Compute the following diversity indices and perform corresponding statistical tests to compare the phenotypic diversity for qualitative traits between entire collection (EC) and core set (CS).
Simpson's and related indices
Simpson's Index (\(d\)) (Simpson 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 (\(D\)) (Gini 1912, 1912; Greenberg 1956; Berger and Parker 1970; Nei 1973; Peet 1974)
Maximum Simpson's Index of Diversity or Maximum Nei's Diversity/Variation Index (\(D_{max}\)) (Hennink and Zeven 1990)
Simpson's Reciprocal Index or Hill's \(N_{2}\) (\(D_{R}\)) (Williams 1964; Hill 1973)
Relative Simpson's Index of Diversity or Relative Nei's Diversity/Variation Index (\(D'\)) (Hennink and Zeven 1990)
Shannon-Weaver and related indices
Shannon or Shannon-Weaver or Shannon-Weiner Diversity Index (\(H\)) (Shannon and Weaver 1949; Peet 1974)
Maximum Shannon-Weaver Diversity Index (\(H_{max}\)) (Hennink and Zeven 1990)
Relative Shannon-Weaver Diversity Index or Shannon Equitability Index (\(H'\)) (Hennink and Zeven 1990)
McIntosh Diversity Index
McIntosh Diversity Index (\(D_{Mc}\)) (McIntosh 1967; Peet 1974)
diversity.evaluate.core(data, names, qualitative, selected, base = 2, R = 1000)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.
Name of column with the individual names as a character string.
Name of columns with the qualitative traits as a character vector.
Character vector with the names of individuals selected in
core collection and present in the names column.
The logarithm base to be used for computation of Shannon-Weaver Diversity Index (\(I\)). Default is 2.
The number of bootstrap replicates. Default is 1000.
A list with three data frames as follows.
The number of classes in the trait for EC.
The number of classes in the trait for CS.
The Simpson's Index (\(d\)) for EC.
The Simpson's Index of Diversity (\(D\)) for EC.
The Maximum Simpson's Index of Diversity (\(D_{max}\)) for EC.
The Simpson's Reciprocal Index (\(D_{R}\)) for EC.
The Relative Reciprocal Index (\(D'\)) for EC.
The variance of \(d\) for EC according to (Simpson 1949) .
The bootstrap variance of \(d\) for EC.
The Simpson's Index (\(d\)) for CS.
The Simpson's Index of Diversity (\(D\)) for CS.
The Maximum Simpson's Index of Diversity (\(D_{max}\)) for CS.
The Simpson's Reciprocal Index (\(D_{R}\)) for CS.
The Relative Reciprocal Index (\(D'\)) for CS.
The variance of \(d\) for CS according to (Simpson 1949) .
The bootstrap variance of \(d\) for CS.
The degrees of freedom for t test.
The t statistic.
The p value for t test.
The significance of t test for t-test
The degrees of freedom for bootstrap z score.
The bootstrap z score.
The p value of z score.
The significance of z score.
The number of classes in the trait for EC.
The number of classes in the trait for CS.
The Shannon-Weaver Diversity Index (\(I\)) for EC.
The Maximum Shannon-Weaver Diversity Index (\(I_{max}\)) for EC.
The Relative Shannon-Weaver Diversity Index (\(I'\)) for EC.
The variance of \(I\) for EC according to (Hutcheson 1970) .
The bootstrap variance of \(I\) for EC.
The Shannon-Weaver Diversity Index (\(I\)) for CS.
The Maximum Shannon-Weaver Diversity Index (\(I_{max}\)) for CS.
The Relative Shannon-Weaver Diversity Index (\(I'\)) for CS.
The variance of \(I\) for CS according to (Hutcheson 1970) .
The bootstrap variance of \(I\) for CS.
The t statistic.
The degrees of freedom for t test.
The p value for t test.
The significance of t test for t-test
The degrees of freedom for bootstrap z score.
The bootstrap z score.
The p value of z score.
The significance of z score.
The number of classes in the trait for CS.
The McIntosh Index (\(D_{Mc}\)) for EC.
The McIntosh Index (\(D_{Mc}\)) for CS.
The bootstrap z score.
The degrees of freedom for bootstrap z score.
The p value of z score.
The significance of z score.
The diversity indices and the corresponding statistical
tests implemented in diversity.evaluate.core are as follows.
