Compute germination indices from a data frame of germination counts recorded at specific time intervals for multiple samples in batch.

germination.indices(
  data,
  total.seeds.col,
  counts.intervals.cols,
  intervals,
  partial = TRUE,
  PeakGermPercent = TRUE,
  FirstGermTime = TRUE,
  LastGermTime = TRUE,
  PeakGermTime = TRUE,
  TimeSpreadGerm = TRUE,
  t50 = TRUE,
  MeanGermTime = TRUE,
  VarGermTime = TRUE,
  SEGermTime = TRUE,
  CVGermTime = TRUE,
  MeanGermRate = TRUE,
  CVG = TRUE,
  VarGermRate = TRUE,
  SEGermRate = TRUE,
  GermRateRecip = TRUE,
  GermSpeed = TRUE,
  GermSpeedAccumulated = TRUE,
  GermSpeedCorrected = TRUE,
  WeightGermPercent = TRUE,
  MeanGermPercent = TRUE,
  MeanGermNumber = TRUE,
  TimsonsIndex = TRUE,
  GermRateGeorge = TRUE,
  max.int,
  GermIndex = TRUE,
  EmergenceRateIndex = TRUE,
  PeakValue = TRUE,
  GermValue = TRUE,
  gv.k = 10,
  CUGerm = TRUE,
  GermSynchrony = TRUE,
  GermUncertainty = TRUE
)

Arguments

data

A data frame with the germination count data. It should possess columns with

  • Partial or cumulative germination counts per time interval (to be indicated by the argument counts.intervals.cols and

  • Total number of seeds tested (to be indicated by the argument total.seeds.col).

total.seeds.col

The name of the column in data with the total number of seeds tested.

counts.intervals.cols

The names of columns in data with the germination counts (partial or cumulative, as indicated by the argument partial) per time interval (indicated by the argument intervals).

intervals

The time intervals at which germination counts (in the columns specified in argument counts.intervals.cols) were recorded.

partial

logical. If TRUE, germination counts in counts.intervals.cols is considered as partial and if FALSE, it is considered as cumulative. Default is TRUE.

PeakGermPercent

logical. If TRUE, then the Peak germination percentage (Vallance 1950; Roh et al. 2004) is computed. Default is TRUE.

FirstGermTime

logical. If TRUE, the Time of first germination or Germination time lag (\(t_{0}\)) (Edwards 1932; Czabator 1962; Goloff and Bazzaz 1975; Labouriau 1983; Ranal 1999; Quintanilla et al. 2000) is computed. Default is TRUE.

LastGermTime

logical. If TRUE, the Time of last germination (\(t_{g}\)) (Edwards 1932; Labouriau 1983; Ranal and de Santana 2006) . is computed. Default is TRUE.

PeakGermTime

logical. If TRUE, the Peak time of germination or Modal time of germination (Ranal and de Santana 2006) is computed. Default is TRUE.

TimeSpreadGerm

logical. If TRUE, the Time spread of germination (Al-Mudaris 1998; Kader 2005) or Germination distribution (Schrader and Graves 2000) . is computed. Default is TRUE.

t50

logical. If TRUE, the Median germination time (\(t_{50}\)) (Coolbear et al. 1984; Farooq et al. 2005) is computed. Default is TRUE.

MeanGermTime

logical. If TRUE, the Mean germination time (\(\overline{T}\)) or Mean length of incubation time (Edmond and Drapala 1958; Czabator 1962; Ellis and Roberts 1980; Labouriau 1983; Ranal and de Santana 2006) . or Sprouting index (\(SI\)) (Smith and Millet 1964) or Germination Resistance (\(GR\)) Gordon (1969, 1971) is computed. Default is TRUE.

VarGermTime

logical. If TRUE, the Variance of germination time (\(s_{T}^{2}\)) (Labouriau 1983; Ranal and de Santana 2006) is computed. Default is TRUE.

SEGermTime

logical. If TRUE, the Standard error of germination time (\(s_{\overline{T}}\)) (Labouriau 1983; Ranal and de Santana 2006) . is computed. Default is TRUE.

CVGermTime

logical. If TRUE, the Coefficient of variation of the germination time (\(CV_{T}\)) (Ranal and de Santana 2006) is computed. Default is TRUE.

MeanGermRate

logical. If TRUE, the Mean germination rate (\(\overline{V}\)) (Labouriau and Valadares 1976; Labouriau 1983; Ranal and de Santana 2006) . is computed. Default is TRUE.

