BACKGROUND
understanding the diversification history of species-rich clades is a major goal in evolutionary biology  <cit>  as they provide important insights into the evolution of life on earth.
with over  <dig>  plant species, magnoliidae, sensu cantino et al.
<cit> , are the largest clade of flowering plants outside monocots and eudicots and comprise four orders: canellales , laurales , magnoliales , and piperales .
investigating the diversification of magnoliidae is of primary importance to provide guidance for future hypotheses on the drivers of diversification of flowering plants as a whole.
in addition, many organisms  are highly dependent on this group for feeding or reproduction  <cit> , and magnoliid species are an important part of tropical ecosystems  <cit> .
as a consequence, investigating their tempo and mode of diversification will provide key knowledge to understand not only the evolutionary history of magnoliidae as a whole, but also that of these related groups  <cit>  and of the environments they live in  <cit> .
it has often been suggested that the biology of angiosperms has a great influence on their own diversification  <cit> .
the biology of magnoliidae differs from that of eudicots and monocots in several respects.
for instance, most members of magnoliidae are mainly pollinated by beetles, flies, or thrips, while, in contrast to eudicots and monocots, bee or wind pollination are rare  <cit> .
in addition, floral and vegetative morphology of magnoliidae is highly variable and several of these variable traits have been shown to be associated with variation of diversification rates in other flowering plant lineages  <cit> .
previous molecular dating studies at large  or narrow  taxonomic scale have suggested that the crown node age of magnoliidae is older than the crown nodes of both eudicots and monocots, ranging from  <dig>  to  <dig>  myr  <cit> , and that several of the  <dig> families of magnoliidae appear to have originated before the end of the cretaceous  <cit> .
in addition, the ages of numerous nodes within magnoliidae have yet to be estimated  <cit> .
in parallel, few studies have focused on the diversification of the group, being either at the scale of all angiosperms  <cit>  or within families  <cit> .
in the present study, we provide for the first time a complete time scale for magnoliidae at the familial level.
we then use this new time scale to test for significant diversification rate shifts during the evolutionary history of the clade.
to do so, we take advantage of a recent improvement in the phylogeny of the group  <cit>  and a new revision of the rich fossil record of magnoliidae providing reliable minimum-age calibration points  <cit> .
in order to conduct these analyses for nodes above and below the family level, we used a dataset including more than 75% of the existing genera and  <dig> molecular markers from the three plant genomes .
RESULTS
temporal analyses
all runs in each of the five beast analyses with different calibration scheme  converged effectively.
the concatenated post-burn-in samples of the four runs in each analyses showed final effective sampling sizes  of the likelihood far above  <dig> .
except for the position of siparunaceae  and magnoliaceae , which remained unresolved in all analyses, the great majority of the relationships among the families received high support values  and is similar in all analyses .
conducting beast analyses without molecular data highlighted the non-uniformity of the temporal constraints effectively used in the analyses .
however, no effective temporal priors violated the paleontological information used to calibrate the present analyses.
in addition, the temporal posterior distributions of calibrated nodes obtained with the molecular data differ from the effective temporal prior distributions obtained without these data.
these mismatches for calibrated nodes suggest that molecular data are well informative.
the 95% credibility intervals of the ages obtained with beast are larger than those obtained with r8s .
when the maximum age of the root varied, only the ages estimated for the crown node of magnoliidae, and the splits between canellales and piperales, and between laurales and magnoliales, are significantly different in the beast analyses .
on the contrary, in the pl analyses, the majority of age estimates are significantly different when the maximum age of the root is changed .figure  <dig>
age estimates for the root and different nodes within the tree of magnoliidae.
estimates are in million years, and the root is constrained with a maximum age.
names of families refer to the crown node ages except when sl  is mentioned.
a, beast analyses with mean age estimates and 95% credibility intervals.
b, r8s  analyses with best-scoring ml tree age and 95% credibility intervals.
*the stem lineage of siparunaceae, in the beast analysis with the maximum age of angiosperms set to  <dig> million years, did not correspond to the same node in other analyses.
abbreviation: sl, stem lineage.
in general, the ages estimated in beast and r8s were similar .
in the present paper, we take into account the overlapping 95% credibility intervals of all  <dig> analyses .
our results support an origin of extant magnoliidae  between  <dig>  and  <dig>  myr, that is, in the lower cretaceous or the jurassic.
the crown nodes of canellales, laurales, magnoliales, and piperales are dated to  <dig> - <dig>  myr,  <dig> - <dig>  myr,  <dig> - <dig>  myr, and  <dig> - <dig>  myr, respectively.
by the end of the cretaceous , most families  were probably present, with the exception of canellaceae, myristicaceae and winteraceae.
the oldest families in terms of crown node age are aristolochiaceae and calycanthaceae  or aristolochiaceae and lauraceae , depending on the relaxed clock method used .table  <dig>
age estimates for selected nodes of magnoliidae
angio 130
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all age estimates are in million years.
the first line corresponds to beast estimates  and the second line to r8s  estimates.
