The overall apparent substitution rate of mtDNA coding region shows no notable change for hundreds of thousands of years implying that the decrease of non-neutral mutations with time must be very slow (). This observation is based on the human-Neandertal comparison and is supported by a comparison between two chimpanzees. We have dated the coalescence ages of these lineage splits according to our newly revised rate of synonymous transitions and by the application of the 3-rates model. This yielded a date of 440 (SD 138) ky ago for the divergence of the human and Neandertal mtDNA lineages. This date estimate makes it unlikely that the direct ancestors of Neandertals would have been around in Europe 800 ky ago, assuming that the human-neanderthal split occurred in Africa. However, the commonly referred divergence dates for the two species, (a) 400–600 kya, assuming the continuity between H. heidelbergensis
and H. neanderthalensis
in Europe 
and (b) 250–300 kya, assuming their split from an intermediate species H. helmei
in Africa 
, both lay within the error margins of our coalescence estimate. The latter hypothesis seems though more consistent with the mtDNA date estimate as it allows for a reasonable convergence time of DNA lineages within the ancestral species: if the species split occurred 250–300 kya then the additional 140–190 ky could be reserved for the coalescence of mtDNA lineages within the ancestral population, which would be comparable to the observed value in modern humans – about 190 ky.
Changes in the overall substitution rate of the coding region.
Our results imply that the change in the apparent substitution rate of mtDNA coding region involves fluctuations (). In addition, the growth trend in the proportion of synonymous substitutions along with growing clade ages is wavy (). Furthermore, this growth trend is lost after sorting the data according to the accumulated total variation, which includes substitutions that are under selection (). The fluctuations in the apparent substitution rate imply interrelated influences of variable strength in natural selection and population size changes. Indeed, the earliest turning point in the apparent substitution rate coincides with the population expansion following the out-of Africa migration of modern humans, associated with the first diversification of the two mtDNA superclades M and N. Notably, a recently proposed correction for the molecular clock of mtDNA was based on a growth function derived from a dataset of proportions of synonymous substitutions that was sorted, like in , according to the accumulated total variation 
. It is possible that the distortion of the growth trend is more evident in our dataset compared to theirs 
because of the larger proportion of non-neutral variation in our data due to the exclusion of the non-coding control region. Detailed understanding of the behavior of mtDNA substitution rate would certainly increase our knowledge on the factors that have conditioned the development of existing genetic variation in human populations.
Changes in the fraction of synonymous substitutions.
Our intrahuman data show systematically lower fraction of synonymous substitutions compared to the results of Soares et al (2009) 
. For instance, the proportion of synonymous substitutions (0.62) found in the clades of about 140 ky makes up 75% of the respective proportion in the human-chimp distance (). The same comparison yields a fraction close to 90% in the dataset of Soares et al (2009). Unaccounted saturation cannot be the explanation for the discrepancy as the extent of saturation in the long branches of human mtDNA tree is very low 
. The difference in the results of the two studies, however, has implications for the strength of purifying selection. According to Soares et al (2009) 
the proportion of synonymous changes would be virtually stable by the time of the divergence of human and Neandertal mtDNA lineages, indicating only marginal role of purifying selection on mutations that have preserved from this time depth. In our dataset, however, the proportion of synonymous substitutions for that time point is only 78% of the respective human-chimp ratio. An indirect support for the weakness of purifying selection comes from the comparison of the two chimp sequences that diverged about 300 ky ago, which show a similar fraction of synonymous substitutions to the human-Neandertal pair. Notably, the estimates for the fraction of synonymous substitutions for the human-chimp distance were similar in our study and Soares et al. (2009): the proportion was 0.81, based on 3 rate classes for the synonymous sites and Jukes-Cantor correction for the distance in non-synonymous and RNA genes substitutions, and it was 0.79, assuming 1.55 times higher substitution rate for the coding region compared to the control region, as determined by Soares et al. (2009) 
Our substitution rate of 7990 years per synonymous mutation is slightly slower than the average result of Soares et al. (2009), 7880 years 
. However, they used a date that was 8% earlier, 7 my, for the divergence time between the human and chimpanzee mtDNA lineages. We chose to retain the commonly used 6.5 my date, given the uncertainties in the phylogenetic relationships of the Miocene hominids and the amount of time that was necessary for the sorting of mtDNA lineages of the ancestral population. Nevertheless, our rate estimate is in the range of the four estimates derived by four different methods applied by Soares et al. (2009) 
, extending from 6690 to 9500 years per synonymous substitution. Notably, there is a difference in the results of the two studies that were both derived from the accumulated amount of synonymous transversions. Soares et al. (2009), however, did not correct for multiple mutation hits and, in addition, the distance was erroneously underestimated (Pedro Soares, personal communication). According to the substitution rate of 7990 years per synonymous substitution, geographically pooled sequences show that the coalescence times for the two non-African superclades, M and N, are in reasonable agreement with the earliest archaeological evidence for the presence of anatomically modern humans outside Africa ().
Dates of expansion of the main clades in human mtDNA tree by different calibrations.
