BACKGROUND
glaciations were frequent throughout the quaternary, with potential consequences for population genetic structure by affecting distribution and demographic dynamics of species through time  <cit> .
recovering population dynamics in response to past climate changes and investigating how the genetic variation was spatially structured are common and fundamental tasks in phylogeography  <cit> .
however, because similar genetic patterns can arise under different demographic processes and selection, conventional methods in phylogeography based on narrative descriptions and patterns-alone interpretations  produce often dubious or indistinguishable historical demographic processes.
to overcome such problem, different approaches exploring statistical and process-based modelling have been recently used for phylogeographic inference  <cit> .
coalescent modelling, for instance, has provided significant advances in hypothesis testing by estimating genetic parameters following predefined demographic histories   <cit> .
the hypothesis describing the most likely processes should then generate the most similar parameters for the observed pattern from real populations.
this reasoning on hypothesis testing came from the multi-model inference approach, i.e.
the simultaneous comparison of data from multiple hypotheses generated by different models, which is increasingly used in ecology, evolution and biogeography  <cit> .
however, defining which demographic hypotheses should be simulated has been hampered by the lack of reliable and complete datasets, such as fossil records for most species worldwide see examples in  <cit> .
hence, subjective hypotheses, with little or no ecological and biogeographic realism, became common.
at the same time, ecological niche modelling  has allowed the exploration of the geographic context of species dynamics through time by hindcasting suitable climatic conditions  currently occupied by species of palaeoclimatic scenarios .
this procedure predicts the species potential distribution over different time periods and can be further used to set demographic hypotheses  <cit> .
a frequent criticism of this approach is that different enm methods  and palaeoclimatic simulations, which are based on different modelling assumptions or types of training data, produce different predictions  <cit> .
also, the difficulty of validating enm projections  when their results are transferred over long time periods is another important matter of discussion  <cit> .
thus, enm uncertainties would challenge objective choices, which are required for inferences of population genetics.
to overcome such problems, the full range of modelling uncertainties should be accounted for as part of the process of exploring the dynamic of species distribution through time.
in this case, by exploring different assumptions about the dynamics of species ecological niche , enms can actually generate multiple and independent hypotheses of species' distributional history that reflect, at the same time, ecological and biogeographical realism  <cit> .
subsequently, demographic hypotheses inferred from the distributional dynamic of species would be tested using coalescent analyses.
again, this idea follows the reasoning of the multi-model inference approach, which advocates that uncertainty should not be ignored, either for parameter estimation or for model setting and selection  <cit> .
furthermore, considering that glaciations caused unequal biotic effects worldwide, this multi-model inference approach may be especially useful to better understand the demographic dynamics of species occupying systems with complex responses to the quaternary climate changes, such as the neotropical savannas  <cit> .
during the glacial periods, for instance, a drier and cooler climate occurred in south and southeastern brazil, and grasslands may have extended from latitudes ~ 28°/27° s to at least 20° s on savanna landscapes, although the precise age of the arid period may differ due to latitude  <cit> .
the climate became moister and arboreal pollen dominated the savanna vegetation record only after  <dig>  14c yr bp, until reaching the current pattern around  <dig>  14c yr bp  <cit> .
this palaeoscenario may have favoured species more adapted to drier and highly seasonal climate, consequently leading to a retraction in the geographical range of many arboreal savanna taxa that became restricted to areas with moist climatic conditions  <cit> .
herein, we implement the multi-model inference approach to address and test multiple hypotheses concerning the effect of the late quaternary climate oscillations on the distribution and demographic history of tabebuia aurea  benth.
& hook.f.
ex s.moore .
tabebuia aurea is a neotropical tree species with a long generation time and life span, widely distributed in the seasonal savannas and wet-savanna grasslands of central brazil , and for which there is a scarce fossil record.
moreover, general palaeovegetation reconstructions for south america constrain hypothesis testing under the coalescent theoretical background.
this focal species is thus inserted into a nice context of the multi-model inference approach to elucidate its efficiency in recovering its demographic history.
in particular, we explore whether the ecological and biographic hypotheses inferred from potential palaeodistribution scenarios , along with the historical demographic dynamics simulated from coalescent analyses, reflect the observed genetic structure of modern populations.figure  <dig>
current geographical distribution of
tabebuia aurea
across the neotropics.
