Florent Mazel
email: mazel@gmail.com.

Julien Renaud
email: julien.renaud.leca@gmail.com

François Guilhaumon
email: francois.guilhaumon@ird.fr

David Mouillot
email: david.mouillot@univ-montp2.fr

Dominique Gravel
email: dominique_gravel@uqar.ca

Wilfried Thuiller
email: wilfried.thuiller@ujf-grenoble.fr

Mammalian phylogenetic diversity-area relationships at a continental scale

Keywords: species area-relationship, strict nested design, null models, phylogenetic diversity

In analogy to the species-area relationship (SAR), one of the few laws in Ecology, the phylogenetic diversity-area relationship (PDAR) describes the tendency of phylogenetic diversity (PD) to increase with area. Although investigating PDAR has the potential to unravel the underlying processes shaping assemblages across spatial scales and to predict PD loss through habitat reduction, it has been little investigated so far. Focusing on PD has noticeable advantages compared to species richness (SR) since PD also gives insights on processes such as speciation/ extinction, assembly rules and ecosystem functioning. Here we investigate the universality and pervasiveness of the PDAR at continental scale using terrestrial mammals as study case. We define the relative robustness of PD (compared to SR) to habitat loss as the area between the standardized PDAR and standardized SAR (i.e. standardized by the diversity of the largest spatial window) divided by the area under the standardized SAR only. This metric quantifies the relative increase of PD robustness compared to SR robustness. We show that PD robustness is higher than

Introduction

The species area relationship (SAR) describes the tendency of species richness (SR) to increase with area [START_REF] Rosenzweig | Species Diversity in Space and Time[END_REF]. This relationship is documented for a wide range of taxonomic groups and ecosystems [START_REF] Guilhaumon | Taxonomic and regional uncertainty in speciesarea relationships and the identification of richness hotspots[END_REF][START_REF] Triantis | The island species-area relationship: biology and statistics[END_REF] and its understanding is central to ecology and conservation biogeography [START_REF] Rosenzweig | Species Diversity in Space and Time[END_REF][START_REF] Whittaker | Conservation Biogeography: assessment and prospect[END_REF]. For instance, the SAR is a key tool to estimate species extinctions from habitat destruction and climate change [START_REF] Pimm | Biodiversity: extinction by numbers[END_REF][START_REF] Thomas | Extinction risk from climate change[END_REF][START_REF] Pereira | Scenarios for global biodiversity in the 21st century[END_REF][START_REF] Matias | Estimates of species extinctions from species-area relationships strongly depend on ecological context[END_REF]). Nevertheless a SAR approach reduces biological diversity to species richness only and fails to include the amount of evolutionary history in species assemblages [START_REF] Mouquet | Ecophylogenetics: advances and perspectives[END_REF]). To fill this gap, the Phylogenetic Diversity Area Relationship (PDAR hereafter; [START_REF] Morlon | Spatial patterns of phylogenetic diversity[END_REF]) can help unravel the processes assembling communities across spatio-temporal scales and provides complementary tools for conserving the Tree of Life [START_REF] Mazel | Multifaceted diversity-area relationships reveal global hotspots of mammalian species, trait and lineage diversity[END_REF]. For instance, translating SAR into PDAR allows to predict the loss of PD through habitat destruction. This prediction is essential since the loss of a given amount of PD or the loss of an entire lineage could have strong negative ecological consequences since distinct lineages are likely to perform different functions [START_REF] Cadotte | Evolutionary history and the effect of biodiversity on plant productivity[END_REF][START_REF] Mouquet | Ecophylogenetics: advances and perspectives[END_REF]).

