Test of genetical isochronism for longitudinal samples of DNA sequences

Longitudinal samples of DNA sequences, the DNA sequences sampled from the same population at different time points, have increasingly been used to study the evolutionary process of fast-evolving organisms, e.g., RNA Virus, in recent years. We propose in this article several methods for testing genetical isochronism or detecting significant genetical heterochronism in this type of sample. These methods can be used to determine the necessary sample size and sampling interval in experimental design or to combine genetically isochronic samples for better data analysis. We investigate the properties of these test statistics, including their powers of detecting heterochronism, assuming different evolutionary processes using simulation. The possible choices and usages of these test statistics are discussed.