CVG

logical. If TRUE, the Coefficient of velocity/rate of germination or Kotowski's coefficient of velocity (\(CVG\)) (Kotowski 1926; Nichols and Heydecker 1968; Labouriau 1983; Scott et al. 1984; Bewley and Black 1994) . is computed. Default is TRUE.

VarGermRate

logical. If TRUE, the Variance of germination rate (\(s_{V}^{2}\)) (Labouriau 1983; Ranal and de Santana 2006) is computed. Default is TRUE.

SEGermRate

logical. If TRUE, the Standard error of germination rate (\(s_{\overline{V}}\)) (Labouriau 1983; Ranal and de Santana 2006) is computed. Default is TRUE.

GermRateRecip

logical. If TRUE, the Germination rate as reciprocal of median time (\(v_{50}\)) (Went 1957; Labouriau 1983; Ranal and de Santana 2006) is computed.

GermSpeed

logical. If TRUE, the Speed of germination or Germination rate index or Index of velocity of germination or Germination index or Emergence rate index (Throneberry and Smith 1955; Maguire 1962; Allan et al. 1962; Kendrick and Frankland 1969; Bouton et al. 1976; AOSA 1983; Khandakar and Bradbeer 1983; Bradbeer 1988; Wardle et al. 1991) considering both counts and percentages is computed.

GermSpeedAccumulated

logical. If TRUE, the Speed of accumulated germination (Bradbeer 1988; Wardle et al. 1991; Haugland and Brandsaeter 1996; de Santana and Ranal 2004) considering both counts and percentages is computed.

GermSpeedCorrected

logical. If TRUE, the Corrected speed of germination or Corrected germination rate index and the Corrected speed of accumulated germination (Evetts and Burnside 1972) is computed.

WeightGermPercent

logical. If TRUE, the Weighted germination percentage \(WGP\) or Weighted germination index \(WGI\) (Reddy 1978; Reddy et al. 1985) is computed.

MeanGermPercent

logical. If TRUE, the Mean/average germination percentage per unit time (\(\overline{GP}\)) (Czabator 1962) is computed.

MeanGermNumber

logical. If TRUE, the Number of seeds germinated per unit time (\(\overline{N}\)) (Khamassi et al. 2013) is computed.

TimsonsIndex

logical. If TRUE, the Timson's index or Timson's germination velocity index (Grose and Zimmer 1958; Timson 1965; Brown and Mayer 1988; Baskin and Baskin 1998) and it's modifications by Labouriau (Ranal and de Santana 2006) and (Khan and Ungar 1984) is computed.

GermRateGeorge

logical. If TRUE, the George's index George (1961) is computed.

max.int

The maximum interval value up to which Timson's index/George's germination rate is to be computed.

GermIndex

logical. If TRUE, the Germination index according to Melville et al. (1980) and its modification by de Santana and Ranal (2004) (Ranal and de Santana 2006) are computed.

EmergenceRateIndex

logical. If TRUE, the Emergence rate index or Germination rate index are computed according to

  • Shmueli and Goldberg (1971) and it's modification by de Santana and Ranal (2004) (Ranal and de Santana 2006) ;

  • Bilbro and Wanjura (1982) ; and

  • Fakorede and Ayoola (1980) , Fakorede and Ojo (1981) , and Fakorede and Agbana (1983) .

PeakValue

logical. If TRUE, the Peak value (\(PV\)) or Emergence Energy (\(EE\)) (Czabator 1962; Bonner 1967) is computed.

GermValue

logical. If TRUE, the Germination value (Czabator 1962; Djavanshir and Pourbeik 1976) and its modification considering duration from start of test instead of from onset of germination (Brown and Mayer 1988) is computed.

gv.k

The k Constant for computation of germination value. Default is 10.

CUGerm

logical. If TRUE, the Coefficient of uniformity of germination (CUG) (Heydecker 1972; Bewley and Black 1994) is computed.

GermSynchrony

logical. If TRUE, the Synchrony of germination (\(Z\) index) (Primack 1985; Ranal and de Santana 2006) is computed.

GermUncertainty

logical. If TRUE, the Synchronization index (\(\overline{E}\)) or Uncertainty of the germination process (\(U\)) or Informational entropy (\(H\)) (Shannon 1948; Labouriau and Valadares 1976; Labouriau 1983) is computed.

