Generate Core collections with Length of Encoded Attribute Values

Based on Length of Encoded Attribute Values (LEAV) (Wallace and Boulton 1968; Balakrishnan and Suresh 2001; Balakrishnan and Suresh 2001; Balakrishnan and Nair 2003) estimated from qualitative and/or quantitative trait data, core collections can be generated by the three following methods.

Method I: Classification based on pre-determined diversity represented by LEAV estimates implemented in LEAVcore1.
Method II: Purposive selection of accessions with highest rank of LEAV estimates implemented in LEAVcore2.
Method III: Stratified sampling of accessions from diversity groups/strata computed from LEAV estimates partially implemented in LEAVcore3.

Usage

LEAVcore1(
  data,
  names,
  quantitative = NULL,
  qualitative = NULL,
  size,
  prop.adj = c("none", "log", "sqrt"),
  e,
  always.selected = NULL
)

LEAVcore2(
  data,
  names,
  quantitative = NULL,
  qualitative = NULL,
  size,
  prop.adj = c("none", "log", "sqrt"),
  e,
  always.selected = NULL
)

LEAVcore3(
  data,
  names,
  quantitative = NULL,
  qualitative = NULL,
  size,
  prop.adj = c("none", "log", "sqrt"),
  e,
  always.selected = NULL
)

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.
qualitative: Name of columns with the qualitative traits as a character vector.
size: The desired core set size proportion.
prop.adj: The method for relative frequency transformation for qualitative traits. Either "none" for no transformation or "log" for log-frequency transformation or "sqrt" for square root-proportion transformation (see prop.adj).
e: A named numeric vector of least count of measurement for each quantitative trait specified in quantitative. The list names should be same as quantitative.
always.selected: Names of accessions to be always included in the core set as a character vector.

Value

LEAVcore1 returns a data frame with one row per accession in data and the following columns:

names: Accession identifiers, as specified by the names argument.
LEAV_core: The total LEAV score for each accession computed under the core group parameterisation (frequencies and moments estimated from the target core subset).
LEAV_noncore: The total LEAV score for each accession computed under the non-core group parameterisation (frequencies and moments estimated from the remainder of the collection).
always.selected: A logical vector indicating whether the accession was pre-specified in always.selected.
core: A logical vector indicating whether the accession is selected into the core collection, either because LEAV_core \(\leq\) LEAV_noncore (selected by the method) or because it appears in always.selected.

LEAVcore2 returns a data frame with one row per accession in data, sorted in decreasing order of LEAV score, with the following columns:

names: Accession identifiers, as specified by the names argument.
lt: The log-ratio message length term \(\log(N / n)\), where \(N\) is the total number of accessions in data and \(n\) is size.count.
<trait columns>: One column per trait specified in qualitative and quantitative, giving the per-accession information length for that trait.
LEAV: The total LEAV score for each accession, equal to the row sum of lt and all trait information length columns.
always.selected: A logical vector indicating whether the accession was pre-specified in always.selected.
core: A logical vector indicating whether the accession is selected into the core collection, either as one of the top size.count ranked accessions among non-always.selected accessions or because it appears in always.selected.

LEAVcore3 returns a data frame with one row per accession in data, sorted in decreasing order of LEAV score, with the following columns:

names: Accession identifiers, as specified by the names argument.
lt: The log-ratio message length term \(\log(N / n)\), where \(N\) is the total number of accessions in data and \(n\) is size.count.
<trait columns>: One column per trait specified in qualitative and quantitative, giving the per-accession information length for that trait.
LEAV: The total LEAV score for each accession, equal to the row sum of lt and all trait information length columns.
LEAVStrata: An integer stratum identifier assigned by the Dalenius-Hodges cumulative root frequency method (Dalenius and Hodges 1959) , indicating the stratum to which each accession belongs for proportional sampling. NA for accessions in always.selected, which are excluded from stratification.
always.selected: A logical vector indicating whether the accession was pre-specified in always.selected and is therefore excluded from stratification.

Details

Balakrishnan and Suresh (2001); Balakrishnan and Suresh (2001) describe three different methods of constructing core collections from estimates of Length of Encoded Attribute Values.

Method I: Classification based on pre-determined diversity represented by LEAV estimates

This is an objective classification scheme that assigns accessions to either a "core" or "non-core" group based on which group model they best fit.

The target frequency patterns for qualitative traits and distribution parameters for quantitative traits are determined first for the two groups: the Core and the Non-Core.

Target proportions for the core group are estimated from the base proportions of the qualitative trait levels. These may be subjected to transformations if required according to "prop.adj" argument to increase rare trait representation. Target counts are set by scaling these to the total count and capping them at the actual frequency available in the collection. Similarly for the non-core group, the target proportions are determined by subtracting the core model's frequencies from the total counts of each trait level in the entire collection.

The target distribution for the core group is modeled by applying a Gaussian kernel density function to the quantitative trait data, scaled to the core size. The non-core parameters are set to the actual mean and standard deviation of the entire collection.

