Advanced seed germination measurements excel tool
- Introduction
- Sections of the tool
- Getting the output
- Methodology for calculations
- Germination percentage
- Relativized percentage
- Mean germination time
- Mean germination rate
- Uncertainty of germination process
- Synchrony of germination process
- Coefficient of variation of germination time
- Germination index
- Coefficient of velocity of germination
- Time to 50% germination
- Mean daily germination percent
- Peak value
- Germination value
- Instructions to download this excel tool
- References
Introduction
Seed germination refers to the physiological process culminating in the emergence of the embryo from its enclosing coverings, which can include the endosperm , perisperm, testa, or pericarp. The visible indication that germination has been completed is when the radicle (or other embryonic tissue) emerges from the tissues enclosing it. This point marks a clear end to germination and the start of seedling growth. There are many ways to measure the attributes related to seed germination.
This effort was made to develop an excel tool for making ease in calculations related to some important seed germination measurements. By using this tool a researcher can enter data up to \(200\) counts. First I shall discuss how to enter data and get the output and then will describe the methodology used for parameters or germination attributes.
Sections of the tool
The first sheet of the tool is a data entry sheet which is comprised of \(4\) different sections. The detail of each section representing how to enter values is given below.
Section-I
First section (section-I) specify the treatments labels. The labels Rep, Factor A, Factor B and Factor C are just to represent the treatment combinations. There is no hard and fast rule to enter exactly the same variable levels in its respective column. However, you can enter any sequence of treatment combinations in this section but make sure the combination entered in this section are in accordance with the germination count values entered in the ni section.
Section-I: Specify treatment labels
Section-II
This section represent the number of seeds used in each experimental unit. According to the section-I treatment level, enter the number of seeds used in that specific experimental unit.
Section-II: Specify number of seeds in each experimental units
Section-III
Third section of the tool represent the time interval (ti) used for each count. The values for time taken for each count will be entered in this section. If time interval is \(24\) hours or \(1\)day and germination completed on \(6\)th day then enter values from 1 to 6 in t1 to t6 in this section.
If time interval for each count is \(8\) hours then enter values in the sequence of \(8\), \(16\), \(24\), \(32\), \(40\) and \(48\) in t1 to t6 in this section. Similarly, count interval can be in minutes, weeks or months so use the values for ti accordingly.
Section-III: Specify time taken for each count
Section-IV
This section is labeled as ni section and it specify the number of seeds germinated in each count. In accordance with the treatment label in section-I and ti section, enter the number of seeds germinated in this ni section.
paste special: Make sure if you are pasting values in each section then right click on the starting cell, choose paste special, check values and number formats and then click OK.
Section-IV: Specify germinated seeds in each count
Getting the output
The second sheet of the tool Analysis result represent the output of the data entry sheet. To get the results from this sheet do the following:
- Select the output including the treatment labels and variable names.
- Press
Ctrl + Nto open a new worksheet - Go to the first cell, right click and choose
paste special - Check the box
values and number formatsand clickOK. - Delete empty column if any
Now the results can be used to further fit analysis of variance model to see the significance of treatment factors followed by suitable mean comparison test if necessary.
Methodology for calculations
The output will show more than 13 attributes related to seed germination measurements. Here, I shall briefly describe how these measurements were computed.
Germination percentage
Germination percentage is an estimate of the germinability of the population of seeds. The equation to calculate germination percentage is:
\[G\: (\%) = \frac{\sum_{i=1}^k\:n_i}{N}\:\times\:100\] Where;
\(n_i=\) number of seeds germinated in the \(i^{th}\) time
\(N=\) Total number of seeds used
Relativized percentage
The germination percentage can be relativized by the following equation (Fitch et al. 2007):
\[R\:(\%) = \frac{AP}{HP}\:\times\:100\]
\(AP=\) actual percentage
\(HP=\) highest percentage amongst group of data
This standardization allow comparisons among treatments equivalent when amount of dormancy broken variedMean germination time
Mean germination time is a measure of the rate and time spread of the germination. It indicates time spent to germinate or emerge. Following formula was used to calculate the mean germination time (Ellis and Roberts 1981):
\[\bar{t} = \frac{\sum_{i=1}^k\:n_it_i}{\sum_{i=1}^k\:n_i}\] Where;
\(n_it_i=\) The product of seeds germinated at interval \(i^{th}\) with the corresponding time interval
\(n_i=\) number of seeds germinated in the \(i^{th}\) time
Mean germination rate
Mean germination rate is the reciprocal of the mean germination time as shown below (Ranal et al. 2009).
\[\bar{v} = \frac{1}{\bar{t}}\] Where;
\(\bar{t} =\) Mean germination time
Uncertainty of germination process
The uncertainty of germination process indicates the degree of uncertainty associated with the distribution of relative frequency of germination. Uncertainty is calculated using the following equation (Labouriau and Valadares 1976):
\[U = \sum_{i=1}^k\:fi\:log_2\:fi\] Where;
\(f_i = \frac{n_i}{\sum_{i=1}^k\:n_i}\) \(f_i=\) Relative frequency of germination
Low values of uncertainity indicate frequencies with few peaks (i.e. germination more concentrated in time)Low value (towards zero) indicates more synchronized germinationSynchrony of germination process
Evaluate the degree of overlapping among individuals of one population. Synchronization index produces a number if and only if there are two seeds finishing the germination process at the same time. It is calculated using the following formula (Labouriau 1978):
\[Z = \frac{\sum_{i=1}^k\:C_{n_i,2}}{C_{\sum n_i,2}}\] Where;
\(C_{n_i,2} = n_i(n_i-1)/2\)
\(C_{ni,2}=\) combination of seeds germinated in the \(i^{th}\) time, two by two.