Several mechanisms have been proposed to explain the SAR, such as sampling effects [START_REF] Rosenzweig | Species Diversity in Space and Time[END_REF], the effect of habitat size on extinction rates [START_REF] Macarthur | The theory of island biography[END_REF], the scaling of environmental heterogeneity with area [START_REF] Kadmon | Integrating the effects of area, isolation, and habitat heterogeneity on species diversity: a unification of island biogeography and niche theory[END_REF] or dispersal limitation [START_REF] Hubbell | The unified neutral theory of biodiversity and biogeography[END_REF]. In complement to the SAR, the PDAR brings unique information about the different processes structuring biodiversity at different spatial scales, helping, for example, to quantify the effects of biotic interactions at small scales versus biogeographical processes at large scale. A particular feature of the PDAR is that the shape of the phylogenetic tree ultimately drives its relative position to the SAR. A star phylogeny would produce a PDAR proportional to the SAR, while a complete and recent polytomy at the tips of the tree would produce an extreme PDAR that would reach its maximum from the smallest area (see Figure 1.A). In addition to those mechanisms, biogeographic history together with ecological processes should also influence the PDAR (see Fig. 1.B). Allopatric speciation and/or competition between close relative species would result in a relatively higher PD than expected for a given SR ('overdispersion'; [START_REF] Webb | Phylogenies and Community Ecology[END_REF][START_REF] O'dwyer | Phylogenetic diversity theory sheds light on the structure of microbial communities[END_REF]. Coexistence theory indeed predicts that similar species will compete more strongly than dissimilar species, leading to the exclusion of one of the similar species [START_REF] Hillerislambers | Rethinking Community Assembly through the Lens of Coexistence Theory[END_REF]). If we assume that niche differences are properly portrayed by phylogenetic differences, we predict a phylogenetic overdispersion (i.e. distantly related species co-occur) under competitive interactions [START_REF] Webb | Phylogenies and Community Ecology[END_REF], but see [START_REF] Mayfield | Opposing effects of competitive exclusion on the phylogenetic structure of communities[END_REF]. Reciprocally, low PD may be expected if close relative species tend to cooccur because of shared environmental niches and/or geographic isolation of land mass (phylogenetic clustering; [START_REF] Webb | Phylogenies and Community Ecology[END_REF], O'Dwyer et al. 2012, see Fig. 1.B). Overall the difference between SAR and PDAR curves is thus very informative on the way the phylogenetic structure of assemblages varies across spatial scales.

In summary the PDAR is ultimately influenced by (1) the shape of the SAR that depends on species range placement over space (e.g. either 'clumped' or random), (2) the structure of the phylogenetic tree and (3) the species range placement in regards to the phylogeny (that ultimately depends on eco-evolutionary processes). Since the pioneering work by [START_REF] Morlon | Spatial patterns of phylogenetic diversity[END_REF], that first introduced PDAR, no study has tried to explain large scale PDARs and to disentangle the relative influence of these three factors.

In this paper we report the first large-scale analysis of PDAR over the globe for mammal assemblages. We used the calibrated and dated ultrametric phylogenetic tree updated by [START_REF] Fritz | Geographical variation in predictors of mammalian extinction risk: big is bad, but only in the tropics[END_REF] from [START_REF] Bininda-Emonds | The delayed rise of present-day mammals[END_REF]. We extracted the distribution maps provided by the Mammal Red List Assessment (http://www.iucnredlist.org/) for 4616 terrestrial species to obtain occurrence data on worldwide grid cells of approximately 110*110 km and used a strictly nested design recently published (SNQ; [START_REF] Storch | Universal species-area and endemics-area relationships at continental scales[END_REF] to produce median SAR and PDAR at a continental scale (i.e. we computed median SR and PD over each spatial scale to produce median SAR and PDAR respectively). First we ask whether PDAR differs from the SAR at a continental scale and how this difference may affect the robustness of PD to habitat loss. To do so we define the relative robustness of PD (compared to SR) to habitat loss as the area between the standardized PDAR and standardized SAR (i.e. standardized by the diversity of the largest spatial window) divided by the area under the standardized SAR only (named 'relative Area Under the Curve', AUC r, ). This metric quantifies the relative increase of PD robustness compared to SR robustness (Fig. 2). Second, we ask whether PDARs is a simple consequence of the observed SAR and a random sampling of species on the phylogenetic tree or if it also depends on eco-evolutionary processes. Assuming that the continental SAR for mammals can be adequately modelled by a random placement model of species ranges [START_REF] Storch | Universal species-area and endemics-area relationships at continental scales[END_REF], we derive PDAR expectations that only rely on the phylogenetic tree shape. To do so we use a tip-shuffling null model that keeps the observed species range distribution, SAR and phylogenetic tree shape while shuffling the phylogenetic relationships among species. Third we ask whether AUC r depends on the phylogenetic tree shape only (see Fig. 1.A) or if it is also an outcome of eco-evolutionary processes (see Fig. 1.B). To do so we take advantage of our null model approach to produce null AUC r expectations. More specifically we estimate the effect of tree structure (see Fig. 1.A) on the relative robustness of PD to habitat loss across continents. Our analyses confirm that PD might be more robust than SR to habitat loss but that this higher robustness differs across continents for different reasons.

