R/percentdiff.evaluate.core.R
percentdiff.evaluate.core.RdCompute the following differences between the entire collection (EC) and core set (CS).
Percentage of significant differences of mean (\(MD\%_{Hu}\)) (Hu et al. 2000)
Percentage of significant differences of variance (\(VD\%_{Hu}\)) (Hu et al. 2000)
Average of absolute differences between means (\(MD\%_{Kim}\)) (Kim et al. 2007)
Average of absolute differences between variances (\(VD\%_{Kim}\)) (Kim et al. 2007)
Percentage difference between the mean squared Euclidean distance among accessions (\(\overline{d}D\%\)) (Studnicki et al. 2013)
Percentage of range ratios smaller than 0.70 (\(S_{RR_{0.7}}\)) (Diwan et al. 1995)
percentdiff.evaluate.core(
data,
names,
quantitative,
selected,
alpha = 0.05,
rr.crit = 0.7
)The data as a data frame object. The data frame should possess one row per individual and columns with the individual names and multiple trait/character data.
Name of column with the individual names as a character string.
Name of columns with the quantitative traits as a character vector.
Character vector with the names of individuals selected in
core collection and present in the names column.
Type I error probability (Significance level) of difference.
The critical value of range ratio considered to be acceptable for a representative CS. The default value is 0.7.
A data frame with the values of \(MD\%_{Hu}\), \(VD\%_{Hu}\), \(MD\%_{Kim}\), \(VD\%_{Kim}\) and \(\overline{d}D\%\).
The differences are computed as follows.
\[MD\%_{Hu} = \left ( \frac{S_{t}}{n} \right ) \times 100\]
Where, \(S_{t}\) is the number of traits with a significant difference between the means of the EC and the CS and \(n\) is the total number of traits. A representative core should have \(MD\%_{Hu}\) < 20 % and \(CR\) > 80 % (Hu et al. 2000) .
\[VD\%_{Hu} = \left ( \frac{S_{F}}{n} \right ) \times 100\]
Where, \(S_{F}\) is the number of traits with a significant difference between the variances of the EC and the CS and \(n\) is the total number of traits. Larger \(VD\%_{Hu}\) value indicates a more diverse core set.
\[MD\%_{Kim} = \left ( \frac{1}{n}\sum_{i=1}^{n} \frac{\left | M_{EC_{i}}-M_{CS_{i}} \right |}{M_{CS_{i}}} \right ) \times 100\]
Where, \(M_{EC_{i}}\) is the mean of the EC for the \(i\)th trait, \(M_{CS_{i}}\) is the mean of the CS for the \(i\)th trait and \(n\) is the total number of traits.
\[VD\%_{Kim} = \left ( \frac{1}{n}\sum_{i=1}^{n} \frac{\left | V_{EC_{i}}-V_{CS_{i}} \right |}{V_{CS_{i}}} \right ) \times 100\]
Where, \(V_{EC_{i}}\) is the variance of the EC for the \(i\)th trait, \(V_{CS_{i}}\) is the variance of the CS for the \(i\)th trait and \(n\) is the total number of traits.
\[\overline{d}D\% = \frac{\overline{d}_{CS}-\overline{d}_{EC}}{\overline{d}_{EC}} \times 100\]
Where, \(\overline{d}_{CS}\) is the mean squared Euclidean distance among accessions in the CS and \(\overline{d}_{EC}\) is the mean squared Euclidean distance among accessions in the EC.
Percentage of range ratios smaller than 0.70 (Diwan et al. 1995) is computed as follows.
\[RR\%_{0.7} = \left ( \frac{S_{RR_{0.7}}}{n} \right ) \times 100\]
Where, \(S_{RR_{0.7}}\) is the number of traits with a range ratio smaller than 0.7 (\(\frac{R_{CS_{i}}}{R_{EC_{i}}} \(R_{CS_{i}}\) is the range of the \(i\)th trait in the CS, \(R_{EC_{i}}\) is the range of the \(i\)th trait in the EC and \(n\) is the total number of traits.
Diwan N, McIntosh MS, Bauchan GR (1995).
“Methods of developing a core collection of annual Medicago species.”
Theoretical and Applied Genetics, 90(6), 755–761.
Hu J, Zhu J, Xu HM (2000).
“Methods of constructing core collections by stepwise clustering with three sampling strategies based on the genotypic values of crops.”
Theoretical and Applied Genetics, 101(1), 264–268.
Kim K, Chung H, Cho G, Ma K, Chandrabalan D, Gwag J, Kim T, Cho E, Park Y (2007).
“PowerCore: A program applying the advanced M strategy with a heuristic search for establishing core sets.”
Bioinformatics, 23(16), 2155–2162.
Studnicki M, Madry W, Schmidt J (2013).
“Comparing the efficiency of sampling strategies to establish a representative in the phenotypic-based genetic diversity core collection of orchardgrass (Dactylis glomerata L.).”
Czech Journal of Genetics and Plant Breeding, 49(1), 36–47.
data("cassava_CC")
data("cassava_EC")
ec <- cbind(genotypes = rownames(cassava_EC), cassava_EC)
ec$genotypes <- as.character(ec$genotypes)
rownames(ec) <- NULL
core <- rownames(cassava_CC)
quant <- c("NMSR", "TTRN", "TFWSR", "TTRW", "TFWSS", "TTSW", "TTPW", "AVPW",
"ARSR", "SRDM")
qual <- c("CUAL", "LNGS", "PTLC", "DSTA", "LFRT", "LBTEF", "CBTR", "NMLB",
"ANGB", "CUAL9M", "LVC9M", "TNPR9M", "PL9M", "STRP", "STRC",
"PSTR")
ec[, qual] <- lapply(ec[, qual],
function(x) factor(as.factor(x)))
percentdiff.evaluate.core(data = ec, names = "genotypes",
quantitative = quant, selected = core)
#> MDPercent_Hu VDPercent_Hu MDPercent_Kim VDPercent_Kim DDPercent RR
#> 1 50 80 13.02737 41.64331 18.2052 20