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Allocation of Entries to be Selected from Clusters/Groups based on Diversity Index Estimates for Core Collection Development

Source: R/allocate.diversity.R
allocate.diversity.Rd

Estimate the number of entries to be allocated from each cluster/group in the entire collection to construct a core collection on the basis of different metrics computed from within cluster/group diversity index estimates. The following strategies are implemented.

  • Diversity

  • Diversity & Proportional

  • Diversity & Logarithmic

  • Diversity & Square root

Usage

allocate.diversity(
  data,
  names,
  group,
  qualitative,
  method = c("div", "div.prop", "div.sqrt", "div.log"),
  div.index = c("richness", "shannon", "simpson", "mcintosh"),
  shannon.base = exp(1),
  div.fun = NULL,
  log.base = exp(1),
  metric = c("pooled", "mean"),
  size
)

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.

qualitative

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

method

The allocation method. Either "div" for constant or "div.prop" for proportional or "div.log" for logarithmic or "div.sqrt" for square root allocation.

div.index

The diversity index to be used to estimate within cluster/group diversity.

shannon.base

The logarithm base to be used for estimation of Shannon diversity index. Default is exp(1).

div.fun

A function to estimate diversity index from a factor vector of qualitative trait data.

log.base

The logarithm base to be used for logarithmic method of sampling. Default is exp(1).

metric

The metric to be computed from the diversity index. Either "pooled" or "mean".

size

The desired core set size proportion.

Value

A named numeric vector specifying the number of entries to be selected from each cluster/group. The vector names correspond to the levels of the ""group" column, and values indicate the number of elements to be selected from each level.

Details

The number of entries to be chosen from each cluster is estimated either on the basis of diversity of entries within that cluster/group alone or in combination with the size of the cluster/group (See Methods).

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) .

The within-cluster/group diversity is estimated as either pooled or mean value of cluster/group-wise diversity indices. The following diversity indices are implemented in this function.

  • Shannon or Shannon-Weaver or Shannon-Wiener Diversity Index or Shannon entropy (\(H\)) (Shannon and Weaver 1949; Peet 1974)

  • Simpson's Index of Diversity or Gini's Diversity Index or Gini-Simpson Index or Nei's Diversity Index or Nei's Variation Index (\(D\)) or Hurlbert’s probability of interspecific encounter (\(PIE\)) (Gini 1912, 1912; Greenberg 1956; Berger and Parker 1970; Hurlbert 1971; Nei 1973; Peet 1974)

  • McIntosh Diversity Index (\(D_{Mc}\)) (McIntosh 1967; Peet 1974)

Methods

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.

Diversity and proportional method

Here the number of entries to be selected is proportional to the diversity of the cluster/group (\(D_{i}\)) weighted by the the cluster/group size (\(N_{i}\)).

\[n_{i} = n \times \frac{N_{i}D_{i}}{\sum_{i=1}^{g}N_{i}D_{i}}\]

Diversity and logarithmic method

Here the number of entries to be selected is proportional to the diversity of the cluster/group (\(D_{i}\)) weighted by the logarithm of the cluster/group size (\(N_{i}\)).

\[n_{i} = n \times \frac{\log(N_{i})D_{i}}{\sum_{i=1}^{g}\log(N_{i})D_{i}}\]

Diversity and square root method

Here the number of entries to be selected is proportional to the diversity of the cluster/group (\(D_{i}\)) weighted by the square root of the cluster/group size (\(N_{i}\)).

\[n_{i} = n \times \frac{\sqrt{N_{i}}D_{i}}{\sum_{i=1}^{g}\sqrt{N_{i}}D_{i}}\]

References

Berger WH, Parker FL (1970). “Diversity of planktonic foraminifera in deep-sea sediments.” Science, 168(3937), 1345–1347.

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.

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.

Gini C (1912). Variabilita e Mutabilita. Contributo allo Studio delle Distribuzioni e delle Relazioni Statistiche. [Fasc. I.]. Tipogr. di P. Cuppini, Bologna.

Gini C (1912). “Variabilita e mutabilita.” In Pizetti E, Salvemini T (eds.), Memorie di Metodologica Statistica. Liberia Eredi Virgilio Veschi, Roma, Italy.