Based on these target values, the message length (\(F\)) is estimated for each accession against both the models using LEAV. An accession is assigned to the core if \(F_{core} \leq F_{non-core}\). If more accessions are selected than the target core size, the core is refined by ranking individuals by \(F_{core}\) values in ascending order and retaining only the top matches.

Method II: Purposive selection of accessions with highest rank of LEAV estimates

This is a directed selection method that captures the most unique and dispersed accessions to maximize diversity and reduce redundancy.

Here the LEAV index for every accession relative to the entire base collection is first estimated. Then the accessions are ranked in descending order of their LEAV estimates.Finally the core collection is constituted by selecting a pre-determined number of top-ranked accessions according to "size" argument.

Method III: Stratified sampling of accessions from diversity groups/strata computed from LEAV estimates

This is a two-step approach that first organizes the collection into optimized diversity groups based on LEAV estimates followed by a group-wise representative sampling.

Here also the LEAV index for every accession relative to the entire base collection is first estimated. These estimates are then divided into \(L\) strata using the Dalenius formula to minimize pooled variance (Dalenius and Hodges 1959) .

The number of entries to be sampled from each stratum is then determined followed by stratified selection from each group to reach the final core size.

In LEAVcore3, only the stratification based on LEAV estimates is implemented. The downstream steps for allocation (allocate.basic, allocate.diversity, allocate.distance) and stratified selection (select.random, select.diversity, select.distance) are available from the sister package SampleCore.

References

Balakrishnan R, Nair NV (2003). “Strategies for developing core collections of sugarcane (Saccharum officinarum L.) germplasm-comparison of sampling from diversity groups constituted by three different methods.” Plant Genetic Resources Newsletter, 134, 33–41.

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.

Balakrishnan R, Suresh KK (2001). “Strategies for developing core collections of safflower (Carthamus tinctorius L.) germplasm-part III. Obtaining diversity groups based on an information measure.” Indian Journal of Plant Genetic Resources, 14(3), 342–349.

Dalenius T, Hodges JL (1959). “Minimum variance stratification.” Journal of the American Statistical Association, 54(285), 88–101.

Wallace CS, Boulton DM (1968). “An information measure for classification.” The Computer Journal, 11(2), 185–194.

Examples

suppressPackageStartupMessages(library(EvaluateCore))

# Get data from EvaluateCore
data("cassava_EC", package = "EvaluateCore")

cassava_EC <- cbind(genotypes = rownames(cassava_EC), cassava_EC)


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")

cassava_EC[, qual] <- lapply(cassava_EC[, qual], as.factor)

e_vec <- rep(1, length(quant))
names(e_vec) <- quant

mand_accns <-
  c("TMe-2018", "TMe-801", "TMe-3191", "TMe-1830", "TMe-1790")

table(cassava_EC$genotypes %in% mand_accns)
#> 
#> FALSE  TRUE 
#>  1679     5 

#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Method I
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

LEAVcore1_out <-
  LEAVcore1(data = cassava_EC, names = "genotypes",
            quantitative = quant, qualitative = qual,
            size = 0.2, prop.adj = "log", e = e_vec,
            always.selected = mand_accns)

head(LEAVcore1_out)
#>   genotypes LEAV_core LEAV_noncore always.selected  core
#> 1    TMe-10  38.65169     39.21512           FALSE FALSE
#> 2  TMe-1003  44.89429     39.45960           FALSE FALSE
#> 3  TMe-1004  59.24587     50.33656           FALSE FALSE
#> 4  TMe-1005  42.29718     41.37500           FALSE FALSE
#> 5  TMe-1006  48.53216     44.48855           FALSE FALSE
#> 6  TMe-1007  70.29001     43.39722           FALSE FALSE