<dig> occurrence records used in ecological niche modelling;   <dig> populations sampled for genetic analyses.
area in grey represents the brazilian savannah in central brazil.
details on the sampled populations are provided in additional file  <dig>  table s <dig>
RESULTS
ecological niche modelling
species niche and consensual palaeodistribution
the present-day geographic range in climatic conditions of t. aurea clearly shows its preference for hot and drier climates, matching the general current conditions of the neotropical savannas .
as expected, such climatic space was more restricted during the last glacial maximum  than the mid-holocene and the present day, mainly due to a temperature decrease, potentially leading to a scenario of population expansion through time in response to the increasing availability of suitable conditions across the neotropics .
the ensembled predictions show that the potential distribution of t. aurea was restricted to central brazil during the lgm , followed by a spatial displacement towards northeast brazil during the mid-holocene , and then returning to central brazil to the present day, expanding also towards the west of central brazil .
despite the spatial displacements, our predictions show a wide historical refugium across central brazil, where higher levels of climatic suitability were maintained throughout the last glacial cycle .figure  <dig>
ecological space of climatic conditions in neotropics during the lgm , mid-holocene  and the present day .
the climatic preferences from current occurrence records of tabebuia aurea are represented by black dots.
note that the climatic conditions in neotropics matching the t. aurea's preferences were less available during the lgm than holocene and present-day, mainly due to temperature decrease, consequently allowing a general scenario of range expansion through the time.
the bioclimatic variables were obtained from aogcm ccsm <dig>
climatic suitability for
tabebuia aurea
.
maps of consensus representing the potential distribution of species across the neotropics during the  lgm ,  mid-holocene , and  present day.
historical refugium  shows areas climatically suitable throughout the time.
predictive uncertainties and alternative distributional hypotheses
considering the predictions across all  <dig> maps  through the three time periods, the greatest variance came from aogcms , followed by time component .
moreover, their higher uncertainties are distributed across northeast and central-northeast brazil, respectively .
the algorithms presented the lowest proportion of uncertainty , which occur outside central brazil, where the consensual distribution of t. aurea does not reach .figure  <dig>
uncertainty from the components of ecological niche modelling.
time,  atmosphere–ocean global circulation models , and  algorithms.
in map classification, the distribution dynamics predicting range expansion through time was the most frequent scenario .
although map classification was not dependent on the modelling components  within both 6–0 ka  and 21–6 ka specific periods , map classification was heterogeneous between time slices .table  <dig>
alternative demographic hypotheses used for multi-model inference
models
aicw
p
rs
enm%
retraction 21–6 ka
stability 21–0 ka
expansion 21–0 ka
expansion 6–0 ka
expansion 21–6 ka
multiple refugia 21–0 ka
aicw, akaike information criterion  weights; p, two-tailed probability of not rejecting the model; rs, relative support.
the support from palaeodistribution modelling  is represented by the percentage of each demographic hypothesis observed through the  <dig> predictive maps.
genetic diversity and demographic parameters
populations of t. aurea were genetically differentiated  with relatively high genetic diversity across its geographical range , high levels of inbreeding within populations  and non-random mating among populations , also evidencing high genetic differentiation among populations .table  <dig> genetic characterisation and demographic parameters for  <dig> populations of tabebuia aurea
pop
n
a
ar
ar*
h
o
h
e
f
θ
θ - 95% interval
n
e
θ - 95% interval
g
g - 95% interval
age
ara
bag
bar
bod
cac
chg
fat
gsv
niq
pan
pne
pot
ptu
sca
sdo
sec
stz
sum
vib
mean
sd
overall
n – number of individuals sampled; a – mean number of alleles per locus; ar – allelic richness; ar* - allelic richness excluding populations sec and sdo; h
o - observed heterozygosity; h
e – expected heterozygosity; f – inbreeding coefficient ; θ - coalescent parameter; 95% credibility interval around the estimate; n
e – effective population size; g - exponential growth parameter .