The results of the present study confirm the higher non-synonymous and RNA variation in human mtDNA genealogy as compared to the level of interspecies variation 
and reveal that the rate of accumulation of substitutions is not gradual but has accelerated since the beginning of the Holocene 11.7 kya. There are three possible explanations for the recent excessive accumulation of functional substitutions in our species: (1) adaptive shifts and positive selection, (2) insufficient time for purifying selection or (3) relaxation of selective constraints. These are not mutually exclusive and probably all of them have shaped the distribution of substitutions in human mtDNA tree. The contribution of adaptive mutations is small 
. The abundance of infrequent non-synonymous variants in human populations has been difficult to explain in terms of adaptive shift. Instead, a transient perpetuation of slightly deleterious variants 
or relaxation of selection 
have been proposed as explanations. The distinction between these two scenarios is difficult to make 
. Comparisons to other species would enable to disentangle the effect of relaxation of natural selection due to technological, cultural and anatomical innovations of modern humans from other factors slowing down the purification of DNA from slightly deleterious mutations, such as post-glacial population growth. Indeed, various other species have been found to have higher intra-species non-synonymous variation than anticipated from interspecies differences 
. There is also evidence of a delayed purifying selection after the rapid population expansion following a severe bottleneck at the LGM for the North American migratory bird species 
. Nevertheless, because of scarcity of data, such interspecies comparisons of variation in mitochondrial genomes are so far very limited. However, the relatively high Ka
value of the two chimpanzee mtDNA sequences that exhibit a coalescence age of 300 ky ago implies sluggishness of purifying selection (). The low efficiency of purifying selection may be a more general pattern as there is no sign of a rapid population growth in the genetic variation of chimpanzees 
. Demography also appears to play a role in the extent of non-synonymous variation in nuclear genes: temporal relaxation of selection after the bottleneck associated with the out-of-Africa migration has been proposed to explain the increase of probably harmful mutations from 12% in African Americans to 16% in European Americans 
. In addition, distribution of fitness effects in a non-stationary population suggested that at least 30% of the non-synonymous or 16% of all mutations in human nuclear genes are highly deleterious 
. An analysis of Craig Venter's exome predicted that 14% of the single nucleotide polymorphisms affect protein function 
It is known that published human mtDNA sequences contain sequencing errors 
, which may bias the results of neutrality tests 
. Sequencing errors mostly occur on terminal branches, where no phylogenetic check or independent confirmation from another study is available. As the share of terminal branches is the largest in the youngest clades, sequencing errors can generate the accumulation of non-synonymous and RNA mutations in the youngest clades. We assessed the effect of putative sequencing errors on the results of this study by three indirect means. First, provided that the sequencing errors in the dataset are random in respect to mutation class, one can presume that the number of errors in each mutation class is proportional to the number of nucleotide positions that allow such mutations. As the number of non-synonymous positions is nearly two times higher than the number of synonymous positions, most of the randomly generated errors should appear as non-synonymous mutations. The number of positions in genes coding for RNAs is comparable to that of synonymous positions and sequencing errors are expected to occur equally likely at the two classes of nucleotide sites. However, the ratio of non-synonymous to synonymous substitutions was not elevated compared to the ratio of RNA to synonymous changes (), suggesting no major impact of sequencing errors on our results.
Secondly, we assessed the effect of sequencing mistakes by removing all non-synonymous and RNA mutation counts from terminal branches (and also from branches that carried 2 individuals) and repeated the sliding window analysis. This reduced the number of non-synonymous mutations in the analysis from 2065 to 605 (or 355) and the number of RNA mutations from 1407 to 442 (or 264). The observed decrease in mutation ratios was expected for all time-windows as the high ratios of external branches also contributed to the ratios of the older clades (). After the removal of the external branches the mutation ratios were still higher for the younger clades.
Temporal changes in the relative rates of non-synonymous (A) and RNA plus intergenic mutations (B) without counting the mutations from the branches that carried only 1 or 2 individuals.
Third, as phantom transversions are a common type of sequencing errors, the ratio of transversions to transitions was compared for the internal and terminal branches. The ratio for the terminal branches was 0.031 (90/2878), it was 0.033 (19/583) for branches that carried 2 individuals and 0.039 (36/929) for all others. These ratios were insignificantly different by chi-squared tests from 0.036 (55/1512), which was the average ratio for all internal branches. In conclusion, we could not find evidence of sequencing errors having major effect on our results but based on these general statistics we cannot exclude that the used dataset included minor problems of sequence quality.
We observed that the fastest evolving synonymous sites exhibited higher than expected interspecies divergence (). It is unlikely that these synonymous sites have been under strong directional selection as even for non-synonymous sites there is no evidence of strong positive selection 
. Alternative explanation, concerning natural selection, would be that the small historical population size of humans has reduced the efficiency of purifying selection, which enabled the mildly deleterious synonymous sites to escape the purifying selection among humans but not in chimpanzees. If the apparently fast-evolving sites were under selective pressure, the saturation hypothesis would not hold. However, the multiple hit correction, as applied on the variable rates model, was able to explain the observed gap between the intra- and interspecies synonymous substitution rates and thus we were unable to reject the null-hypothesis of neutrality. Under neutrality, an explanation would be that the mechanisms that determine the differential rate of substitution for synonymous sites are species-specific, possibly sequence context dependent, and differ in between humans and chimpanzees. Possible interspecies shifts in the synonymous substitution rates at specific sites 
would then explain the excess of higher than expected divergence rate at sites that are also highly variable within a species. This would also further complicate the correction of observed distances for multiple hits at longer evolutionary distances as well as interspecies application of molecular clock.
In conclusion, human mitochondrial DNA clock is time-dependent mainly because of the time-dependence of purifying selection. There is also evidence that purifying selection has been counteracted by other population genetic factors during the course of human history. Our results imply that the proportion of synonymous substitutions has alternated between growth and decrease. This interpretation is strengthened given the shape of the human mtDNA tree, which reflects the bottlenecks and subsequent population expansions associated with the out-of-Africa migration and the hectic climatic conditions of the last glacial period. The wavy growth of the proportion of synonymous substitutions implies biases in the published correction of the mtDNA clock, which assumed a monotonic growth curve 
. Therefore, the clock of synonymous substitutions should be preferred. In addition, it seems that a good consensus has been achieved on the rate of accumulation of synonymous substitutions in human mtDNA, which applies at the population as well as the interspecies level (this study,