95% credibility intervals  are followed in brackets by mean estimates for beast analyses and best-scoring ml tree estimates for r8s analyses.
abbreviations: angio- <dig>  angio- <dig>  angio- <dig>  angio- <dig>  and angio- <dig> correspond to the different maximum age constraints applied to the root .
the names of taxa refer to their crown node except if sl  is mentioned.
*the stem lineage of siparunaceae, in the beast analysis with the maximum age of angiosperms set to  <dig> million years, did not correspond with the same crown node than in other analyses.
diversification analyses
our medusa analyses on  <dig> posterior beast trees of the angio- <dig> and angio- <dig> calibration schemes resulted in very similar scenarios for the mode of diversification within magnoliidae .
the two maximum clade credibility trees used to summarize results are identical in terms of relationships.
we identified six to  <dig> significant diversification rate shifts across magnoliidae.
in both cases, models including nine shifts were the most often selected among the  <dig> trees sampled .
the mean of the initial net diversification rate  at the crown node of magnoliidae is estimated to  <dig>  ±  <dig>  species per million years  in angio- <dig>  and  <dig>  ±  <dig>  sp.myr− <dig> in angio- <dig>  when considering shifts present in more than 50% of the trees , five main shifts in net diversification rates within magnoliidae are identified .
three are decreases and two are increases: 1) at the crown node of the clade of piperaceae and saururaceae ; 2) at the crown node of piperaceae excluding verhuellia ; 3) at the crown node of calycanthaceae ; 4) at the crown node of the clade of degeneria and galbulimima ; 5) at the stem node of tribe miliuseae of annonaceae .
in addition to those five main shifts, the net diversification rate averaged over the sample of  <dig> trees show a general increase both within the laurales and within the magnoliales .
our estimates of the relative extinction rate  at the crown node of magnoliidae are  <dig>  ±  <dig>   and  <dig>  ±  <dig>   .
this rate remained relatively high  in magnoliidae except in laurales and part of piperales.figure  <dig>
diversification analyses.
results of the medusa analyses obtained using  <dig> posterior trees randomly sampled from the beast posterior: a, angio- <dig>  b, angio- <dig>  topologies are the maximum clade credibility tree of  <dig> randomly selected trees .
names of terminals refer to compartments defined in the methods sections and detailed in additional file  <dig>  branch colors illustrate the mean net diversification rate .
red dots denote significant shifts in r, their size being proportional to their frequency among the  <dig> trees tested.
numbered shifts in figure 2a:  <dig>  crown node of the clade of piperaceae and saururaceae;  <dig>  crown node of the clade of piperaceae excluding verhuellia;  <dig>  crown node of calycanthaceae;  <dig>  crown node of the clade of himantandraceae and degeneriaceae;  <dig>  crown node of the clade of miliuseae and monocarpia.
the diagram in the top-right corner represents the frequency of the different model sizes  in the 1000-model collections for the two analyses .
abbreviations: sp., species; myr, million years.
discussion
tempo of magnoliidae evolution
we provide here for the first time a near complete temporal framework for the evolution of magnoliidae above the generic level.
applying different maximum age constraints to the crown node of angiosperms highlighted the sensitivity of inferred ages estimated for the deepest nodes of magnoliidae .
although previous studies have recognized a long gap in the fossil record of the angiosperm stem lineage  <cit> , there is no indisputable argument in favor of one particular maximum age constraint for the crown node of angiosperms.
here we will systematically consider the whole range of age estimates obtained across our five maximum age calibration schemes and both molecular dating approaches used.
we restricted ourselves to conservative fossil age constraints based on phylogenetic analyses of fossil and extant taxa  <cit> .
this led us to consider only  <dig> out of more than  <dig> described fossils putatively belonging to magnoliidae  <cit> .
however, our new age estimates for families and orders of magnoliidae appear, in general, to be compatible with the putative fossil record attributed to each of these taxa.
future investigations of the phylogenetic placement of other magnoliid fossils will likely provide additional minimum age constraints, which could push back in time several young estimates supported in the present study, and decrease the size of the credibility intervals.
this study further illustrates that, just as paleontological dating, molecular dating estimates are often associated with large uncertainties.
the latter approach has to be seen as an attempt to reduce the range of the most likely ages for nodes constrained by the age of the fossil record securely placed and dated, and to evaluate the probability of the ages of nodes for which there is no direct fossil record.
because all the ambiguity of our current knowledge has to be taken into account, the molecular dating approach cannot provide exact secure ages, except for exceptionally fossil-rich clades.
based on this most reliable knowledge in the field of paleobotany of magnoliidae  <cit>  and chrono-stratigraphy  <cit> , combined with a comprehensive sample of taxa and molecular markers, our data support an origin of extant lineages of magnoliidae  during the jurassic or lower cretaceous between  <dig>  and  <dig>  myr.
this result tend to be older than previously suggested  <cit> .
for example, the angiosperm-wide study of bell et al.
