Compute the following metrics to compare quantitative traits of the entire collection (EC) and core set (CS).

• Changeable Rate of Maximum ($$CR_{\max}$$) (Wang et al. 2007)

• Changeable Rate of Minimum ($$CR_{\min}$$) (Wang et al. 2007)

• Changeable Rate of Mean ($$CR_{\mu}$$) (Wang et al. 2007)

cr.evaluate.core(data, names, quantitative, selected)

## 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.

## Value

The $$CR$$ value.

## Details

The Coincidence Rate of Range ($$CR$$) is computed as follows.

$CR = \left ( \frac{1}{n} \sum_{i=1}^{n} \frac{R_{CS_{i}}}{R_{EC_{i}}} \right ) \times 100$

Where, $$R_{CS_{i}}$$ 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.

A representative CS should have a $$CR$$ value no less than 70% (Diwan et al. 1995) or 80% (Hu et al. 2000) .

The Changeable Rate of Maximum ($$CR_{\max}$$) is computed as follows.

$CR_{\max} = \left ( \frac{1}{n} \sum_{i=1}^{n} \frac{\max_{CS_{i}}}{\max_{EC_{i}}} \right ) \times 100$

Where, $$\max_{CS_{i}}$$ is the maximum value of the $$i$$th trait in the CS, $$\max_{EC_{i}}$$ is the maximum value of the $$i$$th trait in the EC and $$n$$ is the total number of traits.

The Changeable Rate of Minimum ($$CR_{\min}$$) is computed as follows.

$CR_{\min} = \left ( \frac{1}{n} \sum_{i=1}^{n} \frac{\min_{CS_{i}}}{\min_{EC_{i}}} \right ) \times 100$

Where, $$\min_{CS_{i}}$$ is the minimum value of the $$i$$th trait in the CS, $$\min_{EC_{i}}$$ is the minimum value of the $$i$$th trait in the EC and $$n$$ is the total number of traits.

The Changeable Rate of Mean ($$CR_{\mu}$$) is computed as follows.

$CR_{\mu} = \left ( \frac{1}{n} \sum_{i=1}^{n} \frac{\mu_{CS_{i}}}{\mu_{EC_{i}}} \right ) \times 100$

Where, $$\mu_{CS_{i}}$$ is the mean value of the $$i$$th trait in the CS, $$\mu_{EC_{i}}$$ is the mean value of the $$i$$th trait in the EC and $$n$$ is the total number of traits.

## Note

NaN or Inf values for $CR_{\min}$ occurs when the minimum values for some of the traits are zero.

wilcox.test

## 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)))

cr.evaluate.core(data = ec, names = "genotypes",
quantitative = quant, selected = core)
#>        CR    CR_Max    CR_Min   CR_Mean
#>  89.23084  93.78085       NaN 112.80763