Compute 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
)

## Arguments

data

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.

names

Name of column with the individual names as a character string

quantitative

Name of columns with the quantitative traits as a character vector.

selected

Character vector with the names of individuals selected in core collection and present in the names column.

alpha

Type I error probability (Significance level) of difference.

rr.crit

The critical value of range ratio considered to be acceptable for a representative CS. The default value is 0.7.

## Value

A data frame with the values of

$$MD\%_{Hu}$$,

$$VD\%_{Hu}$$,

$$MD\%_{Kim}$$,

$$VD\%_{Kim}$$ and

$$\overline{d}D\%$$.

## Details

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 ($$\frac{R_{CS_{i}}}{R_{EC_{i}}} < 0.7$$) $$R_{CS_{i}}$$ 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.

snk.evaluate.core, snk.evaluate.core

## Examples


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