<cit> , in which  <dig> magnoliid genera were sampled, estimated the crown node of magnoliidae to be between  <dig> and  <dig> myr.
in another, more recent angiosperm-wide analysis sampling  <dig> species of magnoliidae and using a pl approach, zanne et al.
<cit>  estimated the age of the crown node of magnoliidae to be  <dig> myr without uncertainty associated.
our new estimates for the crown-group age of orders also tend to be older than previously inferred  <cit>  .
however, some studies have supported much older ages for these nodes  <cit> .
at the familial level, in addition to providing the first estimates for the ages of crown-group canellaceae , saururaceae , and winteraceae , the crown nodes of families are also generally dated to an older range of dates than previously estimated  <cit> , with the exception of atherospermataceae  for which we found a younger age than previously suggested  <cit> .
the large amount of combinations of parameters influencing age estimates limits straightforward explanations of these differences with previous studies .
despite variation among the ages obtained for the crown ages of families, our results confirm that magnoliidae diversified into morphologically distinct clades  by the end of the cretaceous , but probably earlier than thought before  <cit> .
this provides arguments in favor of an earlier diversification of angiosperms altogether, with the presence of more flowering plant lineages in the cretaceous than previously thought.
finally, taking into account the whole range of age estimates obtained across our five different calibration schemes, leads to long ranges of age estimates that are compatible with biogeographic scenarios previously suggested in magnoliidae  <cit> .
however, viewed in isolation, the different assumptions about the maximum age of angiosperms lead to alternative time scales for the evolutionary history of the families of magnoliidae.
therefore, biogeographic scenarios will need to be reevaluated in the context of explicit assumptions on the age of the angiosperms.
mode of diversification of magnoliidae
the new timetree obtained for magnoliidae in this study allowed us to detect an average of nine significant diversification rate shifts across lineages, implying that diversification has not been a homogeneous process throughout the history of the clade .
explaining the present day diversity of species-rich clades has generally required several diversification rate shifts, but previous studies using the same statistical approach in other large angiosperm clades found, in general, fewer shifts than in the present analysis.
within eudicots, beaulieu and donoghue  <cit>  detected six shifts in campanulidae , koenen et al.
<cit>  detected nine shifts in fabaceae , xi et al.
<cit>  found five significant shifts in malpighiales , and arakaki et al.
<cit>  found seven shifts in cactaceae .
within monocots, escudero and hipp  <cit>  supported three shifts in the family cyperaceae  while baker and couvreur  <cit>  identified up to  <dig> shifts in palms .
despite the dependence of the number of shifts detected on the taxonomic level of tips in the chronograms used , it seems that magnoliidae experienced a high variation in diversification rates.
because of their longer evolutionary history in comparison with these other clades and because their fossil record supports a global distribution during the cretaceous and the paleogene  <cit> , magnoliidae as a whole may have been affected by more events potentially influencing the speciation and extinction rates .
establishing the causes affecting diversification-rate variation can be difficult.
there is a large diversity of intrinsic and extrinsic traits known to influence speciation and extinction  <cit> , all of them being potentially correlated to each other  <cit> .
the influence of a trait on the birth and death of species is dependent on other taxa, other traits of the same organism, and its physical environment  <cit> , implying that a trait could have different effects on different clades.
finally, the actual shift of diversification may happen several nodes after the evolution of an influencing trait.
one explanation could be that an isolated trait will influence diversification in combination with other characters, the effect appearing when the entire set of traits needed is present  <cit> .
for these reasons, the investigation of the correlation between traits and diversification rates will need to take into account as many potential factors as possible  <cit> .
the older estimates of the ages in the “angio-200” hypothesis led to slightly lower absolute rates of diversification than in the “angio-140” hypothesis, as expected.
because the general pattern  is the same in both analyses, in the present paragraph we refer only to rates of the angio- <dig> analysis.
the background net diversification rate obtained in the tree of magnoliidae  is comparable to those found in angiosperms  <cit> .
in the present study, the lowest net diversification rates, resulting from shifts  <dig> and  <dig> , were found in the crown group of calycanthaceae , and in the branches of degeneriaceae and himantandraceae .
these three families share distinctive floral features not or seldom found in other magnoliidae groups, such as the presence of inner staminodes that cover the stigma at the end of the female phase  <cit> , and spiral phyllotaxy of all floral organs  <cit> .
however, it is difficult to link these two characters with mechanisms sustaining a low diversification rate .
within calycanthaceae, the low rate of net diversification is associated with a low speciation rate for the entire clade  and near-zero extinction .
the absence of extinction would seem contradictory with the presence of several fossils in the cretaceous  <cit>  and could be an artefact of the method which does not take into account the extinct diversity .
however, because the phylogenetic position of these fossils within the family has not been tested , it is difficult to draw conclusions about extinction within the family.
the pollination systems of calycanthaceae involve trapping of a large variety of beetles and thrips  <cit> .
in comparison with specific pollination systems involving a unique relationship for the two partners, this generalist interaction is not favorable for genetic isolation promoting diversification  <cit> .
