Relative Frequency Adjustments

Compute and transform relative frequencies for a qualitative trait in a germplasm collection by the following methods (Balakrishnan and Suresh 2001) :

• Square root-proportion

• Log-frequency

Usage

prop.adj(x, method = c("none", "log", "sqrt"), size.count = NULL)

Arguments

x

Data of a qualitative trait for accessions in a collection as a vector of type factor.

method

The method for transformation. Either "none" for no transformation or "log" for log-frequency transformation or "sqrt" for square root-proportion transformation.

size.count

A positive integer specifying the target size of the core collection. The sum of frequencies allocated across levels of each qualitative trait will not exceed this value, and serves as the upper bound for iterative proportion clamping when size.count is supplied. If NULL, no clamping is performed and the adjusted proportions are returned as-is.

Value

The relative frequencies as a named numeric vector.

Details

If \(p_{i}\) is the relative frequency of the \(i\)th descriptive state for a qualitative trait in a collection, then the square root-proportion transformed relative \(q_{i}\) is computed as

\[q_{i} = \frac{\sqrt{p_{i}}}{\sum_{i=1}^{s}\sqrt{p_{i}}}\]

Where \(s\) is the number of possible descriptor states for the qualitative trait in the collection.

Similarly, the log-frequency transformed relative \(q_{i}\) is computed as

\[q_{i} = \frac{\log(F_{i} + k)}{\sum_{i=1}^{s}\log(F_{i} + k)}\]

Where \(F_{i}\) is the absolute frequency of the \(i\)th descriptive state for a qualitative trait in a collection. It is incremented by a constant \(k = 0.000001\) prior to log transformation. This ensures that singleton descriptor states (where \(F_{i} = 1\)) yield a small but non-zero proportion rather than being assigned a zero proportion due to \(\log(1) = 0\), which would otherwise exclude all accessions of that descriptor state from core selection irrespective of size.count.

When size.count is supplied, the transformed proportions \(q_{i}\) are subject to iterative clamping to ensure that the implied frequency \(q_{i} \times n\) for any descriptor state \(i\) does not exceed its actual count in the collection, where \(n\) is size.count. Excess proportion from clamped states is redistributed proportionally among unclamped states and the process repeats until no state exceeds its maximum allowable proportion \(F_{i} / n\).

References

Balakrishnan R, Suresh KK (2001). “Strategies for developing core collections of safflower (Carthamus tinctorius L.) germplasm-part II. Using an information measure for obtaining a core sample with pre-determined diversity levels for several descriptors simultaneously.” Indian Journal of Plant Genetic Resources, 14(1), 32–42.

Examples

suppressPackageStartupMessages(library(EvaluateCore))

library(EvaluateCore)

# Get data from EvaluateCore

data("cassava_EC", package = "EvaluateCore")

# Data of 'Colour of unexpanded apical leaves' qualitative trait
CUAL <- as.factor(cassava_EC$CUAL)

# Raw relative frequencies
prop.adj(CUAL, method = "none")
#>   Dark green        Green Green purple  Light green       Purple 
#>  0.190617577  0.001187648  0.527909739  0.028503563  0.251781473 

# Square root-proportion transformed relative frequencies
prop.adj(CUAL, method = "sqrt")
#>   Dark green        Green Green purple  Light green       Purple 
#>   0.23369439   0.01844636   0.38890779   0.09036836   0.26858311 

# Square log-frequency transformed relative frequencies
prop.adj(CUAL, method = "log")
#>   Dark green        Green Green purple  Light green       Purple 
#>   0.24903071   0.02990848   0.29298448   0.16703764   0.26103868