Time Dependency of Molecular Rates in Ancient DNA Data Sets, A Sampling Artifact?

It is common knowledge that the instantaneous rate of mutation (RoM) in DNA sequences exceeds the long-term rate of substitution (RoS) when measured in interspecific phylogenetic analyses. The neutral theory of molecular evolution describes this temporary excess diversity as transient polymorphisms either removed from the population through the actions of purifying selection or fixed by random genetic drift over a few generations (Kimura 1983). Observations of these “accelerations” in the molecular rates within recent evolutionary time have been documented (Parsons et al. 1997; Lambert et al. 2002); however, they did not resolve the magnitude and duration of this phenomenon. Howell et al. (2003) have addressed these issues through pedigree analyses of human mitochondrial (mt) hypervariable region (HVR) sequences and have suggested a 5- to 10-fold acceleration compared with the long-term RoS. In addition, Burridge et al. (2008) have shown that the calibration of the mt clock for galaxiid fishes using geological divergence dates with cytochrome b and control region sequences supports a transition period during which the RoM would decrease toward the RoS extending up to ∼200 kyr (Burridge et al. 2008). However, the general applicability of these specific results remains untested. The recent publication (Ho, Phillips, Cooper, et al. 2005) of a Bayesian analysis supporting that a drastic acceleration in the molecular rates as time approaches 0 is a general and predictable feature has become a hotly debated topic in both systematics and evolutionary biology (Bandelt 2007; Emerson 2007; Ho, Kolokotronis, et al. 2007; Ho, Shapiro, et al. 2007; Howell et al. 2008). When using the program BEAST (Drummond and Rambaut 2007), with data sets containing sequences of vertebrate taxa in conjunction with a wide range of calibration points, Ho, Phillips, Cooper, et al. (2005) have proposed a “time-dependency” model in which the rate reflects a direct response of the divergence time between the terminals. In this model, the molecular rate, referred to as the rate of change (RoC), is allowed to decrease rapidly along a vertically translated exponential decay curve until the long-term RoS reaches equilibrium. Ho, Phillips, Cooper, et al. (2005) have evaluated the putative effects of sequencing and calibration errors as well as mutational saturation in their model and have concluded that purifying selection was the most likely contributing factor involved in the variation of the RoC over time. This model, however, describes a phenomenon an order of magnitude beyond all previous reports of such accelerations, as it allows the RoC to vary over a wide range of rates (up to and beyond 20-fold) during an extended period of time (up to 2 million years). Although intuitively appealing and explaining the data analyzed by Ho, Phillips, Cooper, et al. (2005) well, this model supports a serious and prolonged impact of deleterious mutations and would thus require a few adjustments to the current evolutionary paradigm of genomes (Penny 2005). Recently, Bandelt (2007) and Emerson (2007) have questioned both the model of the time dependency and the significance of the rate acceleration phenomenon. Emerson (2007) has emphasized the critical role of the selection of priors in BEAST analyses and has shown that the results described by Ho, Phillips, Cooper, et al. (2005) could only be retrieved under specific conditions within a full Bayesian framework (where the level of enforcement over the priors is minimal). In this paper, our primary objective was thus to re-address the nature of the causal factor(s) of the rate acceleration described by Ho, Phillips, Cooper, et al. (2005) as well as their biological meaning. Based on previously published material, we suggest that the emphasis placed on the divergence time in the current explanation of this phenomenon might have hidden other relevant factors such as the information content of the data sets. In order to compare the performance of the strict “time-dependency” model with a more inclusive “signal-dependency” hypothesis, we examine the impact of sequence length over the estimates of the RoC for 2 different calibrations. We show that our hypothesis for a signal-dependent artifact appearstomodelthedatapresentedheremoreaccurately and may explain some inconsistencies between published reports on evolutionary rates. In their original paper, Ho, Phillips, Cooper, et al. (2005) reported an apparent acceleration of the RoC in recent times ( < 2 Ma) for 3 groups of mt data sets calibrated with dates ranging from 29 to 42 ka for tip 14C calibrations to 0.125–35 Ma for node (internal) calibrations using the software application BEAST. This software, developed by Drummond and Rambaut (2007), simultaneously analyzes genetic data with their associated dates/ages of terminals and/or nodes, in order to infer, under various clock models within a Bayesian framework, the substitution rates, phylogenetic structure, branch lengths, and demographic parameters, which the data In of the data Emerson (2007) has documented of 3 of the