Comparative studies of molecular substitution rates between lineages provide insights into the mechanisms that cause evolution of DNA sequences. Under the neutral theory [1, 2] rates of nucleotide substitutions are expected to be equal to rates of mutation, thus a constant rate of nucleotide substitution in homologous DNA sequences should be observed among lineages that share mutation rates. Neutral theory assumes that genetic drift is the primary evolutionary mechanism causing molecular evolution and predicts that rates of sequence change would be both constant over time and independent of the effective population size. Heterogeneity in substitution rates can be explained under neutral theory by either unevenness of mutation rates at individual loci (manifested as locus effects) or correlated mutation rates across all loci within species (manifested as lineage effects). Alternatively, natural selection may cause rate heterogeneity among loci and lineages via purifying selection that reduces the probability of substitution due to functional constraint or through the increased probability of substitution associated with positive natural selection [3–6]. Identifying causes of rate heterogeneity as well as specific variables that affect underlying mutation and substitution rates is fundamental to understanding the mechanisms that cause evolution of DNA sequences (reviewed in ).
Differences in generation time could affect substitution rates, causing lineage effects on substitution rates if organisms with shorter generation times experience more mutations per unit of chronological time than organisms with longer generation times. This neutral explanation for rate heterogeneity among lineages is commonly called the generation time hypothesis. Under the generation time hypothesis, lineage-specific heterogeneity in rates of divergence can be explained by differences in the number of germ line cell divisions per unit time among lineages that otherwise share constant mutation rates. Therefore, under the generation time hypothesis substitution rates are expected to be negatively correlated with generation time [5, 8, 9]. Generation time effects on synonymous substitution rates have been widely observed at multiple loci for several mammalian species [2, 3, 9–15]. Generation-time-like effects have also been tested for in organism such as RNA viruses where faster substitution rates were correlated with higher frequencies of replication  and in spore-forming bacteria where rates of divergence were not related to spore dormancy .
In angiosperms, expected generation time impacts on rates of molecular evolution are not as clear as in animals since plants lack distinct germ and somatic cell lines. Plant cells are totipotent and the number of cell divisions between germination and gamete production can vary from individual to individual and even among parts of a single individual. The generation time hypothesis modified for plants assumes that variation in the frequency of cell replication is correlated with differences in annual/perennial habit. Since annuals have shorter minimum time to first flowering than perennials, it has been assumed that annuals would also experience a higher frequency of cell replication per chronological time and thereby a faster rate of divergence when compared to perennials . The generation time hypothesis has been invoked to explain why annual species exhibited higher rates of molecular evolution than perennial species for several nuclear, mitochondrial and chloroplast loci (e.g. [19–23]). However, results from studies that support a generation time effect in plants have two primary limitations . First, some studies used multiple non-independent comparisons in their analyses that may lead to statistical difficulties as well as potential phylogenetic bias. Second, the taxa compared were highly divergent so that other evolved differences in addition to generation time could also have caused the rate variation observed. Comparing divergence rates in phylogenetically-independent sets of annual/perennial pairs that are recently diverged can correct for these two pitfalls when testing for a generation time effect in angiosperms .
Loci that can be used to estimate divergence rates are limited in the vast majority of angiosperms, which restricts comparisons of substitution rates in multiple independent sets of recently diverged plant taxa. For example, the plant mitochondrial genome exhibits a fast pace of structural evolution but the lowest rate of nucleotide substitutions of all three plant genomes making it especially difficult to obtain sequences in multiple plant lineages with sufficient divergence [18, 25–28]. Universal primers are available for multiple chloroplast regions but, like mitochondrial regions, the utility of these regions is often limited by low sequence divergence at shallow phylogenetic relatedness. Nuclear loci are not widely available in multiple plant lineages since nuclear genomes have variable architecture, abundant multigene families with rapid duplication and loss complicating the identification of orthologous loci [18, 27]. There is also a wide range of substitution rates among nuclear DNA sequences in plants , requiring multiple loci in comparative studies to average rates over independent loci.