Simpson's index (\(d\)) which estimates the probability that two accessions randomly selected will belong to the same phenotypic class of a trait, is computed as follows (Simpson 1949; Peet 1974) .
\[d = \sum_{i = 1}^{k}p_{i}^{2}\]
Where, \(p_{i}\) denotes the proportion/fraction/frequency of accessions in the \(i\)th phenotypic class for a trait and \(k\) is the number of phenotypic classes for the trait.
The value of \(d\) can range from 0 to 1 with 0 representing maximum diversity and 1, no diversity.
\(d\) is subtracted from 1 to give Simpson's index of diversity (\(D\)) (Greenberg 1956; Berger and Parker 1970; Peet 1974; Hennink and Zeven 1990) originally suggested by Gini (1912, 1912) and described in literature as Gini's diversity index or Gini-Simpson index. It is the same as Nei's diversity index or Nei's variation index (Nei 1973; Hennink and Zeven 1990) . Greater the value of \(D\), greater the diversity with a range from 0 to 1.
\[D = 1 - d\]
The maximum value of \(D\), \(D_{max}\) occurs when accessions are uniformly distributed across the phenotypic classes and is computed as follows (Hennink and Zeven 1990) .
\[D_{max} = 1 - \frac{1}{k}\]
Reciprocal of \(d\) gives the Simpson's reciprocal index (\(D_{R}\)) (Williams 1964; Hennink and Zeven 1990) and can range from 1 to \(k\). This was also described in Hill (1973) as (\(N_{2}\)).
\[D_{R} = \frac{1}{d}\]
Relative Simpson's index of diversity or Relative Nei's diversity/variation index (\(H'\)) (Hennink and Zeven 1990) is defined as follows (Peet 1974) .
\[D' = \frac{D}{D_{max}}\]
Differences in Simpson's diversity index for qualitative traits of EC and CS can be tested by a t-test using the associated variance estimate described in Simpson (1949) (Lyons and Hutcheson 1978) .
The t statistic is computed as follows.
\[t = \frac{d_{EC} - d_{CS}}{\sqrt{V_{d_{EC}} + V_{d_{CS}}}}\]
Where, the variance of \(d\) (\(V_{d}\)) is,
\[V_{d} = \frac{4N(N-1)(N-2)\sum_{i=1}^{k}(p_{i})^{3} + 2N(N-1)\sum_{i=1}^{k}(p_{i})^{2} - 2N(N-1)(2N-3) \left( \sum_{i=1}^{k}(p_{i})^{2} \right)^{2}}{[N(N-1)]^{2}}\]
The associated degrees of freedom is computed as follows.
\[df = (k_{EC} - 1) + (k_{CS} - 1)\]
Where, \(k_{EC}\) and \(k_{CS}\) are the number of phenotypic classes in the trait for EC and CS respectively.
An index of information \(H\), was described by Shannon and Weaver (1949) as follows.
\[H = -\sum_{i=1}^{k}p_{i} \log_{2}(p_{i})\]
\(H\) is described as Shannon or Shannon-Weaver or Shannon-Weiner diversity index in literature.
Alternatively, \(H\) is also computed using natural logarithm instead of logarithm to base 2.
\[H = -\sum_{i=1}^{k}p_{i} \ln(p_{i})\]
The maximum value of \(H\) (\(H_{max}\)) is \(\ln(k)\). This value occurs when each phenotypic class for a trait has the same proportion of accessions.
\[H_{max} = \log_{2}(k)\;\; \textrm{OR} \;\; H_{max} = \ln(k)\]
The relative Shannon-Weaver diversity index or Shannon equitability index (\(H'\)) is the Shannon diversity index (\(I\)) divided by the maximum diversity (\(H_{max}\)).
\[H' = \frac{H}{H_{max}}\]
Differences in Shannon-Weaver diversity index for qualitative traits of EC and CS can be tested by Hutcheson t-test (Hutcheson 1970) .
