Wen‐Hsiung Li

A mathematical model for the evolutionary change of restriction sites in mitochondrial DNA is developed. Formulas based on this model are presented for estimating the number of nucleotide substitutions between two populations or species. To express the degree of polymorphism in a population at the nucleotide level, a measure called "nucleotide diversity" is proposed.

Mutations in the genealogy of the sequences in a random sample from a population can be classified as external and internal. External mutations are mutations that occurred in the external branches and internal mutations are mutations that occurred in the internal branches of the genealogy. Under the assumption of selective neutrality, the expected number of external mutations is equal to theta = 4Ne mu, where Ne is the effective population size and mu is the rate of mutation per gene per generation. Interestingly, this expectation is independent of the sample size. The number of external mutations is likely to deviate from its neutral expectation when there is selection while the number of internal mutations is less affected by the presence of selection. Statistical properties of the numbers of external mutations and of internal mutations are studied and their relationships to two commonly used estimates of theta are derived. From these properties, several new statistical tests based on a random sample of DNA sequences from the population are developed for testing the hypothesis that all mutations at a locus are neutral.

A simple, effective measure of synonymous codon usage bias, the Codon Adaptation Index, is detailed. The index uses a reference set of highly expressed genes from a species to assess the relative merits of each codon, and a score for a gene is calculated from the frequency of use of all codons in that gene. The index assesses the extent to which selection has been effective in moulding the pattern of codon usage. In that respect it is useful for predicting the level of expression of a gene, for assessing the adaptation of viral genes to their hosts, and for making comparisons of codon usage in different organisms. The index may also give an approximate indication of the likely success of heterologous gene expression.

Comparison of plant mitochondrial (mt), chloroplast (cp) and nuclear (n) DNA sequences shows that the silent substitution rate in mtDNA is less than one-third that in cpDNA, which in turn evolves only half as fast as plant nDNA. The slower rate in mtDNA than in cpDNA is probably due to a lower mutation rate. Silent substitution rates in plant and mammalian mtDNAs differ by one or two orders of magnitude, whereas the rates in nDNAs may be similar. In cpDNA, the rate of substitution both at synonymous sites and in noncoding sequences in the inverted repeat is greatly reduced in comparison to single-copy sequences. The rate of cpDNA evolution appears to have slowed in some dicot lineages following the monocot/dicot split, and the slowdown is more conspicuous at nonsynonymous sites than at synonymous sites.