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Table 3 Inference of the optimal numbers of clusters existed in Ethiopian durum wheat panel using Delta K Statistics

From: Genetic diversity and population structure analysis based on the high density SNP markers in Ethiopian durum wheat (Triticum turgidum ssp. durum)

K

L(K)

stdev

L’(K)

L”(K)

|L”(K)|

Delta K

1

−157,376

3.369

2

−138,930

1370.013

18,446.93

− 3224.75

3224.75

2.35

3

− 123,708

543.0884

15,222.19

− 5458.76

5458.76

10.05

4

−113,944

1149.967

9763.425

− 1419.46

1419.46

1.23

5

− 105,600

708.175

8343.965

− 3511.28

3511.28

4.96

6

−100,768

677.594

4832.685

− 1326.03

1326.025

1.96

7

−97,261

1353.421

3506.66

580.6019

580.6019

0.43

8

−93,173

1398.676

4087.262

− 1491.05

1491.054

1.07

9

−90,577

1708.376

2596.208

635.7119

635.7119

0.37

10

−87,345

2170.333

3231.92

   
  1. Where;
  2. K = Subpopulations;
  3. Ln (PD) = The log likelihood for each K;
  4. L (K) = An average of 20 values of Ln P(D);
  5. stdev = Standard deviation for 20 values of Ln P(D);
  6. L’(K) = L(K) n – L(K) n-1;
  7. L”(K) = L′(K) n+ 1 − L′(K);
  8. ∆K = |L”(K)|/Stdev;
  9. The gray color of the third line designates the optimal sub-populations of the panel based on the highest delta K value