in addition, calycanthaceae have a temperate distribution, except for the monospecific genus idiospermum growing in a restricted area in north-east australia.
the low ecological limits on species richness in temperate areas  <cit>  could provide an explanation for the low diversification of the lineage leading to the genera calycanthus and chimonanthus.
on the other hand, the apparent lack of diversification of the lineage leading to idiospermum could be explained by different causes.
individuals of this species are long-living trees  <cit>  involving low fixation rates in diverging populations.
the genus is restricted to the very wet humid tropical lowland rainforests of australia  <cit> .
idiospermum presents one of the heaviest seeds among australian plants and is therefore probably not dispersed by animals, limiting its capacity of dispersion  <cit> .
if this low capacity of dispersion is ancestral in the lineage leading to the extant species of the genus, it restrained the number of available areas promoting diversification  <cit> .
this latter explanation might be generalized for all calycanthaceae as the seeds of the family contain secondary metabolites that are toxic at least for mammals  <cit> .
the highest diversification rate inferred in this study was found on the branch leading to the terminal compartment miliuseae in subfamily malmeoideae of annonaceae .
a shift of + <dig>  ±  <dig>  sp.myr− <dig> at the node sustaining the branch of this clade was present in 71% of the trees tested and the associated rate of speciation on the branch is on average equal to  <dig>  sp.myr− <dig>  couvreur et al.
<cit>  found that major clades in annonaceae have undergone different rates of diversification, with subfamily malmeoideae  having significantly higher rates than subfamily annonoideae .
however, analyses of family-level lineage-through-time plots  did not detect significant shits in diversification rates during most of the evolutionary history of annonaceae  <cit> .
erkens et al.
<cit> , using a tree with fewer taxa and two alternative approaches to detect rate shifts, identified up to three diversification rate shifts in annonaceae, including the one we detected here at the crown of miliuseae.
reasons for an increase in diversification within miliuseae are not yet well known but could be related to founder effects after dispersal into south-east asia or distinctive pollen characters  <cit> .
canellales and piperales have, on average, higher speciation rates than magnoliales and laurales.
within piperales, this may be explained by widespread herbaceous habits, resulting in faster life history  and higher fixation rates in divergent populations  <cit> .
in addition, within this order, aristolochiaceae typically have zygomorphic flowers, which has been shown to have a positive impact on diversification  <cit> .
however, canellales and piperales also share the highest extinction rates, making laurales and magnoliales the most productive orders in terms of net diversification.
differences in extinction rates are difficult to explain.
for instance, there are no major differences in pollination systems among the four orders  <cit> , and their current geographic distributions are similar  <cit> .
however, doyle and endress  <cit>  found several synapomorphies for the clade of laurales and magnoliales, specifically the presence of more than two whorls of stamens and more than one whorl or series of carpels.
these characters might have played a role in relation to pollination, but the underlying mechanisms remain unknown.
finally, even though the medusa approach represents a significant conceptual improvement over previous models, it still requires several important assumptions that may have influenced our results.
first, medusa does not implement diversification models in which the extinction rate can be higher than speciation rates.
second, the rates are assumed to be constant in each part of the tree, and only abrupt variations are evaluated, probably not in accordance with the biological reality in which rates could gradually fluctuate.
morlon et al.,  <cit>  recently developed an approach specifically to relax these two assumptions, but it is not implemented yet to detect shifts automatically nor to analyze higher-level phylogenies with terminally unresolved clades.
in addition, rabosky  <cit>  recently developed a new bayesian framework to detect multiple diversification processes in a tree while allowing the speciation rate to vary continuously through time, but it is not available yet for a set of multiple trees and therefore cannot take phylogenetic and dating uncertainty into account.
last, because the fossil record is not taken into account in the diversification rate analyses, very low rates of speciation and extremely low extinction rates are always allocated to the old lineages with few species , which have probably been more diverse in the past .
new research efforts are currently being made in this area  <cit> .
therefore, our understanding of magnoliidae diversification may further improve in the future when more realistic methods and more complete phylogenies are available.
CONCLUSIONS
the present study suggests that magnoliidae began to diversify somewhere between the toarcian  and the barremian , or  <dig> - <dig>  myr ago.
several key nodes within magnoliidae are dated here for the first time.
in general, our age estimates suggest a possibly older diversification of the group than previously inferred.
the rich fossil record of magnoliidae may eventually provide additional calibration points to refine the time scale proposed here.
however, considerable work remains to be done to securely relate this extinct diversity to the extant one, a task for which an integrated morphological dataset will be essential.
the tempo and mode of diversification within this clade appears to be characterized by several increases and decreases of diversification rates, suggesting that magnoliidae have not undergone constant diversification but have instead been shaped by alternative, yet to be determined evolutionary processes.
our new dated trees provide a solid basis for future biogeographical studies and robust statistical tests of correlation among intrinsic traits, extrinsic factors, and diversification rates within magnoliidae.