# Selected accessions for core
core1 <- LEAVcore1_out[LEAVcore1_out$core == TRUE, "genotypes"]

core1
#>   [1] "TMe-1020" "TMe-1083" "TMe-1099" "TMe-1147" "TMe-116"  "TMe-1174"
#>   [7] "TMe-1184" "TMe-1204" "TMe-1218" "TMe-123"  "TMe-1232" "TMe-1238"
#>  [13] "TMe-1250" "TMe-1262" "TMe-130"  "TMe-1305" "TMe-132"  "TMe-1353"
#>  [19] "TMe-1360" "TMe-1375" "TMe-1383" "TMe-1385" "TMe-1391" "TMe-1392"
#>  [25] "TMe-1403" "TMe-1409" "TMe-1419" "TMe-1421" "TMe-1423" "TMe-1428"
#>  [31] "TMe-1461" "TMe-15"   "TMe-1505" "TMe-1506" "TMe-1511" "TMe-1518"
#>  [37] "TMe-154"  "TMe-1564" "TMe-1566" "TMe-1577" "TMe-1579" "TMe-160" 
#>  [43] "TMe-1608" "TMe-1661" "TMe-167"  "TMe-1716" "TMe-1732" "TMe-1744"
#>  [49] "TMe-1775" "TMe-1776" "TMe-1790" "TMe-1809" "TMe-181"  "TMe-1814"
#>  [55] "TMe-1819" "TMe-1820" "TMe-1830" "TMe-184"  "TMe-185"  "TMe-186" 
#>  [61] "TMe-1875" "TMe-1883" "TMe-1897" "TMe-190"  "TMe-1902" "TMe-1956"
#>  [67] "TMe-1960" "TMe-1964" "TMe-2"    "TMe-2004" "TMe-2018" "TMe-203" 
#>  [73] "TMe-2033" "TMe-2041" "TMe-205"  "TMe-2055" "TMe-2058" "TMe-206" 
#>  [79] "TMe-2064" "TMe-2067" "TMe-2069" "TMe-2077" "TMe-208"  "TMe-210" 
#>  [85] "TMe-2121" "TMe-215"  "TMe-2158" "TMe-2216" "TMe-2217" "TMe-2240"
#>  [91] "TMe-225"  "TMe-2307" "TMe-2308" "TMe-2352" "TMe-2383" "TMe-241" 
#>  [97] "TMe-2413" "TMe-25"   "TMe-2510" "TMe-2532" "TMe-2534" "TMe-2552"
#> [103] "TMe-259"  "TMe-266"  "TMe-267"  "TMe-268"  "TMe-270"  "TMe-2748"
#> [109] "TMe-2751" "TMe-2756" "TMe-276"  "TMe-2761" "TMe-2769" "TMe-277" 
#> [115] "TMe-2776" "TMe-2779" "TMe-2785" "TMe-279"  "TMe-2790" "TMe-2791"
#> [121] "TMe-280"  "TMe-2800" "TMe-2809" "TMe-2810" "TMe-2811" "TMe-2823"
#> [127] "TMe-2824" "TMe-2835" "TMe-289"  "TMe-2897" "TMe-290"  "TMe-2901"
#> [133] "TMe-2903" "TMe-2907" "TMe-2915" "TMe-2917" "TMe-2926" "TMe-2928"
#> [139] "TMe-2944" "TMe-2945" "TMe-2954" "TMe-2957" "TMe-2958" "TMe-2965"
#> [145] "TMe-2970" "TMe-2971" "TMe-2975" "TMe-2979" "TMe-2980" "TMe-2985"
#> [151] "TMe-2998" "TMe-3006" "TMe-3007" "TMe-3030" "TMe-3032" "TMe-3043"
#> [157] "TMe-3046" "TMe-3048" "TMe-3053" "TMe-3054" "TMe-3055" "TMe-306" 
#> [163] "TMe-3066" "TMe-3071" "TMe-3088" "TMe-3095" "TMe-3111" "TMe-3114"
#> [169] "TMe-3116" "TMe-3118" "TMe-3127" "TMe-3140" "TMe-3141" "TMe-3148"
#> [175] "TMe-3151" "TMe-3167" "TMe-3189" "TMe-3191" "TMe-3196" "TMe-3198"
#> [181] "TMe-3200" "TMe-3207" "TMe-3209" "TMe-3210" "TMe-3222" "TMe-3234"
#> [187] "TMe-3236" "TMe-3253" "TMe-3256" "TMe-3257" "TMe-326"  "TMe-3261"
#> [193] "TMe-3262" "TMe-3264" "TMe-3265" "TMe-3273" "TMe-3275" "TMe-3276"
#> [199] "TMe-3277" "TMe-3278" "TMe-3284" "TMe-3291" "TMe-3299" "TMe-3302"
#> [205] "TMe-3312" "TMe-3314" "TMe-3346" "TMe-3354" "TMe-3356" "TMe-3362"
#> [211] "TMe-3382" "TMe-3383" "TMe-3394" "TMe-3397" "TMe-34"   "TMe-3401"
#> [217] "TMe-3411" "TMe-3417" "TMe-3418" "TMe-3422" "TMe-3433" "TMe-3437"
#> [223] "TMe-3438" "TMe-344"  "TMe-3443" "TMe-3445" "TMe-3452" "TMe-3466"
#> [229] "TMe-3467" "TMe-3478" "TMe-3480" "TMe-3481" "TMe-35"   "TMe-3518"
#> [235] "TMe-352"  "TMe-3544" "TMe-3549" "TMe-3558" "TMe-3568" "TMe-3571"
#> [241] "TMe-3572" "TMe-3575" "TMe-3576" "TMe-3591" "TMe-3592" "TMe-3594"
#> [247] "TMe-3599" "TMe-3606" "TMe-3619" "TMe-3620" "TMe-3625" "TMe-3663"
#> [253] "TMe-3679" "TMe-3690" "TMe-3719" "TMe-3721" "TMe-3729" "TMe-3760"
#> [259] "TMe-3766" "TMe-3771" "TMe-3772" "TMe-378"  "TMe-38"   "TMe-3804"
#> [265] "TMe-383"  "TMe-385"  "TMe-39"   "TMe-397"  "TMe-40"   "TMe-41"  
#> [271] "TMe-410"  "TMe-418"  "TMe-419"  "TMe-420"  "TMe-425"  "TMe-43"  
#> [277] "TMe-434"  "TMe-457"  "TMe-460"  "TMe-469"  "TMe-478"  "TMe-480" 
#> [283] "TMe-5"    "TMe-514"  "TMe-528"  "TMe-536"  "TMe-540"  "TMe-550" 
#> [289] "TMe-551"  "TMe-57"   "TMe-575"  "TMe-59"   "TMe-594"  "TMe-606" 
#> [295] "TMe-620"  "TMe-635"  "TMe-64"   "TMe-650"  "TMe-656"  "TMe-660" 
#> [301] "TMe-67"   "TMe-674"  "TMe-696"  "TMe-70"   "TMe-712"  "TMe-735" 
#> [307] "TMe-74"   "TMe-748"  "TMe-754"  "TMe-766"  "TMe-768"  "TMe-771" 
#> [313] "TMe-773"  "TMe-774"  "TMe-778"  "TMe-78"   "TMe-801"  "TMe-82"  
#> [319] "TMe-821"  "TMe-828"  "TMe-830"  "TMe-838"  "TMe-842"  "TMe-85"  
#> [325] "TMe-86"   "TMe-867"  "TMe-875"  "TMe-878"  "TMe-887"  "TMe-897" 
#> [331] "TMe-925"  "TMe-93"   "TMe-930"  "TMe-945"  "TMe-950"  "TMe-972" 
#> [337] "TMe-985" 