of the phylogenetic to lengths, the of the molecular and the of the time calibrations. has shown that when different sets of priors in the exponential decay rate as by Ho, Phillips, Cooper, et al. (2005) could either not be retrieved the data sets using control region and or not with the magnitude data sets of in the original data only the human sequences sequences of with a RoC in both when the calibration was on the 14C dates of the However, Emerson (2007) rate acceleration when the time of the most recent common of the sequences was as a node results the rate acceleration to be on the framework of BEAST analyses. Ho, Phillips, Cooper, et al. (2005) for a Bayesian with models and Emerson (2007) and Bandelt (2007) more priors and calibrations within a full Bayesian framework, Ho, Kolokotronis, et al. (2007) have documented for BEAST analyses on data sets DNA sequences and calibrations for a data the calibration analyses with the original human all from sequences all using time calibration priors that on 14C dates of the and all associated with We the these conditions might be from the rate acceleration phenomenon described by Ho, Phillips, Cooper, et al. of the RoC through BEAST analyses using or data sets The of the for the data sets is in order to compare with the data sets. the of Ho, Kolokotronis, et al. Although recent the of the rate Emerson (2007) has that this might be In response to this Ho, Kolokotronis, et al. (2007) have BEAST analyses on data sets. The for this analysis was that BEAST estimates of the RoC that been as a to the data sets in a full Bayesian framework recent tip calibration it would the of the rate estimates for the However, for to be the data and results from the and data sets be as as Ho, Kolokotronis, et al. (2007) sequences of in length of variation with a RoS as as the of the substitution rate for the mt of such a would on change sequence that a of their divergence could be within time. these data the of the RoC using BEAST was not only The the of the for the which of the substitution for a RoC of However, the of the RoC for the mt data sets analyzed in the was (Ho, Kolokotronis, et al. with the of the the for the rates on times for the of the their the data sets not the of most data sets in which the rate is associated with a wide could be the of remains to be would the and of the RoC be a in the range of interspecific mt substitution rates and substitution and to the sequence the rate through the Bayesian or an RoC with a wide it to that the data sets to data sets. the acceleration in the estimates of the RoC in the data sets analyzed by Ho, Kolokotronis, et al. (2007) it is the have that it is not the of an of the rate we examine the analysis of Ho, Shapiro, et al. (2007) of an data et al. in which the sequences to to In with their model, they the decrease in time with an in the This however, is only on the of the the analysis of that the of the is when the calibration a between time and molecular rate, might suggest a between time and level of on the of the time of the data with the of and the RoC using data from 2 in Ho, Shapiro, et al. is shown in exponential of the of with time was and for the RoC The from the analysis of the was to show the with the from the more inclusive time We to an exponential between the calibration and the level of between the sequences by the of supporting the decrease in the information content of the data when the divergence time toward 0 these a between the of sequence variation and the not the of the estimates of the This was by Ho, Shapiro, et al. of the could be to a as the calibrations to the is a of information in the is on the rates, that the and the However, they that magnitude of the is not to explain the rate in our (Ho, Shapiro, et al. 2 this as the the time range Ho, Phillips, Cooper, et al. Ho, Kolokotronis, et al. 2007; Ho, Shapiro, et al. have that was an between the divergence time and the acceleration of the the published for more to that phenomenon. The variation in the range of the that factors might be for that phenomenon a strict time dependency of the It has been previously that the information content of the published data sets to the hypothesis might be Ho, Phillips, Cooper, et al. (2005) have on the rate estimates from recent calibration which they to sequence variation in these (Ho, Phillips, Cooper, et al. Bandelt (2007) has the original human data to resolve the time Emerson (2007) issues BEAST to a of phylogenetic in the human data However, the impact of the information content of the data sets in the rate acceleration phenomenon has been to we an framework to the of a “signal-dependency” hypothesis, which that the and of the RoC estimates by the of sequence divergence the calibration The phylogenetic in a molecular data is on the divergence between to which we to as the of change by with the of the rates. a fixed of the is and with 3 the the sequence and the evolutionary time. for a the be the in a DNA sequence as in a sequence This from when mutational saturation a in the data sets previously analyzed (Ho, Kolokotronis, et al. 2007), their of a of mutational would all the sequence a of it is thus to the