 understanding the diversification history of species-rich clades is a major goal in evolutionary biology as they provide important insights into the evolution of life on earth. with over plant species, magnoliidae, sensu cantino et al., are the largest clade of flowering plants outside monocots and eudicots and comprise four orders: canellales, laurales, magnoliales, and piperales. investigating the diversification of magnoliidae is of primary importance to provide guidance for future hypotheses on the drivers of diversification of flowering plants as a whole. in addition, many organisms are highly dependent on this group for feeding or reproduction, and magnoliid species are an important part of tropical ecosystems. as a consequence, investigating their tempo and mode of diversification will provide key knowledge to understand not only the evolutionary history of magnoliidae as a whole, but also that of these related groups and of the environments they live in. it has often been suggested that the biology of angiosperms has a great influence on their own diversification. the biology of magnoliidae differs from that of eudicots and monocots in several respects. for instance, most members of magnoliidae are mainly pollinated by beetles, flies, or thrips, while, in contrast to eudicots and monocots, bee or wind pollination are rare. in addition, floral and vegetative morphology of magnoliidae is highly variable and several of these variable traits have been shown to be associated with variation of diversification rates in other flowering plant lineages. previous molecular dating studies at large or narrow taxonomic scale have suggested that the crown node age of magnoliidae is older than the crown nodes of both eudicots and monocots, ranging from to myr, and that several of the families of magnoliidae appear to have originated before the end of the cretaceous. in addition, the ages of numerous nodes within magnoliidae have yet to be estimated. in parallel, few studies have focused on the diversification of the group, being either at the scale of all angiosperms or within families. in the present study, we provide for the first time a complete time scale for magnoliidae at the familial level. we then use this new time scale to test for significant diversification rate shifts during the evolutionary history of the clade. to do so, we take advantage of a recent improvement in the phylogeny of the group and a new revision of the rich fossil record of magnoliidae providing reliable minimum-age calibration points. in order to conduct these analyses for nodes above and below the family level, we used a dataset including more than 75% of the existing genera and molecular markers from the three plant genomes.  temporal analyses all runs in each of the five beast analyses with different calibration scheme converged effectively. the concatenated post-burn-in samples of the four runs in each analyses showed final effective sampling sizes of the likelihood far above. except for the position of siparunaceae and magnoliaceae, which remained unresolved in all analyses, the great majority of the relationships among the families received high support values and is similar in all analyses. conducting beast analyses without molecular data highlighted the non-uniformity of the temporal constraints effectively used in the analyses. however, no effective temporal priors violated the paleontological information used to calibrate the present analyses. in addition, the temporal posterior distributions of calibrated nodes obtained with the molecular data differ from the effective temporal prior distributions obtained without these data. these mismatches for calibrated nodes suggest that molecular data are well informative. the 95% credibility intervals of the ages obtained with beast are larger than those obtained with r8s. when the maximum age of the root varied, only the ages estimated for the crown node of magnoliidae, and the splits between canellales and piperales, and between laurales and magnoliales, are significantly different in the beast analyses. on the contrary, in the pl analyses, the majority of age estimates are significantly different when the maximum age of the root is changed.figure age estimates for the root and different nodes within the tree of magnoliidae. estimates are in million years, and the root is constrained with a maximum age. names of families refer to the crown node ages except when sl is mentioned. a, beast analyses with mean age estimates and 95% credibility intervals. b, r8s analyses with best-scoring ml tree age and 95% credibility intervals. *the stem lineage of siparunaceae, in the beast analysis with the maximum age of angiosperms set to million years, did not correspond to the same node in other analyses. abbreviation: sl, stem lineage. in general, the ages estimated in beast and r8s were similar. in the present paper, we take into account the overlapping 95% credibility intervals of all analyses. our results support an origin of extant magnoliidae between and myr, that is, in the lower cretaceous or the jurassic. the crown nodes of canellales, laurales, magnoliales, and piperales are dated to - myr, - myr, - myr, and - myr, respectively. by the end of the cretaceous, most families were probably present, with the exception of canellaceae, myristicaceae and winteraceae. the oldest families in terms of crown node age are aristolochiaceae and calycanthaceae or aristolochiaceae and lauraceae, depending on the relaxed clock method used.table age estimates for selected nodes of magnoliidae angio 130 angio 140 angio 150 angio 170 angio 200 node - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - x-x * - - - - - - - - all age estimates are in million years. the first line corresponds to beast estimates and the second line to r8s estimates. 