Value

A data frame with the original data along with the various single-value germination indices specified in the function arguments.

References

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Allan RE, Vogel OA, Peterson CJ (1962). “Seedling emergence rate of fall-sown wheat and its association with plant height and coleoptile length.” Agronomy Journal, 54(4), 347.

AOSA (1983). Seed Vigor Testing Handbook. Association of Official Seed Analysts, Ithaca, NY, USA.

Baskin CC, Baskin JM (1998). Seeds: Ecology, Biogeography, and Evolution of Dormancy and Germination. Academic Press, San Diego. ISBN 0-12-080260-0.

Bewley JD, Black M (1994). Physiology of Development and Germination. Plenum Publishing Corporation, New York, USA. ISBN 0-306-44748-7, tex.ids= bewley_ seeds:_1994, bewley_ seeds:_1994-1, bewley_ seeds:_1994-2 googlebooksid: W6EbrewcpDwC.

Bilbro JD, Wanjura DF (1982). “Soil crusts and cotton emergence relationships.” Transactions of the ASAE, 25(6), 1484--1487.

Bonner FT (1967). “Ideal sowing depth for sweetgum seed.” Tree Planters' Notes, 18(1), 1--1.

Bouton JH, Dudeck AE, Smith RL (1976). “Germination in freshly harvested seed of centipedegrass.” Agronomy Journal, 68(6), 991.

Bradbeer JW (1988). Seed Dormancy and Germination. Blackie, Glasgow and London.

Brown RF, Mayer DG (1988). “Representing cumulative germination. 1. A critical analysis of single-value germination indices.” Annals of Botany, 61(2), 117--125.

Coolbear P, Francis A, Grierson D (1984). “The effect of low temperature pre-sowing treatment on the germination performance and membrane integrity of artificially aged tomato seeds.” Journal of Experimental Botany, 35(11), 1609--1617.

Czabator FJ (1962). “Germination value: An index combining speed and completeness of pine seed germination.” Forest Science, 8(4), 386--396.

de Santana DG, Ranal MA (2004). Analise Da Germinacao: Um Enfoque Estatistico. Universidade de Brasilia, Brasilia.

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Fakorede MAB, Agbana SB (1983). “Heterotic effects and association of seedling vigour with mature characteristics and grain yield in some tropical maize cultivars.” Maydica, 28, 327--338.

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Gordon AG (1969). “Some observations on the germination energy tests for cereals.” Proceedings of the Association of Official Seed Analysts, 59, 58--72.

Gordon AG (1971). “The germination resistance test - A new test for measuring germination quality of cereals.” Canadian Journal of Plant Science, 51(2), 181--183.

Grose RJ, Zimmer WJ (1958). “Some laboratory germination responses of the seeds of river red gum, Eucalyptus camaldulensis Dehn. Syn. Eucalyptus rostrata Schlecht.” Australian Journal of Botany, 6(2), 129.

Haugland E, Brandsaeter LO (1996). “Experiments on bioassay sensitivity in the study of allelopathy.” Journal of Chemical Ecology, 22(10), 1845--1859.

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Kader MA (2005). “A comparison of seed germination calculation formulae and the associated interpretation of resulting data.” Journal and Proceedings of the Royal Society of New South Wales, 138, 65--75.

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Khamassi K, Harbaoui K, Jaime ATdS, Jeddi FB (2013). “Optimal germination temperature assessed by indices and models in field bean (Vicia faba L. var. minor).” Agriculturae Conspectus Scientificus, 78(2), 131--136.

Khan MA, Ungar IA (1984). “The effect of salinity and temperature on the germination of polymorphic seeds and growth of Atriplex triangularis Willd.” American Journal of Botany, 71(4), 481--489.

Khandakar AL, Bradbeer JW (1983). Jute seed quality. Bangladesh Agricultural Research Council, Dhaka.

Kotowski F (1926). “Temperature relations to germination of vegetable seeds.” Proceedings of the American Society for Horticultural Science, 23, 176--184.

Labouriau LG (1983). A Germinacao Das Sementes. Organizacao dos Estados Americanos. Programa Regional de Desenvolvimento Cientifico e Tecnologico. Serie de Biologia. Monografia 24.

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).

Maguire JD (1962). “Speed of germination - Aid in selection and evaluation for seedling emergence and vigor.” Crop Science, 2(2), 176--177.