coalescent analyses supported a low mutation parameter  and small effective population sizes for all populations .
using the mutation parameter over all populations , tmrca dated  <dig>  ka  and effective population size was ne =  <dig>  .
gene flow was high among all population pairs .
model selection
similar to the enms predictions, the two models of population expansion through time  were the best-supported hypotheses for predicting the observed genetic parameters for t. aurea, using either two-tailed probability  or aicw  criteria for model selection .
hypotheses predicting population retraction or stability retrieved 100% of the values  above the observed mean genetic diversity for the  <dig> populations of t. aurea.
thus, relative support  was  <dig>  and aicw and p could not be estimated.
in addition, the hypotheses "expansion 21–6 ka" and "multiple refugia 21–0 ka" retrieved a greater proportion of genetic diversity below the observed values .figure  <dig>
demographic history scenarios simulated for
tabebuia aurea
and their palaeodistributional representations.
circles represent hypothetical demes and indicate population stability or shrinkage through the time.
lgm, last glacial maximum; hol, mid-holocene; pres, present day; n <dig>  n <dig> and n <dig>  effective population size at time t <dig> , time t <dig> , and time t <dig> , respectively; nt, logarithm function for effective population size variation in coalescent simulation.
the migration rate was  <dig> /generation.
spatial patterns in genetic diversity
we found no significant relationship between the geographical distance and the genetic differentiation among pairs of populations .
however, quantile regressions showed clear effects of climate change on the genetic structure of t. aurea.
relationships resembling triangular-shaped envelopes show that populations in less climatically suitable areas during the lgm and present day presented high or low genetic diversity  and allelic richness , whereas populations in more suitable areas had only high he and ar*.
an inverse pattern occurred at 6 ka .
notwithstanding, distances from the centroids often showed weak or no significant relationships with either he or ar* .
discussion
inferences on demographic history
our findings showed clear evidence that the current pattern in t. aurea genetic diversity is the result of population expansion through time.
the general scenarios predicting "expansion" were the most frequent among enm predictions and the best-supported models among demographic simulations.
moreover, genetic analyses also showed that all populations present a negative growth parameter  and small effective population sizes, which in turn may also be the outcome of smaller populations in the past than in the present.
in fact, a slow and long population expansion lasting  <dig> generations from the lgm to the present  or a fast and brief expansion from the mid-holocene  to present  retrieved similar results of genetic diversity and were equally supported in our analyses.
however, some theoretical expectations favour the scenario of "expansion 6–0 ka".
for example, the probability of coalescence is inversely related to the number of gene copies  <cit> , therefore populations that experienced population retraction followed by expansion may present the most coalescence just before the demographic expansion when population size was small .
thus, because the tmrca for t. aurea lineages dated from the early- to mid-holocene , our results are more congruent with the hypothesis "expansion 6–0 ka".
we believe therefore that this scenario of a fast and brief population expansion from the mid-holocene  to the present should be considered for t. aurea hereafter.
geographical context: inferences on genetic and spatial connectivity
along with population expansion from the mid-holocene, the spatial displacements in climatically suitable areas through time also affected the current genetic pattern in t. aurea.
populations with lower values of both genetic diversity and allelic richness are located in the northeast edge of the t. aurea geographical range, a region potentially occupied only during the mid-holocene.
following the abundant-centre model , we hypothesize that populations of t. aurea at the northeast edge already had depleted genetic diversity due to small effective sizes, which may have in turn reduced individual fitness and population adaptability, and constrained the scale up in genetic diversity.
moreover, the northeastward range shift may have led to the colonisation of new sites with low genetic diversity and allelic richness due to allele surfing .
