TimsonsIndex: Timson's index

In germinationmetrics: Seed Germination Indices and Curve Fitting

Timson's index

Description

Compute George's index \insertCitegeorge_influence_1961,tucker_estimating_1965,nichols_two_1968,chopra_effect_1980germinationmetrics, Timson's index or Timson's germination velocity index \insertCitegrose_laboratory_1958,timson_new_1965,lyon_rapid_1966,chaudhary_effect_1970,negm_effects_1978,brown_representing_1988,baskin_seeds_1998germinationmetrics and it's modifications by Labouriau \insertCiteranal_how_2006germinationmetrics and \insertCitekhan_effect_1984germinationmetrics. \loadmathjax

Usage

TimsonsIndex(
  germ.counts,
  intervals,
  partial = TRUE,
  total.seeds,
  max,
  modification = c("none", "labouriau", "khanungar")
)

GermRateGeorge(germ.counts, intervals, partial = TRUE, max)

Arguments

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.
max	The maximum interval value up to which Timson's index/George's germination rate is to be computed.
modification	The modification to be applied. Either "none", "labouriau" or "khanungar". Default is "none" (see Details).

Details

Timson's index \insertCitetimson_new_1965germinationmetrics is computed as follows \insertCitegrose_laboratory_1958,brown_representing_1988,baskin_seeds_1998germinationmetrics.

\mjsdeqn\Sigma

k = \sum_i=1^kG_i

Where, \mjseqnG_i is the cumulative germination percentage in time interval \mjseqni and \mjseqnk is the total number of time intervals.

For example ten summation (\mjseqn\Sigma 10) is expressed as follows.

\mjsdeqn\Sigma

10 = G_1+G_2+\cdots+G_10

Where \mjseqnG_1,G_2,\cdots G_10 are the cumulative germination percentage at day 1, 2, 3, \mjseqn\cdots, 10 respectively.

Similarly \mjseqn\Sigma 5 or \mjseqn\Sigma 20 can be estimated. For \mjseqn\Sigma 10, the value can range from 0 (no germination) to 1,000 (100% germination after 24 hours).

It is the progressive total of cumulative germination percentage recorded at specific intervals for a set period of time. It combines onset, rate and total percentage of germination and estimates the area under the cumulative germination percentage curve. It is same as the indices for area under time course curve of germination described by \insertCitelyon_rapid_1966;textualgerminationmetrics as well as \insertCitenegm_effects_1978;textualgerminationmetrics. It is also described as Emergence Rate Index (\mjseqnERI) by \insertCitechaudhary_effect_1970;textualgerminationmetrics.

\insertCite

goodchild_method_1971;textualgerminationmetrics, described the same in terms of partial germination percentage as follows.

\mjsdeqn\Sigma

k = \sum_i=1^kg_i(k-j)

Where, \mjseqng_i is the germination (not cumulative, but partial germination) in time interval \mjseqni (\mjseqni varying from \mjseqn0 to \mjseqnk), \mjseqnk is the total number of time intervals, and \mjseqnj = i - 1.

Timson's index is equivalent to the Germination Energy Index \mjseqnGEI proposed by \insertCitegrose_laboratory_1958;textualgerminationmetrics.

As Timson's index is useful for comparison only when samples have similar germinabilities or final germination percentage, the following modification was suggested by Labouriau \insertCiteranal_how_2006germinationmetrics (Specified by the argument modification = "labouriau").

\mjsdeqn\Sigma

k_mod = \frac\Sigma k\sum_i=1^kg_i

Here Timson's index (\mjseqn\Sigma k) is divided by the sum of partial germination percentages.

Similarly another modification was proposed by \insertCitekhan_effect_1984germinationmetrics, where Timson's index (\mjseqn\Sigma k) is divided by the total time period of germination (\mjseqnT_k) (Specified by the argument modification = "khanungar").

