BACKGROUND
molecular-clock dating of long-stemmed clades  is prone to large estimation errors partly because calibration points can be placed only at nodes, not part-way along stems  <cit> .
likewise, shifts in substitution rate along lineages can be detected only at nodes, and cannot be placed within unbroken stems.
as molecular dating depends upon accuracy of rate modelling, inferred rate variation within long branches has been hypothesized to contribute to dating error, e.g.
in the crown node of angiosperms  <cit> .
calibration is critically important for reducing error in molecular dating  <cit> , for instance by improving estimates of rate heterogeneity among lineages  <cit> .
conversely, estimation error is greater in target clades when calibrations are experimentally omitted  <cit> .
furthermore, abrupt rate shifts in some lineages of a phylogeny, followed by rate conservation, can mislead rate and age estimation, even when the node of interest is calibrated  <cit> .
a strict molecular clock has been rejected in analyses of most empirical datasets, and is inapplicable to data in which rate shifts occur, so relaxed molecular clock models are used widely .
commonly used relaxed clocks include uncorrelated, autocorrelated and local clocks.
in an autocorrelated clock, the rate along a given branch is more similar to its parent branch than a branch chosen at random, though autocorrelation models differ in the degree to which they restrict rate variation between parent and daughter branches.
a local clocks model differs from an autocorrelated clock by setting a single rate throughout a contiguous section of the tree, allowing relatively few such clocks in different parts of the tree, with abrupt shifts in rate between these clocks.
an uncorrelated clock has a distinct rate along each branch, with the rates drawn at random from a specified probability distribution, thus allowing random and frequent rate shifts.
the uncorrelated lognormal  model draws its rates from a lognormal distribution and appears to be more robust to violation of assumptions about clock rate variation, and a better fit to simulated and empirical datasets, than are strict or autocorrelated clock models  <cit> .
moreover, studies differ in whether they find support for uncorrelated clocks  <cit>  or correlated clocks  <cit> .
if rates shift infrequently and are conserved along lineages, then dating using either an uncorrelated or correlated model could be inaccurate and local models can be a better fit  <cit> .
having the means to detect if and when rates shift, and to correct branch lengths accordingly, could be critically important to evolutionary analysis using molecular phylogenies.
the random local clocks  model proposes and compares a series of alternative local molecular clocks, each potentially arising on any branch and extending over a contiguous part of the phylogeny.
in beast, the rlc model parameters  are estimated simultaneously with phylogenetic relationships in a bayesian framework  <cit> .
in a real and a simulated phylogeny that included abrupt and sustained rate shifts, rlc outperformed ucln in terms of accuracy of divergence-time estimates, and ucln estimates were misleadingly precise  <cit> .
to date, there have not been comparisons of rlc and ucln models based on multiple phylogenies exhibiting rate heterogeneity among lineages.
as modelling of dna substitution rates directly affects estimation of dates, the assumptions of underlying rate models should be biologically realistic.
for example, if substitution rates depend upon certain life history traits, then abrupt shifts in these traits might suggest an rlc clock model is preferable to ucln.
although the determinants of rate variation among lineages are often unclear  <cit> , undoubtedly there are lineage-specific effects that result from shifts in life history and life forms in different clades of organisms.
among mammals, generation time is strongly negatively correlated with substitution rate, and is explained by the sequestering of the female germ line  early in the development of the female  <cit> .
plants also show a negative relationship between substitution rate and generation time  <cit> , though the primary cause is unclear because, in contrast to mammals, female gametes are produced multiple times during the life of the individual.
recently, it has been shown that plant height correlates better with rate than does generation time – taller plants have slower rates  <cit> .
these authors suggest that the rate of mitosis in apical meristems may be the determining factor because taller plants have slower growth at their tips.
here, we use a simulation approach to evaluate the performance of rlc and ucln models.
we simulate multiple trees having a long-stemmed clade with a known crown age, and then simulate dna datasets on these trees so that there is a large downward shift in substitution rate associated with the long stem.
we compare the accuracy of the rlc and ucln clock models in retrieving the known crown age of the long-stemmed clade, and also use marginal likelihoods to determine which model is the better fit.
we compare these results with those we obtain using australian grass trees , a group that is expected to show a slower substitution rate than their relatives.
as the crown age of xanthorrhoea is unknown, we compare the performance of the ucln and rlc clock models using marginal likelihoods to determine which is the better fit.
xanthorrhoea is a genus of arborescent grasstrees and a characteristic plant of the fire-dependent sclerophyll biome with nutrient-poor soils in western, southern and eastern australia, sometimes dominating the shrub layer.
it is the only genus in xanthorrhoeaceae subfamily xanthorrhoeoideae.
extant xanthorrhoea appears to have undergone major morphological and ecological transformations compared with the last common ancestor that it shared with its worldwide sister groups .
the latter clades have diverse morphologies and life histories but most are smaller and faster-maturing plants than xanthorrhoea.
several traits in xanthorrhoea lead us to predict that this lineage evolves more slowly than its sister groups.
the plants have a palm-like form with one or few apical meristems and are long-lived  with slow apical growth   <cit>  and reproductive maturity may not be reached until 20– <dig> years of age  <cit> .
reproduction in xanthorrhoea occurs mainly in the first spring following a wildfire  <cit>   and, in the sclerophyll biome, estimates of intervals between fires range from 3– <dig> to 10– <dig> yr  <cit> .
thus, generation time is likely longer even than is indicated by the slow growth rates alone.
it has been suggested that both generation time  and the rate of apical growth  are negatively related to dna substitution rate in plants  <cit> .
mutations occur when dna is replicated and cells divide  and are passed to the next generation; thus variation in both generation time  <cit>  and plant height  <cit>  are likely to explain variation in dna substitution rates.
we test the hypothesis of a substitution rate shift downwards in xanthorrhoea by using the well-known relative rates test that assumes no phylogeny  <cit> , followed by a phylogenetic test that corrects for the confounding effect of within-clade rate variation .
we then use bayesian phylogenetics  to estimate the crown age for xanthorrhoea with the same combinations of clock and tree models as used on the simulated datasets.
we consider the implications of our results for the estimation of clade ages when rates vary among lineages.
RESULTS
simulations of strong among-clade substitution rate variation
our simulated datasets were designed to mirror our understanding of the evolution of the xanthorrhoeaceae, i.e.
a phylogenetic tree including a long-stemmed “broom” clade, a slow molecular clock and a crown with no internal calibration, and a “bush” sister clade with a short stem, faster clock and internal calibration .
the major difference was that, in the simulated dataset, the crown age of the slow-clock clade was known in advance.
as expected, in the beast analyses, the rlc clock model  outperformed ucln  and accurately reconstructed the abrupt and sustained change in substitution rate occurring along the long internal branch of the broom clade .
the true crown age of the broom clade in each simulated dataset was  <dig> ma.
under rlc, the mean age estimate for this node was  <dig>  ma  with a birth-death phylogenetic tree model, and  <dig>   ma with a yule model .
in all rlc analyses, the true age fell within the 95% bci of the estimate.
by contrast, under ucln, the mean estimates were much younger, being  <dig>   ma  and  <dig>   ma , and the upper  limit of the 95% bci never contained the true age .
age estimates under the two clock models were significantly different  for both tree models .
by contrast, comparisons between the yule and birth-death age estimates within each clock model did not find significant differences .
under rlc , the number of rate shifts inferred was small  across all ten simulated datasets.
the simulated trees varied in size from  <dig> to  <dig> terminals, and in the proportion of terminals in the bush vs broom clades, from  <dig> vs  <dig> to  <dig> vs  <dig> .
there was no evidence that the date estimates showed a systematic relationship with either tree size  or relative clade sizes.