#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Method II
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

LEAVcore2_out <-
  LEAVcore2(data = cassava_EC, names = "genotypes",
            quantitative = quant, qualitative = qual,
            size = 0.2, prop.adj = "log", e = e_vec,
            always.selected = mand_accns)

head(LEAVcore2_out)
#>      genotypes       lt     CUAL     LNGS     PTLC     DSTA     LFRT    LBTEF
#> 942   TMe-3163 1.623792 1.171319 1.018756 1.001667 1.383677 1.034312 1.609178
#> 1432   TMe-603 1.623792 1.171319 1.009479 1.001667 1.383677 1.034312 1.570564
#> 1221  TMe-3605 1.623792 1.171319 1.292631 1.001667 1.383677 2.627081 1.602382
#> 1251  TMe-3685 1.623792 1.287220 1.018756 1.001667 1.622932 1.034312 1.795852
#> 1033  TMe-3292 1.623792 1.287220 1.018756 1.001667 1.913500 1.034312 1.795852
#> 1312   TMe-399 1.623792 1.171319 1.018756 1.001667 1.622932 1.464561 1.570564
#>           CBTR     NMLB     ANGB   CUAL9M    LVC9M   TNPR9M      PL9M     STRP
#> 942  0.8126782 1.720141 1.226096 1.406059 1.147944 1.577724 0.7000020 1.214631
#> 1432 0.7318245 1.804366 1.144471 1.353840 1.202224 1.486676 0.7167117 1.233826
#> 1221 0.8126782 1.760304 1.252595 1.363820 1.147944 1.608716 0.7167117 1.233826
#> 1251 0.8126782 1.720141 1.144471 1.406059 1.516240 1.486676 0.7000020 1.214631
#> 1033 0.8126782 1.760304 1.252595 1.353840 1.147944 1.577724 0.7000020 1.233826
#> 1312 0.7318245 1.886362 1.144471 1.353840 1.202224 1.486676 0.7167117 1.233826
#>           STRC      PSTR     NMSR     TTRN     TFWSR      TTRW     TFWSS
#> 942  0.7148823 0.6508703 3.148152 2.920333  7.725617 62.300599  3.184656
#> 1432 0.6718744 0.7563591 4.231506 1.688734 28.186653  7.329838 20.356342
#> 1221 0.7148823 0.6508703 3.931099 2.682888  2.438998  4.479733  5.948706
#> 1251 0.7148823 0.7563591 5.195730 1.983253 31.447430  8.187797 11.931777
#> 1033 0.6718744 0.6508703 3.406218 2.407173 18.553374 14.557196  7.171076
#> 1312 0.6718744 0.6508703 4.447229 2.351584  9.257126  3.845843 20.356342
#>           TTSW      TTPW      AVPW     ARSR     SRDM     LEAV always.selected
#> 942  15.116045  5.414342 38.522834 1.800534 2.572890 162.7197           FALSE
#> 1432  6.113131 27.021538  8.184969 1.859701 2.704807 127.5742           FALSE
#> 1221 49.534465  4.470612 26.950597 2.067785 2.652030 127.1218           FALSE
#> 1251  3.676607 21.904679  6.697428 1.800534 2.633677 116.3156           FALSE
#> 1033  5.818571 13.020808 11.171692 1.800534 2.538544 101.2819           FALSE
#> 1312  9.807997 17.188937  8.236776 2.067785 2.546281 100.6582           FALSE
#>      core
#> 942  TRUE
#> 1432 TRUE
#> 1221 TRUE
#> 1251 TRUE
#> 1033 TRUE
#> 1312 TRUE