Greenberg JH (1956). “The measurement of linguistic diversity.” Language, 32(1), 109.

Hurlbert SH (1971). “The nonconcept of species diversity: A critique and alternative parameters.” Ecology, 52(4), 577–586.

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.

McIntosh RP (1967). “An index of diversity and the relation of certain concepts to diversity.” Ecology, 48(3), 392–404.

Nei M (1973). “Analysis of gene diversity in subdivided populations.” Proceedings of the National Academy of Sciences, 70(12), 3321–3323.

Peet RK (1974). “The measurement of species diversity.” Annual Review of Ecology and Systematics, 5(1), 285–307.

Peet RK (1974). “The measurement of species diversity.” Annual Review of Ecology and Systematics, 5(1), 285–307.

Shannon CE, Weaver W (1949). The Mathematical Theory of Communication, number v. 2 in The Mathematical Theory of Communication. University of Illinois Press.

Yonezawa K, Nomura T, Morishima H (1995). “Sampling strategies for use in stratified germplasm collections.” In Hodkin T, Brown ADH, van Hintum TJL, Morales EAV (eds.), Core Collections of Plant Genetic Resources, 35–53. John Wiley & Sons, New York. ISBN 0-471-95545-0.

See also

allocate.basic, allocate.distance

Examples

#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Prepare example data
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

# Get data
data("cassava_EC_gp")

set.seed(123)
cassava_EC_gp <- cassava_EC_gp[sample(1:nrow(cassava_EC_gp), 500), ]

data <- cbind(genotypes = rownames(cassava_EC_gp), cassava_EC_gp)
row.names(data) <- NULL

# Column names of traits
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")

# Convert qualitative data columns to factor
data[, qual] <- lapply(data[, qual], as.factor)

# Convert quantitative data columns to qualitative scores
quant_to_score5 <- function(x) {

  brks <- unique( quantile(x,
                           probs = seq(0, 1, 0.2),
                           na.rm = TRUE))
  cut(x, breaks = brks,
      include.lowest = TRUE,
      labels = seq_len(length(brks) - 1))
}

data[, quant] <- lapply(data[, quant], quant_to_score5)

traits <- c(quant, qual)

#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Custom diversity index functions
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

div_fun_brillouin <- function(x) {
  n <- tabulate(x)
  n <- n[n > 0]
  N <- sum(n)
  if (N <= 1) {
    return(0)
  }
  (lgamma(N + 1) - sum(lgamma(n + 1)))/N
}

div_fun_margalef <- function(x) {
  tab <- tabulate(x)
  tab <- tab[tab > 0]
  S <- length(tab)
  N <- length(x)
  if (N <= 1) {
    return(0)
  }
  (S - 1)/log(N)
}

#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Diversity allocation
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

## Shannon-Weaver Diversity Index
div_out_shannon1 <-
  allocate.diversity(data = data, names = "genotypes",
                    group = "Cluster",
                    qualitative = traits,
                    method = "div",
                    div.index = "shannon", metric = "pooled",
                    size = 0.2)
div_out_shannon1
#>   I  II III  IV   V  VI 
#>  17  14  16  18  16  19 

div_out_shannon2 <-
  allocate.diversity(data = data, names = "genotypes",
                     group = "Cluster",
                     qualitative = traits,
                     method = "div",
                     div.index = "shannon", metric = "mean",
                     size = 0.2)
div_out_shannon2
#>   I  II III  IV   V  VI 
#>  17  14  16  18  16  19 

##  Gini-Simpson Index
div_out_simpson1 <-
  allocate.diversity(data = data, names = "genotypes",
                     group = "Cluster",
                     qualitative = traits,
                     method = "div",
                     div.index = "simpson", metric = "pooled",
                     size = 0.2)
div_out_simpson1
#>   I  II III  IV   V  VI 
#>  17  14  16  18  16  18 

div_out_simpson2 <-
  allocate.diversity(data = data, names = "genotypes",
                     group = "Cluster",
                     qualitative = traits,
                     method = "div",
                     div.index = "simpson", metric = "mean",
                     size = 0.2)
div_out_simpson2
#>   I  II III  IV   V  VI 
#>  17  14  16  18  16  18 