Methods

Datasets and diversity metrics

We used the distribution maps provided by the Mammal Red List Assessment (http:// www.iucnredlist.org/) for 4616 terrestrial species to obtain occurrence data on worldwide grid cells of approximately 110*110 km. The best resolution to use the IUCN maps is still under discussion in the literature [START_REF] Storch | Universal species-area and endemics-area relationships at continental scales[END_REF][START_REF] Jenkins | Global patterns of terrestrial vertebrate diversity and conservation[END_REF]. We here used the resolution commonly used at global scale [START_REF] Belmaker | Cross-scale variation in species richness-environment associations[END_REF]Jetz 2011, Storch et al. 2012). This was our basic unit to construct SAR and PDAR. Domestic, aquatic and semi aquatic mammals were excluded from the analysis. We used the calibrated and dated ultrametric phylogenetic tree updated by [START_REF] Fritz | Geographical variation in predictors of mammalian extinction risk: big is bad, but only in the tropics[END_REF] from [START_REF] Bininda-Emonds | The delayed rise of present-day mammals[END_REF].

To characterize the PD of an assemblage we used the Faith's measure [START_REF] Faith | Conservation evaluation and phylogenetic diversity[END_REF]. This metric represents a 'richness' or 'volume' of diversity [START_REF] Pavoine | Measuring biodiversity to explain community assembly: a unified approach[END_REF] and simply sums up branch lengths of the given species assemblage phylogeny [START_REF] Rodrigues | Maximising phylogenetic diversity in the selection of networks of conservation areas[END_REF]). Faith's measure is an intuitive and relatively simple measure of PD. It is also, by construction, generally highly correlated with SR (Huang et al. 2012, Tucker and[START_REF] Tucker | Unifying measures of biodiversity: understanding when richness and phylogenetic diversity should be congruent[END_REF]. The use of any PD metric theoretically linked with SR in the description of PDAR has been criticized because PDAR would be biased by "spurious artefacts of a statistical relationship between species richness and area " [START_REF] Helmus | Phylogenetic diversity-area curves[END_REF]. Here the comparison of the SAR and the PDAR within the standardisation and the null model that removes the effect of SR on PD (see section describing our null model approach) we propose avoid this artefact while it allows a simple interpretation of the results.

Constructing SAR & PDAR

Median and Median absolute deviance (MAD) of SR/PD were reported for each spatial scale (from 110*110 km up to 2200*2200 km) by using the framework proposed by [START_REF] Storch | Universal species-area and endemics-area relationships at continental scales[END_REF]. We do not use mean SR and PD as the data was highly non-normal (see Supplementary Material 1 for examples of distributions of diversity). It uses a strictly nested quadrat design where a moving window [START_REF] Leitner | Nested species-area curves and stochastic sampling: a new theory[END_REF]Rosenzweig 1997, Lennon et al. 2001) reports the SR/PD of all possible windows of a given size within a continent. The median and MAD of SR/PD are then computed for each spatial scale. This procedure implies that some cells are counted several time for a given spatial windows and thus some pseudoreplication is inevitably introduced. Nevertheless all designs have their own drawbacks and SNQ have several important advantages [START_REF] Storch | Universal species-area and endemics-area relationships at continental scales[END_REF]. We implemented the algorithm within a reduced subset of the five continents (see Supp. Mat. 2 for further details) to avoid some border effect: i.e. for each scale (whatever its size) all pixels of the selected area of the continent will be sampled at least one time. The spectrum of spatial scale analysed was set between 1*1 to 14*14 cells for Australia (i.e. from approximately 110*110 km to 1540*1540 km) and from 1*1 to 20*20 cells for North and South America, Africa and Eurasia (i.e. from approximately 110*110 km to 2200*2200 km) following [START_REF] Storch | Universal species-area and endemics-area relationships at continental scales[END_REF]. Note that the resulting curve corresponds to a type I curve in the terminology proposed by [START_REF] Scheiner | Six types of species-area curves[END_REF].