# Selected accessions for core
core2 <- LEAVcore2_out[LEAVcore2_out$core == TRUE, "genotypes"]

core2
#>   [1] "TMe-3163" "TMe-603"  "TMe-3605" "TMe-3685" "TMe-3292" "TMe-399" 
#>   [7] "TMe-3800" "TMe-3736" "TMe-616"  "TMe-3667" "TMe-2853" "TMe-3705"
#>  [13] "TMe-2943" "TMe-3628" "TMe-3701" "TMe-3573" "TMe-901"  "TMe-2035"
#>  [19] "TMe-3730" "TMe-3223" "TMe-2050" "TMe-2967" "TMe-3415" "TMe-812" 
#>  [25] "TMe-390"  "TMe-3353" "TMe-1730" "TMe-2996" "TMe-707"  "TMe-815" 
#>  [31] "TMe-731"  "TMe-608"  "TMe-3406" "TMe-761"  "TMe-412"  "TMe-2905"
#>  [37] "TMe-717"  "TMe-3025" "TMe-2983" "TMe-3694" "TMe-798"  "TMe-1261"
#>  [43] "TMe-2963" "TMe-1416" "TMe-3297" "TMe-2531" "TMe-373"  "TMe-13"  
#>  [49] "TMe-588"  "TMe-2204" "TMe-2513" "TMe-863"  "TMe-3040" "TMe-1307"
#>  [55] "TMe-2984" "TMe-861"  "TMe-1004" "TMe-3581" "TMe-427"  "TMe-1919"
#>  [61] "TMe-3089" "TMe-997"  "TMe-1985" "TMe-3641" "TMe-3392" "TMe-929" 
#>  [67] "TMe-3034" "TMe-3319" "TMe-2940" "TMe-623"  "TMe-2952" "TMe-1723"
#>  [73] "TMe-659"  "TMe-27"   "TMe-3337" "TMe-432"  "TMe-2955" "TMe-1646"
#>  [79] "TMe-2913" "TMe-2953" "TMe-725"  "TMe-2043" "TMe-705"  "TMe-1294"
#>  [85] "TMe-3329" "TMe-421"  "TMe-3065" "TMe-3249" "TMe-1472" "TMe-584" 
#>  [91] "TMe-1248" "TMe-2196" "TMe-832"  "TMe-3698" "TMe-1283" "TMe-1479"
#>  [97] "TMe-527"  "TMe-2604" "TMe-700"  "TMe-1806" "TMe-3130" "TMe-1272"
#> [103] "TMe-3565" "TMe-3396" "TMe-728"  "TMe-926"  "TMe-1079" "TMe-2912"
#> [109] "TMe-1286" "TMe-2916" "TMe-47"   "TMe-3485" "TMe-1311" "TMe-2977"
#> [115] "TMe-2688" "TMe-3475" "TMe-1011" "TMe-694"  "TMe-3076" "TMe-2966"
#> [121] "TMe-1124" "TMe-44"   "TMe-1945" "TMe-1425" "TMe-1339" "TMe-35"  
#> [127] "TMe-3054" "TMe-3601" "TMe-3281" "TMe-2860" "TMe-2937" "TMe-500" 
#> [133] "TMe-1762" "TMe-1098" "TMe-1348" "TMe-2914" "TMe-3345" "TMe-391" 
#> [139] "TMe-1769" "TMe-2329" "TMe-994"  "TMe-2010" "TMe-1158" "TMe-2551"
#> [145] "TMe-1796" "TMe-2226" "TMe-3471" "TMe-2040" "TMe-289"  "TMe-3222"
#> [151] "TMe-1958" "TMe-1273" "TMe-1129" "TMe-835"  "TMe-631"  "TMe-3185"
#> [157] "TMe-3428" "TMe-3363" "TMe-3087" "TMe-756"  "TMe-729"  "TMe-2973"
#> [163] "TMe-2355" "TMe-3633" "TMe-2906" "TMe-2518" "TMe-3659" "TMe-3398"
#> [169] "TMe-1300" "TMe-3501" "TMe-7"    "TMe-1388" "TMe-3272" "TMe-1293"
#> [175] "TMe-2968" "TMe-2151" "TMe-3531" "TMe-438"  "TMe-600"  "TMe-2843"
#> [181] "TMe-2439" "TMe-3282" "TMe-742"  "TMe-585"  "TMe-3368" "TMe-1581"
#> [187] "TMe-3596" "TMe-845"  "TMe-1137" "TMe-1580" "TMe-1101" "TMe-3085"
#> [193] "TMe-867"  "TMe-1988" "TMe-487"  "TMe-2060" "TMe-2441" "TMe-3255"
#> [199] "TMe-745"  "TMe-937"  "TMe-2993" "TMe-787"  "TMe-3132" "TMe-2567"
#> [205] "TMe-86"   "TMe-473"  "TMe-3351" "TMe-1042" "TMe-5"    "TMe-3055"
#> [211] "TMe-736"  "TMe-2733" "TMe-1600" "TMe-362"  "TMe-2956" "TMe-4"   
#> [217] "TMe-2119" "TMe-2304" "TMe-3387" "TMe-751"  "TMe-3547" "TMe-1401"
#> [223] "TMe-1078" "TMe-698"  "TMe-737"  "TMe-645"  "TMe-2976" "TMe-2939"
#> [229] "TMe-606"  "TMe-1074" "TMe-1174" "TMe-609"  "TMe-2270" "TMe-2203"
#> [235] "TMe-1312" "TMe-1756" "TMe-2257" "TMe-1239" "TMe-1511" "TMe-2802"
#> [241] "TMe-361"  "TMe-241"  "TMe-1269" "TMe-1700" "TMe-3175" "TMe-1501"
#> [247] "TMe-1924" "TMe-3773" "TMe-154"  "TMe-1366" "TMe-3639" "TMe-2374"
#> [253] "TMe-174"  "TMe-209"  "TMe-975"  "TMe-1564" "TMe-976"  "TMe-1995"
#> [259] "TMe-569"  "TMe-3575" "TMe-1376" "TMe-3299" "TMe-1987" "TMe-1233"
#> [265] "TMe-3707" "TMe-579"  "TMe-1715" "TMe-696"  "TMe-1621" "TMe-750" 
#> [271] "TMe-3496" "TMe-3266" "TMe-1975" "TMe-3401" "TMe-3389" "TMe-3463"
#> [277] "TMe-2057" "TMe-876"  "TMe-2855" "TMe-481"  "TMe-501"  "TMe-1643"
#> [283] "TMe-2166" "TMe-1397" "TMe-1256" "TMe-410"  "TMe-1875" "TMe-6"   
#> [289] "TMe-3323" "TMe-196"  "TMe-3440" "TMe-2862" "TMe-1310" "TMe-2128"
#> [295] "TMe-1526" "TMe-3466" "TMe-1053" "TMe-3437" "TMe-2530" "TMe-2318"
#> [301] "TMe-3366" "TMe-2910" "TMe-3072" "TMe-2027" "TMe-2589" "TMe-2985"
#> [307] "TMe-2032" "TMe-3110" "TMe-3533" "TMe-3112" "TMe-893"  "TMe-1232"
#> [313] "TMe-1589" "TMe-3382" "TMe-601"  "TMe-394"  "TMe-2779" "TMe-665" 
#> [319] "TMe-1738" "TMe-66"   "TMe-2809" "TMe-1020" "TMe-1051" "TMe-3572"
#> [325] "TMe-826"  "TMe-3545" "TMe-1257" "TMe-414"  "TMe-3273" "TMe-3479"
#> [331] "TMe-1199" "TMe-2757" "TMe-1790" "TMe-801"  "TMe-1830" "TMe-2018"
#> [337] "TMe-3191"

