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Premise of the Study: Next‐generation sequencing facilitates rapid production of well‐sampled phylogenies built from very large genetic data sets, which can then be subsequently exploited to examine the molecular evolution of the genes themselves. We present an evolutionary analysis of 83 gene families (19 containing carbon‐concentrating mechanism (CCM) genes, 64 containing non‐CCM genes) in the portullugo clade (Caryophyllales), a diverse lineage of mostly arid‐adapted plants that contains multiple evolutionary origins of all known photosynthesis types in land plants (C3, C4, CAM, C4‐CAM, and various intermediates). Methods: We inferred a phylogeny of 197 individuals from 167 taxa using coalescent‐based approaches and individual gene family trees using maximum likelihood. Positive selection analyses were conducted on individual gene family trees with a mixed effects model of evolution (MEME). We devised new indices to compare levels of convergence and prevalence of particular residues between CCM and non‐CCM genes and between species with different photosynthetic pathways. Key Results: Contrary to expectations, there were no significant differences in the levels of positive selection detected in CCM versus non‐CCM genes. However, we documented a significantly higher level of convergent amino acid substitutions in CCM genes, especially in C4 taxa. Conclusions: Our analyses reveal a new suite of amino acid residues putatively important for C4 and CAM function. We discuss both the advantages and challenges of using targeted enrichment sequence data for exploratory studies of molecular evolution. [ABSTRACT FROM AUTHOR]