Compute the Emergence rate index or Germination rate index according to

Shmueli and Goldberg (1971) and it's modification by de Santana and Ranal (2004) (Ranal and de Santana 2006) ;

Bilbro and Wanjura (1982) ; and

Fakorede and Ayoola (1980) , Fakorede and Ojo (1981) , and Fakorede and Agbana (1983) .

```
EmergenceRateIndex(
germ.counts,
intervals,
partial = TRUE,
total.seeds = NULL,
method = c("shmueligoldberg", "sgsantanaranal", "bilbrowanjura", "fakorede")
)
```

- 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`

.- total.seeds
Total number of seeds.

- method
The method to be used. Either

`"shmueligoldberg"`

,`"sgsantanaranal"`

,`"bilbrowanjura"`

or`"fakorede"`

. Default is`"shmueligoldberg"`

(see**Details**).

The value of the Emergence rate index with the units according to

`method`

as follows.

`shmueligoldberg`

\(\mathrm{count}\)

`sgsantanaranal`

\(\mathrm{no \, unit}\)

`bilbrowanjura`

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

`fakorede`

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

Several germination indices are referred to as Emergence rate Index (\(ERI\)).

With argument `method`

specified as `"shmueligoldberg"`

\(ERI\) is estimated as follows.

\[ERI = \sum_{i=i_{0}}^{k-1}N_{i}(k-i)\]

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), \(i_{0}\) is the time interval when emergence/germination started, and \(k\) is the total number of time intervals.

A modification for the same was suggested by
de Santana and Ranal (2004)
(Ranal and de Santana 2006)
and is estimated by
dividing Emergence rate index (\(ERI\)) by total number of emerged
seedlings (or germinated seeds) as follows with argument `method`

specified as `"sgsantanaranal"`

).

\[ERI_{mod} = \frac{\sum_{i=i_{0}}^{k-1}N_{i}(k-i)}{N_{g}} = \frac{ERI}{N_{g}}\]

Where, \(N_{g}\) is the total number of germinated seeds at the end of the test, \(N_{i}\) 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), \(i_{0}\) is the time interval when emergence/germination started, and \(k\) is the total number of time intervals.

With argument `method`

specified as `"bilbrowanjura"`

\(ERI\) is the estimated as follows.

\[ERI = \frac{\sum_{i=1}^{k}N_{i}}{\overline{T}} = \frac{N_{g}}{\overline{T}}\]

Where, \(N_{g}\) is the total number of germinated seeds at the end of the test, \(N_{i}\) 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 \(\overline{T}\) is the mean germination time or mean emergence time.

With argument `method`

specified as `"fakorede"`

\(ERI\) is
the estimated as follows.

\[ERI = \frac{\overline{T}}{FGP/100}\]

Where, \(\overline{T}\) is the Mean germination time and \(FGP\) is the final germination time.

Apart from the above the above, the name Emergence
rate index (\(ERI\)) has also been used to for the mathematical
expressions for Speed of germination
(`GermSpeed`

)
(Allan et al. 1962; Erbach 1982)
,
Timson's index (`TimsonsIndex`

)
(Chaudhary and Ghildyal 1970)
,
and George's index
(`GermRateGeorge`

)
(Chopra and Chaudhary 1980)
.

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.

Bilbro JD, Wanjura DF (1982).
“Soil crusts and cotton emergence relationships.”
*Transactions of the ASAE*, **25**(6), 1484--1487.

Chaudhary TN, Ghildyal BP (1970).
“Effect of temperature associated with levels of bulk density on rice seedling emergence.”
*Plant and Soil*, **33**(1), 87--90.

Chopra UK, Chaudhary TN (1980).
“Effect of soil temperature alteration by soil covers on seedling emergence of wheat (*Triticum aestivum* L.) sown on two dates.”
*Plant and Soil*, **57**(1), 125--129.

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.

Fakorede MAB, Agbana SB (1983).
“Heterotic effects and association of seedling vigour with mature characteristics and grain yield in some tropical maize cultivars.”
*Maydica*, **28**, 327--338.

Fakorede MAB, Ayoola AO (1980).
“Relation between seedling vigor and selection for yield improvement in maize.”
*Maydica*, **25**(3), 135--147.

Fakorede MAB, Ojo DK (1981).
“Variability for seedling vigour in maize.”
*Experimental Agriculture*, **17**(2), 195--201.

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

Shmueli M, Goldberg D (1971).
“Emergence, early growth, and salinity of five vegetable crops germinated by sprinkle and trickle irrigation in an arid zone.”
*HortScience*, **6**, 563--565.

```
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
#----------------------------------------------------------------------------
EmergenceRateIndex(germ.counts = x, intervals = int)
#> [1] 292
EmergenceRateIndex(germ.counts = x, intervals = int,
method = "shmueligoldberg")
#> [1] 292
EmergenceRateIndex(germ.counts = x, intervals = int,
method = "sgsantanaranal")
#> [1] 7.3
EmergenceRateIndex(germ.counts = x, intervals = int,
method = "bilbrowanjura")
#> [1] 5.970149
EmergenceRateIndex(germ.counts = x, intervals = int,
total.seeds = 50, method = "fakorede")
#> [1] 8.375
# From cumulative germination counts
#----------------------------------------------------------------------------
EmergenceRateIndex(germ.counts = y, intervals = int, partial = FALSE)
#> [1] 292
EmergenceRateIndex(germ.counts = y, intervals = int, partial = FALSE,
method = "shmueligoldberg")
#> [1] 292
EmergenceRateIndex(germ.counts = y, intervals = int, partial = FALSE,
method = "sgsantanaranal")
#> [1] 7.3
EmergenceRateIndex(germ.counts = y, intervals = int, partial = FALSE,
method = "bilbrowanjura")
#> [1] 5.970149
EmergenceRateIndex(germ.counts = y, intervals = int, partial = FALSE,
total.seeds = 50, method = "fakorede")
#> [1] 8.375
```