for all  <dig> simulated datasets, bayes factors calculated from marginal likelihoods found “very strong” support  for rlc over ucln under both the birth-death and yule phylogenetic tree models.figure  <dig>
example of a simulated chronogram .
tree parameters were based on those of xanthorrhoeaceae and were simulated using tess using a birth-death model, and “broom” and “bush” sister clades.
the age of the root was fixed at  <dig> ma, that of the broom crown node at  <dig> ma, as marked with open circles.
dna sequences were then simulated along the branches of the trees using a gtr + Γ substitution model with slow  and fast  rates , as in xanthorrhoeaceae, to test the relative performance of the ucln and rlc clock models.
the simulated trees varied in size from  <dig> to  <dig> terminals, and also in the proportion of terminals in the bush vs broom clades, from  <dig> vs  <dig> to  <dig> vs  <dig>  for the beast analyses, three log-normal age-calibration priors were used: one was placed on the stem of the broom clade and two were placed on the stem of each of two clades internal to the bush clade .
the mean and offset of each calibration prior were equal to half the distance between the crown and stem nodes of the respective clade.
a maximum likelihood phylogram estimated from dna sequences simulated on the tree in figure
1
.
we simulated a  <dig> kb sequence set using the r package phylosim with a gtr + Γ model of substitution , with the alpha parameter set to  <dig>  substitution rates were modelled by setting the probability of each particular substitution in a q matrix, with a probability  <dig> times higher in the bush clade than in the broom clade.
see text for the full set of parameter values.
branch lengths are proportional to the substitution rates and illustrate the overall 10x rate difference between the broom and bush clades, and additionally, the stochasticity built into the model.
the phylogram was generated in cipres using raxml with a gtr + Γ model.
reconstruction of the simulated chronogram  using beast with the rlc clock model and calibration priors as shown on figure
1
.
each estimate assumed a gtr + Γ substitution model.
branches are colored by inferred local clock rates in the introns partition: red = fast, blue = slow, and each branch is labelled with the estimated rate .
estimated age with 95% bci is shown for the broom crown node .
reconstruction of the simulated chronogram  using beast with the ucln clock model and calibration priors as shown on figure
1
.
each estimate assumed a gtr + Γ substitution model.
branches are colored by inferred local clock rates in the introns partition: red = fast, blue = slow, and each branch is labelled with the estimated rate .
estimated age  is shown for the broom crown node .
estimated crown ages of long-stemmed “broom” clades in simulated trees using beast with ucln and rlc clock models in combination with birth-death  and yule  phylogenetic tree models.
trees were simulated using tess with a bd model and sequences simulated on the trees using phylosim with a local clock model in which the substitution rate was 10x slower in the broom clade than in its sister “bush” clade.
each large dot represents the mean age across  <dig> simulated trees, error bars are mean 95% bcis, and small open circles represent the extreme 95% bcis across all  <dig> datasets.
the horizontal broken line shows the true age  of the broom crown node.
xanthorrhoeaceae phylogeny
to derive a secondary age calibration for the crown node of xanthorrhoeaceae, a phylogenetic dating analysis was carried out on a broad sample of monocots including multiple fossil calibration points and using sequences of the chloroplast regions ndhf and trnl-f. the resulting topologies of both the raxml and beast trees  were congruent with published trees  <cit>  and returned strong support for monophyly of xanthorrhoeaceae and its subfamilies, and for a sister group relationship between xanthorrhoea and hemerocallidoideae.
partitioned and non-partitioned models made little difference to the topologies, except in clades with poor resolution, e.g., within the crown of xanthorrhoea.
the maximum likelihood  analysis indicated rate heterogeneity within xanthorrhoeaceae, insofar as xanthorrhoeoideae have much shorter branches than in the other two subfamilies .from the xanthorrhoeaceae-only datasets, which were comprehensively sampled at the species level, cpdna and rpb <dig> both yielded maximum likelihood trees in which the branch lengths were conspicuously shorter within xanthorrhoea than in the sister groups .
the cpdna tree differs from the monocot tree in placing xanthorrhoea sister to asphodeloideae but with weak support .
in contrast, the rpb <dig> tree shows xanthorrhoea nested within successively paraphyletic groups of hemerocallidoideae and asphodeloideae.
paralogous copies of rpb <dig> are evident, e.g.
clones from individuals of phormium are in separate lineages , though xanthorrhoea is monophyletic .
with both loci and under both clock models, beast gave topologies  that were substantively the same as those from raxml , at least for well-supported nodes.figure  <dig>
random local clocks  chronogram of xanthorrhoeaceae from combined
ndhf
and
trnl
-
trnf
sequences.
analysis used beast with a yule tree model.
branches are colored by inferred local clock rates: red = fastest, blue = slowest, orange and green = intermediate, and each branch is labelled with the actual rate .
filled pointers show likely rate shifts ; open pointers show possible alternatives.
clade labels with bars indicate subfamilies.
the scale indicates time before present .
rlc chronogram of xanthorrhoeaceae derived from sequences of
rpb2
.
analysis used beast with a yule tree model.
branches are colored by inferred local clock rates in the introns partition: red = fast, blue = slow, and each branch is labelled with the actual rate .
pointers show the two inferred rate shifts: one downwards in the mrca of xanthorrhoeoideae , followed by a second shift , which was either a further downward shift in the stem of the large upper clade or a small upward shift in the stem of the x. macronema + x. gracilis clade.
the pattern of exon rates and shifts is essentially similar but slower .
clade labels with bars indicate subfamilies.
the scale indicates time before present .
bayesian model fitting in xanthorrhoeaceae
a posteriori bayes factor tests using the marginal likelihoods from the beast analyses found a clear preference among alternative models in all three datasets .
partitioned loci were preferred to non-partitioned “very strongly”  <cit>  in both the monocots-cpdna and xanthorrhoeaceae-rpb <dig> datasets, while non-partitioned loci were preferred in the xanthorrhoeaceae-cpdna dataset.
all tests indicated a preference for yule over birth-death tree models, very strongly in most cases.
comparison of clock models in the xanthorrhoeaceae-only datasets  found a strong preference for rlc over ucln in both loci .
clock comparisons could not be made in the large monocot-cpdna dataset because twelve separate analyses using rlc did not reach stationarity or convergence after  <dig> m generations.
this failure is not surprising given reports of similar difficulties with estimating the parameters for this model  <cit> .
the problem appears to arise from inefficient sampling by the markov chains when transitions between alternative states require large moves  <cit>  and is exacerbated in large and/or complex datasets.
results presented from the beast analyses are all from the preferred model combinations shown in table  <dig>  except where specified otherwise for comparative purposes.table  <dig>
model comparisons using bayes factors calculated from marginal likelihoods in beast
dataset
preferred model combination
non-preferred model combination
bayes factor with interpretation
within each dataset, model comparisons follow the nested sequence: partitioned  vs non-partitioned  loci; birth-death  vs yule phylogenetic tree models; and uncorrelated lognormal  vs random local clocks .
each row compares the bolded models, with other models held constant.
for each dataset, the best model combination overall  is indicated, and in each case is  strongly preferred to the second best.
asterisks after the bayes factors indicate their interpretation according to  <cit> : ** = “strong”  and *** = “very strong”  evidence favouring the model with the higher lnl.
results are shown for path sampling only because those from stepping stone sampling were identical.
are substitution rates slow in xanthorrhoea?
substitution rates were compared across xanthorrhoea and its outgroups using the relative rates test, local clock permutation test and results of the beast analyses, and all indicated a markedly slower rate in xanthorrhoea than in its close relatives.
the simple relative rate test  <cit>  does not assume a phylogenetic tree and makes pairwise comparisons of sequence dissimilarities between two groups relative to an outgroup to assess whether the two sets of dissimilarities are significantly different.
