it requires fewer assumptions. Complications There is often a systematic bias in the frequency at which various nucleotides are swapped, as certain mutations are more probable than others. For instance, some lineages may swap C to T more frequently than they swap C to A. In the case of the amino acid Asparagine, which is coded by the codons AAT or AAC, a high C->T exchange rate will increase the proportion of synonymous substitutions at this codon, whereas a high C→A exchange rate will increase the rate of non-synonymous substitutions. Because it is rather common for transitions (T↔C & A↔G) to be favoured over transversions (other changes), models must account for the possibility of non-homogeneous rates of exchange. Some simpler approximate methods, such as those of Miyata & Yasunaga and Nei & Gojobori, neglect to take these into account, which generates a faster computational time at the expense of accuracy; these methods will systematically overestimate N and underestimate S. Further, there may be a bias in which certain codons are preferred in a gene, as a certain combination of codons may improve translational efficiency. A 2022 study reported that synonymous mutations in representative yeast genes are mostly strongly non-neutral, which calls into question the assumptions underlying use of the Ka/Ks ratio. In addition, as time progresses, it is possible for a site to undergo multiple modifications. For instance, a codon may switch from AAA→AAC→AAT→AAA. There is no way of detecting multiple substitutions at a single site, thus the estimate of the number of substitutions is always an underestimate. In addition, in the example above two non-synonymous and one synonymous substitution occurred at the third site; however, because substitutions restored the original sequence, there is no evidence of any substitution. As the divergence time between two sequences increases, so too does the amount of multiple substitutions. Thus "long branches" in a dN/dS analysis can lead to underestimates of both dN and dS, and the longer the branch, the harder it is to correct for the introduced noise. Of course, the ancestral sequence is usually unknown, and two lineages being compared will have been evolving in parallel since their last common ancestor. This effect can be mitigated by constructing the ancestral sequence; the accuracy of this sequence is enhanced by having a large number of sequences descended from that common ancestor to constrain its sequence by phylogenetic methods. Methods that account for