Analysing SAR & PDAR

3.1. Comparing the relative shape of SAR & PDAR-We compared the shape of PDAR and SAR using two complementary approaches. First we fitted a power model [START_REF] Rosenzweig | Species Diversity in Space and Time[END_REF] to each SAR and PDAR. We then reported the slope (z) value of the linear model in a log-log space. These values were then used to depict in a simple way the relative shape of PDAR and SAR. Because PDAR and SAR are not necessarily best modelled by a power function [START_REF] Guilhaumon | Taxonomic and regional uncertainty in speciesarea relationships and the identification of richness hotspots[END_REF][START_REF] Mazel | Multifaceted diversity-area relationships reveal global hotspots of mammalian species, trait and lineage diversity[END_REF] we also (1) fitted alternative statistical models (see Supp. Matt. 3) and ( 2) directly compared PDAR and SAR without an a-priori function. As PD is expressed in units of times while SR in number of species, they are not directly comparable. Therefore we used a basic standardization procedure by rescaling each sampling windows PD/SR value by the value reached at the maximum sample size [START_REF] Mazel | Multifaceted diversity-area relationships reveal global hotspots of mammalian species, trait and lineage diversity[END_REF]). This gives a relative diversity value for each sampling windows, compared to the largest one (that thus represents 100%). We define the relative robustness of PD (compared to SR) to habitat loss as the area between the standardized PDAR and standardized SAR divided by the area under the standardized SAR only (eq. 1 and Fig. 2).

Eq.1

If we define the absolute robustness of PD/SR as the AUC under the PDAR/SAR, our metric quantifies the relative increase of absolute PD robustness compared to absolute SR robustness (Fig. 1). To study the relative increase of PD and SR with area we simply computed the local slope (or derivative) of PDAR & SAR on the standardized coordinates assuming a first point of null diversity and area. Indeed when area tends to zero, diversity also necessarily tends to zero (as sampled area becomes smaller than a single individual).

Understanding the absolute value of PDAR-Second

we used a null model approach to describe and investigate the absolute value of PDAR. This approach allows to compare null expectations with the observed PDAR and avoids the bias caused by the correlation between PD and SR.

We chose to use the observed SAR as a starting point because it has already been shown to be modelled by a simple null model where species ranges are randomly distributed within the continent [START_REF] Storch | Universal species-area and endemics-area relationships at continental scales[END_REF]. Assuming the SAR, we computed a null PDAR expectation by randomly shuffling the tips of the phylogeny within a given pool of species. This procedure breaks the link between species range size/position and phylogenetic relationships but keep unchanged the distribution of range size and the local species richness [START_REF] Hardy | Testing the spatial phylogenetic structure of local communities: statistical performances of different null models and test statistics on a locally neutral community[END_REF]. By repeating this procedure n times (see below), we were able to assess the significance of the observed PDAR relative to our null expectation (using a two-sided test).

In other words, for each randomization, we (1) shuffled the tips of the phylogeny within a given species pool (see below). The resulting randomized phylogeny was used to (2) compute null PD values for each basic grid cells (approximately 110*110 km) and we (3) applied the methodology described above to compute the resulting null median and MAD PDARs. Such null model may help unravel the determinants of the PDAR. For example we may expect competition [START_REF] Pigot | Species interactions constrain geographic range expansion over evolutionary time[END_REF] or environmental filtering to occur at smaller scale, potentially leading to phylogenetic overdispersion or clustering respectively [START_REF] Webb | Phylogenies and Community Ecology[END_REF]; but note that competition may also lead to clustering, see [START_REF] Mayfield | Opposing effects of competitive exclusion on the phylogenetic structure of communities[END_REF]. Also, phylogenetic clustering could be detected at larger scales because of biogeographical effect [START_REF] Rosenzweig | Species Diversity in Space and Time[END_REF]. We used two null models that use either a (1) continental or a (2) biogeographic pool of species. We restricted the analysis of the biogeographic pool of species for Eurasia only because it is the only continent in our design that is a mix of distantly related zoogeographic regions (Wallace 1876[START_REF] Holt | An Update of Wallace's Zoogeographic Regions of the World[END_REF].

