Comparative gene retention analysis in barley, wild emmer, and bread wheat pangenome lines reveals factors affecting gene retention following gene duplication

Table 1 Natural selection tests on HPT genes

Model	np	l = ln L	Estimates of parameters	Positively selected sites
One-ratio
ω_HPT2 = ω_BR = ω_TA = ω_PC	1	−8204.98	ω_HPT2=ω_BR=ω_TA=ω_PC = 0.29798	Not allowed (NA)
Branch-specific models
ω_HPT2 ≠ ω_BR = ω_TA = ω_PC (2 ratio)	2	−8199.87	ω_HPT2=0.81568; ω_BR=ω_TA=ω_PC=0.28457	NA
ω_HPT2 ≠ ω_BR = ω_TA ≠ ω_PC (3 ratio)	3	−8199.06	ω_HPT2=0.75587; ω_PC=0.28095 ω_HPT2=ω_TA= 0.48924	NA
ω_HPT2 ≠ ω_BR ≠ ω_TA ≠ ω_PC (4 ratios)	4	−8199.36	ω_HPT2= 0.81975; ω_BR= 0.24071; ω_TA= 0.18172; ω_PC= 0.28853	NA
Branch-site-specific models (selection test of HPT2 as the foreground lineage)
Model A (4 site classes)	4	−8034.75	p₀=0.65921, p₁=0.25827 (p₂+p₃=0.08252); ω₀=0.09024, (ω₁=1.0), ω₂=4.92076	Selected sites in HPT2: 9P, 79M, 89N, 100T, 103D, 149S, 164S, 167D, 204F, 212L, 217I, 246V, 270M, 271A, 356V (Probability > 0.6)
Model A Null (4 site classes)	3	−8036.70	p₀=0.55094, p₁=0.21917 (p₂+p₃=0.22990), ω₀=0.08916 (ω₁=1.0, ω₂=1.0)	NA

In one-ratio and branch-specific models, ω_HPT2, ω_BR, ω_TA, and ω_PC stand for Ka/Ks values for HPT2, Brachipoideae HPT1, Triticeae-Aveninae HPT1, and Panicoideae HPT1 branches in Fig. 1B. In the site-specific model M1, two site classes were specified: highly conserved sites (ω₀) and neutral sites (ω₁=1). For the branch-site models, HPT2 was specified as the foreground group. In the branch-site model A, four site classes were specified. The first two classes have ω ratios of ω₀ and ω₁ respectively, corresponding to highly conserved sites and neutral sites across all lineages. In the other two site classes, the background lineages have ω₀ or ω₁ while the foreground lineages have ω₂. p₀, p₁, and p₂ represent the percentages of the corresponding site classes. Np: number of parameters. L: likelihood value. Amino acid sites were numbered according to HvHPT2 (HORVU.MOREX.r2.2HG0173050.1) in barley. (see Additional file 5 for detailed data)

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