we used uncorrected p-distances among sequences and found significant substitution rate differences between xanthorrhoea and its sister groups  in both loci  and relative to both alternate outgroup sequences : two-tailed mann–whitney u-test, p <  <dig>  in every case.
the local-clock permutation test  <cit>  is a phylogenetic tree-based randomisation test that corrects for within-clade rate variation.
we performed one-tailed lcpt tests, which showed that substitution rate has been significantly slower in xanthorrhoea than in its sister groups, both in cpdna  and in rpb <dig> .
from the beast posteriors, estimated rates in cpdna were slower in xanthorrhoeaceae than in monocots as a whole and, within the family, slower for both loci in xanthorrhoeoideae than in the other two subfamilies .
the median substitution rate in xanthorrhoeaceae was considerably slower in cpdna than in rpb <dig> introns, under both the ucln  and rlc  clocks, and marginally slower than in the exons .
this result was consistent with the pattern observed across plants generally .
for example, gaut  <cit>  estimated the synonymous rate across multiple plastid genes to be  <dig>  , which overlaps our estimate of  <dig>   across monocots .
his estimate for nuclear genes of  <dig>   is faster than ours but this could reflect conservatism in rpb <dig>  or the generally slower rates in xanthorrhoeaceae, or that we have not distinguished synonymous from non-synonymous rates.
rate shifts within xanthorrhoeaceae
the pattern of rate variation within the trees inferred by beast differed considerably between clock models, as expected.
for both loci, under the ucln clock most branches had a different rate from their parent , though rates within xanthorrhoea varied less, and were generally lower, than in the sister groups.
by contrast, the rlc model inferred a small number of local clocks, with few shifts between them .
for both loci, substitution rates inferred within the xanthorrhoea crown by rlc were much lower than from ucln, by an order of magnitude or more, and were significantly different because the 95% bcis do not overlap .
this result was expected following the relative rates tests.
by contrast, the ucln clock-rate differences between these taxa were neither as large nor significant, though cpdna rates in xanthorrhoeaceae were significantly slower than in monocots overall .
to test whether the number of rate shifts inferred under the rlc model using the real data departed significantly from the null expectation , we ran priors-only analyses  and compared overlap between the two distributions for this parameter .
the relaxed local clocks  model inferred 3– <dig>  substitution rate shifts in the cpdna posterior and ≤  <dig> in rpb <dig> .
in both loci , the prior expectation of a single  molecular clock was rejected, as there was essentially no overlap between the 95% bcis of the prior and posterior distributions of the “ratechangecount” parameter, the priors being 0– <dig> in both loci .
additionally, fisher exact tests indicate that each pair of prior and posterior distributions is significantly different .
downward rate shifts in xanthorrhoea were inferred either at the base of the stem  or within the crown  and these low rates were sustained throughout the crown in all three partitions.
within the rpb <dig> crown of xanthorrhoea, the rlc clock inferred two shifts to rates that are slower than in the stem but it is unclear whether these shifts occurred sequentially or independently .
in cpdna, one or two sequential downward rate shifts are inferred in xanthorrhoea: one shift in the stem, possibly followed by a smaller shift at the crown node .
although neither individual shift was significant , the cumulative change between the mrca of asphodeloideae + xanthorrhoea  and the crown of the latter  was significant.
given that rate shifts can be detected only at nodes, this result is consistent with either  one or more incremental downward shifts along the stem of xanthorrhoea  and/or  independent shifts within the xanthorrhoea crown.
age estimates within xanthorrhoea
age estimates within xanthorrhoea by beast varied among loci and clock models, though the effect of clocks was greater .
the most significant differences occurred in the xanthorrhoea crown age estimates .
when comparing the same model across the different loci, the estimates were almost identical  but the differences were large and significant between clock models.
estimates under ucln  were much younger than those under rlc .
moreover, the 95% bcis did not overlap between estimates from the different clocks .
stem-age estimates varied less between models than did crown ages .
from the xanthorrhoeaceae-cpdna dataset, the estimate for the xanthorrhoea stem was almost identical under both clock models  and older in the monocot-cpdna dataset , though the 95% bcis overlap .
from rpb <dig>  the median stem ages were very similar under both models and younger  than the estimates from cpdna, though the bcis overlapped .table  <dig>
ages of selected nodes estimated by beast
dataset
clock model
tree model
partitioned
node age estimates
xanthorr-hoeaceae crown
xanthorr-hoea
stem
xanthorrhoea
crown
hemerocall-idoideae crown
asphodel-oideae crown
ucln
yule
yes
<dig>
<dig>
<dig>
<dig>
<dig>
rlc
yule
no
<dig>
<dig>
<dig>
<dig>
<dig>
xanthorrhoeaceae, rpb2
rlc
yule
yes
<dig>
<dig>
<dig>
-
-
the xanthorrhoea crown was the target node for dating, being the broom clade with no internal calibration.
in the two xanthorrhoeaceae datasets , the root  was calibrated with a normal prior, mean =  <dig>  sd =  <dig> .
rows with bolded text have the best-fit model combination for each dataset as assessed by bayes factors using marginal likelihoods estimated from beast using path and stepping-stone sampling.
bci = 95% bayesian confidence internal.
ucln = uncorrelated lognormal clock.
rlc = random local clocks.
estimated age of the
xanthorrhoea
crown from three datasets.
estimates are from beast with ucln and rlc clock models in combination with birth-death and yule speciation models.
dna substitution models were partitioned  based on the results of bayes factor tests for each dataset.
each data point represents the median age estimate for a different combination of data and models and error bars are 95% bcis.
asterisks mark the best combination of models for each dataset , as indicated by bayes factors.
abbreviation: xanth = xanthorrhoeaceae.
against the general trend, the age estimated for the xanthorrhoea crown under rlc with birth-death for rpb <dig>  was much younger than the other rlc estimates and within the range of estimates from ucln .
this reconstruction infers a downward rate shift in the xanthorrhoea stem that remains unchanged throughout the crown for the introns , and a single rate throughout xanthorrhoeaceae for the exons .
however, it should be noted that the yule model was very strongly preferred to birth-death for rpb <dig>  and gave an age estimate well within the range of other rlc estimates for this node .
discussion
node age estimates differ significantly between uncorrelated and correlated clock models
our beast analyses of the simulated datasets returned accurate dates under the rlc clock whereas ucln invariably failed to retrieve the true date, even within the 95% bcis.
using a single simulated tree, dornburg et al.
<cit>  also obtained more accurate age estimates with rlc than ucln.
with the latter clock, their estimates were misleadingly precise, i.e.
ulcn gave narrower bcis than did rlc, but was less accurate.
the simulations presented here go further than  <cit>  by using multiple simulated datasets with different tree sizes and relative clade sizes, and by explicitly testing the accuracy of age estimation in uncalibrated “broom” clades.
thus we have shown that accurate age estimates depend upon accurate clock modelling, and that these results are not an artefact of a particular tree shape or relative clade sizes.
we conclude that, for data predicted to include local clocks, dating with rlc is much more likely to be accurate than with ucln.
median age estimates within xanthorrhoeaceae differ by an order of magnitude under the two clock models .
this is the direct consequence of the differences in substitution rates inferred under each model.
the most striking differences lie in estimates for the xanthorrhoea crown: the median ages vary from  <dig>  to  <dig> ma and, with a single exception , the 95% bcis do not overlap between the different clocks for a given locus and phylogenetic tree model combination .
in contrast, crown age estimates from different loci under the same clock are close , and the bcis overlap substantially.
median age estimates also differ between clocks, by 10– <dig> ma, for the xanthorrhoea stem and the asphodeloideae crown .
as the bayes factor tests indicated a clear preference  for the rlc model over ucln, combined with the yule tree model, it appears likely that the age of the xanthorrhoea crown is about  <dig>  to  <dig>  ma with a wide range of uncertainty .