(1) Continental pool of species: This null model simply shuffles the tips within the entire continental phylogeny. The significance of the observed values of PDAR was assessed by comparing observed values with 1000 randomized PDARs. We further confirmed this simulation approach by using analytical expectations of PD based on the framework of Nipperess and Matsen (2013, Supp. Mat. 4) (2) Biogeographical pool of species: First we defined zoogeographic regions following the methodology of [START_REF] Holt | An Update of Wallace's Zoogeographic Regions of the World[END_REF]. To do so we computed phylogenetic beta diversity values between each pair of grid cells from the Eurasian continent by using an index independent of species richness [START_REF] Lennon | The geographical structure of British bird distributions: diversity, spatial turnover and scale[END_REF][START_REF] Holt | An Update of Wallace's Zoogeographic Regions of the World[END_REF]):

(Eq. 1)

where a = the branch lengths shared by the two grid cells and b and c represent the branch lengths unique to each grid cell.

Then we identified group of grid cells (=zoogeographic regions) using the unweighted pair group method with arithmetic mean (UPGMA, function hclust in R; R Development Core Team 2014). We varied the number of delimited zoogeographic regions from 1 to 30 (see Supp. Mat. 5 for examples). We then used these regions to construct a biogeographical null model of the PDAR. While we were shuffling species within the entire continental pool of species in the previous null model, we shuffled here species within the pool of species belonging to a specific zoogeographic region. Because all species are not restricted to one unique zoogeographic region, we adopted a probabilistic approach where, for each randomization independently, a zoogeographic region k is assigned to a species i with a probability of Pi,k depending on its coverage C i,k in this region with respect to its total coverage across all regions:

(Eq. 2)

where K represents the entire set of regions (from 2 to 30). For each randomization, we computed a null PDAR and tested significance by comparing the observed PDAR and 100 null PDAR for each number of zoogeographic regions defined.

Results & Discussion

To visually compare the PDAR and the SAR of mammals we standardized the two curves by the maximal diversity reached in the data set. The two resulting curves are thus expressed in % of maximal diversity and are directly comparable (Fig. 3). We show that PDARs approach their maximum faster than SARs for all continents (Fig. 3). To describe the rate of PD and SR accumulation as a function of area, we estimated local derivatives and show that PDARs accelerate much faster than SARs for small areas and that this tendency reverses for large areas (see subplots of Fig. 3). We show that the power model is among the best model to fit the dataset (Supplementary Mat. 6) but fails to model the upward acceleration of PD on a log-log scale (e.g. Fig. 4). The slope of the power model is lower for the PDARs than for the SAR (z PDAR < z SAR , see Supplementary Mat. 7). The last point has been previously reported at this scale [START_REF] Mazel | Multifaceted diversity-area relationships reveal global hotspots of mammalian species, trait and lineage diversity[END_REF]) but with a different PDAR/SAR reconstruction based on non-overlapping ecoregions [START_REF] Olson | Terrestrial Ecoregions of the World: A New Map of Life on Earth[END_REF]). This result is thus independent of the sampling procedure and approaches, and is, overall, not surprising. Indeed the SAR fully represents the PDAR in the case of a star phylogeny (in this case the PD is proportional to SR). As the phylogenetic tree departs from a star phylogeny (i.e. as some branches start to be shared between species), the relationship between PD and SR becomes concave and the PDAR deviates from the SAR (because redundancies between species are introduced, see Fig. 1.A). As a consequence, AUC r values are positives but we find that they differ across continents (see Fig. 23). The use of the SAR to predict species extinction from habitat loss [START_REF] Pimm | Biodiversity: extinction by numbers[END_REF][START_REF] Thomas | Extinction risk from climate change[END_REF][START_REF] Halley | Extinction debt and the species-area relationship: a neutral perspective[END_REF]) has been questioned [START_REF] He | Species-area relationships always overestimate extinction rates from habitat loss[END_REF]) but remains useful (e.g. [START_REF] Axelsen | Species-area relationships always overestimate extinction rates from habitat loss: comment[END_REF][START_REF] Hanski | Species-fragmented area relationship[END_REF][START_REF] Matias | Estimates of species extinctions from species-area relationships strongly depend on ecological context[END_REF], especially when species ranges are randomly distributed [START_REF] He | Species-area relationships always overestimate extinction rates from habitat loss[END_REF]). If we assume that the SAR and the PDAR can be used to predict the loss of species and PD, respectively, through habitat loss [START_REF] Mazel | Multifaceted diversity-area relationships reveal global hotspots of mammalian species, trait and lineage diversity[END_REF], the AUC r (Fig. 2) then represents the relative robustness of PD (compared to SR) to habitat destruction. In this case, we show, for example, that the Australian PD will be relatively more robust-at the continental scale-than the Eurasian PD to habitat loss (note that at the global scale, the evolutionary history of Australia is particularly unique; [START_REF] Holt | An Update of Wallace's Zoogeographic Regions of the World[END_REF]. This difference could be explained by the different structure of the two trees (see Fig. 1.A) and/or by different eco-evolutionary processes leading to a different spatial pattern of PD (e.g. either clustered, random or overdispersed; see Fig. 1.B). Teasing apart these two mechanisms called for using appropriate null models.

