Compute the following metrics:
GermSynchronySynchrony of germination (\(Z\) index) (Primack 1985; Ranal and de Santana 2006) .
GermUncertaintySynchronization index (\(\overline{E}\)) or Uncertainty of the germination process (\(U\)) or Informational entropy (\(H\)) (Shannon 1948; Labouriau and Valadares 1976; Labouriau 1983) .
GermSynchrony(germ.counts, intervals, partial = TRUE)
GermUncertainty(germ.counts, intervals, partial = TRUE)Germination counts at each time interval. Can be partial
or cumulative as specified in the argument partial.
The time intervals.
logical. If TRUE, germ.counts is considered as
partial and if FALSE, it is considered as cumulative. Default is
TRUE.
For GermUncertainty, the value of uncertainty of germination
process in \(\mathrm{bit}\).
For GermSynchrony, the value of synchrony of germination.
GermSynchrony computes the value of synchrony of germination
(\(Z\) index) as follows
(Primack 1985; Ranal and de Santana 2006)
.
\[Z=\frac{\sum_{i=1}^{k}C_{N_{i},2}}{C_{\Sigma N_{i},2}}\]
Where, \(C_{N_{i},2}\) is the partial combination of the two germinated seeds from among \(N_{i}\), the number of seeds germinated on the \(i\)th time interval (estimated as \(C_{N_{i},2}=\frac{N_{i}(N_{i}-1)}{2}\)), and \(C_{\Sigma N_{i},2}\) is the partial combination of the two germinated seeds from among the total number of seeds germinated at the final count, assuming that all seeds that germinated did so simultaneously.
GermUncertainty computes the value of synchronization index
(\(\overline{E}\)) or uncertainty of the germination process
(\(U\)) or informational entropy (\(H\)) as follows
(Shannon 1948; Labouriau and Valadares 1976; Labouriau 1983)
.
\[\overline{E} = -\sum_{i=1}^{k}f_{i}\log_{2}f_{i}\]
Where, \(f_{i}\) is the relative frequency of germination (estimated as \(f_{i}=\frac{N_{i}}{\sum_{i=1}^{k}N_{i}}\)), \(N_{i}\) is the number of seeds germinated on the \(i\)th time interval, and \(k\) is the total number of time intervals.
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).
Primack RB (1985).
“Longevity of individual flowers.”
Annual Review of Ecology and Systematics, 16(1), 15--37.
Ranal MA, de Santana DG (2006).
“How and why to measure the germination process?”
Brazilian Journal of Botany, 29(1), 1--11.
Shannon CE (1948).
“A mathematical theory of communication.”
Bell System Technical Journal, 27(3), 379--423.
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
#----------------------------------------------------------------------------
GermSynchrony(germ.counts = x, intervals = int)
#> [1] 0.2666667
GermUncertainty(germ.counts = x, intervals = int)
#> [1] 2.062987
# From cumulative germination counts
#----------------------------------------------------------------------------
GermSynchrony(germ.counts = y, intervals = int, partial = FALSE)
#> [1] 0.2666667
GermUncertainty(germ.counts = y, intervals = int, partial = FALSE)
#> [1] 2.062987