in 2 as in the of the rate acceleration by Ho, Phillips, Cooper, et al. Ho, Shapiro, et al. 2007), vary the calibration or vary the sequence the of calibration time has been the of sequence length over the RoC has been compare the performance of the and the with our analyses have been placed in a framework the molecular rate is allowed to vary along the divergence time and length In the model, variation of length have on the RoC However, the rate is by the between it a when both factors vary the RoC decrease rapidly when sequence length a rate to the interspecific as it when the calibration of the data (Ho, Phillips, Cooper, et al. 2005). the variation of the RoC to sequence be to which hypothesis of either the time dependency or the dependency describes the data and either of explain all the of the variation of the RoC and of the 2 to explain the variation for the RoC reported with BEAST. Ho, Phillips, Cooper, et al. model the substitution rate is a only to the time of The hypothesis of a signal-dependent artifact the substitution rate is to the in it has been to the of sequence length on sequences to their length and Ho, Kolokotronis, et al. for a The recent publication of mt genomes et al. et al. et al. et al. has a data of It is placed phylogenetic with the mt genomes of 2 et al. et al. et al. and et al. mt the of the data in and 14C as calibration in both sets of on The in the of analysis is on the The 2 for with using the in with and between the region and of the control region of The of the was analyzed as a In order to the impact of sequence of the mt and up to of the Although the mt is to as a molecular with in genetic and phylogenetic content along In order to the impact of of the we of length by random using the within the 2005). of the variation of the RoC through the of to suggested that to of the analyzed for length not of the data sets was evaluated using the information of and to the most substitution in the model was with model ranging from to the impact of models over the variation of the all Bayesian analyses under the analyses of a of length under the RoC estimates and suggest the of the of rate variation over length from the substitution model not In their Ho, Kolokotronis, et al. (2007) have shown that the demographic model in BEAST impact on the In order to the of when the our analyses using a demographic factor of the analyses of the full mt data Rambaut and Drummond a of in of the clock model over the strict clock < the analysis under the clock a level of variation of the rate along of a length under a clock the of rate variation as the strict clock with the of not Although not as as a clock model (Ho, Phillips, et al. the strict clock model was thus in our analysis of the sets of Bayesian which only by the calibration of the strict in for all data analyses in calibration calibration to as and to the conditions rate acceleration might be In the we our calibration to the of the terminals dates or In to tip we a on the of the Ma for the of analyses. This time range to the current of the divergence between the of the the and the and is well by et al. calibration was analyzed with BEAST Drummond and Rambaut in order to a RoC and associated for the most the of length using to RoC associated compared with the when using the to as This is to the developed by Ho, Phillips, Cooper, et al. Ho, Shapiro, et al. and by Emerson (2007) to the rate acceleration the in our analyses was the length the calibration for generations within the full Bayesian framework by Ho, Shapiro, et al. for all generations a period of was to for as well as of priors as (Drummond and Rambaut The of 3 was the RoC clock rate in as well as the of 2 that to the of the and the of our sequences The of was not their was to in both the full mt and the analyses to of the original In the analyses the when using the with the node not as of the full Bayesian framework previously by Emerson the results of the Bayesian analyses for the of the RoC over the range of sequence to full for both and calibration This under conditions with the which have rates for other in the for sequences with the data an RoC by a wide for of the the calibration that vary from to the RoS published by et al. (2007) for the with between and of their and with the RoC proposed by Ho, Kolokotronis, et al. (2007) for a data of mt of length when the calibration is the sequence of the which with the RoS of the to the sequence length and for the calibration or the calibration and referred to in the of a signal-dependent The of the was to the of both The of the full Bayesian analysis is by the The is the previously published phylogenetic rate for the full mt of substitution et al. 2007), the to the rate by Ho, Kolokotronis, et al. (2007) in their results the of rate acceleration when the calibration approaches with the as previously However, when compared with the on the 2 shown in the not the hypothesis the only the of variation of the RoC with length between the The in length has on the RoC from the it is ranging from up to the range and with the RoS The variation is more over the of that which with sequence the from of the for the sequences to only over