SeedCalc, a new automated R software tool for germination and seedling length data processing

The need to optimize seed quality assessment using new, more accessible, and modern computational resources has led to the emergence of new tools. In this paper, we introduce SeedCalc, a new R software package developed to process germination and seedling length data. The functions included in SeedCalc allow fast and efficient data processing, offering greater reliability to the variables generated and facilitating statistical analysis itself since the data are already processed with the appropriate structure to be statistically analyzed in the R software. SeedCalc is available free of charge at https://CRAN.R-project.org/package=SeedCalc.

Index terms:
R package; germination indexes; seedling uniformity; seed vigor; data analysis

Authorship

Laércio Junio da Silva ^**Corresponding author <laercio.silva@ufv.br>

Departamento de Fitotecnia, Universidade Federal de Viçosa, 36570-900 - Viçosa, MG, Brasil.Universidade Federal de ViçosaBrazilViçosa, MG, BrazilDepartamento de Fitotecnia, Universidade Federal de Viçosa, 36570-900 - Viçosa, MG, Brasil.

André Dantas de Medeiros

http://orcid.org/0000-0002-1097-0292

Ariadne Morbeck Santos Oliveira

*Corresponding author <laercio.silva@ufv.br>

SCIMAGO INSTITUTIONS RANKINGS

Figures | Tables | Formulas

Figures (5)
Tables (2)
Formulas (26)

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Figure 1
Presentation of the germination count data organized for processing by SeedCalc.

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Figure 2
Presentation of the seedling data organized for processing by SeedCalc. In (A) are the seedling length data and in (B) are the germination values of the treatments/lots, corresponding to the ones in the first column of the data file of seedling length (A). The germination data (B) are optional and necessary for calculation of the corrected vigor index.

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Figure 3
Example of results output of the functions applied to the daily counting data of the germination test of soybean seeds by SeedCalc.

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Figure 4
Example of results output of the functions applied to seedling lengths of soybean seeds by SeedCalc.

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Figure 5
Soybean seedlings originated from seeds with different levels of vigor and their respective quality indexes. (A) higher vigor and (B) lower vigor.

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Table 1
Functions contained in the SeedCalc package for calculation of indexes, using data from daily counting of seedling on germination/emergence test.

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Table 2
Functions contained in the SeedCalc package for obtaining indexes using seedling length measurement data.

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Figure 1 Presentation of the germination count data organized for processing by SeedCalc.

Figure 2 Presentation of the seedling data organized for processing by SeedCalc. In (A) are the seedling length data and in (B) are the germination values of the treatments/lots, corresponding to the ones in the first column of the data file of seedling length (A). The germination data (B) are optional and necessary for calculation of the corrected vigor index.

Figure 3 Example of results output of the functions applied to the daily counting data of the germination test of soybean seeds by SeedCalc.

Figure 4 Example of results output of the functions applied to seedling lengths of soybean seeds by SeedCalc.

Figure 5 Soybean seedlings originated from seeds with different levels of vigor and their respective quality indexes. (A) higher vigor and (B) lower vigor.

Table 1 Functions contained in the SeedCalc package for calculation of indexes, using data from daily counting of seedling on germination/emergence test.