where rlc locates rate shifts influences dates
in both the simulated and empirical datasets, a relatively small number of rate shifts, with rate conservation along lineages between shifts, are inferred by rlc.
however, the exact number of rate shifts under rlc , and their location on the phylogeny, are usually uncertain.
even when it appears clear that a rate shift has occurred between a parent node and its immediate daughter, the shift could have occurred anywhere along the branch connecting these nodes.
this uncertainty is greater in longer branches, e.g., the stem of xanthorrhoea.
another source of uncertainty is whether a net directional rate shift in a clade has occurred in a single large step or cumulatively in several smaller steps along successive branches.
such uncertainty can critically affect dating of a particular node.
for example, an anomalously young date  was estimated for the xanthorrhoea crown node using rlc with a birth-death speciation prior from the rpb <dig> dataset .
this analysis reconstructed a single downward rate shift at the stem node  but, in contrast, rlc with yule reconstructed two smaller shifts, both within the crown  and, consequently, a much older age  for the crown node .
thus, the rlc clock, even if appropriate for the data, does not necessarily reconstruct dates accurately .
as the combination of yule with rlc was very strongly preferred to birth-death + rlc by the marginal likelihood tests, the anomalously young date from the latter combination could be discounted in this case.
nevertheless, the question remains of why the birth-death and yule models returned a large difference in age estimates for the xanthorrhoea crown and reconstructed rate shifts that were similar but at different nodes.
perhaps the difference resulted from an interaction between the phylogenetic-branching and rate-shift parameters along the stem of xanthorrhoea .
it could have arisen from mis-specification of the phylogenetic branching model, a known issue  <cit> , because the only difference between these two analyses was the use of the alternative phylogenetic branching models.
substitution rates have slowed in xanthorrhoea
we have found strong evidence in favour of a lineage effect  <cit>  in substitution rates within xanthorrhoeaceae.
that is, the molecular clock ticks much more slowly in xanthorrhoea than in the rest of the family in general.
multiple lines of evidence support these conclusions:  significant results from both relative rates tests ;  rejection of a single clock across the family by comparing the prior versus posterior estimates of the number of rate shifts under the rlc  model;  inference by beast of downward rate shifts, of about an order of magnitude, in the stem and/or crown of xanthorrhoea; and  replication of these findings in two loci from genomes  with different modes of inheritance.
life history and substitution rates
given that two unlinked loci in different genomes show the downward rate shift in xanthorrhoea, the likely cause is a factor that affects both genomes rather than locus-specific factors such as selection, or genome-specific effects such as polymerase error rate or efficiency of dna repair  <cit> .
instead, the concerted rate shifts in these unlinked loci suggest a factor external to the genomes, such as life-history, speciation rate, or environmental factors that affect the metabolic rate  <cit> .
given that xanthorrhoea occurs across a wide range of latitude and moisture regimes, and co-occurs with multiple species from its sister groups, environment is unlikely to be the cause of the rate shift.
our results are consistent with previous studies that found that plant lineages with life history traits similar to xanthorrhoea also have slow rates of molecular evolution.
these traits include an arborescent palm-like life form, longevity, slow growth rate and single or few-branched stems.
the palm-like life form has one or few apical meristems and is likely to have a slower overall rate of mitosis than much-branched plants with many growing tips.
our results are also consistent with earlier findings that speciation rate and substitution rate are positively correlated, though the causal factors are unclear  <cit> : xanthorrhoea has fewer species  and a slower rate of substitution than its sister groups   <cit> .
within xanthorrhoea, rates appear to vary with growth habit: x. macronema and x. gracilis have rpb <dig> substitution rates at least twice as fast as in other grasstrees  and differ from them in being trunkless, softer and grass-like.
xanthorrhoea gracilis is shallow-rooted and can be killed by fire more readily than the other species  <cit> .
however, the underlying factors linking multiple correlated life-history traits to molecular evolutionary rates remain unclear.
as fewer-branched plants have fewer apical meristems, the mitosis hypothesis  <cit> , which posits that substitution rate is correlated with the number of mitotic events, could be tested by comparing substitution rates among plant lineages that differ in their degree of branching but have otherwise similar life histories.
implications for macroevolution
the possibility that ucln significantly under-estimates the age of broom clades has implications for macroevolutionary investigations using molecular dating.
for example, in xanthorrhoea, the rlc model preferred by our analyses suggests a crown age of 24– <dig> ma, implying that xanthorrhoea diversified from about the end of the eocene.
the broom crown of this clade, combined with the long stem, suggests that an extinction event  occurred at this time, when global climate deteriorated significantly, and then the clade re-diversified through the oligocene and miocene.
this timing and diversification pattern are congruent with those in other taxa co-occurring with xanthorrhoea in the australian temperate sclerophyll biome, such as callitris , casuarinaceae, eucalypteae , and pea-flowered legumes , which are considered to have responded to the same climate-change event  <cit> .
in contrast, the much younger crown ages obtained using ucln for xanthorrhoea , but rejected by our tests, would favour a conclusion that extinction and re-radiation occurred during the pliocene and pleistocene.
this timing does not coincide with the similar diversification shifts in the other taxa.
other areas of investigation might also be biased by clock model mis-specification.
for example, vicariance hypotheses for the origins of the new caledonian biota have been rejected after divergence times for multiple clades with sisters in other landmasses were found to be too young compared with geological separation  <cit> .
similarly, claims that new zealand drowned completely during the oligocene have gained support from clade-age estimates that post-date the geological emergence of the islands as subaerial land  <cit> .
the age of any such clades that were broom-shaped and dated using ucln should be reassessed using rlc and marginal likelihood model comparisons.
CONCLUSIONS
we have shown that large dating errors can result from the ucln clock model  if its assumptions are violated.
neither clock is necessarily superior in general: model choice should be contingent upon how well a given dataset meets its assumptions.
in datasets with clade-specific substitution rates, the rlc model provides a significantly more accurate approach than the ucln model, especially in long-branch clades that lack calibrations.
we found significant differences in age estimates using these models with such datasets, whether simulated or empirical .
in simulated rate-heterogeneous phylogenies with a slowly evolving “broom” clade, the uncorrelated clocks model always significantly underestimated the true age of the broom crown, whereas the random local clocks model consistently succeeded.
ucln likely underestimates the age of uncalibrated broom clades because the uncorrelated model is poor at detecting rate shifts  <cit> .
calibration of the broom can reduce this dating error but it does not correct model mis-specification  <cit> .
therefore, it is important to compare the suitability of both models by using a priori criteria  or a posteriori marginal likelihood tests.
more extensive studies of clock models are needed to determine their applicability to different kinds of datasets  <cit> .
for instance, local clocks and autocorrelated clocks are similar in principle but differ in the number of rate shifts allowed and we did not compare these clocks in this study.
in analyses of xanthorrhoea, the two clock models led to very different conclusions about the evolution of the genus: rapid diversification with severe aridification in the pliocene/pleistocene  or diversification following the onset of global cooling and drying in the miocene .
life history traits of xanthorrhoea suggested that the substitution rate might be slower than in its sister groups, and use of the rlc clock was supported by relative rate testing and marginal likelihood tests.
the older crown age  estimated for xanthorrhoea by the preferred rlc model is consistent with re-diversification following the end-eocene extinctions, as inferred in co-occurring taxa and attributed to global climate change.
a challenge for the future will be to determine the timing of substitution rate shifts more accurately because uncertainty can severely affect dating.
currently, resolution of this uncertainty requires independent evidence, such as fossil-based calibration at critical nodes, e.g.
in broom clades.

