Urnal.pone.0052974.gacid sites. The tree length value obtained from the model M0 was compared with tree length values obtained from other models to control for consistency among models. We performed two LRTs to compare null models which assume the same selective pressure along all Title Loaded From File branches of a phylogeny and do not allow positive Mp mode [16]. Bacteria were fixed to polystyrene spin-coated glass slides. Carboxylated selection (dN/dS .1) with nested models which do allow it [33]. The first LRT, M1a-M2a, compares the M1a model (Nearly Neutral) which allows 0# dN/dS #1 with the M2a model (Selection model; same as the M1a model plus an extra class under positive selection with dN/dS .1). The second LRT, M8aM8, compares the M8a model which assumes a discrete beta distribution for dN/dS, which is constrained between 0 and 1 including a class with dN/dS = 1 with the M8 model which allows the same distribution as M8a but an extra class under positive selection with dN/dS .1. Finally, we performed two branch-site tests of positive selection along prespecified foreground branches [33,34,35]. The first was the A model for basal C4 branches only where positive selection was allowed only on branches leading to C4 clades. The second was the A model for all C4 branches where positive selection was allowed on branches leading to C4 clades and branches within C4 clades. The A1-A LRT compares the null model A1 with the nested model A. Both the A1 and A models allow dN/dS ratios to vary among sites and among lineages. The A1 model allows 0, dN/dS ,1 and dN/dS = 1 for all branches, and also two additional classes of codons with fixed dN/dS = 1 along prespecified foreground branches while restricted as 0, dN/dS ,1 and dN/dS = 1 on background branches. The alternative A model allows 0, dN/dS ,1 and dN/dS = 1 for all branches, and also two additional classes of codons under positive selection with dN/dS .1 along prespecified foreground branches while restricted as 0, dN/ dS ,1 and dN/dS = 1 on background branches. C4 lineages were marked as foreground branches. For all LRTs, the first model is a simplified version of the second, with fewer parameters, and is thus expected to provide a poorer fit to the data (lower maximum likelihood). The M1a, M8a and A1 models are null models which do not allow codons with dN/dS .1, whereas the M2a, M8 and A models are alternative models which do allow codons with dN/dS .1. The significance of the LRTs was calculated assuming that twice the difference in the log of maximum likelihood between the two models was distributed as a chi-square distribution with the degrees of freedom (df) given by the difference in the numbers of parameters in the two nested models [34,36]. For the M1a-M2a comparison df = 2, and for M8a-M8, A1-A and M0 vs 2-rates model comparisons df = 1. Each LRT was run two times using different initial dN/dS values (0.1 and 0.4) to test for suboptimal local peaks. To identify amino acid sites potentially under positive selection, the parameter estimates from M2a, M8 and A models were used to calculate the posterior probabilities that an amino acid belongs to a class with dN/dS .1 using the Bayes Empirical Bayes (BEB) approaches implemented in PAML [37]. Independently from codeml we used the SLR program which implements “sitewise likelihood-ratio” (SLR) method for detecting non-neutral evolution, a statistical testTable 1. Analysis of the Amaranthaceae rbcL genes for positively selected sites.a b c a b dModel with positive selection log-likelihoodNull model Positively selected sitesLRT Parameters.Urnal.pone.0052974.gacid sites. The tree length value obtained from the model M0 was compared with tree length values obtained from other models to control for consistency among models. We performed two LRTs to compare null models which assume the same selective pressure along all branches of a phylogeny and do not allow positive selection (dN/dS .1) with nested models which do allow it [33]. The first LRT, M1a-M2a, compares the M1a model (Nearly Neutral) which allows 0# dN/dS #1 with the M2a model (Selection model; same as the M1a model plus an extra class under positive selection with dN/dS .1). The second LRT, M8aM8, compares the M8a model which assumes a discrete beta distribution for dN/dS, which is constrained between 0 and 1 including a class with dN/dS = 1 with the M8 model which allows the same distribution as M8a but an extra class under positive selection with dN/dS .1. Finally, we performed two branch-site tests of positive selection along prespecified foreground branches [33,34,35]. The first was the A model for basal C4 branches only where positive selection was allowed only on branches leading to C4 clades. The second was the A model for all C4 branches where positive selection was allowed on branches leading to C4 clades and branches within C4 clades. The A1-A LRT compares the null model A1 with the nested model A. Both the A1 and A models allow dN/dS ratios to vary among sites and among lineages. The A1 model allows 0, dN/dS ,1 and dN/dS = 1 for all branches, and also two additional classes of codons with fixed dN/dS = 1 along prespecified foreground branches while restricted as 0, dN/dS ,1 and dN/dS = 1 on background branches. The alternative A model allows 0, dN/dS ,1 and dN/dS = 1 for all branches, and also two additional classes of codons under positive selection with dN/dS .1 along prespecified foreground branches while restricted as 0, dN/ dS ,1 and dN/dS = 1 on background branches. C4 lineages were marked as foreground branches. For all LRTs, the first model is a simplified version of the second, with fewer parameters, and is thus expected to provide a poorer fit to the data (lower maximum likelihood). The M1a, M8a and A1 models are null models which do not allow codons with dN/dS .1, whereas the M2a, M8 and A models are alternative models which do allow codons with dN/dS .1. The significance of the LRTs was calculated assuming that twice the difference in the log of maximum likelihood between the two models was distributed as a chi-square distribution with the degrees of freedom (df) given by the difference in the numbers of parameters in the two nested models [34,36]. For the M1a-M2a comparison df = 2, and for M8a-M8, A1-A and M0 vs 2-rates model comparisons df = 1. Each LRT was run two times using different initial dN/dS values (0.1 and 0.4) to test for suboptimal local peaks. To identify amino acid sites potentially under positive selection, the parameter estimates from M2a, M8 and A models were used to calculate the posterior probabilities that an amino acid belongs to a class with dN/dS .1 using the Bayes Empirical Bayes (BEB) approaches implemented in PAML [37]. Independently from codeml we used the SLR program which implements “sitewise likelihood-ratio” (SLR) method for detecting non-neutral evolution, a statistical testTable 1. Analysis of the Amaranthaceae rbcL genes for positively selected sites.a b c a b dModel with positive selection log-likelihoodNull model Positively selected sitesLRT Parameters.