#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Method III
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

LEAVcore3_out <-
  LEAVcore3(data = cassava_EC, names = "genotypes",
            quantitative = quant, qualitative = qual,
            size = 0.2, prop.adj = "log", e = e_vec,
            always.selected = mand_accns)

head(LEAVcore3_out)
#>      genotypes       lt     CUAL     LNGS     PTLC     DSTA     LFRT    LBTEF
#> 942   TMe-3163 1.623792 1.171319 1.018756 1.001667 1.383677 1.034312 1.609178
#> 1432   TMe-603 1.623792 1.171319 1.009479 1.001667 1.383677 1.034312 1.570564
#> 1221  TMe-3605 1.623792 1.171319 1.292631 1.001667 1.383677 2.627081 1.602382
#> 1251  TMe-3685 1.623792 1.287220 1.018756 1.001667 1.622932 1.034312 1.795852
#> 1033  TMe-3292 1.623792 1.287220 1.018756 1.001667 1.913500 1.034312 1.795852
#> 1312   TMe-399 1.623792 1.171319 1.018756 1.001667 1.622932 1.464561 1.570564
#>           CBTR     NMLB     ANGB   CUAL9M    LVC9M   TNPR9M      PL9M     STRP
#> 942  0.8126782 1.720141 1.226096 1.406059 1.147944 1.577724 0.7000020 1.214631
#> 1432 0.7318245 1.804366 1.144471 1.353840 1.202224 1.486676 0.7167117 1.233826
#> 1221 0.8126782 1.760304 1.252595 1.363820 1.147944 1.608716 0.7167117 1.233826
#> 1251 0.8126782 1.720141 1.144471 1.406059 1.516240 1.486676 0.7000020 1.214631
#> 1033 0.8126782 1.760304 1.252595 1.353840 1.147944 1.577724 0.7000020 1.233826
#> 1312 0.7318245 1.886362 1.144471 1.353840 1.202224 1.486676 0.7167117 1.233826
#>           STRC      PSTR     NMSR     TTRN     TFWSR      TTRW     TFWSS
#> 942  0.7148823 0.6508703 3.148152 2.920333  7.725617 62.300599  3.184656
#> 1432 0.6718744 0.7563591 4.231506 1.688734 28.186653  7.329838 20.356342
#> 1221 0.7148823 0.6508703 3.931099 2.682888  2.438998  4.479733  5.948706
#> 1251 0.7148823 0.7563591 5.195730 1.983253 31.447430  8.187797 11.931777
#> 1033 0.6718744 0.6508703 3.406218 2.407173 18.553374 14.557196  7.171076
#> 1312 0.6718744 0.6508703 4.447229 2.351584  9.257126  3.845843 20.356342
#>           TTSW      TTPW      AVPW     ARSR     SRDM     LEAV LEAVStrata
#> 942  15.116045  5.414342 38.522834 1.800534 2.572890 162.7197         12
#> 1432  6.113131 27.021538  8.184969 1.859701 2.704807 127.5742         12
#> 1221 49.534465  4.470612 26.950597 2.067785 2.652030 127.1218         12
#> 1251  3.676607 21.904679  6.697428 1.800534 2.633677 116.3156         12
#> 1033  5.818571 13.020808 11.171692 1.800534 2.538544 101.2819         12
#> 1312  9.807997 17.188937  8.236776 2.067785 2.546281 100.6582         12
#>      always.selected
#> 942            FALSE
#> 1432           FALSE
#> 1221           FALSE
#> 1251           FALSE
#> 1033           FALSE
#> 1312           FALSE

