Calculating germination T50 using coolbear

library(seedTools)

Germination T₅₀ is the time at which 50% of the viable seeds in an experiment have germinated. One approach to calculate T₅₀ values is to use Coolbear et al. (1984) formula modified by Farooq et al.(2005).

Coolbear et al. (1984) formula modified by Farooq et al.(2005)

where N is the final number of germinating seeds and n_j and n_i are the cumulative number of seeds germinated by adjacent counts at times t_j and t_i , respectively, when n_i < N/2 < n_j. In essence, this formula identifies the midpoint of the cumulative germination sigmoidal curve, where the slope is steepest.

coolbear() requires a vector of cumulative germination, a vector of the dates or times at which these germinations were recorded, and the total number of viable seeds in the experiment.

total_viable_seeds<-25
time_germination_recorded<-c(seq(1,12,1)) #germination scored daily for 12 days
cumulative_germination<-c(0,0,0,0,1,3,6,7,15,16,23,25)

coolbear(time_germination_recorded,cumulative_germination,total_viable_seeds)
#> [1] 8.6875

If T₅₀ can’t be calculated (e.g. not enough seeds germinated) the function will output NA. ‘coolbear()’ can efficiently be used within a loop to calculate T₅₀ of several experiments at a time. Given the following germination experiment results (including a row with final viability):

germination_results<-data.frame(days=c(seq(1,12,1)),
                                exp1=c(0,0,0,0,0,0,0,9,9,9,9,9),
                                exp2=c(0,2,5,6,7,12,16,25,25,25,25,25),
                                exp3=c(0,0,0,10,15,20,25,26,27,28,28,30))

germination_results
#>    days exp1 exp2 exp3
#> 1     1    0    0    0
#> 2     2    0    2    0
#> 3     3    0    5    0
#> 4     4    0    6   10
#> 5     5    0    7   15
#> 6     6    0   12   20
#> 7     7    0   16   25
#> 8     8    9   25   26
#> 9     9    9   25   27
#> 10   10    9   25   28
#> 11   11    9   25   28
#> 12   12    9   25   30

coolbear() can easily be implemented like:

for (col in colnames(germination_results)[-1]) {
  
  T50<-coolbear(day=germination_results$days,
           cumulative=germination_results[[col]],
           n=25)
  
  print(paste(col,"- T50:", T50))
}
#> [1] "exp1 - T50: NA"
#> [1] "exp2 - T50: 6.125"
#> [1] "exp3 - T50: 4.5"

Note the function has been feed with a fixed number of viable seeds, but this can be modified to be a vector to adapt for different viabilities across experiments and replicates