Genies to test the significance of correlation between pairs of discrete characters: (1) the presence/absence of C4 photosynthesis and (2) the presence/absence of particular amino-acid at sites found to be under positive selection along C4 branches in the A model of codeml. For this purpose, we used the phylogeny obtained using RAxML (see above) and performed Pagel’s test of correlated (discrete) character evolution [40] implemented in the Mesquite package (K162 site version 2.72) [41]. Test was performed separately 1676428 for each Rubisco residue under positive selection along C4 branches and Bonferroni correction was performed for simultaneous statistical testing.Structural analysis of RubiscoWe used the published Rubisco protein structure from spinach (Spinacia oleracea, Amaranthaceae) from data file 1RBO [42] obtained from the RCSB Protein Data Bank. Throughout the paper, the numbering of Rubisco large subunit residues is based on the spinach sequence. The Lecirelin locations and properties of individual amino acids in the Rubisco structure were analysed using DeepView ?Swiss-PdbViewer v.3.7 [43] and by CUPSAT [44].Discussion Widespread positive selection on RubiscoAs the performance of Rubisco can directly affect plant growth and crop yields, substantial efforts have been made to study its structure and function, with the ultimate aim of trying to improve Rubisco performance [50]. The last few years have brought new approaches to improving our understanding of Rubisco evolution and its genetic mechanisms. The initial molecular-phylogenetic analysis of rbcL showed that positive selection is widespread among all main lineages of land plants, but is restricted to a relatively small number of Rubisco amino 
acid residues within functionally important sites [6]. Following studies showed that rbcL is under positive selection in particular taxonomic groups [26,27,51,52,53,54,55,56]. Coevolution of residues is common in Rubisco of land plants as well as positive selection and there is an overlap between coevolving and positively selected residues [57]. Hence, phylogeny-based genetic analyses suggest there has been a constant fine-tuning of Rubisco to optimize its performance in specific conditions, in agreement with empirical observations that Rubisco enzymes from different organisms show diversity of kinetics better related to species ecology than phylogeny [4]. All eight residues shown under selection in Amaranthaceae using SLR and PAML models M2 and M8 were already shown to be under Darwinian selection in other groups of plants [6]. Five of these residues (145, 225, 262, 279 and 439) were among twenty most commonly selected Rubisco large subunit residues [6]. Findings in Amaranthaceae are in agreement with the previously described uneven distribution of putative fine-tuning residues in Rubisco [6]. Residues 43, 145, 225, 262 and 279 had only twoResults Phylogenetic analysisThe ML phylogenetic tree (Fig. 1) for rbcL sequences from 179 Amaranthaceae species was largely congruent with previously obtained phylogenies and accepted taxonomic subdivisions of the family [19,28,29,30,45,46,47,48]; however no statistical tests for topological similarity between our tree and previously published trees were performed because of different sizes and species compositions of datasets. A minimum of 16 independent origins of C4 photosynthesis were represented in the Amaranthaceae phylogeny if conservative approach for observed polytomies had been taken (Fig. 1), which is consistent.Genies to test the significance of correlation between pairs of discrete characters: (1) the presence/absence of C4 photosynthesis and (2) the presence/absence of particular amino-acid at sites found to be under positive selection along C4 branches in the A model of codeml. For this purpose, we used the phylogeny obtained using RAxML (see above) and performed 
Pagel’s test of correlated (discrete) character evolution [40] implemented in the Mesquite package (version 2.72) [41]. Test was performed separately 1676428 for each Rubisco residue under positive selection along C4 branches and Bonferroni correction was performed for simultaneous statistical testing.Structural analysis of RubiscoWe used the published Rubisco protein structure from spinach (Spinacia oleracea, Amaranthaceae) from data file 1RBO [42] obtained from the RCSB Protein Data Bank. Throughout the paper, the numbering of Rubisco large subunit residues is based on the spinach sequence. The locations and properties of individual amino acids in the Rubisco structure were analysed using DeepView ?Swiss-PdbViewer v.3.7 [43] and by CUPSAT [44].Discussion Widespread positive selection on RubiscoAs the performance of Rubisco can directly affect plant growth and crop yields, substantial efforts have been made to study its structure and function, with the ultimate aim of trying to improve Rubisco performance [50]. The last few years have brought new approaches to improving our understanding of Rubisco evolution and its genetic mechanisms. The initial molecular-phylogenetic analysis of rbcL showed that positive selection is widespread among all main lineages of land plants, but is restricted to a relatively small number of Rubisco amino acid residues within functionally important sites [6]. Following studies showed that rbcL is under positive selection in particular taxonomic groups [26,27,51,52,53,54,55,56]. Coevolution of residues is common in Rubisco of land plants as well as positive selection and there is an overlap between coevolving and positively selected residues [57]. Hence, phylogeny-based genetic analyses suggest there has been a constant fine-tuning of Rubisco to optimize its performance in specific conditions, in agreement with empirical observations that Rubisco enzymes from different organisms show diversity of kinetics better related to species ecology than phylogeny [4]. All eight residues shown under selection in Amaranthaceae using SLR and PAML models M2 and M8 were already shown to be under Darwinian selection in other groups of plants [6]. Five of these residues (145, 225, 262, 279 and 439) were among twenty most commonly selected Rubisco large subunit residues [6]. Findings in Amaranthaceae are in agreement with the previously described uneven distribution of putative fine-tuning residues in Rubisco [6]. Residues 43, 145, 225, 262 and 279 had only twoResults Phylogenetic analysisThe ML phylogenetic tree (Fig. 1) for rbcL sequences from 179 Amaranthaceae species was largely congruent with previously obtained phylogenies and accepted taxonomic subdivisions of the family [19,28,29,30,45,46,47,48]; however no statistical tests for topological similarity between our tree and previously published trees were performed because of different sizes and species compositions of datasets. A minimum of 16 independent origins of C4 photosynthesis were represented in the Amaranthaceae phylogeny if conservative approach for observed polytomies had been taken (Fig. 1), which is consistent.
