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

Miyazawa, Sanzo

doi:10.1186/1471-2148-13-257

BMC Ecology and Evolution

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 model^a	K^b	Δℓ^c	ΔAIC^c	ΔxBIC^c	β ^de	w ₀ ^d	${〈 e^{w_{ab}} 〉}^{F}$	${\hat{m}}^{g}$	^h	${\hat{α}}^{i}$
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

^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.
^bThe number of adjustable parameters.
^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].
^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.
^eThe value parenthesized means that the parameter is fixed at the value specified.
^fThe average of $e^{w_{ab}}$ over all amino acid pairs {a,b}; $〈 e^{w_{ab}} 〉 \equiv \frac{1}{190} \sum_{a} \sum_{b > a} e^{w_{ab}}$ .
^gThe ratio of double to single and of triple to double nucleotide change exchangeability; $\hat{m} \equiv {\hat{m}}_{[tc] [ag]}$ .
^hThe ratio of mean transitional to mean transversional exchangeability; ${\hat{m}}_{tc | ag} / {\hat{m}}_{[tc] [ag]}$ .
ⁱThe shape parameter of a discrete gamma distribution for the variation of mutation rate or selective constraint across sites.

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