## McIntosh Diversity Index
div_out_mcintosh1 <-
  allocate.diversity(data = data, names = "genotypes",
                     group = "Cluster",
                     qualitative = traits,
                     method = "div",
                     div.index = "mcintosh", metric = "pooled",
                     size = 0.2)
div_out_mcintosh1
#>   I  II III  IV   V  VI 
#>  18  15  16  17  17  19 

div_out_mcintosh2 <-
  allocate.diversity(data = data, names = "genotypes",
                     group = "Cluster",
                     qualitative = traits,
                     method = "div",
                     div.index = "mcintosh", metric = "mean",
                     size = 0.2)
div_out_mcintosh2
#>   I  II III  IV   V  VI 
#>  18  15  16  17  17  19 

## Richness
div_out_richness1 <-
  allocate.diversity(data = data, names = "genotypes",
                     group = "Cluster",
                     qualitative = traits,
                     method = "div",
                     div.index = "richness", metric = "pooled",
                     size = 0.2)
div_out_richness1
#>   I  II III  IV   V  VI 
#>  17  15  17  18  16  18 

div_out_richness2 <-
  allocate.diversity(data = data, names = "genotypes",
                     group = "Cluster",
                     qualitative = traits,
                     method = "div",
                     div.index = "richness", metric = "mean",
                     size = 0.2)
div_out_richness2
#>   I  II III  IV   V  VI 
#>  17  15  17  18  16  18 

## Brillouin Diversity Index
div_out_brillouin1 <-
  allocate.diversity(data = data, names = "genotypes",
                     group = "Cluster",
                     qualitative = traits,
                     method = "div",
                     div.fun = div_fun_brillouin, metric = "pooled",
                     size = 0.2)
div_out_brillouin1
#>   I  II III  IV   V  VI 
#>  17  14  16  18  16  19 

div_out_brillouin2 <-
  allocate.diversity(data = data, names = "genotypes",
                     group = "Cluster",
                     qualitative = traits,
                     method = "div",
                     div.fun = div_fun_brillouin, metric = "mean",
                     size = 0.2)
div_out_brillouin2
#>   I  II III  IV   V  VI 
#>  17  14  16  18  16  19 

## Margalef's richness Index
div_out_margalef1 <-
  allocate.diversity(data = data, names = "genotypes",
                     group = "Cluster",
                     qualitative = traits,
                     method = "div",
                     div.fun = div_fun_margalef, metric = "pooled",
                     size = 0.2)
div_out_margalef1
#>   I  II III  IV   V  VI 
#>  19  15  16  16  16  18 

div_out_margalef2 <-
  allocate.diversity(data = data, names = "genotypes",
                     group = "Cluster",
                     qualitative = traits,
                     method = "div",
                     div.fun = div_fun_margalef, metric = "mean",
                     size = 0.2)
div_out_margalef2
#>   I  II III  IV   V  VI 
#>  19  15  16  16  16  18 


#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Diversity allocation & Proportional
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

## Shannon-Weaver Diversity Index
dist_prop_out_shannon1 <-
  allocate.diversity(data = data, names = "genotypes",
                     group = "Cluster",
                     qualitative = traits,
                     method = "div.prop",
                     div.index = "shannon", metric = "pooled",
                     size = 0.2)
dist_prop_out_shannon1
#>   I  II III  IV   V  VI 
#>  18  10  11  29  23  10 

dist_prop_out_shannon2 <-
  allocate.diversity(data = data, names = "genotypes",
                     group = "Cluster",
                     qualitative = traits,
                     method = "div.prop",
                     div.index = "shannon", metric = "mean",
                     size = 0.2)
dist_prop_out_shannon2
#>   I  II III  IV   V  VI 
#>  18  10  11  29  23  10 

##  Gini-Simpson Index
dist_prop_out_simpson1 <-
  allocate.diversity(data = data, names = "genotypes",
                     group = "Cluster",
                     qualitative = traits,
                     method = "div.prop",
                     div.index = "simpson", metric = "pooled",
                     size = 0.2)
dist_prop_out_simpson1
#>   I  II III  IV   V  VI 
#>  18  10  11  29  23  10 

dist_prop_out_simpson2 <-
  allocate.diversity(data = data, names = "genotypes",
                     group = "Cluster",
                     qualitative = traits,
                     method = "div.prop",
                     div.index = "simpson", metric = "mean",
                     size = 0.2)
dist_prop_out_simpson2
#>   I  II III  IV   V  VI 
#>  18  10  11  29  23  10 

