

`GermSpeed`

Speed of germination (\(S\)) or Germination rate index or Index of velocity of germination or Germination index or Emergence rate index (Throneberry and Smith 1955; Maguire 1962; Allan et al. 1962; Kendrick and Frankland 1969; Bouton et al. 1976; Erbach 1982; AOSA 1983; Khandakar and Bradbeer 1983; Hsu and Nelson 1986; Bradbeer 1988; Wardle et al. 1991) .

`GermSpeedAccumulated`

Speed of accumulated germination (\(S_{accumulated}\)) (Bradbeer 1988; Wardle et al. 1991; Haugland and Brandsaeter 1996; de Santana and Ranal 2004) .

`GermSpeedCorrected`

Corrected speed of germination (\(\hat{S}\)) or Corrected germination rate index (Evetts and Burnside 1972) .

```
GermSpeed(
germ.counts,
intervals,
partial = TRUE,
percent = FALSE,
total.seeds = NULL
)
GermSpeedAccumulated(
germ.counts,
intervals,
partial = TRUE,
percent = FALSE,
total.seeds = NULL
)
GermSpeedCorrected(
germ.counts,
intervals,
partial = TRUE,
total.seeds,
method = c("normal", "accumulated")
)
```

- germ.counts
Germination counts at each time interval. Can be partial or cumulative as specified in the argument

`partial`

.- intervals
The time intervals.

- partial
logical. If

`TRUE`

,`germ.counts`

is considered as partial and if`FALSE`

, it is considered as cumulative. Default is`TRUE`

.- percent
logical. If

`TRUE`

, germination percentage is used instead of counts for computation. Default is`FALSE`

.- total.seeds
Total number of seeds. Mandatory for computation when

`percent = TRUE`

.- method
The method for computing germination speed in

`GermSpeedCorrected`

. Either`"normal"`

(`GermSpeed`

) or`"accumulated"`

(`GermSpeedAccumulated`

).

For `GermSpeed`

, the value of germination speed as

\(\mathrm{count \, time^{-1}}\) or % \(\mathrm{time^{-1}}\).

For `GermSpeedAccumulated`

, the value of accumulated germination speed
as \(\mathrm{count \, time^{-1}}\) or % \(\mathrm{time^{-1}}\).

For `GermSpeedCorrected`

, the corrected speed of germination as

\(\mathrm{time^{-1}}\).

`GermSpeed`

computes the speed of germination according to the following
formula
(Throneberry and Smith 1955; Maguire 1962; Allan et al. 1962; Kendrick and Frankland 1969; Bouton et al. 1976; Erbach 1982; AOSA 1983; Khandakar and Bradbeer 1983; Hsu and Nelson 1986; Bradbeer 1988; Wardle et al. 1991)
.

\[S = \frac{N_{1}}{T_{1}} + \frac{N_{2}}{T_{2}} + \frac{N_{3}}{T_{3}} + \cdots + \frac{N_{k}}{T_{k}}\]

Where, \(N_{1}\), \(N_{2}\), \(N_{3}\), \(\cdots\), \(N_{k}\) are the number of germinated seeds observed at time (days or hours) \(T_{1}\), \(T_{2}\), \(T_{3}\), \(\cdots\), \(T_{k}\) after sowing (Not accumulated/cumulative number, but the number of seeds that germinated at the specific time) and \(k\) is the total number of time intervals.

It is the same as Emergence Rate Index (\(ERI\)) described by Allan et al. (1962) , Erbach (1982) and Hsu and Nelson (1986) as well as Germination Index (\(GI\)) according to AOSA (1983) .

The formula can also be described as follows.

\[S = \sum_{i=1}^{k}\frac{N_{i}}{T_{i}}\]

Where, \(T_{i}\) is the time from the start of the experiment to the \(i\)th interval, \(N_{i}\) 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), and \(k\) is the total number of time intervals.

`GermSpeedAccumulated`

computes the speed of accumulated germination as
follows
(Bradbeer 1988; Wardle et al. 1991; Haugland and Brandsaeter 1996; de Santana and Ranal 2004)
.

\[S_{accumulated} = \frac{N_{1}}{T_{1}} + \frac{N_{1} + N_{2}}{T_{2}} + \frac{N_{1} + N_{2} + N_{3}}{T_{3}} + \cdots +\frac{N_{1} + N_{2} + \cdots + N_{k}}{T_{k}}\]

Where, \(N_{1}\), \(N_{2}\), \(N_{3}\), \(\cdots\), \(N_{k}\) are the number of germinated seeds observed at time (days or hours) \(T_{1}\), \(T_{2}\), \(T_{3}\), \(\cdots\), \(T_{k}\) after sowing (Not accumulated/cumulative number, but the number of seeds that germinated at the specific time), and \(k\) is the total number of time intervals.

The formula can also be described as follows.

\[S_{accumulated} = \sum_{i=1}^{k}\frac{\sum_{j=1}^{i}N_{j}}{T_{i}}\]

Where, \(T_{i}\) is the time from the start of the experiment to the \(i\)th interval, \(\sum_{j=1}^{i}N_{j}\) is the cumuative/accumulated number of seeds germinated in the \(i\)th time interval, and \(k\) is the total number of time intervals.

