Compute the following metrics:

`MeanGermRate`

Mean germination rate (\(\overline{V}\)) (Labouriau and Valadares 1976; Labouriau 1983; Ranal and de Santana 2006) .

`VarGermRate`

Variance of germination rate (\(s_{V}^{2}\)) (Labouriau 1983; Ranal and de Santana 2006) .

`SEGermRate`

Standard error of germination rate (\(s_{\overline{V}}\)) (Labouriau 1983; Ranal and de Santana 2006) .

`CVG`

Coefficient of velocity/rate of germination or Kotowski's coefficient of velocity (\(CVG\)) (Kotowski 1926; Nichols and Heydecker 1968; Labouriau 1983; Scott et al. 1984; Bewley and Black 1994) .

`GermRateRecip`

Germination rate as reciprocal of median time (\(v_{50}\)) (Went 1957; Labouriau 1983; Ranal and de Santana 2006) .

```
MeanGermRate(germ.counts, intervals, partial = TRUE)
CVG(germ.counts, intervals, partial = TRUE)
VarGermRate(germ.counts, intervals, partial = TRUE)
SEGermRate(germ.counts, intervals, partial = TRUE)
GermRateRecip(
germ.counts,
intervals,
partial = TRUE,
method = c("coolbear", "farooq")
)
```

- 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`

.- method
The method for computing median germination time. Either

`"coolbear"`

or`"farooq"`

.

For `MeanGermRate`

, the mean germination rate value as

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

For `VarGermTime`

, the variance of germination rate value as

\(\mathrm{time^{-2}}\).

For `SEGermTime`

, the standard error of germination rate as

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

For `CVG`

, the value of Coefficient of of velocity/rate of germination
or Kotowski's coefficient of velocity as % \(\mathrm{time^{-1}}\).

For `GermRateRecip`

, the value of germination rate as

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

`MeanGermRate`

computes the mean germination rate
(\(\overline{V}\)) according to the following formula
(Labouriau and Valadares 1976; Labouriau 1983; Ranal and de Santana 2006)
.

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

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.

It is the inverse of mean germination time (\(\overline{T}\)).

\[\overline{V} = \frac{1}{\overline{T}}\]

`VarGermRate`

computes the variance of germination rate
(\(s_{V}^{2}\)) according to the following formula
(Labouriau 1983; Ranal and de Santana 2006)
.

\[s_{V}^{2} = \overline{V}^{4} \times s_{T}^{2}\]

Where, \(s_{T}^{2}\) is the variance of germination time.

`SEGermRate`

computes the standard error of germination time
(\(s_{\overline{V}}\)) according to the following formula
(Labouriau 1983; Ranal and de Santana 2006)
.

\[s_{\overline{V}} = \sqrt{\frac{s_{V}^{2}}{\sum_{i=1}^{k}N_{i}}}\]

Where, \(N_{i}\) 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.

`CVG`

computes the coefficient of velocity/rate of germination or
Kotowski's coefficient of velocity (\(CVG\)) according to the following
formula
(Kotowski 1926; Nichols and Heydecker 1968; Labouriau 1983; Scott et al. 1984; Bewley and Black 1994)
.

\[CVG = \frac{\sum_{i=1}^{k}N_{i}}{\sum_{i=1}^{k}N_{i}T_{i}} \times 100\]

\[CVG = \overline{V} \times 100\]

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.

`GermRateRecip`

computes the germination rate (\(v_{50}\)) as the
reciprocal of the median germination time (\(t_{50}\))
(Went 1957; Labouriau 1983; Ranal and de Santana 2006)
according to the methods of
Coolbear et al. (1984)
(Specified by
the argument `method = "coolbear"`

) or
Farooq et al. (2005)
(Specified by
the argument `method = "farooq"`

) as follows.

\[v_{50} = \frac{1}{t_{50}}\]

Bewley JD, Black M (1994).
*Physiology of Development and Germination*.
Plenum Publishing Corporation, New York, USA.
ISBN 0-306-44748-7, tex.ids= bewley_ seeds:_1994, bewley_ seeds:_1994-1, bewley_ seeds:_1994-2 googlebooksid: W6EbrewcpDwC.

Coolbear P, Francis A, Grierson D (1984).
“The effect of low temperature pre-sowing treatment on the germination performance and membrane integrity of artificially aged tomato seeds.”
*Journal of Experimental Botany*, **35**(11), 1609--1617.

Farooq M, Basra SMA, Ahmad N, Hafeez K (2005).
“Thermal hardening: A new seed vigor enhancement tool in rice.”
*Journal of Integrative Plant Biology*, **47**(2), 187--193.

Kotowski F (1926).
“Temperature relations to germination of vegetable seeds.”
*Proceedings of the American Society for Horticultural Science*, **23**, 176--184.

Labouriau LG (1983).
“Uma nova linha de pesquisa na fisiologia da germinacao das sementes.”
In *Anais do XXXIV Congresso Nacional de Botanica. SBB, Porto Alegre*, 11--50.

Labouriau LG, Valadares MEB (1976).
“On the germination of seeds of *Calotropis procera* (Ait.) Ait. f.”
*Anais da Academia Brasileira de Ciencias*, **48**(263-284).

Nichols MA, Heydecker W (1968).
“Two approaches to the study of germination data.”
*Proceedings of the International Seed Testing Association*, **33**(3), 531--540.

Ranal MA, de Santana DG (2006).
“How and why to measure the germination process?”
*Brazilian Journal of Botany*, **29**(1), 1--11.

Scott SJ, Jones RA, Williams WA (1984).
“Review of data analysis methods for seed germination.”
*Crop Science*, **24**(6), 1192--1199.

Went FW (1957).
*The experimental control of plant growth*, volume 17.
Chronica Botanica Co., Waltham, Mass., USA and The Ronald Press Co., New York, USA.

```
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
#----------------------------------------------------------------------------
MeanGermRate(germ.counts = x, intervals = int)
#> [1] 0.1492537
CVG(germ.counts = x, intervals = int)
#> [1] 14.92537
VarGermRate(germ.counts = x, intervals = int)
#> [1] 0.0007176543
SEGermRate(germ.counts = x, intervals = int)
#> [1] 0.004235724
GermRateRecip(germ.counts = x, intervals = int, method = "coolbear")
#> [1] 0.1674877
GermRateRecip(germ.counts = x, intervals = int, method = "farooq")
#> [1] 0.1683168
# From cumulative germination counts
#----------------------------------------------------------------------------
MeanGermRate(germ.counts = y, intervals = int, partial = FALSE)
#> [1] 0.1492537
CVG(germ.counts = y, intervals = int, partial = FALSE)
#> [1] 14.92537
VarGermRate(germ.counts = y, intervals = int, partial = FALSE)
#> [1] 0.0007176543
SEGermRate(germ.counts = y, intervals = int, partial = FALSE)
#> [1] 0.004235724
GermRateRecip(germ.counts = y, intervals = int,
method = "coolbear", partial = FALSE)
#> [1] 0.1674877
GermRateRecip(germ.counts = y, intervals = int,
method = "farooq", partial = FALSE)
#> [1] 0.1683168
```