 molecular-clock dating of long-stemmed clades is prone to large estimation errors partly because calibration points can be placed only at nodes, not part-way along stems. likewise, shifts in substitution rate along lineages can be detected only at nodes, and cannot be placed within unbroken stems. as molecular dating depends upon accuracy of rate modelling, inferred rate variation within long branches has been hypothesized to contribute to dating error, e.g. in the crown node of angiosperms. calibration is critically important for reducing error in molecular dating, for instance by improving estimates of rate heterogeneity among lineages. conversely, estimation error is greater in target clades when calibrations are experimentally omitted. furthermore, abrupt rate shifts in some lineages of a phylogeny, followed by rate conservation, can mislead rate and age estimation, even when the node of interest is calibrated. a strict molecular clock has been rejected in analyses of most empirical datasets, and is inapplicable to data in which rate shifts occur, so relaxed molecular clock models are used widely. commonly used relaxed clocks include uncorrelated, autocorrelated and local clocks. in an autocorrelated clock, the rate along a given branch is more similar to its parent branch than a branch chosen at random, though autocorrelation models differ in the degree to which they restrict rate variation between parent and daughter branches. a local clocks model differs from an autocorrelated clock by setting a single rate throughout a contiguous section of the tree, allowing relatively few such clocks in different parts of the tree, with abrupt shifts in rate between these clocks. an uncorrelated clock has a distinct rate along each branch, with the rates drawn at random from a specified probability distribution, thus allowing random and frequent rate shifts. the uncorrelated lognormal model draws its rates from a lognormal distribution and appears to be more robust to violation of assumptions about clock rate variation, and a better fit to simulated and empirical datasets, than are strict or autocorrelated clock models. moreover, studies differ in whether they find support for uncorrelated clocks or correlated clocks. if rates shift infrequently and are conserved along lineages, then dating using either an uncorrelated or correlated model could be inaccurate and local models can be a better fit. having the means to detect if and when rates shift, and to correct branch lengths accordingly, could be critically important to evolutionary analysis using molecular phylogenies. the random local clocks model proposes and compares a series of alternative local molecular clocks, each potentially arising on any branch and extending over a contiguous part of the phylogeny. in beast, the rlc model parameters are estimated simultaneously with phylogenetic relationships in a bayesian framework. in a real and a simulated phylogeny that included abrupt and sustained rate shifts, rlc outperformed ucln in terms of accuracy of divergence-time estimates, and ucln estimates were misleadingly precise. to date, there have not been comparisons of rlc and ucln models based on multiple phylogenies exhibiting rate heterogeneity among lineages. as modelling of dna substitution rates directly affects estimation of dates, the assumptions of underlying rate models should be biologically realistic. for example, if substitution rates depend upon certain life history traits, then abrupt shifts in these traits might suggest an rlc clock model is preferable to ucln. although the determinants of rate variation among lineages are often unclear, undoubtedly there are lineage-specific effects that result from shifts in life history and life forms in different clades of organisms. among mammals, generation time is strongly negatively correlated with substitution rate, and is explained by the sequestering of the female germ line early in the development of the female. plants also show a negative relationship between substitution rate and generation time, though the primary cause is unclear because, in contrast to mammals, female gametes are produced multiple times during the life of the individual. recently, it has been shown that plant height correlates better with rate than does generation time – taller plants have slower rates. these authors suggest that the rate of mitosis in apical meristems may be the determining factor because taller plants have slower growth at their tips. here, we use a simulation approach to evaluate the performance of rlc and ucln models. we simulate multiple trees having a long-stemmed clade with a known crown age, and then simulate dna datasets on these trees so that there is a large downward shift in substitution rate associated with the long stem. we compare the accuracy of the rlc and ucln clock models in retrieving the known crown age of the long-stemmed clade, and also use marginal likelihoods to determine which model is the better fit. we compare these results with those we obtain using australian grass trees, a group that is expected to show a slower substitution rate than their relatives. as the crown age of xanthorrhoea is unknown, we compare the performance of the ucln and rlc clock models using marginal likelihoods to determine which is the better fit. xanthorrhoea is a genus of arborescent grasstrees and a characteristic plant of the fire-dependent sclerophyll biome with nutrient-poor soils in western, southern and eastern australia, sometimes dominating the shrub layer. it is the only genus in xanthorrhoeaceae subfamily xanthorrhoeoideae. extant xanthorrhoea appears to have undergone major morphological and ecological transformations compared with the last common ancestor that it shared with its worldwide sister groups. the latter clades have diverse morphologies and life histories but most are smaller and faster-maturing plants than xanthorrhoea. several traits in xanthorrhoea lead us to predict that this lineage evolves more slowly than its sister groups. the plants have a palm-like form with one or few apical meristems and are long-lived with slow apical growth and reproductive maturity may not be reached until 20– years of age. reproduction in xanthorrhoea occurs mainly in the first spring following a wildfire and, in the sclerophyll biome, estimates of intervals between fires range from 3– to 10– yr. thus, generation time is likely longer even than is indicated by the slow growth rates alone. it has been suggested that both generation time and the rate of apical growth are negatively related to dna substitution rate in plants. mutations occur when dna is replicated and cells divide and are passed to the next generation; thus variation in both generation time and plant height are likely to explain variation in dna substitution rates. we test the hypothesis of a substitution rate shift downwards in xanthorrhoea by using the well-known relative rates test that assumes no phylogeny, followed by a phylogenetic test that corrects for the confounding effect of within-clade rate variation. we then use bayesian phylogenetics to estimate the crown age for xanthorrhoea with the same combinations of clock and tree models as used on the simulated datasets. we consider the implications of our results for the estimation of clade ages when rates vary among lineages.  simulations of strong among-clade substitution rate variation our simulated datasets were designed to mirror our understanding of the evolution of the xanthorrhoeaceae, i.e. a phylogenetic tree including a long-stemmed “broom” clade, a slow molecular clock and a crown with no internal calibration, and a “bush” sister clade with a short stem, faster clock and internal calibration. the major difference was that, in the simulated dataset, the crown age of the slow-clock clade was known in advance. as expected, in the beast analyses, the rlc clock model outperformed ucln and accurately reconstructed the abrupt and sustained change in substitution rate occurring along the long internal branch of the broom clade. the true crown age of the broom clade in each simulated dataset was ma. under rlc, the mean age estimate for this node was ma with a birth-death phylogenetic tree model, and ma with a yule model. in all rlc analyses, the true age fell within the 95% bci of the estimate. by contrast, under ucln, the mean estimates were much younger, being ma and ma, and the upper limit of the 95% bci never contained the true age. age estimates under the two clock models were significantly different for both tree models. by contrast, comparisons between the yule and birth-death age estimates within each clock model did not find significant differences. under rlc, the number of rate shifts inferred was small across all ten simulated datasets. the simulated trees varied in size from to terminals, and in the proportion of terminals in the bush vs broom clades, from vs to vs. there was no evidence that the date estimates showed a systematic relationship with either tree size or relative clade sizes. for all simulated datasets, bayes factors calculated from marginal likelihoods found “very strong” support for rlc over ucln under both the birth-death and yule phylogenetic tree models.figure example of a simulated chronogram. tree parameters were based on those of xanthorrhoeaceae and were simulated using tess using a birth-death model, and “broom” and “bush” sister clades. the age of the root was fixed at ma, that of the broom crown node at ma, as marked with open circles. dna sequences were then simulated along the branches of the trees using a gtr + Γ substitution model with slow and fast rates, as in xanthorrhoeaceae, to test the relative performance of the ucln and rlc clock models. the simulated trees varied in size from to terminals, and also in the proportion of terminals in