and full However, the length has a on the RoC when the calibration is the RoC a for to for the full associated with a of the the wide the range by to the rate, of the of the decrease of the RoC is in the and when or more of the the RoC approaches the for the full This the in Ho, Phillips, Cooper, et al. analyses of the variation of RoC with time that the is the sequence Although this is not by the model it is by our hypothesis the rate acceleration is to the divergence between sequences and strict hypothesis is likely to be for it only describes of the the hypothesis of a causal role of the for the variation of RoC in both The of the hypothesis in biological the hypothesis be a to the for it is not the of evolutionary It is to that the results in the analyses of the full calibration is or or for the data under from these that when data sets under the be as we the (up to for the RoC under calibration as a the apparent time dependency of the rate acceleration as a of a signal-dependent The of our framework both time and that the with for likely to be the results of an phylogenetic content to the calibrations. the Bayesian analyses not random sets of different from the data a RoC estimates with a of the when the length This is we for the RoC when we on the calibration analyses the however, the of the is by a in the RoC when length that the not only the of the This artifact has been previously as a by Ho, Shapiro, et al. estimates of with they by or that the sequences and that the in the impact of this be this we the of the impact of this by the of sequences and which that it has been in the of the results that the calibration has a the variation of the the tip calibrations only the kyr when the variation by the is their calibration over data sets of information content using a calibration for the in of the tip calibrations when sequences We this as the RoC for calibration is the published RoS the sequence range This the RoC from calibration be that calibration is not The enforcement of a calibration might not be the only to a signal-dependent In the developed by Emerson (2007), the of the range for most priors was in BEAST results by the of in the This be for by our current hypothesis might be the results of 2 this might be by different of errors as proposed by Emerson the on the calibration of the that the for the sequence by have a on the associated with the calibration of the Ma could have an impact on the calibration sequencing errors or to explain a acceleration phenomenon (Ho, Phillips, Cooper, et al. 2005) might be in some sequences to explain the the mutational saturation between the and the might to an of the RoC on the calibration not by the substitution all putative of the in the and might a acceleration of the rate only when the recent calibrations by a to purifying selection (Penny 2005). In a primary is placed on of divergence the evolutionary rate has been until on the variation of the divergence estimates that on the results of the Bayesian analyses for the of the for both the node and the the results for the 2 we on the node which is associated with and 2005) for of the estimates of the for the and and with The for the node is it is on by the of the and on the other by the of and and and 2005). The is the between estimates from both the and the calibration when the full mt data is Although the when the is calibrated a both approaches for the with estimates from other by This that an acceleration of the RoC documented by the between and calibrations for the full mt data may not in the The calibration which with the estimates when of the original sequence length was analyzed However, in the sequence length not the of that and to an sequences or of the mitochondrial more which on of in the the node is not a which This is in the of the estimates of the RoC for the sequence we show that estimates of the RoC to The calibration more and estimates of the when of the original sequence length is analyzed when sequence length to the on the estimates and the is it that the calibration might a of the artifact for the RoC in the calibration to the estimates of This beyond the of the paper, it is that a calibration with a in the priors of BEAST analyses not to estimates for other on the analyses thus that of the 2 calibration approaches to and for divergence when sequences have the in from sequences under full Bayesian using BEAST. we 3 and to the general significance of the signal-dependent 3 published data sets of mitochondrial DNA from which be In the published paper, et al. (2007) 2 to as and their they analyzed sequences with BEAST to a full Bayesian framework using only 14C tip dates as calibrations. the model they an RoC with a wide to with the results of Ho, Kolokotronis, et al. (2007) from the data Based on this they a for the of ka This with both and estimates from our which an time as as ka for the node all the in the to the original of this et al. (2008) have mt genomes from both and BEAST analyses of all sequences under a full Bayesian using either only 14C tip calibrations or by the calibration of the of their using the divergence as in the current for the using a et al. (2008) the from