95% credibility intervals are followed in brackets by mean estimates for beast analyses and best-scoring ml tree estimates for r8s analyses. abbreviations: angio- angio- angio- angio- and angio- correspond to the different maximum age constraints applied to the root. the names of taxa refer to their crown node except if sl is mentioned. *the stem lineage of siparunaceae, in the beast analysis with the maximum age of angiosperms set to million years, did not correspond with the same crown node than in other analyses. diversification analyses our medusa analyses on posterior beast trees of the angio- and angio- calibration schemes resulted in very similar scenarios for the mode of diversification within magnoliidae. the two maximum clade credibility trees used to summarize results are identical in terms of relationships. we identified six to significant diversification rate shifts across magnoliidae. in both cases, models including nine shifts were the most often selected among the trees sampled. the mean of the initial net diversification rate at the crown node of magnoliidae is estimated to  ±  species per million years in angio- and  ±  sp.myr− in angio- when considering shifts present in more than 50% of the trees, five main shifts in net diversification rates within magnoliidae are identified. three are decreases and two are increases: 1) at the crown node of the clade of piperaceae and saururaceae; 2) at the crown node of piperaceae excluding verhuellia; 3) at the crown node of calycanthaceae; 4) at the crown node of the clade of degeneria and galbulimima; 5) at the stem node of tribe miliuseae of annonaceae. in addition to those five main shifts, the net diversification rate averaged over the sample of trees show a general increase both within the laurales and within the magnoliales. our estimates of the relative extinction rate at the crown node of magnoliidae are  ±  and  ± . this rate remained relatively high in magnoliidae except in laurales and part of piperales.figure diversification analyses. results of the medusa analyses obtained using posterior trees randomly sampled from the beast posterior: a, angio- b, angio- topologies are the maximum clade credibility tree of randomly selected trees. names of terminals refer to compartments defined in the methods sections and detailed in additional file branch colors illustrate the mean net diversification rate. red dots denote significant shifts in r, their size being proportional to their frequency among the trees tested. numbered shifts in figure 2a: crown node of the clade of piperaceae and saururaceae; crown node of the clade of piperaceae excluding verhuellia; crown node of calycanthaceae; crown node of the clade of himantandraceae and degeneriaceae; crown node of the clade of miliuseae and monocarpia. the diagram in the top-right corner represents the frequency of the different model sizes in the 1000-model collections for the two analyses. abbreviations: sp., species; myr, million years. discussion tempo of magnoliidae evolution we provide here for the first time a near complete temporal framework for the evolution of magnoliidae above the generic level. applying different maximum age constraints to the crown node of angiosperms highlighted the sensitivity of inferred ages estimated for the deepest nodes of magnoliidae. although previous studies have recognized a long gap in the fossil record of the angiosperm stem lineage, there is no indisputable argument in favor of one particular maximum age constraint for the crown node of angiosperms. here we will systematically consider the whole range of age estimates obtained across our five maximum age calibration schemes and both molecular dating approaches used. we restricted ourselves to conservative fossil age constraints based on phylogenetic analyses of fossil and extant taxa. this led us to consider only out of more than described fossils putatively belonging to magnoliidae. however, our new age estimates for families and orders of magnoliidae appear, in general, to be compatible with the putative fossil record attributed to each of these taxa. future investigations of the phylogenetic placement of other magnoliid fossils will likely provide additional minimum age constraints, which could push back in time several young estimates supported in the present study, and decrease the size of the credibility intervals. this study further illustrates that, just as paleontological dating, molecular dating estimates are often associated with large uncertainties. the latter approach has to be seen as an attempt to reduce the range of the most likely ages for nodes constrained by the age of the fossil record securely placed and dated, and to evaluate the probability of the ages of nodes for which there is no direct fossil record. because all the ambiguity of our current knowledge has to be taken into account, the molecular dating approach cannot provide exact secure ages, except for exceptionally fossil-rich clades. based on this most reliable knowledge in the field of paleobotany of magnoliidae and chrono-stratigraphy, combined with a comprehensive sample of taxa and molecular markers, our data support an origin of extant lineages of magnoliidae during the jurassic or lower cretaceous between and myr. this result tend to be older than previously suggested. for example, the angiosperm-wide study of bell et al., in which magnoliid genera were sampled, estimated the crown node of magnoliidae to be between and myr. in another, more recent angiosperm-wide analysis sampling species of magnoliidae and using a pl approach, zanne et al. estimated the age of the crown node of magnoliidae to be myr without uncertainty associated. our new estimates for the crown-group age of orders also tend to be older than previously inferred. however, some studies have supported much older ages for these nodes. at the familial level, in addition to providing the first estimates for the ages of crown-group canellaceae, saururaceae, and winteraceae, the crown nodes of families are also generally dated to an older range of dates than previously estimated, with the exception of atherospermataceae for which we found a younger age than previously suggested. the large amount of combinations of parameters influencing age estimates limits straightforward explanations of these differences with previous studies. despite variation among the ages obtained for the crown ages of families, our results confirm that magnoliidae diversified into morphologically distinct clades by the end of the cretaceous, but probably earlier than thought before. this provides arguments in favor of an earlier diversification of angiosperms altogether, with the presence of more flowering plant lineages in the cretaceous than previously thought. finally, taking into account the whole range of age estimates obtained across our five different calibration schemes, leads to long ranges of age estimates that are compatible with biogeographic scenarios previously suggested in magnoliidae. however, viewed in isolation, the different assumptions about the maximum age of angiosperms lead to alternative time scales for the evolutionary history of the families of magnoliidae. therefore, biogeographic scenarios will need to be reevaluated in the context of explicit assumptions on the age of the angiosperms. mode of diversification of magnoliidae the new timetree obtained for magnoliidae in this study allowed us to detect an average of nine significant diversification rate shifts across lineages, implying that diversification has not been a homogeneous process