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)`

- 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.

The \(CR\) value.

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.

`NaN`

or `Inf`

values for \[CR_{\min}\] occurs when the
minimum values for some of the traits are zero.

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.

Wang J, Hu J, Zhang C, Zhang S (2007).
“Assessment on evaluating parameters of rice core collections constructed by genotypic values and molecular marker information.”
*Rice Science*, **14**(2), 101--110.

```
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
```