Estimate the number of accessions to be sampled from each group/cluster in the entire collection to construct a core collection. The following strategies are implemented.
Basic methods (Brown 1989; Huaman et al. 1999)
Constant
Proportional
Logarithmic
Square root
Diversity dependent methods (Yonezawa et al. 1995; Schoen and Brown 1993; Bisht et al. 1999; Mahajan et al. 1999; Franco et al. 2005)
Diversity
Diversity & Proportional
Diversity & Logarithmic
Diversity & Square root
Usage
sample.size(
data,
names,
group,
dist,
quantitative,
qualitative,
size = 0.2,
sample.method = c("const", "prop", "log", "sqrt", "diversity", "diverstiy.prop",
"diversity.sqrt", "diversity.log")
)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 accession names as a character string.
- group
Name of column with the accession group/cluster names as a character string.
- dist
A precomputed distance matrix of distance measures between the accessions in
data.- size
The desired core set size proportion.
- sample.method
Details
The different methods to determine the number of entries
from each group or clusters implemented in sample.size are as
follows.
Basic methods
These are different methods which estimate the number of entries only on the basis of total number of accessions in each group/cluster. Brown (1989) proposed the constant (C), proportional (P) and logarithmic (L) methods and later a similar square root method was proposed by Huaman et al. (1999) .
Constant method
From an entire collection of size \(N\), to construct a core set of sample size \(n\), the number of entries to be selected from the \(i\)th group among \(1 \cdots g\) groups (\(n_{i}\)) is estimated as below.
\[n_{i} = \frac{n}{g} \times N\]
Proportional method
Here the number of entries to be selected is proportional to the group/cluster size (\(N_{i}\)) as below.
\[n_{i} = n \times \frac{N_{i}}{\sum_{i=1}^{g}N_{i}}\]
\[n_{i} = n \times \frac{N_{i}}{N}\]
Diversity dependent methods
These are different methods which estimate the number of entries on the basis of how diverse are the accessions in each group/cluster. There are several methods proposed on the basis of diversity indices such as genetic multiplicity (G) dependent method based on the range of genetic diversity (Yonezawa et al. 1995) , H strategy based on Nei's gene diversity (Nei 1973) and a method based on the pooled Shannon diversity index (Bisht et al. 1999; Mahajan et al. 1999) . Similarly, measures such as expected proportion of heterozygous loci per individual and effective number of alleles have also been employed as a diversity measure for determining sample size (Franco et al. 2006) . Franco et al. (2005) proposed a method based on mean Gower's distance (Gower 1971) which was also extended to other distance measure averages named D Allocation strategy (Franco et al. 2006) . These methods were also combined with the proportional and logarithmic methods. For example, the GP and GL strategy of Bisht et al. (1999) and Mahajan et al. (1999) as well as the NY and LD allocation methods of Franco et al. (2005) .
Diversity method
From an entire collection of size \(N\), to construct a core set of sample size \(n\), the number of entries to be selected from the \(i\)th group among \(1 \cdots g\) groups (\(n_{i}\)) is estimated as below.
\[n_{i} = n \times \frac{D_{i}}{\sum_{i=1}^{g}D_{i}}\]
Where, \(D_{i}\) is a measure of the extent of diversity present in the \(i\)th cluster.
\(D\) can be either 1) Range of a diversity index 2) Pooled value of a diversity index or 3) Mean genetic distance.
Diversity and proportional method
Here the number of entries to be selected is proportional to the diversity of the group/cluster (\(D_{i}\)) weighted by the the group/cluster size (\(N_{i}\)).
\[n_{i} = n \times \frac{N_{i}D_{i}}{\sum_{i=1}^{g}N_{i}D_{i}}\]
References
Bisht IS, Mahajan RK, Gautam PL (1999).
“Assessment of genetic diversity, stratification of germplasm accessions in diversity groups and sampling strategies for establishing a core collection of Indian sesame (Sesamum indicum L.).”
Plant Genetic Resources Newsletter, 199 Supp., 35–46.
Brown AHD (1989).
“Core collections: A practical approach to genetic resources management.”
Genome, 31(2), 818–824.
Franco J, Crossa J, Taba S, Shands H (2005).
“A sampling strategy for conserving genetic diversity when forming core subsets.”
Crop Science, 45(3), 1035–1044.
Franco J, Crossa J, Warburton ML, Taba S (2006).
“Sampling strategies for conserving maize diversity when forming core subsets using genetic markers.”
Crop Science, 46(2), 854–864.
Gower JC (1971).
“A general coefficient of similarity and some of its properties.”
Biometrics, 27(4), 857–871.
Huaman Z, Aguilar C, Ortiz R (1999).
“Selecting a Peruvian sweetpotato core collection on the basis of morphological, eco-geographical, and disease and pest reaction data:.”
Theoretical and Applied Genetics, 98(5), 840–844.
Mahajan RK, Bisht IS, Gautam PL (1999).
“Sampling strategies for developing Indian sesame core collection.”
Indian Journal of Plant Genetic Resources, 12(01), 1–9.
Nei M (1973).
“Analysis of gene diversity in subdivided populations.”
Proceedings of the National Academy of Sciences, 70(12), 3321–3323.
Schoen DJ, Brown AH (1993).
“Conservation of allelic richness in wild crop relatives is aided by assessment of genetic markers.”
Proceedings of the National Academy of Sciences, 90(22), 10623–10627.
Yonezawa K, Nomura T, Morishima H (1995).
“Sampling strategies for use in stratified germplasm collections.”
In Hodkin T, Brown ADH, Hintum TJLv, Morales EAV (eds.), Core Collections of Plant Genetic Resources, 35–53.
John Wiley \& Sons, New York.
ISBN 0-471-95545-0.