in addition, evidence that most populations are inside the historical refugium suggests that even under demographic retraction or spatial displacements, a wide climatically stable area available throughout the last glacial cycle favoured population persistence and genetic connectivity across central brazil, hence the high genetic diversity and polymorphism observed in modern populations.
interestingly, the two populations outside the historical refugium, sca and sum, which were potentially disconnected from the others in some periods, presented the lowest values of both genetic diversity  and allelic richness .
moreover, the evidence of historical connectivity among populations of t. aurea also reinforces the observed pattern of high gene flow  and low genetic differentiation .
the genetic connectivity is also in agreement with patterns of pollen dispersal observed elsewhere.
tabebuia aurea has a mixed mating system, with potential long distance pollen  and seed dispersal  <cit> .
however, high proportions of self-pollination and biparental inbreeding have been observed, which may have led to high inbreeding within population and a high fixation index .
predictive uncertainties: are the hypotheses and inferences reliable?
the spatial pattern of predictive uncertainties suggests that algorithms converge in their main prediction about the distribution of the species across central brazil through time.
moreover, the high levels of variance of the time component indicate that enms were able to get the effects of climate changes from the t. aurea distributional dynamics throughout the last glacial cycle, despite some methodological noise.
the set of  <dig> maps from ecological niche modelling thus reflects a full range of potential climate change effects on the distributional dynamics of t. aurea across neotropics, supporting alternative demographic hypotheses that are ecologically and biogeographically valid.
along with enms, the validity of such hypotheses is still evident by the fact that the expected demographic histories realistically predicted the current genetic structure of t. aurea when simulated using coalescent models.
therefore, we consider both hypotheses and inferences built by coupling niche modelling and coalescent simulations to be reliable as approached here.
most importantly, our framework provides explicit mechanisms to include and analyse a complete range of uncertainties as required for hypothesis testing in any multi-model inference approach.
CONCLUSIONS
exploring uncertainties inherent to the different modelling techniques, we recovered the demographic history of t. aurea and showed that the pattern of genetic diversity and allelic richness may be the outcome of range expansion from the lgm to the present.
besides range expansion, a wide suitable region throughout the last glacial cycle was evidenced in central brazil.
this wide historical refugium may have buffered the deleterious effect of demographical retraction on genetic diversity due to the long-term population persistence and connectivity, maintaining a relatively high level of genetic diversity and allelic richness in most populations with significant but low genetic differentiation among them.
although we could not validate the palaeodistribution hypotheses due to the lack of fossil records , we believe that our biogeographic hypothesis is reliable because it matches the general pattern of fossil records for central brazil  <cit> .
also, the demographic hypotheses tested here reflect a complete range of potential climatic effects on species distributional dynamic through the time.
moreover, the ensemble among predictions also reflects a likely spatial context of the demographic dynamic with explicit mechanisms to analyse uncertainties and hypothesis reliability, although with some methodological noise .
thus, we believe that the multi-model inference approach used in this study is a useful framework to recover the nature, timing and geographical context of population dynamics in response to quaternary climate changes, as well as to better understand the mechanisms involved in the origin and maintenance of species genetic diversity.