the bush vs broom clades, from vs to vs for the beast analyses, three log-normal age-calibration priors were used: one was placed on the stem of the broom clade and two were placed on the stem of each of two clades internal to the bush clade. the mean and offset of each calibration prior were equal to half the distance between the crown and stem nodes of the respective clade. a maximum likelihood phylogram estimated from dna sequences simulated on the tree in figure 1. we simulated a kb sequence set using the r package phylosim with a gtr + Γ model of substitution, with the alpha parameter set to substitution rates were modelled by setting the probability of each particular substitution in a q matrix, with a probability times higher in the bush clade than in the broom clade. see text for the full set of parameter values. branch lengths are proportional to the substitution rates and illustrate the overall 10x rate difference between the broom and bush clades, and additionally, the stochasticity built into the model. the phylogram was generated in cipres using raxml with a gtr + Γ model. reconstruction of the simulated chronogram using beast with the rlc clock model and calibration priors as shown on figure 1. each estimate assumed a gtr + Γ substitution model. branches are colored by inferred local clock rates in the introns partition: red = fast, blue = slow, and each branch is labelled with the estimated rate. estimated age with 95% bci is shown for the broom crown node. reconstruction of the simulated chronogram using beast with the ucln clock model and calibration priors as shown on figure 1. each estimate assumed a gtr + Γ substitution model. branches are colored by inferred local clock rates in the introns partition: red = fast, blue = slow, and each branch is labelled with the estimated rate. estimated age is shown for the broom crown node. estimated crown ages of long-stemmed “broom” clades in simulated trees using beast with ucln and rlc clock models in combination with birth-death and yule phylogenetic tree models. trees were simulated using tess with a bd model and sequences simulated on the trees using phylosim with a local clock model in which the substitution rate was 10x slower in the broom clade than in its sister “bush” clade. each large dot represents the mean age across simulated trees, error bars are mean 95% bcis, and small open circles represent the extreme 95% bcis across all datasets. the horizontal broken line shows the true age of the broom crown node. xanthorrhoeaceae phylogeny to derive a secondary age calibration for the crown node of xanthorrhoeaceae, a phylogenetic dating analysis was carried out on a broad sample of monocots including multiple fossil calibration points and using sequences of the chloroplast regions ndhf and trnl-f. the resulting topologies of both the raxml and beast trees were congruent with published trees and returned strong support for monophyly of xanthorrhoeaceae and its subfamilies, and for a sister group relationship between xanthorrhoea and hemerocallidoideae. partitioned and non-partitioned models made little difference to the topologies, except in clades with poor resolution, e.g., within the crown of xanthorrhoea. the maximum likelihood analysis indicated rate heterogeneity within xanthorrhoeaceae, insofar as xanthorrhoeoideae have much shorter branches than in the other two subfamilies.from the xanthorrhoeaceae-only datasets, which were comprehensively sampled at the species level, cpdna and rpb both yielded maximum likelihood trees in which the branch lengths were conspicuously shorter within xanthorrhoea than in the sister groups. the cpdna tree differs from the monocot tree in placing xanthorrhoea sister to asphodeloideae but with weak support. in contrast, the rpb tree shows xanthorrhoea nested within successively paraphyletic groups of hemerocallidoideae and asphodeloideae. paralogous copies of rpb are evident, e.g. clones from individuals of phormium are in separate lineages, though xanthorrhoea is monophyletic. with both loci and under both clock models, beast gave topologies that were substantively the same as those from raxml, at least for well-supported nodes.figure random local clocks chronogram of xanthorrhoeaceae from combined ndhf and trnl - trnf sequences. analysis used beast with a yule tree model. branches are colored by inferred local clock rates: red = fastest, blue = slowest, orange and green = intermediate, and each branch is labelled with the actual rate. filled pointers show likely rate shifts; open pointers show possible alternatives. clade labels with bars indicate subfamilies. the scale indicates time before present. rlc chronogram of xanthorrhoeaceae derived from sequences of rpb2. analysis used beast with a yule tree model. branches are colored by inferred local clock rates in the introns partition: red = fast, blue = slow, and each branch is labelled with the actual rate. pointers show the two inferred rate shifts: one downwards in the mrca of xanthorrhoeoideae, followed by a second shift, which was either a further downward shift in the stem of the large upper clade or a small upward shift in the stem of the x. macronema + x. gracilis clade. the pattern of exon rates and shifts is essentially similar but slower. clade labels with bars indicate subfamilies. the scale indicates time before present. bayesian model fitting in xanthorrhoeaceae a posteriori bayes factor tests using the marginal likelihoods from the beast analyses found a clear preference among alternative models in all three datasets. partitioned loci were preferred to non-partitioned “very strongly” in both the monocots-cpdna and xanthorrhoeaceae-rpb datasets, while non-partitioned loci were preferred in the xanthorrhoeaceae-cpdna dataset. all tests indicated a preference for yule over birth-death tree models, very strongly in most cases. comparison of clock models in the xanthorrhoeaceae-only datasets found a strong preference for rlc over ucln in both loci. clock comparisons could not be made in the large monocot-cpdna dataset because twelve separate analyses using rlc did not reach stationarity or convergence after m generations. this failure is not surprising given reports of similar difficulties with estimating the parameters for this model. the problem appears to arise from inefficient sampling by the markov chains when transitions between alternative states require large moves and is exacerbated in large and/or complex datasets. results presented from the beast analyses are all from the preferred model combinations shown in table  except where specified otherwise for comparative purposes.table model comparisons using bayes factors calculated from marginal likelihoods in beast dataset preferred model combination non-preferred model combination bayes factor with interpretation within each dataset, model comparisons follow the nested sequence: partitioned vs non-partitioned loci; birth-death vs yule phylogenetic tree models; and uncorrelated lognormal vs random local clocks. each row compares the bolded models, with other models held constant. for each dataset, the best model combination overall is indicated, and in each case is strongly preferred to the second best. asterisks after the bayes factors indicate their interpretation according to: ** = “strong” and *** = “very strong” evidence favouring the model with the higher lnl. results are shown for path sampling only because those from stepping stone sampling were identical. are substitution rates slow in xanthorrhoea? substitution rates were compared across xanthorrhoea and its outgroups using the relative rates test, local clock permutation test and results of the beast analyses, and all indicated a markedly slower rate in xanthorrhoea than in its close relatives. the simple relative rate test does not assume a phylogenetic tree and makes pairwise comparisons of sequence dissimilarities between two groups relative to an outgroup to assess whether the two sets of dissimilarities are significantly different. we used uncorrected p-distances among sequences and found significant substitution rate differences between xanthorrhoea and its sister groups in both loci and relative to both alternate outgroup sequences: two-tailed mann–whitney u-test, p <  in every case. the local-clock permutation test is a phylogenetic tree-based randomisation test that corrects for within-clade rate variation. we performed one-tailed lcpt tests, which showed that substitution rate has been significantly slower in xanthorrhoea than in its sister groups, both in cpdna and in rpb. from the beast posteriors, estimated rates in cpdna were slower in xanthorrhoeaceae than in monocots as a whole and, within the family, slower for both loci in xanthorrhoeoideae than in the other two subfamilies. the median substitution rate in xanthorrhoeaceae was considerably slower in cpdna than in rpb introns, under both the ucln and rlc clocks, and marginally slower than in the exons. this result was consistent with the pattern observed across plants generally. for example, gaut estimated the synonymous rate across multiple plastid genes to be, which overlaps our estimate of across monocots. his estimate for nuclear genes of is faster than ours but this could reflect conservatism in rpb or the generally slower rates in xanthorrhoeaceae, or that we have not distinguished synonymous from non-synonymous rates. rate shifts within xanthorrhoeaceae the pattern of rate variation within the trees inferred by beast differed considerably between clock models, as expected. for both loci, under the ucln clock most branches had a different rate from their parent, though rates within xanthorrhoea varied less, and were generally lower, than in the sister groups. by contrast, the rlc model inferred a small number of local clocks, with few shifts between