\(n_i=\) number of seeds germinated in the \(i^{th}\) time
Z=1: when germination of all seeds occur at the same time
Z=0: when at least two seeds could germinate, one at each time
Coefficient of variation of germination time
Coefficient of variation of the germination time is calculated by the following expression (Ranal et al. 2009)
\[CV_t=\frac{S_t}{\bar{t}}\times100\] Where;
\(S_t=\sqrt{\frac{\sum_{i=1}^k\:n_i(t_i-\bar{t})^2}{\sum_{i=1}^k\:n_i-1}}\)
\(S_t=\) standard deviation of germination time
\(\bar{t}=\) mean germination time
Samples with only one seed germinated do not have the value of this measurement because the divisor of variance of germination time is zeroGermination index
Germination index is an estimate of the time (in days) it takes a certain germination percentage to occur.Germination index can be calculated by using following expression (AOSA and SCST 1993):
\[GI=\sum_{i=1}^k\:{n_i}/{t_i}\] Where;
\(n_i=\) number of seeds germinated in the \(i^{th}\) time
\(t_i=\) time taken for seeds to germinate at \(i^{th}\) count
Coefficient of velocity of germination
Coefficient of velocity of germination can be calculated using the following expression (Jones and Sanders 1987):
\[CVG=\frac{\sum_{i=1}^k\:n_it_i}{\sum_{i=1}^k\:n_i}\times100\]
Time to 50% germination
Time to 50% germination (\(T_{50}\)) indicates that how much time was taken for half of the seeds to germinate. \(T_{50}\) can be calculated using the following expression (Coolbear, Francis, and Grierson 1984):
\[T_{50}=\frac{t_i\:+\:(\frac{\sum_{i=1}^k\:n_i}{2}-n_i)(t_j-t_i)}{n_j-n_i}\] In the above equation to find out the value of \(n_i\) and \(n_j\) there is need to look in the cumulative number of seeds germinated for which the condition is given below.
\(n_i<\frac{\sum_{i=1}^k\:n_i}{2}<n_j\)
Where;
\(n_i =\) nearest cumulative number of seeds germinated (\(Cn_i\)) \(<\frac{\sum_{i=1}^k\:n_i}{2}\)
\(n_j=\) nearest cumulative number of seeds germinated (\(Cn_j\)) \(>\frac{\sum_{i=1}^k\:n_i}{2}\)
\(t_i=\) the time interval corresponding to \(n_i\)
\(t_j=\) the time interval corresponding to \(n_j\)
Other time related germination parameters like \(T_{10}\), \(T_{25}\), \(T_{75}\) and \(T_{90}\) were calculated using the same above formula by replacing \(\frac{\sum_{i=1}^k\:n_i}{2}\) with \(\frac{\sum_{i=1}^k\:n_i}{10}\), \(\frac{\sum_{i=1}^k\:n_i}{4}\), \(\frac{3\sum_{i=1}^k\:n_i}{4}\) and \(\frac{9\sum_{i=1}^k\:n_i}{10}\), respectively.
Mean daily germination percent
It represents the mean number of seeds germinated per day. This can also be defined as the number of seeds germinating daily relative to the maximum number of germinated seeds. It is calculated using the following expression (Adams and Farrish 1992):
\[\bar{G}=\frac{GP}{T_n}\] Where;
\(GP=\) final cumulative germination percentage
\(T_n=\) total number of intervals required for final germination
Peak value
It is the accumulated number of seeds germinated at the point on the germination curve at which the rate of germination starts to decrease. It is computed as the maximum quotient obtained by dividing successive cumulative germination values by the relevant incubation time (Adams and Farrish 1992).
Germination value
Germination value is obtained by combining both speed and completeness of germination into a composite score as described by Czabator (1962).
\[GV=MDG\:\times\:PV\] Where;
\(MDG=\) mean daily germination
\(PV=\) peak value or largest quotient obtained when all of the cumulative germination percentages were divided by the respective time interval.
Instructions to download this excel tool
To download this excel tool please follow the instructions as given below:
- Click on the download link given below
- A new window will appear, go to
Fileand selectSave As - Click on
Download a Copy
The excel tool will download in a very short time.
Please comment below if you have any questionsReferences
Downloads:
Download this excel tool —
Click here
Thank you very much for sharing.
ReplyDeleteYou are most welcome. Your support highly encourage me to bring valuable content for you.
ReplyDeletethank you very much for sharing. but sir i have one quastion the result directly come in excel through papar command or put seperate formula for every value . plz sir gauid me
ReplyDeleteThe result are obtained by formulas which are present in hidden sheets and by entering data you get the output. The formula used in this excel tool are discussed in this blog post.
DeleteI want to add the data but it is set as read only file
ReplyDeleteThis file is password protected so that no one could change it but you can enter data in data entry sheet and also can copy the output from results sheet. Please follow the steps on how to enter data in data entry sheet or send me a dummy data set and I will send you the tool with data properly entered. You can send your data at agron.infotech@gmail.com
Deletesir im agri student i need this software please send me
Deleteim agri student please send me
DeleteYou can download this excel tool from the link provided at the end of this blog post. See instructions (in this blog post) on how to download this tool.
DeleteSir, in the analysis part, more than half of of the data is blank? What might be the reason for this?
ReplyDeleteBlank spaces may be possible in the results sheet because of in complete number of values. These may not fulfill the formula requirements and thus unable to compute it. You can put NAs for such treatment levels in your final table. However to make sure whether the blanks are because of above reason or you may not properly enter the data. You can share data at agron.infotech@gmail.com and I shall see how to fix it
ReplyDeleteSir, some values are coming in negative number.
ReplyDeleteYou may have entered data in a wrong way. Send me data file at agron.infotech@gmail.com
ReplyDelete