throughout the history of the clade. explaining the present day diversity of species-rich clades has generally required several diversification rate shifts, but previous studies using the same statistical approach in other large angiosperm clades found, in general, fewer shifts than in the present analysis. within eudicots, beaulieu and donoghue detected six shifts in campanulidae, koenen et al. detected nine shifts in fabaceae, xi et al. found five significant shifts in malpighiales, and arakaki et al. found seven shifts in cactaceae. within monocots, escudero and hipp supported three shifts in the family cyperaceae while baker and couvreur identified up to shifts in palms. despite the dependence of the number of shifts detected on the taxonomic level of tips in the chronograms used, it seems that magnoliidae experienced a high variation in diversification rates. because of their longer evolutionary history in comparison with these other clades and because their fossil record supports a global distribution during the cretaceous and the paleogene, magnoliidae as a whole may have been affected by more events potentially influencing the speciation and extinction rates. establishing the causes affecting diversification-rate variation can be difficult. there is a large diversity of intrinsic and extrinsic traits known to influence speciation and extinction, all of them being potentially correlated to each other. the influence of a trait on the birth and death of species is dependent on other taxa, other traits of the same organism, and its physical environment, implying that a trait could have different effects on different clades. finally, the actual shift of diversification may happen several nodes after the evolution of an influencing trait. one explanation could be that an isolated trait will influence diversification in combination with other characters, the effect appearing when the entire set of traits needed is present. for these reasons, the investigation of the correlation between traits and diversification rates will need to take into account as many potential factors as possible. the older estimates of the ages in the “angio-200” hypothesis led to slightly lower absolute rates of diversification than in the “angio-140” hypothesis, as expected. because the general pattern is the same in both analyses, in the present paragraph we refer only to rates of the angio- analysis. the background net diversification rate obtained in the tree of magnoliidae is comparable to those found in angiosperms. in the present study, the lowest net diversification rates, resulting from shifts and, were found in the crown group of calycanthaceae, and in the branches of degeneriaceae and himantandraceae. these three families share distinctive floral features not or seldom found in other magnoliidae groups, such as the presence of inner staminodes that cover the stigma at the end of the female phase, and spiral phyllotaxy of all floral organs. however, it is difficult to link these two characters with mechanisms sustaining a low diversification rate. within calycanthaceae, the low rate of net diversification is associated with a low speciation rate for the entire clade and near-zero extinction. the absence of extinction would seem contradictory with the presence of several fossils in the cretaceous and could be an artefact of the method which does not take into account the extinct diversity. however, because the phylogenetic position of these fossils within the family has not been tested, it is difficult to draw conclusions about extinction within the family. the pollination systems of calycanthaceae involve trapping of a large variety of beetles and thrips. in comparison with specific pollination systems involving a unique relationship for the two partners, this generalist interaction is not favorable for genetic isolation promoting diversification. in addition, calycanthaceae have a temperate distribution, except for the monospecific genus idiospermum growing in a restricted area in north-east australia. the low ecological limits on species richness in temperate areas could provide an explanation for the low diversification of the lineage leading to the genera calycanthus and chimonanthus. on the other hand, the apparent lack of diversification of the lineage leading to idiospermum could be explained by different causes. individuals of this species are long-living trees involving low fixation rates in diverging populations. the genus is restricted to the very wet humid tropical lowland rainforests of australia. idiospermum presents one of the heaviest seeds among australian plants and is therefore probably not dispersed by animals, limiting its capacity of dispersion. if this low capacity of dispersion is ancestral in the lineage leading to the extant species of the genus, it restrained the number of available areas promoting diversification. this latter explanation might be generalized for all calycanthaceae as the seeds of the family contain secondary metabolites that are toxic at least for mammals. the highest diversification rate inferred in this study was found on the branch leading to the terminal compartment miliuseae in subfamily malmeoideae of annonaceae. a shift of +  ±  sp.myr− at the node sustaining the branch of this clade was present in 71% of the trees tested and the associated rate of speciation on the branch is on average equal to sp.myr− couvreur et al. found that major clades in annonaceae have undergone different rates of diversification, with subfamily malmeoideae having significantly higher rates than subfamily annonoideae. however, analyses of family-level lineage-through-time plots did not detect significant shits in diversification rates during most of the evolutionary history of annonaceae. erkens et al., using a tree with fewer taxa and two alternative approaches to detect rate shifts, identified up to three diversification rate shifts in annonaceae, including the one we detected here at the crown of miliuseae. reasons for an increase in diversification within miliuseae are not yet well known but could be related to founder effects after dispersal into south-east asia or distinctive pollen characters. canellales and piperales have, on average, higher speciation rates than magnoliales and laurales. within piperales, this may be explained by widespread herbaceous habits, resulting in faster life history and higher fixation rates in divergent populations. in addition, within this order, aristolochiaceae typically have zygomorphic flowers, which has been shown to have a positive impact on diversification. however, canellales and piperales also share the highest extinction rates, making laurales and magnoliales the most