Function	Measure	Formula	Reference
FGP	Final germination percentage	$FGP=(n/N) × 100$ n is the number of seeds germinated, and N is the total number of seeds.	ISTA (2015)ISTA. The germination test. In: International rules for seed testing. Zurich, Switzerland: International Seed Testing Association, 2015. http://dx.doi.org/10.15258/istarules.2015.05. p. i-5-56. http://dx.doi.org/10.15258/istarules.201...
GI	Germination speed index	$GI= \sum_{i=1}^{k} (n_{i} / t_{i})$ n is the number of seeds germinated on each day of daily counting up to the last count, and t is the number of days after the beginning of the test in each count.	Maguire (1962MAGUIRE, J.D. Speed of germination-aid selection and evaluation for seedling emergence and vigor. Crop Science, v.2, p.176-177, 1962. http://dx.doi.org/http://dx.doi.org/10.2135/cropsci1962.0011183X000200020033x. http://dx.doi.org/http://dx.doi.org/10.2... )
T10	Time required for germination of 10% of the seeds	$T_{10} = \frac{t i + \{[\frac{N}{(\frac{100}{10})}] - n i\} (t j - t i)}{(n j - n i)}$ N is the final number of seeds germinated, and n_i and n_j are the total number of seeds germinated in adjacent counts in time t_i and t_j, respectively, when $n i < \frac{N + 1}{2} < n j$ .	Adapted from Farooq et al. (2005FAROOQ, M.; BASRA, S.M.A.; AHMAD, N.; HAFEEZ, K. Thermal Hardening: A New Seed Vigor Enhancement Tool in Rice. Journal of Integrative Plant Biology, v.47, n.2, p.187-193, 2005. http://dx.doi.org/10.1111/j.1744-7909.2005.00031.x. http://dx.doi.org/10.1111/j.1744-7909.20... )
T50	Time required for germination of 50% of the seeds	$T_{50} = \frac{t i + \{[\frac{N}{(\frac{100}{50})}] - n i\} (t j - t i)}{(n j - n i)}$ Same codification as for T10.	Farooq et al. (2005FAROOQ, M.; BASRA, S.M.A.; AHMAD, N.; HAFEEZ, K. Thermal Hardening: A New Seed Vigor Enhancement Tool in Rice. Journal of Integrative Plant Biology, v.47, n.2, p.187-193, 2005. http://dx.doi.org/10.1111/j.1744-7909.2005.00031.x. http://dx.doi.org/10.1111/j.1744-7909.20... )
T90	Time required for germination of 90% of the seeds	$T_{90} = \frac{t i + \{[\frac{N}{(\frac{100}{90})}] - n i\} (t j - t i)}{(n j - n i)}$ Same codification as for T10.	Adapted from Farooq et al. (2005FAROOQ, M.; BASRA, S.M.A.; AHMAD, N.; HAFEEZ, K. Thermal Hardening: A New Seed Vigor Enhancement Tool in Rice. Journal of Integrative Plant Biology, v.47, n.2, p.187-193, 2005. http://dx.doi.org/10.1111/j.1744-7909.2005.00031.x. http://dx.doi.org/10.1111/j.1744-7909.20... )
MGT	Mean germination time	$MGT= \sum_{i=1}^{k} n_{i} t_{i} / \sum_{i=1}^{k} n_{i}$ n_i is the number of seeds germinated per day (not the accumulated number, but the number corresponding to the i-th observation), and t _i is the time since the beginning of the germination test up to the i-th observation.	Labouriau (1983LABOURIAU, L.G. Uma nova linha de pesquisa na fisiologia da germinação das sementes. Anais do XXXIV Congresso Nacional de Botânica. SBB, Porto Alegre, 11-50, 1983.)