 glaciations were frequent throughout the quaternary, with potential consequences for population genetic structure by affecting distribution and demographic dynamics of species through time. recovering population dynamics in response to past climate changes and investigating how the genetic variation was spatially structured are common and fundamental tasks in phylogeography. however, because similar genetic patterns can arise under different demographic processes and selection, conventional methods in phylogeography based on narrative descriptions and patterns-alone interpretations produce often dubious or indistinguishable historical demographic processes. to overcome such problem, different approaches exploring statistical and process-based modelling have been recently used for phylogeographic inference. coalescent modelling, for instance, has provided significant advances in hypothesis testing by estimating genetic parameters following predefined demographic histories. the hypothesis describing the most likely processes should then generate the most similar parameters for the observed pattern from real populations. this reasoning on hypothesis testing came from the multi-model inference approach, i.e. the simultaneous comparison of data from multiple hypotheses generated by different models, which is increasingly used in ecology, evolution and biogeography. however, defining which demographic hypotheses should be simulated has been hampered by the lack of reliable and complete datasets, such as fossil records for most species worldwide see examples in. hence, subjective hypotheses, with little or no ecological and biogeographic realism, became common. at the same time, ecological niche modelling has allowed the exploration of the geographic context of species dynamics through time by hindcasting suitable climatic conditions currently occupied by species of palaeoclimatic scenarios. this procedure predicts the species potential distribution over different time periods and can be further used to set demographic hypotheses. a frequent criticism of this approach is that different enm methods and palaeoclimatic simulations, which are based on different modelling assumptions or types of training data, produce different predictions. also, the difficulty of validating enm projections when their results are transferred over long time periods is another important matter of discussion. thus, enm uncertainties would challenge objective choices, which are required for inferences of population genetics. to overcome such problems, the full range of modelling uncertainties should be accounted for as part of the process of exploring the dynamic of species distribution through time. in this case, by exploring different assumptions about the dynamics of species ecological niche, enms can actually generate multiple and independent hypotheses of species' distributional history that reflect, at the same time, ecological and biogeographical realism. subsequently, demographic hypotheses inferred from the distributional dynamic of species would be tested using coalescent analyses. again, this idea follows the reasoning of the multi-model inference approach, which advocates that uncertainty should not be ignored, either for parameter estimation or for model setting and selection. furthermore, considering that glaciations caused unequal biotic effects worldwide, this multi-model inference approach may be especially useful to better understand the demographic dynamics of species occupying systems with complex responses to the quaternary climate changes, such as the neotropical savannas. during the glacial periods, for instance, a drier and cooler climate occurred in south and southeastern brazil, and grasslands may have extended from latitudes ~ 28°/27° s to at least 20° s on savanna landscapes, although the precise age of the arid period may differ due to latitude. the climate became moister and arboreal pollen dominated the savanna vegetation record only after 14c yr bp, until reaching the current pattern around 14c yr bp. this palaeoscenario may have favoured species more adapted to drier and highly seasonal climate, consequently leading to a retraction in the geographical range of many arboreal savanna taxa that became restricted to areas with moist climatic conditions. herein, we implement the multi-model inference approach to address and test multiple hypotheses concerning the effect of the late quaternary climate oscillations on the distribution and demographic history of tabebuia aurea benth. & hook.f. ex s.moore. tabebuia aurea is a neotropical tree species with a long generation time and life span, widely distributed in the seasonal savannas and wet-savanna grasslands of central brazil, and for which there is a scarce fossil record. moreover, general palaeovegetation reconstructions for south america constrain hypothesis testing under the coalescent theoretical background. this focal species is thus inserted into a nice context of the multi-model inference approach to elucidate its efficiency in recovering its demographic history. in particular, we explore whether the ecological and biographic hypotheses inferred from potential palaeodistribution scenarios, along with the historical demographic dynamics simulated from coalescent analyses, reflect the observed genetic structure of modern populations.figure current geographical distribution of tabebuia aurea across the neotropics. occurrence records used in ecological niche modelling; populations sampled for genetic