Speed of germination expresses the rate of germination in terms of the total number of seeds that germinate in a time interval. Higher values indicate greater and faster germination. This is useful for comparisons only when samples or treatments possess similar germinabilities. This is overcome by either using the corrected speed of germination or by using germination percentages instead of counts for computing speed.

`GermSpeedCorrected`

computes the corrected speed of germination
\(S\) or corrected speed of accumulated germination \(\hat{S}\) as
follows (Evetts and Burnside 1972)
.

\[\hat{S} = \frac{S}{FGP}\]

\[\hat{S}_{accumulated} = \frac{S_{accumulated}}{FGP}\]

Where, \(S\) is the germination speed or \(\hat{S}\) is the
accumulated speed of germination (as
specified by the argument `method = "normal"`

or ```
method =
"accumulated"
```

respectively) computed with germination percentage instead of
counts and \(FGP\) is the final germination percentage or germinability.

With `percent = TRUE`

, germination percentage is used instead of counts
for computation in `GermSpeed`

and `GermSpeedAccumulated`

. In case
of `GermSpeedCorrected`

, germination percentage is always used for the
numerator.

Allan RE, Vogel OA, Peterson CJ (1962).
“Seedling emergence rate of fall-sown wheat and its association with plant height and coleoptile length.”
*Agronomy Journal*, **54**(4), 347.

AOSA (1983).
*Seed Vigor Testing Handbook*.
Association of Official Seed Analysts, Ithaca, NY, USA.

Bouton JH, Dudeck AE, Smith RL (1976).
“Germination in freshly harvested seed of centipedegrass.”
*Agronomy Journal*, **68**(6), 991.

Bradbeer JW (1988).
*Seed Dormancy and Germination*.
Blackie, Glasgow and London.

de Santana DG, Ranal MA (2004).
*Analise Da Germinacao: Um Enfoque Estatistico*.
Universidade de Brasilia, Brasilia.

Erbach DC (1982).
“Tillage for continuous corn and corn-soybean rotation.”
*Transactions of the ASAE*, **25**(4), 906--0911.

Evetts LL, Burnside OC (1972).
“Germination and seedling development of common milkweed and other species.”
*Weed Science*, **20**(4), 371--378.

Haugland E, Brandsaeter LO (1996).
“Experiments on bioassay sensitivity in the study of allelopathy.”
*Journal of Chemical Ecology*, **22**(10), 1845--1859.

Hsu FH, Nelson CJ (1986).
“Planting date effects on seedling development of perennial warm-season forage grasses. I. Field emergence.”
*Agronomy Journal*, **78**(1), 33--38.

Kendrick RE, Frankland B (1969).
“Photocontrol of germination in *Amaranthus caudatus*.”
*Planta*, **85**(4), 326--339.

Khandakar AL, Bradbeer JW (1983).
*Jute seed quality*.
Bangladesh Agricultural Research Council, Dhaka.

Maguire JD (1962).
“Speed of germination - Aid in selection and evaluation for seedling emergence and vigor.”
*Crop Science*, **2**(2), 176--177.

Throneberry GO, Smith FG (1955).
“Relation of respiratory and enzymatic activity to corn seed viability.”
*Plant Physiology*, **30**(4), 337--343.

Wardle DA, Ahmed M, Nicholson KS (1991).
“Allelopathic influence of nodding thistle (*Carduus nutans* L.) seeds on germination and radicle growth of pasture plants.”
*New Zealand Journal of Agricultural Research*, **34**(2), 185--191.

```
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)
int <- 1:length(x)
# From partial germination counts
#----------------------------------------------------------------------------
GermSpeed(germ.counts = x, intervals = int)
#> [1] 6.138925
GermSpeedAccumulated(germ.counts = x, intervals = int)
#> [1] 34.61567
GermSpeedCorrected(germ.counts = x, intervals = int, total.seeds = 50,
method = "normal")
#> [1] 0.1534731
GermSpeedCorrected(germ.counts = x, intervals = int, total.seeds = 50,
method = "accumulated")
#> [1] 0.8653917
# From partial germination counts (with percentages instead of counts)
#----------------------------------------------------------------------------
GermSpeed(germ.counts = x, intervals = int,
percent = TRUE, total.seeds = 50)
#> [1] 12.27785
GermSpeedAccumulated(germ.counts = x, intervals = int,
percent = TRUE, total.seeds = 50)
#> [1] 69.23134
# From cumulative germination counts
#----------------------------------------------------------------------------
GermSpeed(germ.counts = y, intervals = int, partial = FALSE)
#> [1] 6.138925
GermSpeedAccumulated(germ.counts = y, intervals = int, partial = FALSE)
#> [1] 34.61567
GermSpeedCorrected(germ.counts = y, intervals = int,
partial = FALSE, total.seeds = 50, method = "normal")
#> [1] 0.1534731
GermSpeedCorrected(germ.counts = y, intervals = int,
partial = FALSE, total.seeds = 50, method = "accumulated")
#> [1] 0.8653917
# From cumulative germination counts (with percentages instead of counts)
#----------------------------------------------------------------------------
GermSpeed(germ.counts = y, intervals = int, partial = FALSE,
percent = TRUE, total.seeds = 50)
#> [1] 12.27785
GermSpeedAccumulated(germ.counts = y, intervals = int, partial = FALSE,
percent = TRUE, total.seeds = 50)
#> [1] 69.23134
```