them. for both loci, substitution rates inferred within the xanthorrhoea crown by rlc were much lower than from ucln, by an order of magnitude or more, and were significantly different because the 95% bcis do not overlap. this result was expected following the relative rates tests. by contrast, the ucln clock-rate differences between these taxa were neither as large nor significant, though cpdna rates in xanthorrhoeaceae were significantly slower than in monocots overall. to test whether the number of rate shifts inferred under the rlc model using the real data departed significantly from the null expectation, we ran priors-only analyses and compared overlap between the two distributions for this parameter. the relaxed local clocks model inferred 3– substitution rate shifts in the cpdna posterior and ≤  in rpb. in both loci, the prior expectation of a single molecular clock was rejected, as there was essentially no overlap between the 95% bcis of the prior and posterior distributions of the “ratechangecount” parameter, the priors being 0– in both loci. additionally, fisher exact tests indicate that each pair of prior and posterior distributions is significantly different. downward rate shifts in xanthorrhoea were inferred either at the base of the stem or within the crown and these low rates were sustained throughout the crown in all three partitions. within the rpb crown of xanthorrhoea, the rlc clock inferred two shifts to rates that are slower than in the stem but it is unclear whether these shifts occurred sequentially or independently. in cpdna, one or two sequential downward rate shifts are inferred in xanthorrhoea: one shift in the stem, possibly followed by a smaller shift at the crown node. although neither individual shift was significant, the cumulative change between the mrca of asphodeloideae + xanthorrhoea and the crown of the latter was significant. given that rate shifts can be detected only at nodes, this result is consistent with either one or more incremental downward shifts along the stem of xanthorrhoea and/or independent shifts within the xanthorrhoea crown. age estimates within xanthorrhoea age estimates within xanthorrhoea by beast varied among loci and clock models, though the effect of clocks was greater. the most significant differences occurred in the xanthorrhoea crown age estimates. when comparing the same model across the different loci, the estimates were almost identical but the differences were large and significant between clock models. estimates under ucln were much younger than those under rlc. moreover, the 95% bcis did not overlap between estimates from the different clocks. stem-age estimates varied less between models than did crown ages. from the xanthorrhoeaceae-cpdna dataset, the estimate for the xanthorrhoea stem was almost identical under both clock models and older in the monocot-cpdna dataset, though the 95% bcis overlap. from rpb the median stem ages were very similar under both models and younger than the estimates from cpdna, though the bcis overlapped.table ages of selected nodes estimated by beast dataset clock model tree model partitioned node age estimates xanthorr-hoeaceae crown xanthorr-hoea stem xanthorrhoea crown hemerocall-idoideae crown asphodel-oideae crown ucln yule yes rlc yule no xanthorrhoeaceae, rpb2 rlc yule yes - - the xanthorrhoea crown was the target node for dating, being the broom clade with no internal calibration. in the two xanthorrhoeaceae datasets, the root was calibrated with a normal prior, mean =  sd = . rows with bolded text have the best-fit model combination for each dataset as assessed by bayes factors using marginal likelihoods estimated from beast using path and stepping-stone sampling. bci = 95% bayesian confidence internal. ucln = uncorrelated lognormal clock. rlc = random local clocks. estimated age of the xanthorrhoea crown from three datasets. estimates are from beast with ucln and rlc clock models in combination with birth-death and yule speciation models. dna substitution models were partitioned based on the results of bayes factor tests for each dataset. each data point represents the median age estimate for a different combination of data and models and error bars are 95% bcis. asterisks mark the best combination of models for each dataset, as indicated by bayes factors. abbreviation: xanth = xanthorrhoeaceae. against the general trend, the age estimated for the xanthorrhoea crown under rlc with birth-death for rpb was much younger than the other rlc estimates and within the range of estimates from ucln. this reconstruction infers a downward rate shift in the xanthorrhoea stem that remains unchanged throughout the crown for the introns, and a single rate throughout xanthorrhoeaceae for the exons. however, it should be noted that the yule model was very strongly preferred to birth-death for rpb and gave an age estimate well within the range of other rlc estimates for this node. discussion node age estimates differ significantly between uncorrelated and correlated clock models our beast analyses of the simulated datasets returned accurate dates under the rlc clock whereas ucln invariably failed to retrieve the true date, even within the 95% bcis. using a single simulated tree, dornburg et al. also obtained more accurate age estimates with rlc than ucln. with the latter clock, their estimates were misleadingly precise, i.e. ulcn gave narrower bcis than did rlc, but was less accurate. the simulations presented here go further than by using multiple simulated datasets with different tree sizes and relative clade sizes, and by explicitly testing the accuracy of age estimation in uncalibrated “broom” clades. thus we have shown that accurate age estimates depend upon accurate clock modelling, and that these results are not an artefact of a particular tree shape or relative clade sizes. we conclude that, for data predicted to include local clocks, dating with rlc is much more likely to be accurate than with ucln. median age estimates within xanthorrhoeaceae differ by an order of magnitude under the two clock models. this is the direct consequence of the differences in substitution rates inferred under each model. the most striking differences lie in estimates for the xanthorrhoea crown: the median ages vary from to ma and, with a single exception, the 95% bcis do not overlap between the different clocks for a given locus and phylogenetic tree model combination. in contrast, crown age estimates from different loci under the same clock are close, and the bcis overlap substantially. median age estimates also differ between clocks, by 10– ma, for the xanthorrhoea stem and the asphodeloideae crown. as the bayes factor tests indicated a clear preference for the rlc model over ucln, combined with the yule tree model, it appears likely that the age of the xanthorrhoea crown is about to ma with a wide range of uncertainty. where rlc locates rate shifts influences dates in both the simulated and empirical datasets, a relatively small number of rate shifts, with rate conservation along lineages between shifts, are inferred by rlc. however, the exact number of rate shifts under rlc, and their location on the phylogeny, are usually uncertain. even when it appears clear that a rate shift has occurred between a parent node and its immediate daughter, the shift could have occurred anywhere along the branch connecting these nodes. this uncertainty is greater in longer branches, e.g., the stem of xanthorrhoea. another source of uncertainty is whether a net directional rate shift in a clade has occurred in a single large step or cumulatively in several smaller steps along successive branches. such uncertainty can critically affect dating of a particular node. for example, an anomalously young date was estimated for the xanthorrhoea crown node using rlc with a birth-death speciation prior from the rpb dataset. this analysis reconstructed a single downward rate shift at the stem node but, in contrast, rlc with yule reconstructed two smaller shifts, both within the crown and, consequently, a much older age for the crown node. thus, the rlc clock, even if appropriate for the data, does not necessarily reconstruct dates accurately. as the combination of yule with rlc was very strongly preferred to birth-death + rlc by the marginal likelihood tests, the anomalously young date from the latter combination could be discounted in this case. nevertheless, the question remains of why the birth-death and yule models returned a large difference in age estimates for the xanthorrhoea crown and reconstructed rate shifts that were similar but at different nodes. perhaps the difference resulted from an interaction between the phylogenetic-branching and rate-shift parameters along the stem of xanthorrhoea. it could have arisen from mis-specification of the phylogenetic branching model, a known issue, because the only difference between these two analyses was the use of the alternative phylogenetic branching models. substitution rates have slowed in xanthorrhoea we have found strong evidence in favour of a lineage effect in substitution rates within xanthorrhoeaceae. that is, the molecular clock ticks much more slowly in xanthorrhoea than in the rest of the family in general. multiple lines of evidence support these conclusions: significant results from both relative rates tests; rejection of a single clock across the family by comparing the prior versus posterior estimates of the number of rate shifts under the rlc model; inference by beast of downward rate shifts, of about an order of magnitude, in the stem and/or crown of xanthorrhoea; and replication of these findings in two loci from genomes with different modes of inheritance. life history and substitution rates given that two unlinked loci in different genomes show the downward rate shift in xanthorrhoea, the