The Hutcheson t statistic is computed as follows.
\[t = \frac{H_{EC} - H_{CS}}{\sqrt{V_{H_{EC}} + V_{H_{CS}}}}\]
Where, the variance of \(H\) (\(V_{H}\)) is,
\[V_{H} = \frac{\sum_{i=1}^{k}n_{i}(\log_{2}{n_{i}})^{2} \frac{(\sum_{i=1}^{k}\log_{2}{n_{i}})^2}{N}}{N^{2}}\]
\[\textrm{OR}\]
\[V_{H} = \frac{\sum_{i=1}^{k}n_{i}(\ln{n_{i}})^{2} \frac{(\sum_{i=1}^{k}\ln{n_{i}})^2}{N}}{N^{2}}\]
The associated degrees of freedom is approximated as follows.
\[df = \frac{(V_{H_{EC}} + V_{H_{CS}})^{2}}{\frac{V_{H_{EC}}^{2}}{N_{EC}} + \frac{V_{H_{CS}}^{2}}{N_{CS}}}\]
A similar index of diversity was described by McIntosh (1967) as follows (\(D_{Mc}\)) (Peet 1974) .
\[D_{Mc} = \frac{N - \sqrt{\sum_{i=1}^{k}n_{i}^2}}{N - \sqrt{N}}\]
Where, \(n_{i}\) denotes the number of accessions in the \(i\)th phenotypic class for a trait and \(N\) is the total number of accessions so that \(p_{i} = {n_{i}}/{N}\).
Bootstrap statistics are employed to test the difference between the Simpson, Shannon-Weaver and McIntosh indices for qualitative traits of EC and CS (Solow 1993) .
If \(I_{EC}\) and \(I_{CS}\) are the diversity indices with the original number of accessions, then random samples of the same size as the original are repeatedly generated (with replacement) \(R\) times and the corresponding diversity index is computed for each sample.
\[I_{EC}^{*} = \lbrace H_{EC_{1}}, H_{EC_{}}, \cdots, H_{EC_{R}} \rbrace\]
\[I_{CS}^{*} = \lbrace H_{CS_{1}}, H_{CS_{}}, \cdots, H_{CS_{R}} \rbrace\]
Then the bootstrap null sample \(I_{0}\) is computed as follows.
\[\Delta^{*} = I_{EC}^{*} - I_{CS}^{*}\]
\[I_{0} = \Delta^{*} - \overline{\Delta^{*}}\]
Where, \(\overline{\Delta^{*}}\) is the mean of \(\Delta^{*}\).
Now the original difference in diversity indices (\(\Delta_{0} = I_{EC} - I_{CS}\)) is tested against mean of bootstrap null sample (\(I_{0}\)) by a z test. The z score test statistic is computed as follows.
\[z = \frac{\Delta_{0} - \overline{H_{0}}}{\sqrt{V_{H_{0}}}}\]
Where, \(\overline{H_{0}}\) and \(V_{H_{0}}\) are the mean and variance of the bootstrap null sample \(H_{0}\).
The corresponding degrees of freedom is estimated as follows.
\[df = (k_{EC} - 1) + (k_{CS} - 1)\]
Berger WH, Parker FL (1970).
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Science, 168(3937), 1345–1347.
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Variabilita e Mutabilita. Contributo allo Studio delle Distribuzioni e delle Relazioni Statistiche. [Fasc. I.].
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Greenberg JH (1956).
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Hennink S, Zeven AC (1990).
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Hill MO (1973).
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Hutcheson K (1970).
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McIntosh RP (1967).