Melville AH, Galletta GJ, Draper AD, Ng TJ (1980). “Seed germination and early seedling vigor in progenies of inbred strawberry selections.” HortScience, 15(6, I), 749--750.

Nichols MA, Heydecker W (1968). “Two approaches to the study of germination data.” Proceedings of the International Seed Testing Association, 33(3), 531--540.

Primack RB (1985). “Longevity of individual flowers.” Annual Review of Ecology and Systematics, 16(1), 15--37.

Quintanilla LG, Pajaron S, Pangua E, Amigo J (2000). “Effect of temperature on germination in northernmost populations of Culcita macrocarpa and Woodwardia radicans.” Plant Biology, 2(6), 612--617.

Ranal MA (1999). “Effects of temperature on spore germination in some fern species from semideciduous mesophytic forest.” American Fern Journal, 89(2), 149.

Ranal MA, de Santana DG (2006). “How and why to measure the germination process?” Brazilian Journal of Botany, 29(1), 1--11.

Reddy LV (1978). Effect of temperature on seed dormancy and alpha-amylase activity during kernel maturation and germination in wheat (Triticum aestivum L.) cultivars. Ph.D. Thesis, Oregon State University.

Reddy LV, Metzger RJ, Ching TM (1985). “Effect of temperature on seed dormancy of wheat.” Crop Science, 25(3), 455.

Roh M, Bentz J, Wang P, Li E, Koshioka M (2004). “Maturity and temperature stratification affect the germination of Styrax japonicus seeds.” The Journal of Horticultural Science and Biotechnology, 79(4), 645--651.

Schrader JA, Graves WR (2000). “Seed germination and seedling growth of Alnus maritima from its three disjunct populations.” Journal of the American Society for Horticultural Science, 125(1), 128--134.

Scott SJ, Jones RA, Williams WA (1984). “Review of data analysis methods for seed germination.” Crop Science, 24(6), 1192--1199.

Shannon CE (1948). “A mathematical theory of communication.” Bell System Technical Journal, 27(3), 379--423.

Shmueli M, Goldberg D (1971). “Emergence, early growth, and salinity of five vegetable crops germinated by sprinkle and trickle irrigation in an arid zone.” HortScience, 6, 563--565.

Smith PG, Millet AH (1964). “Germinating and sprouting responses of the tomato at low temperatures.” Proceedings of the American Society for Horticultural Science, 84, 480--484.

Throneberry GO, Smith FG (1955). “Relation of respiratory and enzymatic activity to corn seed viability.” Plant Physiology, 30(4), 337--343.

Timson J (1965). “New method of recording germination data.” Nature, 207(4993), 216.

Vallance KB (1950). “Studies on the germination of the seeds of Striga hermonthica I. The influence of moisture-treatment, stimulant-dilution, and after-ripening on germination.” Annals of Botany, 14(55), 347--363.

Wardle DA, Ahmed M, Nicholson KS (1991). “Allelopathic influence of nodding thistle (Carduus nutans L.) seeds on germination and radicle growth of pasture plants.” New Zealand Journal of Agricultural Research, 34(2), 185--191.