\mjsdeqn\Sigma

k_mod = \frac\Sigma kT_k

Timson's index is similar to the Germination Rate (\mjseqnGR) proposed by \insertCitegeorge_influence_1961;textualgerminationmetrics as follows \insertCitetucker_estimating_1965,nichols_two_1968germinationmetrics.

\mjsdeqn

GR = \sum_i=1^kN_iK_i

Where \mjseqnN_i is the number of seeds germinated by \mjseqnith interval, \mjseqnK_i is the number of intervals(e.g. days) until the end of the test, and \mjseqnk is the total number of time intervals.

This index uses number of seeds germinated instead of germination percentage. It is also described as Emergence Rate Index (\mjseqnERI) by \insertCitechopra_effect_1980;textualgerminationmetrics.

So germination rate (\mjseqnGR) can also be described in terms of partial (\mjseqnN_i) and cumulative (\mjseqn\sum_j=1^iN_j) number of seeds germinated in each time interval (\mjseqni) as follows.

\mjsdeqn

GR = \sum_i=1^k\sum_j=1^iN_j

\mjsdeqn

GR = \sum_i=1^kN_i(k-j)

Value

For TimsonsIndex, the value of Timson's index (%) if modification = "none". If modification = "labouriau", then value with no unit and if modification = "khanungar", then value as % \mjseqn\mathrmtime^-1.

For GermRateGeorge The value of George's germination rate as \mjseqncount time.

References

\insertAllCited

Examples

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
#----------------------------------------------------------------------------
# Without max specified
TimsonsIndex(germ.counts = x, intervals = int, total.seeds = 50)
TimsonsIndex(germ.counts = x, intervals = int, total.seeds = 50,
             modification = "none")
TimsonsIndex(germ.counts = x, intervals = int, total.seeds = 50,
             modification = "labouriau")
TimsonsIndex(germ.counts = x, intervals = int, total.seeds = 50,
             modification = "khanungar")
GermRateGeorge(germ.counts = x, intervals = int)

# With max specified
TimsonsIndex(germ.counts = x, intervals = int, total.seeds = 50, max = 10)
TimsonsIndex(germ.counts = x, intervals = int, total.seeds = 50,
             max = 10, modification = "none")
TimsonsIndex(germ.counts = x, intervals = int, total.seeds = 50,
             max = 10, modification = "labouriau")
TimsonsIndex(germ.counts = x, intervals = int, total.seeds = 50,
             max = 10, modification = "khanungar")
GermRateGeorge(germ.counts = x, intervals = int, max = 10)
GermRateGeorge(germ.counts = x, intervals = int, max = 14)


# From cumulative germination counts
#----------------------------------------------------------------------------
# Without max specified
TimsonsIndex(germ.counts = y, intervals = int, partial = FALSE,
             total.seeds = 50)
TimsonsIndex(germ.counts = y, intervals = int, partial = FALSE,
             total.seeds = 50,
             modification = "none")
TimsonsIndex(germ.counts = y, intervals = int, partial = FALSE,
             total.seeds = 50,
             modification = "labouriau")
TimsonsIndex(germ.counts = y, intervals = int, partial = FALSE,
             total.seeds = 50,
             modification = "khanungar")
GermRateGeorge(germ.counts = y, intervals = int, partial = FALSE)

# With max specified
TimsonsIndex(germ.counts = y, intervals = int, partial = FALSE,
             total.seeds = 50, max = 10)
TimsonsIndex(germ.counts = y, intervals = int, partial = FALSE,
             total.seeds = 50,
             max = 10, modification = "none")
TimsonsIndex(germ.counts = y, intervals = int, partial = FALSE,
             total.seeds = 50,
             max = 10, modification = "labouriau")
TimsonsIndex(germ.counts = y, intervals = int, partial = FALSE,
             total.seeds = 50,
             max = 10, modification = "khanungar")
GermRateGeorge(germ.counts = y, intervals = int, partial = FALSE,
               max = 10)
GermRateGeorge(germ.counts = y, intervals = int, partial = FALSE,
               max = 14)

germinationmetrics documentation built on Aug. 19, 2023, 1:07 a.m.