analyses. area in grey represents the brazilian savannah in central brazil. details on the sampled populations are provided in additional file table s  ecological niche modelling species niche and consensual palaeodistribution the present-day geographic range in climatic conditions of t. aurea clearly shows its preference for hot and drier climates, matching the general current conditions of the neotropical savannas. as expected, such climatic space was more restricted during the last glacial maximum than the mid-holocene and the present day, mainly due to a temperature decrease, potentially leading to a scenario of population expansion through time in response to the increasing availability of suitable conditions across the neotropics. the ensembled predictions show that the potential distribution of t. aurea was restricted to central brazil during the lgm, followed by a spatial displacement towards northeast brazil during the mid-holocene, and then returning to central brazil to the present day, expanding also towards the west of central brazil. despite the spatial displacements, our predictions show a wide historical refugium across central brazil, where higher levels of climatic suitability were maintained throughout the last glacial cycle.figure ecological space of climatic conditions in neotropics during the lgm, mid-holocene and the present day. the climatic preferences from current occurrence records of tabebuia aurea are represented by black dots. note that the climatic conditions in neotropics matching the t. aurea's preferences were less available during the lgm than holocene and present-day, mainly due to temperature decrease, consequently allowing a general scenario of range expansion through the time. the bioclimatic variables were obtained from aogcm ccsm climatic suitability for tabebuia aurea. maps of consensus representing the potential distribution of species across the neotropics during the lgm, mid-holocene, and present day. historical refugium shows areas climatically suitable throughout the time. predictive uncertainties and alternative distributional hypotheses considering the predictions across all maps through the three time periods, the greatest variance came from aogcms, followed by time component. moreover, their higher uncertainties are distributed across northeast and central-northeast brazil, respectively. the algorithms presented the lowest proportion of uncertainty, which occur outside central brazil, where the consensual distribution of t. aurea does not reach.figure uncertainty from the components of ecological niche modelling. time, atmosphere–ocean global circulation models, and algorithms. in map classification, the distribution dynamics predicting range expansion through time was the most frequent scenario. although map classification was not dependent on the modelling components within both 6–0 ka and 21–6 ka specific periods, map classification was heterogeneous between time slices.table alternative demographic hypotheses used for multi-model inference models aicw p rs enm% retraction 21–6 ka stability 21–0 ka expansion 21–0 ka expansion 6–0 ka expansion 21–6 ka multiple refugia 21–0 ka aicw, akaike information criterion weights; p, two-tailed probability of not rejecting the model; rs, relative support. the support from palaeodistribution modelling is represented by the percentage of each demographic hypothesis observed through the predictive maps. genetic diversity and demographic parameters populations of t. aurea were genetically differentiated with relatively high genetic diversity across its geographical range, high levels of inbreeding within populations and non-random mating among populations, also evidencing high genetic differentiation among populations.table genetic characterisation and demographic parameters for populations of tabebuia aurea pop n a ar ar* h o h e f θ θ - 95% interval n e θ - 95% interval g g - 95% interval age ara bag bar bod cac chg fat gsv niq pan pne pot ptu sca sdo sec stz sum vib mean sd overall n – number of individuals sampled; a – mean number of alleles per locus; ar – allelic richness; ar* - allelic richness excluding populations sec and sdo; h o - observed heterozygosity; h e – expected heterozygosity; f – inbreeding coefficient; θ - coalescent parameter; 95% credibility interval around the estimate; n e – effective population size; g - exponential growth parameter. coalescent analyses supported a low mutation parameter and small effective population sizes for all populations. using the mutation parameter over all populations, tmrca dated  ka and effective population size was ne = . gene flow was high among all population pairs. model selection similar to the enms predictions, the two models of population expansion through time were the best-supported hypotheses for predicting the observed genetic parameters for t. aurea, using either two-tailed probability or aicw criteria for model selection. hypotheses predicting population retraction or stability retrieved 100% of the values above the observed mean genetic diversity for the populations of t. aurea. thus, relative support was and aicw and p could not be estimated. in addition, the hypotheses "expansion 21–6 ka" and "multiple refugia 21–0 ka" retrieved a greater proportion of genetic diversity below the observed values.figure demographic history scenarios simulated for tabebuia aurea and their palaeodistributional representations. circles represent hypothetical demes and indicate population stability or shrinkage