An Extension of the Kimura Two-Parameter Model to the Natural Evolutionary Process

Accurate estimates of genetic difference are required for research in evolutionary biology. Here we extend the Kimura two-parameter (K2P) model by considering gaps (insertions and/or deletions) and introduce a new measure for estimating genetic difference between two nucleotide sequences in terms of nucleotide changes that have occurred during the evolutionary process. Using the nuclear ribosomal DNA internal transcribed spacer 2 region from the genus Physalis, we demonstrate that species identification and phylogenetic studies strongly depend on evolutionary models. It is especially noteworthy that the use of different models affects the degree of overlap between intraspecific and interspecific genetic differences. We observe that the percentage of interspecific sequence pairs with values less than the maximum intraspecific genetic difference is 43.2% for the K2P model which is calculated by removing gap sites across all sequences, 22.7% for the K2P model which is calculated by removing gap sites for sequence pairs, and 16.9% for our model which is calculated without removing gap sites. Additionally, the numbers of sequence pairs with interspecific genetic differences of zero are 50 for the K2P model and 29 for our model. The genetic difference measure based on the K2P model, compared to our model, overestimates 21 sequence pairs that are not originally identical. These results indicate the importance of estimating genetic differences under the model of sequence evolution that includes insertions and deletions in addition to substitutions.