## McIntosh Diversity Index
dist_prop_out_mcintosh1 <-
  allocate.diversity(data = data, names = "genotypes",
                     group = "Cluster",
                     qualitative = traits,
                     method = "div.prop",
                     div.index = "mcintosh", metric = "pooled",
                     size = 0.2)
dist_prop_out_mcintosh1
#>   I  II III  IV   V  VI 
#>  18  10  10  28  23  10 

dist_prop_out_mcintosh2 <-
  allocate.diversity(data = data, names = "genotypes",
                     group = "Cluster",
                     qualitative = traits,
                     method = "div.prop",
                     div.index = "mcintosh", metric = "mean",
                     size = 0.2)
dist_prop_out_mcintosh2
#>   I  II III  IV   V  VI 
#>  18  10  10  28  23  10 

## Richness
div_out_richness1 <-
  allocate.diversity(data = data, names = "genotypes",
                     group = "Cluster",
                     qualitative = traits,
                     method = "div.log",
                     div.index = "richness", metric = "pooled",
                     size = 0.2)
div_out_richness1
#>   I  II III  IV   V  VI 
#>  17  14  16  21  17  16 

div_out_richness2 <-
  allocate.diversity(data = data, names = "genotypes",
                     group = "Cluster",
                     qualitative = traits,
                     method = "div.log",
                     div.index = "richness", metric = "mean",
                     size = 0.2)
div_out_richness2
#>   I  II III  IV   V  VI 
#>  17  14  16  21  17  16 

## Brillouin Diversity Index
div_out_brillouin1 <-
  allocate.diversity(data = data, names = "genotypes",
                     group = "Cluster",
                     qualitative = traits,
                     method = "div.prop",
                     div.fun = div_fun_brillouin, metric = "pooled",
                     size = 0.2)
div_out_brillouin1
#>   I  II III  IV   V  VI 
#>  17   9  11  30  22  11 

div_out_brillouin2 <-
  allocate.diversity(data = data, names = "genotypes",
                     group = "Cluster",
                     qualitative = traits,
                     method = "div.prop",
                     div.fun = div_fun_brillouin, metric = "mean",
                     size = 0.2)
div_out_brillouin2
#>   I  II III  IV   V  VI 
#>  17   9  11  30  22  11 

## Margalef's richness Index
div_out_margalef1 <-
  allocate.diversity(data = data, names = "genotypes",
                     group = "Cluster",
                     qualitative = traits,
                     method = "div.prop",
                     div.fun = div_fun_margalef, metric = "pooled",
                     size = 0.2)
div_out_margalef1
#>   I  II III  IV   V  VI 
#>  19  10  10  27  23  10 

div_out_margalef2 <-
  allocate.diversity(data = data, names = "genotypes",
                     group = "Cluster",
                     qualitative = traits,
                     method = "div.prop",
                     div.fun = div_fun_margalef, metric = "mean",
                     size = 0.2)
div_out_margalef2
#>   I  II III  IV   V  VI 
#>  19  10  10  27  23  10 

#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Diversity allocation & Logarithmic
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

## Shannon-Weaver Diversity Index
dist_log_out_shannon1 <-
  allocate.diversity(data = data, names = "genotypes",
                     group = "Cluster",
                     qualitative = traits,
                     method = "div.log",
                     div.index = "shannon", metric = "pooled",
                     size = 0.2)
dist_log_out_shannon1
#>   I  II III  IV   V  VI 
#>  18  13  15  20  18  17 

dist_log_out_shannon2 <-
  allocate.diversity(data = data, names = "genotypes",
                     group = "Cluster",
                     qualitative = traits,
                     method = "div.log",
                     div.index = "shannon", metric = "mean",
                     size = 0.2)
dist_log_out_shannon2
#>   I  II III  IV   V  VI 
#>  18  13  15  20  18  17 