through the time. lgm, last glacial maximum; hol, mid-holocene; pres, present day; n n and n effective population size at time t, time t, and time t, respectively; nt, logarithm function for effective population size variation in coalescent simulation. the migration rate was /generation. spatial patterns in genetic diversity we found no significant relationship between the geographical distance and the genetic differentiation among pairs of populations. however, quantile regressions showed clear effects of climate change on the genetic structure of t. aurea. relationships resembling triangular-shaped envelopes show that populations in less climatically suitable areas during the lgm and present day presented high or low genetic diversity and allelic richness, whereas populations in more suitable areas had only high he and ar*. an inverse pattern occurred at 6 ka. notwithstanding, distances from the centroids often showed weak or no significant relationships with either he or ar*. discussion inferences on demographic history our findings showed clear evidence that the current pattern in t. aurea genetic diversity is the result of population expansion through time. the general scenarios predicting "expansion" were the most frequent among enm predictions and the best-supported models among demographic simulations. moreover, genetic analyses also showed that all populations present a negative growth parameter and small effective population sizes, which in turn may also be the outcome of smaller populations in the past than in the present. in fact, a slow and long population expansion lasting generations from the lgm to the present or a fast and brief expansion from the mid-holocene to present retrieved similar results of genetic diversity and were equally supported in our analyses. however, some theoretical expectations favour the scenario of "expansion 6–0 ka". for example, the probability of coalescence is inversely related to the number of gene copies, therefore populations that experienced population retraction followed by expansion may present the most coalescence just before the demographic expansion when population size was small. thus, because the tmrca for t. aurea lineages dated from the early- to mid-holocene, our results are more congruent with the hypothesis "expansion 6–0 ka". we believe therefore that this scenario of a fast and brief population expansion from the mid-holocene to the present should be considered for t. aurea hereafter. geographical context: inferences on genetic and spatial connectivity along with population expansion from the mid-holocene, the spatial displacements in climatically suitable areas through time also affected the current genetic pattern in t. aurea. populations with lower values of both genetic diversity and allelic richness are located in the northeast edge of the t. aurea geographical range, a region potentially occupied only during the mid-holocene. following the abundant-centre model, we hypothesize that populations of t. aurea at the northeast edge already had depleted genetic diversity due to small effective sizes, which may have in turn reduced individual fitness and population adaptability, and constrained the scale up in genetic diversity. moreover, the northeastward range shift may have led to the colonisation of new sites with low genetic diversity and allelic richness due to allele surfing. in addition, evidence that most populations are inside the historical refugium suggests that even under demographic retraction or spatial displacements, a wide climatically stable area available throughout the last glacial cycle favoured population persistence and genetic connectivity across central brazil, hence the high genetic diversity and polymorphism observed in modern populations. interestingly, the two populations outside the historical refugium, sca and sum, which were potentially disconnected from the others in some periods, presented the lowest values of both genetic diversity and allelic richness. moreover, the evidence of historical connectivity among populations of t. aurea also reinforces the observed pattern of high gene flow and low genetic differentiation. the genetic connectivity is also in agreement with patterns of pollen dispersal observed elsewhere. tabebuia aurea has a mixed mating system, with potential long distance pollen and seed dispersal. however, high proportions of self-pollination and biparental inbreeding have been observed, which may have led to high inbreeding within population and a high fixation index. predictive uncertainties: are the hypotheses and inferences reliable? the spatial pattern of predictive uncertainties suggests that algorithms converge in their main prediction about the distribution of the species across central brazil through time. moreover, the high levels of variance of the time component indicate that enms were able to get the effects of climate changes from the t. aurea distributional dynamics throughout the last glacial cycle, despite some methodological noise. the set of maps from ecological niche modelling thus reflects a full range of potential climate change effects on the distributional dynamics of t. aurea across neotropics, supporting alternative demographic hypotheses that are ecologically and biogeographically valid. along with enms, the validity of such hypotheses is still evident by the fact that the expected demographic histories realistically predicted the current genetic structure of t. aurea when simulated using coalescent models. therefore, we consider both hypotheses and inferences built by coupling niche modelling and coalescent simulations to be reliable as approached here. most importantly, our framework provides explicit mechanisms to include and analyse a complete range of uncertainties as required for hypothesis testing in any multi-model inference approach.  