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Table 3 Comparisons between various amino acid and codon substitution models for the reference phylogenetic tree of the mammalian-mtProt

From: Superiority of a mechanistic codon substitution model even for protein sequences in Phylogenetic analysis

Substitution modela

Kb

Δℓc

ΔAICc

ΔxBICc

β de

w 0 d

〈 e w ab 〉 F

m Ì‚ g

h

α ̂ i

 Amino acid substitution models

mtREV-dG4r

1

-96.5

154.9

37.2

     

0.471

cpREV64-F-dG4r

20

-3733.4

7466.9

7466.9

     

0.426

WAG-F-dG4r

20

-2667.4

5334.7

5334.7

     

0.443

LG-F-dG4r

20

-2617.5

5235.1

5235.1

     

0.438

cpREV10-F-dG4r

20

-2316.2

4632.4

4632.4

     

0.445

FLU-F-dG4r

20

-2249.4

4498.8

4498.8

     

0.433

JTT-F-dG4r

20

-1255.8

2511.6

2511.6

     

0.436

mtREV-F-dG4r

20

0.0

0.0

0.0

     

0.469

 Mechanistic codon substitution models

Equal-Constraint-10-F-dG4r

30

-3356.4

6732.7

6794.6

(0.0)

-0.000

1.000

0.338

2.887

0.407

EI-11-F-dG4r

31

-1663.4

3348.8

3417.0

0.463

0.012

0.276

0.369

4.061

0.424

WAG-ML91+-11-F-dG4r

31

356.4

-690.9

-622.8

1.140

0.017

0.122

0.336

3.978

0.427

LG-ML91+-11-F-dG4r

31

621.5

-1221.1

-1152.9

0.962

0.585

0.194

0.269

4.029

0.418

KHG-ML200-11-F-dG4r

31

701.5

-1380.9

-1312.8

1.321

0.944

0.223

0.196

1.939

0.415

JTT-ML91+-11-F-dG4r

31

712.6

-1403.2

-1335.1

1.354

0.539

0.137

0.348

2.417

0.421

JTT-ML91+-11-F-dG8r

31

1328.0

-2634.0

-2565.8

1.363

0.483

0.129

0.304

2.480

0.302

Equal-Constraint-10-F-dG4s

30

-3346.1

6712.1

6774.1

(0.0)

-0.000

1.000

0.300

2.950

0.396

EI-11-F-dG4s

31

-1164.7

2351.4

2419.5

0.553

-0.511

0.136

0.344

3.772

0.288

WAG-ML91+-11-F-dG4s

31

509.8

-997.6

-929.4

1.355

0.147

0.106

0.403

3.534

0.418

KHG-ML200-11-F-dG4s

31

511.1

-1000.2

-932.1

1.259

0.069

0.115

0.192

2.044

0.485

LG-ML91+-11-F-dG4s

31

637.6

-1253.2

-1185.1

0.994

-0.108

0.097

0.268

3.897

0.436

JTT-ML91+-11-F-dG4s

31

909.2

-1796.5

-1728.3

1.587

0.425

0.094

0.398

2.190

0.452

JTT-ML91+-11-F-dG8s

31

1712.7

-3403.4

-3335.2

1.739

0.409

0.078

0.348

2.250

0.328

Equal-Constraint-10-F-dG4sf

87

-1878.8

3891.7

4306.7

(0.0)

-0.000

1.000

0.283

2.967

0.390

EI-11-F-dG4sf

88

444.0

-752.0

-330.8

0.541

-0.678

0.117

0.310

3.914

0.265

JTT-ML91+-11-F-dG4sf

88

1226.6

-2317.2

-1896.0

1.495

0.358

0.098

0.373

2.350

0.442

WAG-ML91+-11-F-dG4sf

88

1290.2

-2444.5

-2023.3

1.339

0.220

0.116

0.375

3.544

0.390

KHG-ML200-11-F-dG4sf

88

1328.4

-2520.8

-2099.6

1.406

0.986

0.208

0.181

2.062

0.574

LG-ML91+-11-F-dG4sf

88

1360.7

-2585.4

-2164.2

0.992

0.122

0.123

0.278

3.769

0.416

  1. a"-F" means that the equilibrium frequencies are estimated to be equal to those in the alignment; equal codon usage is assumed. "-dGmr" and "-dGms" mean discrete gamma distributions with m categories of unequal probabilities for the rate variation and the variation of selective constraint across sites, respectively. "-dGmsf" means the equilibrium frequencies for respective categories are estimated from their posterior probabilities for sites. The number string in the model name indicates the number of parameters optimized for the substitution rate matrix, and the remaining strings denote a rate matrix or a selective constraint matrix used.
  2. bThe number of adjustable parameters.
  3. cDifference from the reference state; Δℓ = ℓ + 122106.2, ΔAIC = AIC - 244252.3, and ΔBIC = BIC - 244376.2. The reference tree topology is Tree-6 in [34].
  4. d w ab =min[ β w ab estimate + w 0 (1- δ ab ),0]; w ab estimate is the one specified by the model name.
  5. eThe value parenthesized means that the parameter is fixed at the value specified.
  6. fThe average of e w ab over all amino acid pairs {a,b};〈 e w ab 〉≡ 1 190 ∑ a ∑ b > a e w ab .
  7. gThe ratio of double to single and of triple to double nucleotide change exchangeability; m ̂ ≡ m ̂ [ tc ] [ ag ] .
  8. hThe ratio of mean transitional to mean transversional exchangeability; m Ì‚ tc | ag / m Ì‚ [ tc ] [ ag ] .
  9. iThe shape parameter of a discrete gamma distribution for the variation of mutation rate or selective constraint across sites.