##  Gini-Simpson Index
dist_log_out_simpson1 <-
  allocate.diversity(data = data, names = "genotypes",
                     group = "Cluster",
                     qualitative = traits,
                     method = "div.log",
                     div.index = "simpson", metric = "pooled",
                     size = 0.2)
dist_log_out_simpson1
#>   I  II III  IV   V  VI 
#>  18  13  15  20  18  16 

dist_log_out_simpson2 <-
  allocate.diversity(data = data, names = "genotypes",
                     group = "Cluster",
                     qualitative = traits,
                     method = "div.log",
                     div.index = "simpson", metric = "mean",
                     size = 0.2)
dist_log_out_simpson2
#>   I  II III  IV   V  VI 
#>  18  13  15  20  18  16 

## McIntosh Diversity Index
dist_log_out_mcintosh1 <-
  allocate.diversity(data = data, names = "genotypes",
                     group = "Cluster",
                     qualitative = traits,
                     method = "div.log",
                     div.index = "mcintosh", metric = "pooled",
                     size = 0.2)
dist_log_out_mcintosh1
#>   I  II III  IV   V  VI 
#>  18  13  14  19  18  16 

dist_log_out_mcintosh2 <-
  allocate.diversity(data = data, names = "genotypes",
                     group = "Cluster",
                     qualitative = traits,
                     method = "div.log",
                     div.index = "mcintosh", metric = "mean",
                     size = 0.2)
dist_log_out_mcintosh2
#>   I  II III  IV   V  VI 
#>  18  13  14  19  18  16 

## Richness
div_out_richness1 <-
  allocate.diversity(data = data, names = "genotypes",
                     group = "Cluster",
                     qualitative = traits,
                     method = "div.log",
                     div.index = "richness", metric = "pooled",
                     size = 0.2)
div_out_richness1
#>   I  II III  IV   V  VI 
#>  17  14  16  21  17  16 

div_out_richness2 <-
  allocate.diversity(data = data, names = "genotypes",
                     group = "Cluster",
                     qualitative = traits,
                     method = "div.log",
                     div.index = "richness", metric = "mean",
                     size = 0.2)
div_out_richness2
#>   I  II III  IV   V  VI 
#>  17  14  16  21  17  16 

## Brillouin Diversity Index
div_out_brillouin1 <-
  allocate.diversity(data = data, names = "genotypes",
                     group = "Cluster",
                     qualitative = traits,
                     method = "div.log",
                     div.fun = div_fun_brillouin, metric = "pooled",
                     size = 0.2)
div_out_brillouin1
#>   I  II III  IV   V  VI 
#>  17  13  15  21  17  17 

div_out_brillouin2 <-
  allocate.diversity(data = data, names = "genotypes",
                     group = "Cluster",
                     qualitative = traits,
                     method = "div.log",
                     div.fun = div_fun_brillouin, metric = "mean",
                     size = 0.2)
div_out_brillouin2
#>   I  II III  IV   V  VI 
#>  17  13  15  21  17  17 

## Margalef's richness Index
div_out_margalef1 <-
  allocate.diversity(data = data, names = "genotypes",
                     group = "Cluster",
                     qualitative = traits,
                     method = "div.log",
                     div.fun = div_fun_margalef, metric = "pooled",
                     size = 0.2)
div_out_margalef1
#>   I  II III  IV   V  VI 
#>  19  14  14  19  18  16 

div_out_margalef2 <-
  allocate.diversity(data = data, names = "genotypes",
                     group = "Cluster",
                     qualitative = traits,
                     method = "div.log",
                     div.fun = div_fun_margalef, metric = "mean",
                     size = 0.2)
div_out_margalef2
#>   I  II III  IV   V  VI 
#>  19  14  14  19  18  16 

#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Diversity allocation & Square root
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

## Shannon-Weaver Diversity Index
dist_sqrt_out_shannon1 <-
  allocate.diversity(data = data, names = "genotypes",
                     group = "Cluster",
                     qualitative = traits,
                     method = "div.sqrt",
                     div.index = "shannon", metric = "pooled",
                     size = 0.2)
dist_sqrt_out_shannon1
#>   I  II III  IV   V  VI 
#>  18  12  13  23  20  14 

dist_sqrt_out_shannon2 <-
  allocate.diversity(data = data, names = "genotypes",
                     group = "Cluster",
                     qualitative = traits,
                     method = "div.sqrt",
                     div.index = "shannon", metric = "mean",
                     size = 0.2)
dist_sqrt_out_shannon2
#>   I  II III  IV   V  VI 
#>  18  12  13  23  20  14 