MGR	Mean germination rate	$\bar{v} = C o V g / 100 = 1 / \bar{t}$ t is the mean germination time, and CoVg is the germination speed coefficient.	Labouriau (1983LABOURIAU, L.G. Uma nova linha de pesquisa na fisiologia da germinação das sementes. Anais do XXXIV Congresso Nacional de Botânica. SBB, Porto Alegre, 11-50, 1983.)
VarGer	Variance of germination time	$s_{t}^{2} = \sum_{i=1}^{k} n_{i} {(t_{i} - \bar{t})}^{2} /(\sum_{i=1}^{k} n_{i} -1)$ t is the mean germination time, t_i is the time between the beginning of the experiment and the i-th observation (day or hour), n_i is the number of seeds germinated in time i, and k is the last count of the germination test.	Labouriau (1983LABOURIAU, L.G. Uma nova linha de pesquisa na fisiologia da germinação das sementes. Anais do XXXIV Congresso Nacional de Botânica. SBB, Porto Alegre, 11-50, 1983.)
CVt	Coefficient of variation of germination time	${CV}_{t} = (S_{t} / \bar{t}) 100$ St is standard deviation of the germination time, and 𝑡 is mean germination time.	Carvalho et al. (2005CARVALHO, M.P.; SANTANA, D.G.; RANAL, M.A. Emergência de plântulas de Anacardium humile A. St.-Hil. (Anacardiaceae) avaliada por meio de amostras pequenas. Revista Brasileira de Botânica, v.28, n.3, p.627-633, 2005. http://dx.doi.org/10.1590/S0100-84042005000300018. http://dx.doi.org/10.1590/S0100-84042005... )
Sinc	Germination synchrony	$Z= \sum C n i, 2 / N$ $Cni, 2 = ni (ni-1)/2$ and $N = {\sum n i (\sum n i - 1) / 2}_{}$ Cni is the combination of the seeds germinated in time i, two by two, and ni is the number of seeds germinated in time i.	Primack (1980PRIMACK, R.B. Variation in the phenology of natural populations of montane shrubs in New Zealand. Journal of Ecology, v.68, n.3, p.849-862, 1980.)
Unc	Uncertainty	$\bar{E} =- \sum_{i=1}^{k} f_{i} log 2 f_{i}$ with f_i given by, $f_{i} = n_{i} / \sum_{i=1}^{k} n_{i}$ f_i is the relative frequency of germination, and n_i is the number of seeds germinated on day i.	Labouriau and Valadares (1976)LABOURIAU L.G.; VALADARES M.B. On the germination of seeds of Calotropis procera. Anais da Academia Brasileira de Ciências v.48, p.174-186, 1976.
CVG	Germination speed coefficient	$CVG=(\sum_{i=1}^{k} f_{i} / \sum_{i=1}^{k} f_{i} x_{i}) 100$ f_i is the number of newly germinated seeds on day i, and x_i is the number of days from sowing.	Nichols and Heydecker (1968NICHOLS, M.A.; HEYDECKER, W. Two approaches to the study of germination data. Proceedings of the International Seed Testing Association, v.33, p.531-540, 1968. )
UnifG	Uniformity of germination	$UnifG=( T90-T10)$ T90 is the time required for germination of 90% of the seeds, and T10 is the time required for germination of 10% of the seeds.	Demilly et al. (2014DEMILLY, D.; DUCOURNAU, S.; WAGNER, M.H.; DÜRR, C. Digital imaging of seed germination. In: GUPTA, S.D.; IBARAKI, Y. (Eds.). Plant Image Analysis: Fundamentals and Applications. 1. ed. CRC Press, 2014. p.147-164. )

