TimsonsIndex: Timson's index

Description

Compute George's index george_influence_1961,tucker_estimating_1965,nichols_two_1968,chopra_effect_1980germinationmetrics, Timson's index or Timson's germination velocity index grose_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 ranal_how_2006germinationmetrics and khan_effect_1984germinationmetrics.

Usage

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

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 % time^-1.

For GermRateGeorge The value of George's germination rate as

count time.

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 timson_new_1965germinationmetrics is computed as follows grose_laboratory_1958,brown_representing_1988,baskin_seeds_1998germinationmetrics.

k = _i=1^kG_i

Where, G_i is the cumulative germination percentage in time interval i and k is the total number of time intervals.

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

10 = G_1+G_2++G_10

Where G_1,G_2, G_10 are the cumulative germination percentage at day 1, 2, 3, , 10 respectively.

Similarly 5 or 20 can be estimated. For 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 lyon_rapid_1966;textualgerminationmetrics as well as negm_effects_1978;textualgerminationmetrics. It is also described as Emergence Rate Index (ERI) by chaudhary_effect_1970;textualgerminationmetrics.

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

k = _i=1^kg_i(k-j)

Where, g_i is the germination (not cumulative, but partial germination) in time interval i (i varying from 0 to k), k is the total number of time intervals, and j = i - 1.

Timson's index is equivalent to the Germination Energy Index GEI proposed by grose_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 ranal_how_2006germinationmetrics (Specified by the argument modification = "labouriau").

k_mod = k_i=1^kg_i

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

Similarly another modification was proposed by khan_effect_1984germinationmetrics, where Timson's index ( k) is divided by the total time period of germination (T_k) (Specified by the argument modification = "khanungar").

k_mod = kT_k

Timson's index is similar to the Germination Rate (GR) proposed by george_influence_1961;textualgerminationmetrics as follows tucker_estimating_1965,nichols_two_1968germinationmetrics.

GR = _i=1^kN_iK_i

Where N_i is the number of seeds germinated by ith interval, K_i is the number of intervals(e.g. days) until the end of the test, and k 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 (ERI) by chopra_effect_1980;textualgerminationmetrics.

So germination rate (GR) can also be described in terms of partial (N_i) and cumulative (_j=1^iN_j) number of seeds germinated in each time interval (i) as follows.

GR = _i=1^k_j=1^iN_j

GR = _i=1^kN_i(k-j)

References

Examples

Run this code

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)

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