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Examples


# \donttest{
data(gcdata)

counts.per.intervals <- c("Day01", "Day02", "Day03", "Day04", "Day05",
                          "Day06", "Day07", "Day08", "Day09", "Day10",
                          "Day11", "Day12", "Day13", "Day14")
germination.indices(gcdata, total.seeds.col = "Total Seeds",
                    counts.intervals.cols = counts.per.intervals,
                    intervals = 1:14, partial = TRUE, max.int = 5)
#>    Genotype Rep Day01 Day02 Day03 Day04 Day05 Day06 Day07 Day08 Day09 Day10
#> 1        G1   1     0     0     0     0     4    17    10     7     1     0
#> 2        G2   1     0     0     0     1     3    15    13     6     2     1
#> 3        G3   1     0     0     0     2     3    18     9     8     2     1
#> 4        G4   1     0     0     0     0     4    19    12     6     2     1
#> 5        G5   1     0     0     0     0     5    20    12     8     1     0
#> 6        G1   2     0     0     0     0     3    21    11     7     1     1
#> 7        G2   2     0     0     0     0     4    18    11     7     1     0
#> 8        G3   2     0     0     0     1     3    14    12     6     2     1
#> 9        G4   2     0     0     0     1     3    19    10     8     1     1
#> 10       G5   2     0     0     0     0     4    18    13     6     2     1
#> 11       G1   3     0     0     0     0     5    21    11     8     1     0
#> 12       G2   3     0     0     0     0     3    20    10     7     1     1
#> 13       G3   3     0     0     0     0     4    19    12     8     1     1
#> 14       G4   3     0     0     0     0     3    21    11     6     1     0
#> 15       G5   3     0     0     0     0     4    17    10     8     1     1
#>    Day11 Day12 Day13 Day14 Total Seeds GermPercent PeakGermPercent
#> 1      1     0     0     0          50    80.00000        34.00000
#> 2      0     1     0     0          51    82.35294        29.41176
#> 3      1     1     0     0          48    93.75000        37.50000
#> 4      1     1     0     0          51    90.19608        37.25490
#> 5      0     1     1     0          50    96.00000        40.00000
#> 6      1     1     0     0          49    93.87755        42.85714
#> 7      1     0     0     0          48    87.50000        37.50000
#> 8      0     1     0     0          47    85.10638        29.78723
#> 9      1     1     0     0          52    86.53846        36.53846
#> 10     0     1     0     0          50    90.00000        36.00000
#> 11     0     1     1     0          51    94.11765        41.17647
#> 12     1     1     0     0          51    86.27451        39.21569
#> 13     0     1     1     0          49    95.91837        38.77551
#> 14     1     1     0     0          48    91.66667        43.75000
#> 15     1     0     0     0          48    87.50000        35.41667
#>    FirstGermTime LastGermTime PeakGermTime TimeSpreadGerm t50_Coolbear
#> 1              5           11            6              6     5.970588
#> 2              4           12            6              8     6.192308
#> 3              4           12            6              8     6.000000
#> 4              5           12            6              7     6.041667
#> 5              5           13            6              8     5.975000
#> 6              5           12            6              7     5.976190
#> 7              5           11            6              6     5.972222
#> 8              4           12            6              8     6.208333
#> 9              4           12            6              8     6.000000
#> 10             5           12            6              7     6.076923
#> 11             5           13            6              8     5.928571
#> 12             5           12            6              7     5.975000
#> 13             5           13            6              8     6.083333
#> 14             5           12            6              7     5.928571
#> 15             5           11            6              6     6.050000
#>    t50_Farooq MeanGermTime VarGermTime SEGermTime CVGermTime MeanGermRate
#> 1    5.941176     6.700000    1.446154  0.1901416  0.1794868    0.1492537
#> 2    6.153846     6.857143    2.027875  0.2197333  0.2076717    0.1458333
#> 3    5.972222     6.866667    2.572727  0.2391061  0.2335882    0.1456311
#> 4    6.000000     6.891304    2.187923  0.2180907  0.2146419    0.1451104
#> 5    5.950000     6.812500    2.368351  0.2221275  0.2259002    0.1467890
#> 6    5.952381     6.869565    2.071498  0.2122088  0.2095140    0.1455696
#> 7    5.944444     6.690476    1.389663  0.1818989  0.1761967    0.1494662
#> 8    6.166667     6.875000    2.112179  0.2297923  0.2113940    0.1454545
#> 9    5.973684     6.866667    2.300000  0.2260777  0.2208604    0.1456311
#> 10   6.038462     6.822222    1.831313  0.2017321  0.1983606    0.1465798
#> 11   5.904762     6.791667    2.381206  0.2227295  0.2272072    0.1472393
#> 12   5.950000     6.886364    2.149577  0.2210295  0.2129053    0.1452145
#> 13   6.041667     6.936170    2.539315  0.2324392  0.2297410    0.1441718
#> 14   5.904762     6.772727    1.900634  0.2078370  0.2035568    0.1476510
#> 15   6.000000     6.809524    1.670151  0.1994129  0.1897847    0.1468531