likely cause is a factor that affects both genomes rather than locus-specific factors such as selection, or genome-specific effects such as polymerase error rate or efficiency of dna repair. instead, the concerted rate shifts in these unlinked loci suggest a factor external to the genomes, such as life-history, speciation rate, or environmental factors that affect the metabolic rate. given that xanthorrhoea occurs across a wide range of latitude and moisture regimes, and co-occurs with multiple species from its sister groups, environment is unlikely to be the cause of the rate shift. our results are consistent with previous studies that found that plant lineages with life history traits similar to xanthorrhoea also have slow rates of molecular evolution. these traits include an arborescent palm-like life form, longevity, slow growth rate and single or few-branched stems. the palm-like life form has one or few apical meristems and is likely to have a slower overall rate of mitosis than much-branched plants with many growing tips. our results are also consistent with earlier findings that speciation rate and substitution rate are positively correlated, though the causal factors are unclear: xanthorrhoea has fewer species and a slower rate of substitution than its sister groups. within xanthorrhoea, rates appear to vary with growth habit: x. macronema and x. gracilis have rpb substitution rates at least twice as fast as in other grasstrees and differ from them in being trunkless, softer and grass-like. xanthorrhoea gracilis is shallow-rooted and can be killed by fire more readily than the other species. however, the underlying factors linking multiple correlated life-history traits to molecular evolutionary rates remain unclear. as fewer-branched plants have fewer apical meristems, the mitosis hypothesis, which posits that substitution rate is correlated with the number of mitotic events, could be tested by comparing substitution rates among plant lineages that differ in their degree of branching but have otherwise similar life histories. implications for macroevolution the possibility that ucln significantly under-estimates the age of broom clades has implications for macroevolutionary investigations using molecular dating. for example, in xanthorrhoea, the rlc model preferred by our analyses suggests a crown age of 24– ma, implying that xanthorrhoea diversified from about the end of the eocene. the broom crown of this clade, combined with the long stem, suggests that an extinction event occurred at this time, when global climate deteriorated significantly, and then the clade re-diversified through the oligocene and miocene. this timing and diversification pattern are congruent with those in other taxa co-occurring with xanthorrhoea in the australian temperate sclerophyll biome, such as callitris, casuarinaceae, eucalypteae, and pea-flowered legumes, which are considered to have responded to the same climate-change event. in contrast, the much younger crown ages obtained using ucln for xanthorrhoea, but rejected by our tests, would favour a conclusion that extinction and re-radiation occurred during the pliocene and pleistocene. this timing does not coincide with the similar diversification shifts in the other taxa. other areas of investigation might also be biased by clock model mis-specification. for example, vicariance hypotheses for the origins of the new caledonian biota have been rejected after divergence times for multiple clades with sisters in other landmasses were found to be too young compared with geological separation. similarly, claims that new zealand drowned completely during the oligocene have gained support from clade-age estimates that post-date the geological emergence of the islands as subaerial land. the age of any such clades that were broom-shaped and dated using ucln should be reassessed using rlc and marginal likelihood model comparisons.  we have shown that large dating errors can result from the ucln clock model if its assumptions are violated. neither clock is necessarily superior in general: model choice should be contingent upon how well a given dataset meets its assumptions. in datasets with clade-specific substitution rates, the rlc model provides a significantly more accurate approach than the ucln model, especially in long-branch clades that lack calibrations. we found significant differences in age estimates using these models with such datasets, whether simulated or empirical. in simulated rate-heterogeneous phylogenies with a slowly evolving “broom” clade, the uncorrelated clocks model always significantly underestimated the true age of the broom crown, whereas the random local clocks model consistently succeeded. ucln likely underestimates the age of uncalibrated broom clades because the uncorrelated model is poor at detecting rate shifts. calibration of the broom can reduce this dating error but it does not correct model mis-specification. therefore, it is important to compare the suitability of both models by using a priori criteria or a posteriori marginal likelihood tests. more extensive studies of clock models are needed to determine their applicability to different kinds of datasets. for instance, local clocks and autocorrelated clocks are similar in principle but differ in the number of rate shifts allowed and we did not compare these clocks in this study. in analyses of xanthorrhoea, the two clock models led to very different conclusions about the evolution of the genus: rapid diversification with severe aridification in the pliocene/pleistocene or diversification following the onset of global cooling and drying in the miocene. life history traits of xanthorrhoea suggested that the substitution rate might be slower than in its sister groups, and use of the rlc clock was supported by relative rate testing and marginal likelihood tests. the older crown age estimated for xanthorrhoea by the preferred rlc model is consistent with re-diversification following the end-eocene extinctions, as inferred in co-occurring taxa and attributed to global climate change. a challenge for the future will be to determine the timing of substitution rate shifts more accurately because uncertainty can severely affect dating. currently, resolution of this uncertainty requires independent evidence, such as fossil-based calibration at critical nodes, e.g. in broom clades. 
estimating divergence times in phylogenies using a molecular clock depends on accurate modeling of nucleotide substitution rates in dna sequences. we compare the results of simulations to empirical results from analyses of a real rate-heterogeneous taxon – australian grass trees – whose substitution rate is slower than in its sister groups, as determined by relative rate tests. divergence timessubstitution rate heterogeneityuncorrelated lognormal clockrandom local clocksrelative rateslife historyxanthorrhoeaissue-copyright-statement© the author 2014 rate heterogeneity among lineages is likely to affect estimates, especially in lineages with long stems and short crowns and no internal calibration. in the simulated datasets, the rlc model performed much better than ucln: rlc correctly estimated the age of the crown node of slow-rate broom clades, whereas ucln estimates were consistently too young. in both real and simulated datasets, bayes factor tests strongly favored the rlc model over the ucln model. we evaluate the performance of the random local clocks model and the more routinely employed uncorrelated lognormal relaxed clock model in situations in which a significant rate shift occurs on the stem branch of a broom clade. in particular, for data predicted to have more rate variation among than within clades, dating with rlc is much more likely to be accurate than with ucln. similarly, in the xanthorrhoea dataset, ucln returned significantly younger crown ages than rlc. the choice of an unsuitable molecular clock model can strongly bias divergence time estimates.
 estimating divergence times in phylogenies using a molecular clock depends on accurate modeling of nucleotide substitution rates in dna sequences. rate heterogeneity among lineages is likely to affect estimates, especially in lineages with long stems and short crowns and no internal calibration. we evaluate the performance of the random local clocks model and the more routinely employed uncorrelated lognormal relaxed clock model in situations in which a significant rate shift occurs on the stem branch of a broom clade. we compare the results of simulations to empirical results from analyses of a real rate-heterogeneous taxon – australian grass trees – whose substitution rate is slower than in its sister groups, as determined by relative rate tests.  in the simulated datasets, the rlc model performed much better than ucln: rlc correctly estimated the age of the crown node of slow-rate broom clades, whereas ucln estimates were consistently too young. similarly, in the xanthorrhoea dataset, ucln returned significantly younger crown ages than rlc. in both real and simulated datasets, bayes factor tests strongly favored the rlc model over the ucln model.  the choice of an unsuitable molecular clock model can strongly bias divergence time estimates. in particular, for data predicted to have more rate variation among than within clades, dating with rlc is much more likely to be accurate than with ucln. the choice of clocks should be informed by the biology of the study group or assessed with relative rate tests and post-hoc model comparisons. electronic supplementary material the online version of this article contains supplementary material, which is available to authorized users. keywords divergence timessubstitution rate heterogeneityuncorrelated lognormal clockrandom local clocksrelative rateslife historyxanthorrhoeaissue-copyright-statement© the author 2014 