productive orders in terms of net diversification. differences in extinction rates are difficult to explain. for instance, there are no major differences in pollination systems among the four orders, and their current geographic distributions are similar. however, doyle and endress found several synapomorphies for the clade of laurales and magnoliales, specifically the presence of more than two whorls of stamens and more than one whorl or series of carpels. these characters might have played a role in relation to pollination, but the underlying mechanisms remain unknown. finally, even though the medusa approach represents a significant conceptual improvement over previous models, it still requires several important assumptions that may have influenced our results. first, medusa does not implement diversification models in which the extinction rate can be higher than speciation rates. second, the rates are assumed to be constant in each part of the tree, and only abrupt variations are evaluated, probably not in accordance with the biological reality in which rates could gradually fluctuate. morlon et al., recently developed an approach specifically to relax these two assumptions, but it is not implemented yet to detect shifts automatically nor to analyze higher-level phylogenies with terminally unresolved clades. in addition, rabosky recently developed a new bayesian framework to detect multiple diversification processes in a tree while allowing the speciation rate to vary continuously through time, but it is not available yet for a set of multiple trees and therefore cannot take phylogenetic and dating uncertainty into account. last, because the fossil record is not taken into account in the diversification rate analyses, very low rates of speciation and extremely low extinction rates are always allocated to the old lineages with few species, which have probably been more diverse in the past. new research efforts are currently being made in this area. therefore, our understanding of magnoliidae diversification may further improve in the future when more realistic methods and more complete phylogenies are available.  the present study suggests that magnoliidae began to diversify somewhere between the toarcian and the barremian, or - myr ago. several key nodes within magnoliidae are dated here for the first time. in general, our age estimates suggest a possibly older diversification of the group than previously inferred. the rich fossil record of magnoliidae may eventually provide additional calibration points to refine the time scale proposed here. however, considerable work remains to be done to securely relate this extinct diversity to the extant one, a task for which an integrated morphological dataset will be essential. the tempo and mode of diversification within this clade appears to be characterized by several increases and decreases of diversification rates, suggesting that magnoliidae have not undergone constant diversification but have instead been shaped by alternative, yet to be determined evolutionary processes. our new dated trees provide a solid basis for future biogeographical studies and robust statistical tests of correlation among intrinsic traits, extrinsic factors, and diversification rates within magnoliidae. 
using a molecular data set of markers and species and six robust, internal fossil age constraints, we estimate divergence times and significant shifts of diversification across the clade. this study provides a new time scale for the evolutionary history of an important, but underexplored, part of the tree of angiosperms. although families vary in crown ages, magnoliidae appear to have diversified into most extant families by the end of the cretaceous. the strongly imbalanced distribution of extant diversity within magnoliidae appears to be best explained by models of diversification with to shifts in net diversification rates. the ages of the main clades of magnoliidae are older than previously thought, and in several lineages, there were significant increases and decreases in net diversification rates. significant increases are inferred within piperaceae and annonaceae, while the low species richness of calycanthaceae, degeneriaceae, and himantandraceae appears to be the result of decreases in both speciation and extinction rates. compared with previous work, our study tends to push back in time the age of the crown node of magnoliidae, and of the four orders, canellales, piperales, laurales, and magnoliales. this study is a new robust framework for future investigations of trait evolution and of factors influencing diversification in this group as well as angiosperms as a whole.
 with species, magnoliidae are the largest clade of flowering plants outside monocots and eudicots. despite an ancient and rich fossil history, the tempo and mode of diversification of magnoliidae remain poorly known. using a molecular data set of markers and species and six robust, internal fossil age constraints, we estimate divergence times and significant shifts of diversification across the clade. in addition, we test the sensitivity of magnoliid divergence times to the choice of relaxed clock model and various maximum age constraints for the angiosperms.  compared with previous work, our study tends to push back in time the age of the crown node of magnoliidae, and of the four orders, canellales, piperales, laurales, and magnoliales. although families vary in crown ages, magnoliidae appear to have diversified into most extant families by the end of the cretaceous. the strongly imbalanced distribution of extant diversity within magnoliidae appears to be best explained by models of diversification with to shifts in net diversification rates. significant increases are inferred within piperaceae and annonaceae, while the low species richness of calycanthaceae, degeneriaceae, and himantandraceae appears to be the result of decreases in both speciation and extinction rates.  this study provides a new time scale for the evolutionary history of an important, but underexplored, part of the tree of angiosperms. the ages of the main clades of magnoliidae are older than previously thought, and in several lineages, there were significant increases and decreases in net diversification rates. this study is a new robust framework for future investigations of trait evolution and of factors influencing diversification in this group as well as angiosperms as a whole. electronic supplementary material the online version of this article contains supplementary material, which is available to authorized users. keywords angiospermsmagnoliidaemolecular datingdiversificationspeciationextinctionissue-copyright-statement© the author 2015 