exploring uncertainties inherent to the different modelling techniques, we recovered the demographic history of t. aurea and showed that the pattern of genetic diversity and allelic richness may be the outcome of range expansion from the lgm to the present. besides range expansion, a wide suitable region throughout the last glacial cycle was evidenced in central brazil. this wide historical refugium may have buffered the deleterious effect of demographical retraction on genetic diversity due to the long-term population persistence and connectivity, maintaining a relatively high level of genetic diversity and allelic richness in most populations with significant but low genetic differentiation among them. although we could not validate the palaeodistribution hypotheses due to the lack of fossil records, we believe that our biogeographic hypothesis is reliable because it matches the general pattern of fossil records for central brazil. also, the demographic hypotheses tested here reflect a complete range of potential climatic effects on species distributional dynamic through the time. moreover, the ensemble among predictions also reflects a likely spatial context of the demographic dynamic with explicit mechanisms to analyse uncertainties and hypothesis reliability, although with some methodological noise. thus, we believe that the multi-model inference approach used in this study is a useful framework to recover the nature, timing and geographical context of population dynamics in response to quaternary climate changes, as well as to better understand the mechanisms involved in the origin and maintenance of species genetic diversity. 
by exploring uncertainties inherent in multiple working hypotheses, we have shown that multi-model inference is a fruitful and efficient approach to recover the nature, timing and geographical context of the tabebuia aurea population dynamic in response to the quaternary climate changes. coalescent simulationecological niche modellinggenetic connectivityhabitat trackingmultiple working hypothesesquaternary climate changesissue-copyright-statement© the author 2014 nevertheless, a wide historical refugium across central brazil likely maintained large populations connected throughout time. comparing predictions from demographic hypotheses with genetic parameters of modern populations, our findings revealed a likely scenario of population decline, with spatial displacement towards northeast brazil from the last glacial maximum to the mid-holocene. glaciations were recurrent throughout the quaternary and potentially shaped species genetic structure worldwide by affecting population dynamics. exploring different algorithms and paleoclimatic simulations, we used ecological niche modelling to generate alternative hypotheses of potential demographic changes through the last glacial cycle and estimated genetic parameters using coalescent modelling. here, we implemented a multi-model inference approach to recover the distribution dynamics and demographic history of a neotropical savanna tree, tabebuia aurea. the expected genetic signatures from such predicted distribution dynamics are also corroborated by spatial genetic structure observed in modern populations. subsequently, populations expanded in response to the return of the climatically suitable conditions in central-west brazil.
 glaciations were recurrent throughout the quaternary and potentially shaped species genetic structure worldwide by affecting population dynamics. here, we implemented a multi-model inference approach to recover the distribution dynamics and demographic history of a neotropical savanna tree, tabebuia aurea. exploring different algorithms and paleoclimatic simulations, we used ecological niche modelling to generate alternative hypotheses of potential demographic changes through the last glacial cycle and estimated genetic parameters using coalescent modelling.  comparing predictions from demographic hypotheses with genetic parameters of modern populations, our findings revealed a likely scenario of population decline, with spatial displacement towards northeast brazil from the last glacial maximum to the mid-holocene. subsequently, populations expanded in response to the return of the climatically suitable conditions in central-west brazil. nevertheless, a wide historical refugium across central brazil likely maintained large populations connected throughout time. the expected genetic signatures from such predicted distribution dynamics are also corroborated by spatial genetic structure observed in modern populations.  by exploring uncertainties inherent in multiple working hypotheses, we have shown that multi-model inference is a fruitful and efficient approach to recover the nature, timing and geographical context of the tabebuia aurea population dynamic in response to the quaternary climate changes. electronic supplementary material the online version of this article contains supplementary material, which is available to authorized users. keywords coalescent simulationecological niche modellinggenetic connectivityhabitat trackingmultiple working hypothesesquaternary climate changesissue-copyright-statement© the author 2014 