For all continents except Eurasia and for most of the spatial scales, we find that PD values are not significantly different from those obtained with the null model randomizing the phylogenetic relationships among species (Fig. 4 and Supplementary Mat. 8). This means that the only significant phylogenetic effect that influences the PDAR is the shape of the observed continental tree. Several non-mutually exclusive hypotheses can be proposed to explain this result. First, we use here an averaged phylogenetic structure across a whole continent and different assembly processes may have been mixed. In North America for example we could expect a phylogenetic clustering at high elevation in the Rocky Mountains (e.g. due to environmental filtering) while overdispersion could be found in the lowland forest (e.g. due to competition, Graham and Parra 2009), resulting in higher MAD of PD than expected by chance (see Supp. Mat. 9). Such distribution may likely compensate each other during the sampling process, resulting in a null random distribution when averaged across assemblages. Second, the spatial and phylogenetic scale of our analysis is perhaps too large to detect any effect of repulsion/attraction of species. Indeed, at the smallest resolution we have used (110*110 km), co-occurring species do not necessarily interact with each other (probably because this scale is still very large) and may, for example, use different habitats (Araújo andRozenfeld 2014, but see Cardillo 2011). Also, specific group of mammals may show repulsion or attraction while others not, blurring the overall pattern (see e.g. [START_REF] Pedersen | Macroecological evidence for competitive regional-scale interactions between the two major clades of mammal carnivores (Feliformia and Caniformia)[END_REF].

The Eurasian PDARs is however much lower than expected by chance at all spatial scales, indicating phylogenetic clustering (Fig. 4 and Supplementary Mat. 8). This continent is a mosaic of biogeographic realms with diverging biogeographic history (Wallace 1876[START_REF] Holt | An Update of Wallace's Zoogeographic Regions of the World[END_REF]) and thus mixes very different faunas: there are many strict Palearctic species (e.g. the wolverine, Gulo gulo) and strict oriental species (e.g. the asiatic elephant, Elephas maximus). The continental null model mixes all these faunas and thus tends to overestimate the expected median PD of assemblages. For example Elephas maximus represents the only afrotherian species present in our data set so it has a very high distinctiveness at the continental scale and will considerably increase relative local PD. We consequently develop a biogeographical null model that takes into account the historical origin of taxa. We show that this null model progressively decreases the random PD expectations (Fig 5) and that 15 realms were sufficient to correctly predict most of the spatial scale median PD and observed c value (Fig. 5 and Supp. Mat. 10-11). Our approach may sound circular at first glance because we use spatial and phylogenetic data (to define zoogeographic regions) to explain spatial and phylogenetic data (the PDAR). Nevertheless the aim of any null models is rather to ask how much synthetic information we need from the initial data to parsimoniously explain this data. The null model is necessarily constrained by the initial data but if this constrain is too high (i.e. a lot of the initial data is used) the null model will necessarily be plausible (the "narcissus effect"; [START_REF] Gotelli | Research frontiers in null model analysis[END_REF]. Here our aim is to quantify how much synthetic information is needed to parsimoniously explain the Eurasian PDAR. Finally it is not directly possible to conclude from the biogeographic null model that the effect we detected is purely 'historic', i.e. that it derives from the mix of fauna due to continental drift. Indeed Eurasia has also a steep North-South gradient in term of climate (and SR) and we cannot reject the hypothesis of a phylogenetic clustering due to environmental filtering [START_REF] Webb | Phylogenies and Community Ecology[END_REF]. One potential future avenue could be to contrast the relative predictive power of biogeographic null model versus a climate based null model.