#>     VarGermRate  SEGermRate      CVG GermRateRecip_Coolbear
#> 1  0.0007176543 0.004235724 14.92537              0.1674877
#> 2  0.0009172090 0.004673148 14.58333              0.1614907
#> 3  0.0011572039 0.005071059 14.56311              0.1666667
#> 4  0.0009701218 0.004592342 14.51104              0.1655172
#> 5  0.0010995627 0.004786184 14.67890              0.1673640
#> 6  0.0009301809 0.004496813 14.55696              0.1673307
#> 7  0.0006935558 0.004063648 14.94662              0.1674419
#> 8  0.0009454531 0.004861721 14.54545              0.1610738
#> 9  0.0010345321 0.004794747 14.56311              0.1666667
#> 10 0.0008453940 0.004334343 14.65798              0.1645570
#> 11 0.0011191581 0.004828643 14.72393              0.1686747
#> 12 0.0009558577 0.004660905 14.52145              0.1673640
#> 13 0.0010970785 0.004831366 14.41718              0.1643836
#> 14 0.0009033254 0.004531018 14.76510              0.1686747
#> 15 0.0007767634 0.004300508 14.68531              0.1652893
#>    GermRateRecip_Farooq GermSpeed_Count GermSpeed_Percent
#> 1             0.1683168        6.138925          12.27785
#> 2             0.1625000        6.362698          12.47588
#> 3             0.1674419        6.882179          14.33787
#> 4             0.1666667        6.927417          13.58317
#> 5             0.1680672        7.318987          14.63797
#> 6             0.1680000        6.931782          14.14649
#> 7             0.1682243        6.448449          13.43427
#> 8             0.1621622        6.053175          12.87909
#> 9             0.1674009        6.830592          13.13575
#> 10            0.1656051        6.812698          13.62540
#> 11            0.1693548        7.342796          14.39764
#> 12            0.1680672        6.622258          12.98482
#> 13            0.1655172        7.052320          14.39249
#> 14            0.1693548        6.706782          13.97246
#> 15            0.1666667        6.363925          13.25818
#>    GermSpeedAccumulated_Count GermSpeedAccumulated_Percent
#> 1                    34.61567                     69.23134
#> 2                    35.54058                     69.68741
#> 3                    38.29725                     79.78594
#> 4                    38.68453                     75.85202
#> 5                    41.00786                     82.01571
#> 6                    38.77620                     79.13509
#> 7                    36.38546                     75.80304
#> 8                    33.77079                     71.85275
#> 9                    38.11511                     73.29829
#> 10                   38.19527                     76.39054
#> 11                   41.17452                     80.73436
#> 12                   37.00640                     72.56158
#> 13                   39.29399                     80.19182
#> 14                   37.69490                     78.53103
#> 15                   35.69697                     74.36868
#>    GermSpeedCorrected_Normal GermSpeedCorrected_Accumulated WeightGermPercent
#> 1                  0.1534731                      0.8653917          47.42857
#> 2                  0.1514928                      0.8462043          47.89916
#> 3                  0.1529373                      0.8510501          54.46429
#> 4                  0.1505960                      0.8409680          52.24090
#> 5                  0.1524789                      0.8543303          56.14286
#> 6                  0.1506909                      0.8429608          54.51895
#> 7                  0.1535345                      0.8663205          51.93452
#> 8                  0.1513294                      0.8442698          49.39210
#> 9                  0.1517909                      0.8470024          50.27473
#> 10                 0.1513933                      0.8487837          52.57143
#> 11                 0.1529749                      0.8578026          55.18207
#> 12                 0.1505059                      0.8410547          50.00000
#> 13                 0.1500494                      0.8360424          55.24781
#> 14                 0.1524269                      0.8567022          53.86905
#> 15                 0.1515220                      0.8499278          51.19048
#>    MeanGermPercent MeanGermNumber TimsonsIndex TimsonsIndex_Labouriau
#> 1         5.714286       2.857143     8.000000                   1.00
#> 2         5.882353       3.000000     9.803922                   1.25
#> 3         6.696429       3.214286    14.583333                   1.40
#> 4         6.442577       3.285714     7.843137                   1.00
#> 5         6.857143       3.428571    10.000000                   1.00
#> 6         6.705539       3.285714     6.122449                   1.00
#> 7         6.250000       3.000000     8.333333                   1.00
#> 8         6.079027       2.857143    10.638298                   1.25
#> 9         6.181319       3.214286     9.615385                   1.25
#> 10        6.428571       3.214286     8.000000                   1.00
#> 11        6.722689       3.428571     9.803922                   1.00
#> 12        6.162465       3.142857     5.882353                   1.00
#> 13        6.851312       3.357143     8.163265                   1.00