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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)))
# \donttest{
diversity.evaluate.core(data = ec, names = "genotypes",
qualitative = qual, selected = core)
#> $simpson
#> Trait EC_No.Classes CS_No.Classes EC_d EC_D
#> 1 CUAL 5 4 0.379231526565524 0.620768473434476
#> 2 LNGS 3 3 0.422400150078142 0.577599849921858
#> 3 PTLC 5 5 0.477398006104682 0.522601993895318
#> 4 DSTA 5 5 0.351400071089646 0.648599928910354
#> 5 LFRT 5 4 0.448935347916114 0.551064652083886
#> 6 LBTEF 6 6 0.223971174841036 0.776028825158964
#> 7 CBTR 3 3 0.51874284166756 0.48125715833244
#> 8 NMLB 10 9 0.206703725435988 0.793296274564012
#> 9 ANGB 4 4 0.350516387291879 0.64948361270812
#> 10 CUAL9M 5 5 0.309073521363567 0.690926478636433
#> 11 LVC9M 5 5 0.425299451029954 0.574700548970046
#> 12 TNPR9M 5 5 0.247165582455527 0.752834417544473
#> 13 PL9M 3 2 0.498635332682619 0.501364667317381
#> 14 STRP 4 4 0.322189843207836 0.677810156792164
#> 15 STRC 2 2 0.510325630074306 0.489674369925694
#> 16 PSTR 3 2 0.555306757465823 0.444693242534177
#> EC_D.max EC_D.inv EC_D.rel EC_d.V
#> 1 0.8 2.63691156971154 0.775960591793095 6.2401326584027e-05
#> 2 0.666666666666667 2.36742340128195 0.866399774882787 2.66303075243519e-05
#> 3 0.8 2.09468826265002 0.653252492369147 6.43256463380354e-05
#> 4 0.8 2.84575924216273 0.810749911137942 4.49202770089222e-05
#> 5 0.8 2.22749223165839 0.688830815104857 3.64033438958825e-05
#> 6 0.833333333333333 4.46486026922774 0.931234590190757 1.01110395238633e-05
#> 7 0.666666666666667 1.92773744459853 0.72188573749866 4.63756492257553e-05
#> 8 0.9 4.83784217188518 0.881440305071124 1.57355754103247e-05
#> 9 0.75 2.85293366089411 0.865978150277494 3.10366375721298e-05
#> 10 0.8 3.23547612745411 0.863658098295541 1.34905804296262e-05
#> 11 0.8 2.35128448338761 0.718375686212558 4.98247003940663e-05
#> 12 0.8 4.04587074812462 0.941043021930592 2.56650302792209e-05
#> 13 0.666666666666667 2.005473608579 0.752047000976072 3.79031161219323e-06
#> 14 0.75 3.10376016215672 0.903746875722886 9.34647324671549e-06
#> 15 0.5 1.9595331707216 0.979348739851389 1.21791747807758e-05
#> 16 0.666666666666667 1.80080646697613 0.667039863801265 6.1357244865428e-05
#> EC_d.boot.V CS_d CS_D CS_D.max
#> 1 6.68533450338314e-05 0.378472222222222 0.621527777777778 0.75
#> 2 2.65879113857189e-05 0.387755102040816 0.612244897959184 0.666666666666667
#> 3 6.50363094034534e-05 0.421343537414966 0.578656462585034 0.8
#> 4 4.79746735208086e-05 0.303500566893424 0.696499433106576 0.8
#> 5 3.49356184489191e-05 0.426587301587302 0.573412698412698 0.75
#> 6 9.78416887814862e-06 0.200538548752834 0.799461451247165 0.833333333333333
#> 7 4.76384743057889e-05 0.487244897959184 0.512755102040816 0.666666666666667
#> 8 1.55424381336112e-05 0.198058390022676 0.801941609977324 0.888888888888889
#> 9 3.19616815160651e-05 0.342120181405896 0.657879818594104 0.75
#> 10 1.35390135457135e-05 0.288052721088435 0.711947278911565 0.8
#> 11 4.73810044068571e-05 0.388676303854875 0.611323696145125 0.8
#> 12 2.63678232813366e-05 0.2218679138322 0.7781320861678 0.8
#> 13 3.95700024252201e-06 0.500283446712018 0.499716553287982 0.5
#> 14 9.00891406453171e-06 0.311862244897959 0.688137755102041 0.75
#> 15 1.11259330666434e-05 0.518140589569161 0.481859410430839 0.5