Table 2 Functions contained in the SeedCalc package for obtaining indexes using seedling length measurement data.

Function	Measurement	Formula	Reference
mean_pa	Mean shoot length	$Mea n_{pa} = \frac{\sum_{i=1}^{k} HL}{n}$ HL is the length of the shoot of each seedling, and n is the total number of seedlings evaluated.	Nakagawa et al. (1999NAKAGAWA, J.; KRZYZANOWSKI, F.C.; VIEIRA, R.D.; FRANÇA-NETO, J.B. Testes de vigor baseados no desempenho das plântulas. In: KRZYANANOWSKI, F.C.; VIEIRA, R.D.; FRANÇA-NETO, J.B. (Eds.). Vigor de sementes: conceitos e testes. Londrina: ABRATES, 1999. p. 9-13. )
mean_raiz	Mean root length	$Mea n_{raiz} = \frac{\sum_{i=1}^{k} RL}{n}$ RL is the length of the root of each seedling, and n is the total number of seedlings evaluated.	Nakagawa et al. (1999NAKAGAWA, J.; KRZYZANOWSKI, F.C.; VIEIRA, R.D.; FRANÇA-NETO, J.B. Testes de vigor baseados no desempenho das plântulas. In: KRZYANANOWSKI, F.C.; VIEIRA, R.D.; FRANÇA-NETO, J.B. (Eds.). Vigor de sementes: conceitos e testes. Londrina: ABRATES, 1999. p. 9-13. )
mean_total	Mean total length	$Mea n_{total} = \frac{\sum_{i=1}^{k} SL}{n}$ SL is the total length of each seedling, and n is the total number of seedlings evaluated.	Nakagawa et al. (1999NAKAGAWA, J.; KRZYZANOWSKI, F.C.; VIEIRA, R.D.; FRANÇA-NETO, J.B. Testes de vigor baseados no desempenho das plântulas. In: KRZYANANOWSKI, F.C.; VIEIRA, R.D.; FRANÇA-NETO, J.B. (Eds.). Vigor de sementes: conceitos e testes. Londrina: ABRATES, 1999. p. 9-13. )
mean_razao	Mean of the root/shoot ratio	$Mea n_{razao} = \frac{\sum_{i=1}^{k} R R A}{n}$ RRA is the ratio between the root and the shoot of each seedling, and n is the total number of seedlings evaluated.	Benincasa (2003BENINCASA, M.M.P. Análise do crescimento em plantas - noções básicas. Jaboticabal: FUNEP, 412p. 2003.)
Unif_1	Uniformity index	$Uniformity_1 = [1- \frac{\sum_{i=1}^{n} \|Xi- \bar{X}\|}{n × X}] ×1000- [n_{dead} × (\frac{50}{n_{total}})]$ Xi is the length of the seedling analyzed, X is the mean length of seedlings of the seed lot analyzed, n is the variable of total number of seedlings evaluated, n_dead is the number of ungerminated or dead seeds present, and n_total is the total number of seedlings.	Christiansen (1942CHRISTIANSEN, J.E. Irrigation by Sprinkling. University of California, Berkeley, CA, USA. (California Agriculture Experiment Station Bulletin, 670). 1942.), adapted by Castan et al. (2018CASTAN, D.O.C.; GOMES-JUNIOR, F.G.; MARCOS-FILHO, J. Vigor-S, a new system for evaluating the physiological potential of maize seeds. Scientia Agricola, v.75, n.2, p.167-172, 2018. http://dx.doi.org/10.1590/1678-992x-2016-0401. http://dx.doi.org/10.1590/1678-992x-2016... )
Unif_2	Uniformity index	$Uniformity_2 = max [1000- (0.75 × sh+0.5 × sr+2.5 × s_{total} +50 ×s rh) -0 × ndead]$ sh, sr, and srh are the standard deviations of the length of the shoot, primary root, and root/shoot ratio, respectively.	Sako et al. (2001SAKO, Y.; MCDONALD, M.B.; FUJIMURA, K.; EVANS, A.F.; BENNETT, M.A. A system for automated seed vigor assessment. Seed Science and Technology, v.29, n.3, p.625-636, 2001. https://www.eurofinsus.com/media/162083/seed-vigor-imaging-system.pdf https://www.eurofinsus.com/media/162083/... )
Growth	Growth index	$Growth= [(mean (h) ×wh) + (mean(r)×wr)]$ mean(h) and mean(r) are the arithmetic means of shoot length and root length, respectively. wh and wr are adjustable weights in the formula for shoot and root, however, with reference values of 10 and 90, respectively.	Sako et al. (2001SAKO, Y.; MCDONALD, M.B.; FUJIMURA, K.; EVANS, A.F.; BENNETT, M.A. A system for automated seed vigor assessment. Seed Science and Technology, v.29, n.3, p.625-636, 2001. https://www.eurofinsus.com/media/162083/seed-vigor-imaging-system.pdf https://www.eurofinsus.com/media/162083/... )
Vigor	Vigor index	$Vigor= (Growth×wg) + (Uniformity×wu)$ Growth is the growth index, and Uniformity is the uniformity index chosen by the user. wg and wu are adjustable weights in the formula for growth and uniformity, however, with standard values of 70 and 30, respectively.	Sako et al. (2001SAKO, Y.; MCDONALD, M.B.; FUJIMURA, K.; EVANS, A.F.; BENNETT, M.A. A system for automated seed vigor assessment. Seed Science and Technology, v.29, n.3, p.625-636, 2001. https://www.eurofinsus.com/media/162083/seed-vigor-imaging-system.pdf https://www.eurofinsus.com/media/162083/... )
Vigor_corr	Corrected vigor index	$Vigor_Corr= [(Growth×wg) + (Uniformity×wu)] × (\frac{G}{100})$ G is the percentage of germination of the seed lot.	Medeiros and Pereira (2018MEDEIROS, A.D.; PEREIRA, M.D. SAPL ® : a free software for determining the physiological potential in soybean seeds. Pesquisa Agropecuária Tropical, v.48, n.3, p.222-228, 2018. http://dx.doi.org/10.1590/1983-40632018v4852340. http://dx.doi.org/10.1590/1983-40632018v... )

