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.

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.

Receptor-like kinases (RLKs) belong to the large RLK/Pelle gene family, and it is known that the Arabidopsis thaliana genome contains >600 such members, which play important roles in plant growth, development, and defense responses. Surprisingly, we found that rice (Oryza sativa) has nearly twice as many RLK/Pelle members as Arabidopsis does, and it is not simply a consequence of a larger predicted gene number in rice. From the inferred phylogeny of all Arabidopsis and rice RLK/Pelle members, we estimated that the common ancestor of Arabidopsis and rice had >440 RLK/Pelles and that large-scale expansions of certain RLK/Pelle members and fusions of novel domains have occurred in both the Arabidopsis and rice lineages since their divergence. In addition, the extracellular domains have higher nonsynonymous substitution rates than the intracellular domains, consistent with the role of extracellular domains in sensing diverse signals. The lineage-specific expansions in Arabidopsis can be attributed to both tandem and large-scale duplications, whereas tandem duplication seems to be the major mechanism for recent expansions in rice. Interestingly, although the RLKs that are involved in development seem to have rarely been duplicated after the Arabidopsis–rice split, those that are involved in defense/disease resistance apparently have undergone many duplication events. These findings led us to hypothesize that most of the recent expansions of the RLK/Pelle family have involved defense/resistance-related genes.