Since January 2020, Elsevier has created a free COVID-19 resource centre with information in English and Mandarin. The centre is hosted on Elsevier Connect, providing access to research on the novel coronavirus. Elsevier grants permission to make all research freely available in PubMed Central and other repositories for unrestricted use. The article discusses statistical methods for detecting molecular adaptation, focusing on the ratio of nonsynonymous (dN) to synonymous (dS) substitution rates in protein-coding genes. This ratio, ω = dN/dS, indicates whether amino acid changes are under positive selection. A ω ratio significantly greater than one suggests diversifying selection. Various methods have been developed to estimate dN and dS, including approximate methods and maximum likelihood (ML) approaches. ML methods are more accurate as they account for factors like transition/transversion rate bias and codon-usage bias. Likelihood-ratio tests are used to determine if dN is significantly higher than dS. The article also addresses limitations of current methods, such as the assumption of constant selective pressure across sites and the potential for biases in ancestral sequence reconstruction. It highlights the importance of considering variable selective pressures among sites and lineages, which can be modeled using likelihood approaches. The text reviews recent statistical models for detecting positive selection, including the use of Bayesian methods and likelihood models with different ω ratios for branches in phylogenies. These methods allow for more accurate identification of sites under positive selection. The article concludes that while current methods are generally conservative, they have improved significantly, allowing for better detection of adaptive molecular evolution. Future research should focus on refining these methods to account for complex evolutionary dynamics and improve the accuracy of detecting positive selection.Since January 2020, Elsevier has created a free COVID-19 resource centre with information in English and Mandarin. The centre is hosted on Elsevier Connect, providing access to research on the novel coronavirus. Elsevier grants permission to make all research freely available in PubMed Central and other repositories for unrestricted use. The article discusses statistical methods for detecting molecular adaptation, focusing on the ratio of nonsynonymous (dN) to synonymous (dS) substitution rates in protein-coding genes. This ratio, ω = dN/dS, indicates whether amino acid changes are under positive selection. A ω ratio significantly greater than one suggests diversifying selection. Various methods have been developed to estimate dN and dS, including approximate methods and maximum likelihood (ML) approaches. ML methods are more accurate as they account for factors like transition/transversion rate bias and codon-usage bias. Likelihood-ratio tests are used to determine if dN is significantly higher than dS. The article also addresses limitations of current methods, such as the assumption of constant selective pressure across sites and the potential for biases in ancestral sequence reconstruction. It highlights the importance of considering variable selective pressures among sites and lineages, which can be modeled using likelihood approaches. The text reviews recent statistical models for detecting positive selection, including the use of Bayesian methods and likelihood models with different ω ratios for branches in phylogenies. These methods allow for more accurate identification of sites under positive selection. The article concludes that while current methods are generally conservative, they have improved significantly, allowing for better detection of adaptive molecular evolution. Future research should focus on refining these methods to account for complex evolutionary dynamics and improve the accuracy of detecting positive selection.