FGP=(n/N) × 100

GI= \sum_{i=1}^{k} (n_{i} / t_{i})

T_{10} = \frac{t i + \{[\frac{N}{(\frac{100}{10})}] - n i\} (t j - t i)}{(n j - n i)}

n i < \frac{N + 1}{2} < n j

T_{50} = \frac{t i + \{[\frac{N}{(\frac{100}{50})}] - n i\} (t j - t i)}{(n j - n i)}

T_{90} = \frac{t i + \{[\frac{N}{(\frac{100}{90})}] - n i\} (t j - t i)}{(n j - n i)}

MGT= \sum_{i=1}^{k} n_{i} t_{i} / \sum_{i=1}^{k} n_{i}

\bar{v} = C o V g / 100 = 1 / \bar{t}

s_{t}^{2} = \sum_{i=1}^{k} n_{i} {(t_{i} - \bar{t})}^{2} /(\sum_{i=1}^{k} n_{i} -1)

{CV}_{t} = (S_{t} / \bar{t}) 100

Z= \sum C n i, 2 / N

Cni, 2 = ni (ni-1)/2

N = {\sum n i (\sum n i - 1) / 2}_{}

\bar{E} =- \sum_{i=1}^{k} f_{i} log 2 f_{i}

f_{i} = n_{i} / \sum_{i=1}^{k} n_{i}

CVG=(\sum_{i=1}^{k} f_{i} / \sum_{i=1}^{k} f_{i} x_{i}) 100

UnifG=( T90-T10)

Mea n_{pa} = \frac{\sum_{i=1}^{k} HL}{n}

Mea n_{raiz} = \frac{\sum_{i=1}^{k} RL}{n}

Mea n_{total} = \frac{\sum_{i=1}^{k} SL}{n}

Mea n_{razao} = \frac{\sum_{i=1}^{k} R R A}{n}

Uniformity_1 = [1- \frac{\sum_{i=1}^{n} |Xi- \bar{X}|}{n × X}] ×1000- [n_{dead} × (\frac{50}{n_{total}})]

Uniformity_2 = max [1000- (0.75 × sh+0.5 × sr+2.5 × s_{total} +50 ×s rh) -0 × ndead]

Growth= [(mean (h) ×wh) + (mean(r)×wr)]

Vigor= (Growth×wg) + (Uniformity×wu)

Vigor_Corr= [(Growth×wg) + (Uniformity×wu)] × (\frac{G}{100})

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SeedCalc, a new automated R software tool for germination and seedling length data processing

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[1] *Corresponding author <laercio.silva@ufv.br>