# Strata/Group-wise counts
table(LEAVcore3_out$LEAVStrata)
#> 
#>   1   2   3   4   5   6   7   8   9  10  11  12 
#> 205 210 205 188 316 168 138  84  69  42  27  27 

# Sample accessions from strata to form core set using SampleCOre
suppressPackageStartupMessages(library(SampleCore))

# Append LEAV strata to original data
data <- merge.data.frame(cassava_EC,
                         LEAVcore3_out[, c("genotypes", "LEAVStrata",
                                           "always.selected")],
                         by = "genotypes")
data$LEAVStrata <- as.factor(data$LEAVStrata)

# Use log allocation
log_alloc <-
  allocate.basic(data = data[data$always.selected != TRUE, ],
                 names = "genotypes",
                 group = "LEAVStrata", method = "log",
                 size = 0.2)

# Use random selection
set.seed(123)
sel_random_out <-
  select.random(data = data[data$always.selected != TRUE, ],
                names = "genotypes",
                group = "LEAVStrata", alloc = log_alloc,
                # Already included in LEAVcore3_out
                always.selected = NULL)

# Append always selected accessions
core3 <-
  c(sel_random_out,
    list(always.selected =
         LEAVcore3_out[LEAVcore3_out$always.selected == TRUE,
                       "genotypes"]))
# Final core
core3
#> $`1`
#>  [1] "TMe-406"  "TMe-685"  "TMe-1151" "TMe-846"  "TMe-548"  "TMe-1678"
#>  [7] "TMe-3003" "TMe-1487" "TMe-960"  "TMe-882"  "TMe-368"  "TMe-2319"
#> [13] "TMe-2326" "TMe-834"  "TMe-786"  "TMe-2332" "TMe-3286" "TMe-2402"
#> [19] "TMe-1930" "TMe-1211" "TMe-1086" "TMe-940"  "TMe-802"  "TMe-450" 
#> [25] "TMe-2026" "TMe-2127" "TMe-866"  "TMe-2543" "TMe-2989" "TMe-2009"
#> [31] "TMe-3427" "TMe-1268"
#> 
#> $`2`
#>  [1] "TMe-3008" "TMe-1123" "TMe-3340" "TMe-467"  "TMe-2192" "TMe-137" 
#>  [7] "TMe-3538" "TMe-684"  "TMe-187"  "TMe-3335" "TMe-878"  "TMe-885" 
#> [13] "TMe-442"  "TMe-1486" "TMe-211"  "TMe-2152" "TMe-2210" "TMe-1981"
#> [19] "TMe-3407" "TMe-2775" "TMe-245"  "TMe-3499" "TMe-1509" "TMe-1368"
#> [25] "TMe-1629" "TMe-565"  "TMe-2435" "TMe-191"  "TMe-1278" "TMe-3128"
#> [31] "TMe-273"  "TMe-1083"
#> 
#> $`3`
#>  [1] "TMe-932"  "TMe-2453" "TMe-967"  "TMe-1592" "TMe-386"  "TMe-321" 
#>  [7] "TMe-1802" "TMe-1470" "TMe-1110" "TMe-1224" "TMe-2041" "TMe-3322"
#> [13] "TMe-3729" "TMe-1831" "TMe-1345" "TMe-2750" "TMe-388"  "TMe-1367"
#> [19] "TMe-1488" "TMe-447"  "TMe-317"  "TMe-142"  "TMe-3527" "TMe-933" 
#> [25] "TMe-3243" "TMe-315"  "TMe-381"  "TMe-1979" "TMe-3540" "TMe-2020"
#> [31] "TMe-3644" "TMe-3261"
#> 
#> $`4`
#>  [1] "TMe-237"  "TMe-2611" "TMe-668"  "TMe-3593" "TMe-1827" "TMe-2268"
#>  [7] "TMe-852"  "TMe-3142" "TMe-3010" "TMe-939"  "TMe-3423" "TMe-813" 
#> [13] "TMe-1351" "TMe-1795" "TMe-186"  "TMe-661"  "TMe-3216" "TMe-2950"
#> [19] "TMe-985"  "TMe-1443" "TMe-323"  "TMe-3149" "TMe-3568" "TMe-480" 