analyses the of the which direct with the previous 3 of their publication et al. it that in our analyses of the full both and calibration approaches estimates and that the of the original by et al. results suggest that the analyses of et al. (2007) on recent calibrations of a have from a signal-dependent which could be by et al. (2008) when using The most recent et al. a of and a more in which the between and 2 is and the length analyzed and the time range of et al. (2008) estimates to of et al. (2007) when a calibration 14C analysis is with BEAST. However, when the estimates of the for the and the from the full mt analysis as priors to the BEAST the acceleration is not the RoC to is to the RoS and is some times the by et al. (2007), in a of the of the of the of all sequences of and 2 an Ma) is with the of the node proposed by et al. (2008) using a calibration of the mt genomes more recent their calibration This in of a sequence length the rate and estimates could be by the of calibration This thus a framework for most that likely to be in sequence length and Ho, Phillips, Cooper, et al. (2005) have analyzed different data sets of that a rate acceleration when calibrated with only 14C dates of sequences of the analysis a RoC of times as as the estimates from a data calibrated with the Recently, and (2008) have published an analysis of a of mt genomes of and 2 have different of the data for which model have been In addition, they have 2 different calibration the using only estimates of divergence within and the was calibrated analyses have an variation of the RoC control region sequences 3 times the as a sequence was the RoC variation over a was between the and the recent calibrations and 2008). for both calibration the estimates with of the RoC and variation when the calibration is that the RoC from the analysis of a of genomes and the previous estimates on supporting a signal-dependent artifact in the original analysis (Ho, Phillips, Cooper, et al. 2005). Emerson suggested the the for the data with the data et al. The 2 most sequence sets by calibration range in the of Ho, Shapiro, et al. (2007) analyzed sequences ka sequences the of sequence we sequence of a of the original data either or the sequence In addition, 3 through the of a and 10-fold of the original 3 and might not compare with The BEAST analyses to the conditions by Ho, Shapiro, et al. (2007) on the generations with a and strict molecular clock substitution model, and demographic the results of these analyses. on the data ka a as for the data is for the When the original sequence length is the RoC (up to and associated from up to of the the the RoC was not only more for the was estimates of the RoC and for the data to and the original the ka calibration range and the ka range The the results from the original data length The to the data by the with associated The of these results with the from the calibration range that the signal-dependent artifact the data more in RoC and when the sequence for the the rate variation for the data sets be by a vary in over of the original data and thus to the RoS for the ka data could be as as the of from the the RoS for the ka range is more This that length and time not the only contributing factors to the rate to the (where the in terminals was the 2 sequence sets analyzed in the of terminals and the phylogenetic 2 factors that may to the signal-dependent the in RoS estimates could a by Emerson that the signal-dependent may not be to explain the phenomenon of rate In all the of the of the original data a to to to the RoC from data in both calibration and sequence length might be to a signal-dependent Bayesian analyses have of general significance for data sets analyzed with BEAST. Based on the mt data we to show that the apparent time dependency of the RoC for on data sets calibrated in time with only recent dates is more likely by an artifact an evolutionary The phylogenetic content of sequences to the over the substitution rates, which vary that their for and to a of the apparent acceleration of the molecular rates. the described from the analyses of the data be extended to other published material, we suggest that all data sets be for such a dependency through the framework to the of such a the effects of the signal-dependent artifact the between the RoC estimates on either or calibrations suggest that this artifact not for the rate It however, show that the acceleration phenomenon is of magnitude has been previously reported by Ho, Phillips, Cooper, et al. We have to the of recent calibration The calibration is more to a full Bayesian framework as it on the and of the data to to both and However, we have this be when the data and both and the and results for the RoC with an calibration for this information is for the the of BEAST in a full Bayesian framework when DNA our analyses suggest that data sets of phylogenetic content might of the range of and estimates of divergence The of divergence using data sets is thus of the for This was by The and the a from the and We and for and critical of our We to and an for their We to and for of the data

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