The internal transcribed spacers (ITS 1 and ITS 2) of nuclear ribosomal DNA (nrDNA) are the only nuclear DNA markers currently available for comparative tests of the generation time hypothesis in a broad range of recently diverged plant taxa for several reasons. First, ITS regions are universally amplifiable in plants and many plant taxa have been sequenced. Second, ITS regions are highly variable at the nucleotide level. Third, it is commonly believed that ITS multicopy arrays are homogenized by concerted evolution so that intraspecific polymorphism does not complicate estimates of divergence [30, 31]. Moreover, ITS regions have been used extensively in molecular evolution studies of plants such as demonstrating that rates of ITS nucleotide substitution are associated with species diversity , reproductive isolation and life history , and environmental variables (; but see ).
Two recent studies compared rates of ITS 1 and ITS 2 divergence using phylogenetically independent sets of angiosperms differing in life history but reached opposite conclusions about whether differences in life history affect rates of divergence. In the first study, Whittle and Johnston  did not find an association between relative rates of nucleotide substitution and annual/perennial life history in 22 species pairs, leading them to conclude that the generation time hypothesis does not apply to angiosperms. In another recent study, clades with a predominantly herbaceous life history exhibited an almost twice-faster average rate of divergence than predominantly long-lived woody clades using 28 independently calibrated absolute rates of ITS nucleotide substitution . Both studies consistently did not reject the null hypothesis of constant divergence rates when comparing life histories. Since low statistical power of rate tests was suspected, both papers also treated substitution rate differences qualitatively or categorically (e.g. annual is faster or perennial is faster regardless of the magnitude of the rate difference). These conflicting results mandate further research into whether differences in generation times are correlated with substitution rates in angiosperms.
Given that ITS 1 and ITS 2 are currently among the only sequences available to test for rate heterogeneity among a wide sampling of plant taxa, it is essential to assess the statistical power of rate heterogeneity tests based on ITS sequences. It is critical to determine the magnitude of rate heterogeneity required to reliably reject the null hypothesis of rate constancy when evaluating whether differences in annual/perennial habit have heterogeneous substitution rates. Low statistical power will result in type II errors (incorrectly failing to reject the null hypothesis of rate constancy) that could lead to an erroneous conclusion that annual/perennial habit is not associated with divergence rates. One main cause of low statistical power is a small number of nucleotide substitutions available to estimate divergence, a common situation when recently diverged species are being compared. Simulations have shown that the power of Tajima's relative rate test , distance-based relative rate tests , and the maximum-likelihood relative ratio test  are all dependent on sequence lengths, the relatedness of the outgroup taxa, and the employment of an appropriate model of nucleotide substitution [37, 38]. The alternative approach of categorical treatment of substitution rate differences in annual/perennial comparisons is based on the assumption that the direction of rate differences would accurately test rate heterogeneity. However, this approach has not yet been subjected to a rigorous power analysis.
In this article, we test whether annual/perennial habit affects rates of divergence by comparing both relative rates of molecular evolution and categorical branch length differences in 16 independent annual/perennial species pairs. ITS 1 and ITS 2 sequences were obtained from GenBank under strict sampling criteria designed to control for artifacts contributing additional variation in divergence rates that could obscure any rate variation caused by differences in life history. The criteria were that each annual/perennial pair was recently diverged, had at least eight nucleotide changes between taxa, had ITS sequences for two outgroup taxa available, and the ITS sequences were originally obtained from a single PCR amplicon. The power of maximum likelihood relative rate tests was investigated by determining the degree of rate heterogeneity required to reliably reject rate constancy for DNA sequences simulated under average nucleotide substitution parameters of ITS sequences. We also used simulations to assess whether categorical treatment of branch length differences is an appropriate method to test for rate heterogeneity when a relative rate test does not reject rate constancy. In addition, we utilized sequences of three nuclear loci, two chloroplast regions and multiple intra-specific nrDNA ribotypes for the annual Arabidopsis thaliana and two closely related perennials (Arabidopsis lyrata subsp. lyrata and A. lyrata subsp. petrea) to test whether substitution rate differences at the ITS regions were correlated across multiple loci as expected under the generation time hypothesis.