#> 14        6.547619       3.142857     6.250000                   1.00
#> 15        6.250000       3.000000     8.333333                   1.00
#>    TimsonsIndex_KhanUngar GermRateGeorge GermIndex GermIndex_mod
#> 1               0.5714286              4  5.840000      7.300000
#> 2               0.7002801              5  5.882353      7.142857
#> 3               1.0416667              7  6.687500      7.133333
#> 4               0.5602241              4  6.411765      7.108696
#> 5               0.7142857              5  6.900000      7.187500
#> 6               0.4373178              3  6.693878      7.130435
#> 7               0.5952381              4  6.395833      7.309524
#> 8               0.7598784              5  6.063830      7.125000
#> 9               0.6868132              5  6.173077      7.133333
#> 10              0.5714286              4  6.460000      7.177778
#> 11              0.7002801              5  6.784314      7.208333
#> 12              0.4201681              3  6.137255      7.113636
#> 13              0.5830904              4  6.775510      7.063830
#> 14              0.4464286              3  6.625000      7.227273
#> 15              0.5952381              4  6.291667      7.190476
#>    EmergenceRateIndex_SG EmergenceRateIndex_SG_mod
#> 1                    292                  7.300000
#> 2                    300                  7.142857
#> 3                    321                  7.133333
#> 4                    327                  7.108696
#> 5                    345                  7.187500
#> 6                    328                  7.130435
#> 7                    307                  7.309524
#> 8                    285                  7.125000
#> 9                    321                  7.133333
#> 10                   323                  7.177778
#> 11                   346                  7.208333
#> 12                   313                  7.113636
#> 13                   332                  7.063830
#> 14                   318                  7.227273
#> 15                   302                  7.190476
#>    EmergenceRateIndex_BilbroWanjura EmergenceRateIndex_Fakorede PeakValue
#> 1                          5.970149                    8.375000  9.500000
#> 2                          6.125000                    8.326531  9.313725
#> 3                          6.553398                    7.324444 10.416667
#> 4                          6.675079                    7.640359 10.049020
#> 5                          7.045872                    7.096354 11.250000
#> 6                          6.696203                    7.317580 10.714286
#> 7                          6.277580                    7.646259 10.416667
#> 8                          5.818182                    8.078125  9.574468
#> 9                          6.553398                    7.934815  9.855769
#> 10                         6.596091                    7.580247 10.250000
#> 11                         7.067485                    7.216146 11.029412
#> 12                         6.389439                    7.981921  9.803922
#> 13                         6.776074                    7.231326 10.969388
#> 14                         6.496644                    7.388430 10.677083
#> 15                         6.167832                    7.782313 10.156250
#>    GermValue_Czabator GermValue_DP GermValue_Czabator_mod GermValue_DP_mod
#> 1            54.28571     57.93890               54.28571         39.56076
#> 2            54.78662     52.58713               54.78662         40.99260
#> 3            69.75446     68.62289               69.75446         53.42809
#> 4            64.74158     70.43331               64.74158         48.86825
#> 5            77.14286     80.16914               77.14286         56.23935
#> 6            71.84506     76.51983               71.84506         53.06435
#> 7            65.10417     69.41325               65.10417         47.37690
#> 8            58.20345     56.00669               58.20345         43.67948
#> 9            60.92165     58.13477               60.92165         45.30801
#> 10           65.89286     70.91875               65.89286         49.10820
#> 11           74.14731     77.39782               74.14731         54.27520
#> 12           60.41632     64.44988               60.41632         44.71582
#> 13           75.15470     78.16335               75.15470         54.94192
#> 14           69.90947     74.40140               69.90947         51.41913
#> 15           63.47656     67.62031               63.47656         46.48043
#>       CUGerm GermSynchrony GermUncertainty
#> 1  0.7092199     0.2666667        2.062987
#> 2  0.5051546     0.2346109        2.321514
#> 3  0.3975265     0.2242424        2.462012
#> 4  0.4672113     0.2502415        2.279215
#> 5  0.4312184     0.2606383        2.146051
#> 6  0.4934701     0.2792271        2.160545
#> 7  0.7371500     0.2729384        2.040796
#> 8  0.4855842     0.2256410        2.357249
#> 9  0.4446640     0.2494949        2.321080
#> 10 0.5584666     0.2555556        2.187983
#> 11 0.4288905     0.2686170        2.128670
#> 12 0.4760266     0.2737844        2.185245
#> 13 0.4023679     0.2506938        2.241181
#> 14 0.5383760     0.2991543        2.037680
#> 15 0.6133519     0.2497096        2.185028
# }