#> 16 5.79882678523648e-05 0.555555555555556 0.444444444444444 0.5
#> CS_D.inv CS_D.rel CS_d.V CS_d.boot.V
#> 1 2.64220183486239 0.828703703703704 0.000664974207441761 0.000711409006695385
#> 2 2.57894736842105 0.918367346938775 0.000253494320337725 0.000240277035602111
#> 3 2.37336024217962 0.723320578231292 0.00106773305088108 0.00104909427501709
#> 4 3.29488676161569 0.87062429138322 0.000464316667250201 0.0004640806330644
#> 5 2.34418604651163 0.764550264550265 0.000434218289438062 0.000428639235160984
#> 6 4.98657243816254 0.959353741496599 6.05627470284696e-05 6.05634678928432e-05
#> 7 2.05235602094241 0.769132653061224 0.000257136051752956 0.000271330248841789
#> 8 5.04901610017889 0.90218431122449 0.000216132859442877 0.000204816497715932
#> 9 2.92294946147473 0.877173091458806 0.000360254817691854 0.0003537099748542
#> 10 3.47158671586716 0.889934098639456 0.000144703074224106 0.000152475008559194
#> 11 2.57283500455789 0.764154620181406 0.000503057233986995 0.000488621895795101
#> 12 4.50718620249122 0.972665107709751 0.000134121919501297 0.000143869065469617
#> 13 1.99886685552408 0.999433106575964 2.11737525161229e-05 1.4057939053243e-05
#> 14 3.20654396728016 0.917517006802721 8.69838142388246e-05 8.64975280349916e-05
#> 15 1.92997811816193 0.963718820861678 0.00022467592663519 0.000201749293623147
#> 16 1.8 0.888888888888889 0.000601970661850899 0.000601085481209453
#> d.t.df d.t.stat d.t.pvalue d.t.significance d.boot.z.df
#> 1 7 0.02815376878219 0.978325351754391 ns 7
#> 2 4 2.06997700767549 0.10723294813912 ns 4
#> 3 8 1.66600295615057 0.134274950280504 ns 8
#> 4 8 2.12261420536943 0.0665538249488766 ns 8
#> 5 7 1.0301574783912 0.337209790540494 ns 7
#> 6 10 2.78735177789005 0.0192068432217533 * 10
#> 7 4 1.80798358527422 0.144886591272101 ns 4
#> 8 17 0.567755084270463 0.577623407084813 ns 17
#> 9 6 0.424456215383704 0.686031514328123 ns 6
#> 10 8 1.6713011659847 0.133206249679844 ns 8
#> 11 8 1.55754090990284 0.157957033254601 ns 8
#> 12 8 2.00128917457502 0.0803555866511265 ns 8
#> 13 3 -0.329859967245677 0.763196306139146 ns 3
#> 14 6 1.05224751693921 0.333206278005286 ns 6
#> 15 2 -0.507791421657648 0.662061546648583 ns 2
#> 16 3 -0.00966012858117729 0.99289893656246 ns 3
#> d.boot.z.stat d.boot.z.pvalue d.boot.z.significance
#> 1 0.0276014468259671 0.97875044140037 ns
#> 2 2.11134701701347 0.10233493680879 ns
#> 3 1.67600791343304 0.132263448642767 ns
#> 4 2.12071979935888 0.0667503673247065 ns
#> 5 1.03756609320658 0.333978621629479 ns
#> 6 2.77065034924187 0.0197652293840094 *
#> 7 1.76028327597653 0.153166166195353 ns
#> 8 0.577008613944405 0.571496330602201 ns
#> 9 0.425217529507766 0.685506175360378 ns
#> 10 1.63791870182241 0.140072980275729 ns
#> 11 1.58556233614025 0.151499007860614 ns
#> 12 1.93374355649653 0.0892037747747804 ns
#> 13 0.39244722767569 0.72094875991824 ns
#> 14 1.03972126692463 0.338541348748645 ns
#> 15 0.54146070930643 0.64244084391876 ns
#> 16 0.00959298293692684 0.992948292625 ns
#>
#> $shannon
#> Trait EC_No.Classes CS_No.Classes EC_I EC_I.max
#> 1 CUAL 5 4 1.60118025300384 1.6094379124341
#> 2 LNGS 3 3 1.34638092645118 1.09861228866811
#> 3 PTLC 5 5 1.29757991678528 1.6094379124341
#> 4 DSTA 5 5 1.75217791456181 1.6094379124341
#> 5 LFRT 5 4 1.32020430332539 1.6094379124341
#> 6 LBTEF 6 6 2.26107917725546 1.79175946922805
#> 7 CBTR 3 3 1.04940762729587 1.09861228866811