##  Gini-Simpson Index
dist_sqrt_out_simpson1 <-
  allocate.diversity(data = data, names = "genotypes",
                     group = "Cluster",
                     qualitative = traits,
                     method = "div.sqrt",
                     div.index = "simpson", metric = "pooled",
                     size = 0.2)
dist_sqrt_out_simpson1
#>   I  II III  IV   V  VI 
#>  18  12  14  23  20  14 

dist_sqrt_out_simpson2 <-
  allocate.diversity(data = data, names = "genotypes",
                     group = "Cluster",
                     qualitative = traits,
                     method = "div.sqrt",
                     div.index = "simpson", metric = "mean",
                     size = 0.2)
dist_sqrt_out_simpson2
#>   I  II III  IV   V  VI 
#>  18  12  14  23  20  14 

## McIntosh Diversity Index
dist_sqrt_out_mcintosh1 <-
  allocate.diversity(data = data, names = "genotypes",
                     group = "Cluster",
                     qualitative = traits,
                     method = "div.sqrt",
                     div.index = "mcintosh", metric = "pooled",
                     size = 0.2)
dist_sqrt_out_mcintosh1
#>   I  II III  IV   V  VI 
#>  18  12  13  22  20  14 

dist_sqrt_out_mcintosh2 <-
  allocate.diversity(data = data, names = "genotypes",
                     group = "Cluster",
                     qualitative = traits,
                     method = "div.sqrt",
                     div.index = "mcintosh", metric = "mean",
                     size = 0.2)
dist_sqrt_out_mcintosh2
#>   I  II III  IV   V  VI 
#>  18  12  13  22  20  14 

## Richness
div_out_richness1 <-
  allocate.diversity(data = data, names = "genotypes",
                     group = "Cluster",
                     qualitative = traits,
                     method = "div.sqrt",
                     div.index = "richness", metric = "pooled",
                     size = 0.2)
div_out_richness1
#>   I  II III  IV   V  VI 
#>  17  12  14  24  19  14 

div_out_richness2 <-
  allocate.diversity(data = data, names = "genotypes",
                     group = "Cluster",
                     qualitative = traits,
                     method = "div.sqrt",
                     div.index = "richness", metric = "mean",
                     size = 0.2)
div_out_richness2
#>   I  II III  IV   V  VI 
#>  17  12  14  24  19  14 

## Brillouin Diversity Index
div_out_brillouin1 <-
  allocate.diversity(data = data, names = "genotypes",
                     group = "Cluster",
                     qualitative = traits,
                     method = "div.sqrt",
                     div.fun = div_fun_brillouin, metric = "pooled",
                     size = 0.2)
div_out_brillouin1
#>   I  II III  IV   V  VI 
#>  17  12  14  24  19  14 

div_out_brillouin2 <-
  allocate.diversity(data = data, names = "genotypes",
                     group = "Cluster",
                     qualitative = traits,
                     method = "div.sqrt",
                     div.fun = div_fun_brillouin, metric = "mean",
                     size = 0.2)
div_out_brillouin2
#>   I  II III  IV   V  VI 
#>  17  12  14  24  19  14 

## Margalef's richness Index
div_out_margalef1 <-
  allocate.diversity(data = data, names = "genotypes",
                     group = "Cluster",
                     qualitative = traits,
                     method = "div.sqrt",
                     div.fun = div_fun_margalef, metric = "pooled",
                     size = 0.2)
div_out_margalef1
#>   I  II III  IV   V  VI 
#>  19  13  13  21  20  14 

div_out_margalef2 <-
  allocate.diversity(data = data, names = "genotypes",
                     group = "Cluster",
                     qualitative = traits,
                     method = "div.sqrt",
                     div.fun = div_fun_margalef, metric = "mean",
                     size = 0.2)
div_out_margalef2
#>   I  II III  IV   V  VI 
#>  19  13  13  21  20  14