#> [25] "TMe-536"  "TMe-3068" "TMe-626"  "TMe-693"  "TMe-54"   "TMe-1147"
#> [31] "TMe-2123"
#> 
#> $`5`
#>  [1] "TMe-610"  "TMe-663"  "TMe-706"  "TMe-650"  "TMe-1572" "TMe-3726"
#>  [7] "TMe-419"  "TMe-1483" "TMe-2891" "TMe-3576" "TMe-1533" "TMe-1873"
#> [13] "TMe-1935" "TMe-3265" "TMe-90"   "TMe-334"  "TMe-456"  "TMe-3118"
#> [19] "TMe-682"  "TMe-2058" "TMe-995"  "TMe-1357" "TMe-3338" "TMe-3097"
#> [25] "TMe-1554" "TMe-1362" "TMe-3219" "TMe-15"   "TMe-1939" "TMe-1192"
#> [31] "TMe-270"  "TMe-194"  "TMe-3326" "TMe-2242"
#> 
#> $`6`
#>  [1] "TMe-2823" "TMe-816"  "TMe-161"  "TMe-551"  "TMe-1301" "TMe-363" 
#>  [7] "TMe-1560" "TMe-1786" "TMe-1221" "TMe-853"  "TMe-1218" "TMe-1198"
#> [13] "TMe-41"   "TMe-25"   "TMe-727"  "TMe-251"  "TMe-2195" "TMe-716" 
#> [19] "TMe-1459" "TMe-85"   "TMe-3443" "TMe-963"  "TMe-2124" "TMe-755" 
#> [25] "TMe-3277" "TMe-123"  "TMe-1442" "TMe-2064" "TMe-70"   "TMe-768" 
#> [31] "TMe-3071"
#> 
#> $`7`
#>  [1] "TMe-2757" "TMe-3572" "TMe-3496" "TMe-1526" "TMe-1341" "TMe-3707"
#>  [7] "TMe-3437" "TMe-696"  "TMe-3575" "TMe-394"  "TMe-277"  "TMe-3266"
#> [13] "TMe-1715" "TMe-1614" "TMe-1621" "TMe-333"  "TMe-1100" "TMe-2809"
#> [19] "TMe-431"  "TMe-618"  "TMe-2027" "TMe-3323" "TMe-1091" "TMe-404" 
#> [25] "TMe-3463" "TMe-174"  "TMe-3460" "TMe-138"  "TMe-2890" "TMe-196" 
#> 
#> $`8`
#>  [1] "TMe-3547" "TMe-1700" "TMe-2567" "TMe-2441" "TMe-487"  "TMe-1101"
#>  [7] "TMe-7"    "TMe-1137" "TMe-2119" "TMe-1269" "TMe-3501" "TMe-3085"
#> [13] "TMe-1581" "TMe-2976" "TMe-241"  "TMe-1174" "TMe-3659" "TMe-3255"
#> [19] "TMe-1580" "TMe-698"  "TMe-2257" "TMe-4"    "TMe-3387" "TMe-2956"
#> [25] "TMe-3773" "TMe-1239" "TMe-867" 
#> 
#> $`9`
#>  [1] "TMe-1806" "TMe-1079" "TMe-3471" "TMe-926"  "TMe-1425" "TMe-2355"
#>  [7] "TMe-835"  "TMe-1098" "TMe-1945" "TMe-756"  "TMe-2977" "TMe-1348"
#> [13] "TMe-44"   "TMe-729"  "TMe-3185" "TMe-1158" "TMe-3633" "TMe-3565"
#> [19] "TMe-3054" "TMe-3428" "TMe-1796" "TMe-2966" "TMe-2973" "TMe-2688"
#> [25] "TMe-3363"
#> 
#> $`10`
#>  [1] "TMe-623"  "TMe-3249" "TMe-1283" "TMe-421"  "TMe-1248" "TMe-929" 
#>  [7] "TMe-861"  "TMe-1919" "TMe-3698" "TMe-832"  "TMe-584"  "TMe-997" 
#> [13] "TMe-1294" "TMe-725"  "TMe-3089" "TMe-3337" "TMe-2196" "TMe-432" 
#> [19] "TMe-2043" "TMe-1646" "TMe-27"   "TMe-1472"
#> 
#> $`11`
#>  [1] "TMe-2996" "TMe-1261" "TMe-588"  "TMe-3025" "TMe-13"   "TMe-707" 
#>  [7] "TMe-373"  "TMe-761"  "TMe-1307" "TMe-412"  "TMe-3406" "TMe-2513"
#> [13] "TMe-798"  "TMe-717"  "TMe-2963" "TMe-731"  "TMe-815"  "TMe-3694"
#> [19] "TMe-2905" "TMe-608" 
#> 
#> $`12`
#>  [1] "TMe-812"  "TMe-3605" "TMe-3736" "TMe-2967" "TMe-616"  "TMe-399" 
#>  [7] "TMe-3292" "TMe-3685" "TMe-3223" "TMe-3163" "TMe-3353" "TMe-1730"
#> [13] "TMe-3667" "TMe-2035" "TMe-3730" "TMe-2050" "TMe-3701" "TMe-3705"
#> [19] "TMe-390"  "TMe-2853"
#> 
#> $always.selected
#> [1] "TMe-1790" "TMe-801"  "TMe-1830" "TMe-2018" "TMe-3191"
#>