#> 8 NMLB 10 9 2.46043656290491 2.30258509299405
#> 9 ANGB 4 4 1.63181278826841 1.38629436111989
#> 10 CUAL9M 5 5 1.81895733334165 1.6094379124341
#> 11 LVC9M 5 5 1.45781261313429 1.6094379124341
#> 12 TNPR9M 5 5 2.15936383275215 1.6094379124341
#> 13 PL9M 3 2 1.02393231699601 1.09861228866811
#> 14 STRP 4 4 1.70471635517281 1.38629436111989
#> 15 STRC 2 2 0.985051563686417 0.693147180559945
#> 16 PSTR 3 2 0.932902628052214 1.09861228866811
#> EC_I.rel EC_I.V EC_I.boot.V
#> 1 0.994869227718287 0.000495550546246209 0.000483808510194458
#> 2 1.22552873323805 0.00026683714279372 0.000269948802236365
#> 3 0.806231732681647 0.00076741293709653 0.000765752404583755
#> 4 1.08868934988106 0.000644551217715297 0.000699283275380162
#> 5 0.820289054412 0.0005480962422548 0.000517842713945963
#> 6 1.26193231630002 0.000259759685726472 0.000271033385039332
#> 7 0.955211987086096 0.000312696844542415 0.000303798121154971
#> 8 1.06855402234261 0.000496178249738945 0.000505626109031182
#> 9 1.17710410864701 0.000306008701151613 0.00030810953251426
#> 10 1.13018173567856 0.000397228605602063 0.000382025104334203
#> 11 0.90578990458197 0.000698631874341118 0.000665418478253527
#> 12 1.34168818571345 0.000264448274894998 0.000279879360986154
#> 13 0.932023360340673 0.000100041535943681 0.000101884272024935
#> 14 1.22969291586506 0.00021912035039574 0.000213652548557445
#> 15 1.42112900595031 2.53468656861686e-05 2.75676958917147e-05
#> 16 0.849164566676391 0.000206905486943159 0.000215549640442331
#> CS_I CS_I.max CS_I.rel CS_I.V
#> 1 1.60715392433211 1.38629436111989 1.15931649828959 0.00466900952090494
#> 2 1.44881563572518 1.09861228866811 1.31876882378736 0.00183098114336171
#> 3 1.60685189446012 1.6094379124341 0.998393216691366 0.00915269666156106
#> 4 1.94652505102181 1.6094379124341 1.20944401519528 0.00501290672204481
#> 5 1.39390699808299 1.38629436111989 1.00549135679738 0.00481441616742965
#> 6 2.3831722498942 1.79175946922805 1.330073757568 0.00172264312694065
#> 7 1.12338192727968 1.09861228866811 1.02254629669362 0.00290287113955504
#> 8 2.56080478714959 2.19722457733622 1.16547248449867 0.00546163553548553
#> 9 1.69700114892879 1.38629436111989 1.22412757097122 0.00354899161566695
#> 10 1.92688046691671 1.6094379124341 1.19723814881589 0.00380714696318465
#> 11 1.59702066650884 1.6094379124341 0.992284731315619 0.00676974620846264
#> 12 2.24730159981114 1.6094379124341 1.39632699245436 0.00129552549169971
#> 13 0.999591034189098 0.693147180559945 1.44210502794168 7.02197242512667e-06
#> 14 1.74920954558179 1.38629436111989 1.26178796844324 0.0020863467552808
#> 15 0.97366806454962 0.693147180559945 1.40470608819769 0.000443961107972778
#> 16 0.91829583405449 0.693147180559945 1.32482084585941 0.00132275132275134
#> CS_I.boot.V I.t.stat I.t.df I.t.pvalue
#> 1 0.0047929123394758 -0.083123660050637 205.323489838581 0.933834195011031
#> 2 0.00187875640207067 -2.23647066374941 220.068588438007 0.0263241034578903
#> 3 0.00931911218476163 -3.10514822627186 197.214845421711 0.00218182272218803
#> 4 0.00517797969455639 -2.58385107753543 213.627424864319 0.0104369229742795
#> 5 0.00488761731418891 -1.00646624014807 208.16009186019 0.315359849464886
#> 6 0.00187862560896072 -2.74217439229004 221.982338302534 0.00660128212793374
#> 7 0.00298070544341396 -1.30452382793487 205.90491319267 0.193511253079244
#> 8 0.00547694938695042 -1.3003275918761 199.746997945695 0.194987041994507
#> 9 0.00362924040839815 -1.04992396937323 198.073409342984 0.295032389672131
#> 10 0.00434669657011922 -1.66442333074281 204.664065671499 0.097558069731458
#> 11 0.00669021208688097 -1.61083557606938 204.247107694347 0.108759859193219
#> 12 0.0013166833981556 -2.22646968440541 242.577447747539 0.0269016983557465
#> 13 4.24533303750304e-05 2.35246259571922 1837.93308927511 0.0187545059227561
#> 14 0.00212088460832853 -0.926646485957522 204.916304701679 0.3552001943646
#> 15 0.000438689236849775 0.52546865211132 187.669671190779 0.599877733009115
#> 16 0.00146139768748281 0.373471875118422 224.120762900574 0.709150296735105
#> I.t.significance I.boot.z.df I.boot.z.stat I.boot.z.pvalue
#> 1 ns 7 0.0817336348245371 0.937146464242981
#> 2 * 4 2.2064267784542 0.0919914613051522
#> 3 ** 8 3.08665470359158 0.0149652109934245
#> 4 * 8 2.57117798516249 0.0330669187074517
#> 5 ns 7 1.01631020857175 0.343315003404297
#> 6 ** 10 2.66359626201418 0.0237522092011334
#> 7 ns 4 1.28540612042092 0.268024804385408
#> 8 ns 17 1.2958056339159 0.212360842372221
#> 9 ns 6 1.04598381571325 0.335865437056982
#> 10 ns 8 1.5855588008592 0.151499807281787
#> 11 ns 8 1.60319190075875 0.147559909191939
#> 12 * 8 2.20200971458306 0.0588093099330856
#> 13 * 3 1.98106680901202 0.141910185247116
#> 14 ns 6 0.935780231278676 0.385503284430038
#> 15 ns 2 0.532654452382285 0.647528455859605
#> 16 ns 3 0.355800409404779 0.745538558892587
#> I.boot.z.significance
#> 1 ns
#> 2 ns
#> 3 *
#> 4 *
#> 5 ns
#> 6 *
#> 7 ns
#> 8 ns
#> 9 ns
#> 10 ns
#> 11 ns
#> 12 ns
#> 13 ns
#> 14 ns
#> 15 ns
#> 16 ns
#>
#> $mcintosh
#> Trait EC_No.Classes CS_No.Classes EC_D.Mc CS_D.Mc
#> 1 CUAL 5 4 0.393778012434178 0.416968887221027
#> 2 LNGS 3 3 0.358820738546382 0.40884307929476
#> 3 PTLC 5 5 0.316779500161785 0.380225207834671
#> 4 DSTA 5 5 0.417380876241608 0.486635921075666
#> 5 LFRT 5 4 0.338215427137732 0.375861861492538
#> 6 LBTEF 6 6 0.539900644138108 0.598348264293068
#> 7 CBTR 3 3 0.286749615427161 0.327215963767637
#> 8 NMLB 10 9 0.558974562677424 0.601358283540837
#> 9 ANGB 4 4 0.418145333938704 0.449791785009108
#> 10 CUAL9M 5 5 0.455147453452433 0.502026774187731
#> 11 LVC9M 5 5 0.356538441668976 0.408042032313971
#> 12 TNPR9M 5 5 0.515402077468806 0.573194332783244
#> 13 PL9M 3 2 0.301198604544138 0.317162433070916
#> 14 STRP 4 4 0.443181993303366 0.478468357680793
#> 15 STRC 2 2 0.292763414762376 0.303603702882552
#> 16 PSTR 3 2 0.261175379595452 0.275932675604997
#> M.boot.z.stat M.boot.z.df M.boot.z.pvalue M.boot.z.significance
#> 1 1.00391168633292 7 0.348854575801086 ns
#> 2 3.39520672163674 4 0.0273980949692247 *
#> 3 2.28323260882762 8 0.051809250272037 ns
#> 4 3.3110316235721 8 0.0106817822611812 *
#> 5 2.15395666678097 7 0.0682139277106039 ns
#> 6 5.96821850593738 10 0.000137837562706689 **
#> 7 2.99754729409007 4 0.0400387096312927 *
#> 8 2.42994156651831 17 0.0264706618143546 *
#> 9 1.80568141934553 6 0.12099659678039 ns
#> 10 3.8867793107122 8 0.00463023359089327 **
#> 11 2.53855378664644 8 0.0347890152183959 *
#> 12 4.24645671583821 8 0.00281266593084537 **
#> 13 4.42355476586344 3 0.0214543888693413 *
#> 14 3.81879071089912 6 0.00877307594548063 **
#> 15 0.913484492624288 2 0.457416629856141 ns
#> 16 0.8043452846734 3 0.480033356696624 ns
#>
# }