We also find that PD at small scale tends to be higher than expected by chance for South America (phylogenetic overdispersion, Fig. 4), leading to a significantly low z value for the PDAR (Supp. mat. 8, p<0.005). This observation may result from allopatric speciation events and/or competition at the smallest scale (Pigot and Tobias 2013) but more work is needed to test these hypotheses. For Eurasia, on the contrary, we observe that small scale PD tends to be relatively lower than expected by chance (phylogenetic clustering, Fig. 4) leading to a significant high z value (p<0.01, Supp. Mat. 8). This could be a possible product of environmental filtering occurring only at small scale.

These last two results shed light on the discrepancy between observed and null AUC r (Supp. mat. 12 black and red lines respectively). Indeed the robustness of PD to habitat loss depends on the structure of the phylogenetic tree (represented here by the null model mean expectation) and also on the spatial pattern of phylogenetic structure (represented by the departure of the observed PDAR from the mean null model, see subplots in Fig. 4). We indeed find that Australian observed AUC r is higher than predicted by the continental tree structure because small scale Australian PD tends to be relatively higher than expected by chance (see Supp. Mat. 12), providing a buffer against the loss of PD. In contrast, observed Eurasia AUC r is lower than expected by the tree shape (see Supp. Mat. 12). This is because Eurasian PD is disproportionately low at small scale, reducing the area between the PDAR and the SAR compared to random expectations and thus being more vulnerable to habitat reduction. Overall, we demonstrate that the additional robustness of PD to habitat loss compared to species richness is determined by the phylogenetic tree shape but also depends on the spatial structure of PD. Note that the red PDAR also corresponds to the observed SAR as the red tree is a star phylogeny. (B) Different eco-evolutionary processes may change the PDAR if they act differently among spatial scales. We expect that competition and/or allopatric speciation may relatively increase the PD at small scale while environmental filtering and/or geographic isolation of biotas may relatively decrease the PD at small scale. The example shows how to quantify the relative PDAR shape by measuring the Area between the two curves (SR, PD and Area are expressed in %) and computing AUC r . For each continent, we report the SAR & the PDAR rescaled by the value of the maximum SR and PD respectively. The two curves are both expressed in percentage of maximum diversity and thus directly comparable. We also report the corresponding AUC r values (see Fig. 2). In the lower-right corner subplots we show the corresponding local derivatives. For each continent, the envelope corresponding to 1000 null continental PDARs is shown in black while the observed PDAR is in red. In the corner of each panel, we plot the relative rank of observed PD value within the null PD distribution as a function of log Area. For each spatial scale, it is computed as the percentage of null PD values that are lower than the observed value (a value of 0.5 indicates that observed PD equals the median of the null distribution). The dashed lines correspond to a relative rank of 2.5% and 97.5%. When the The biogeographical null models shuffle the tips of the phylogeny according to biogeographical origin (see methods). We present the results from null models containing different numbers of biogeographical regions. The top panel presents the median PDAR obtained for different number of biogeographic regions (see legend). The four other panels represent the details of four biogeographic null models that used 1 (=continental null model), 2, 15 or 30 biogeographic regions, respectively. The * indicates if the relative rank of observed PD value within the null PD distribution is lower (or higher) than 0.025 (or 0.975) for a given area.

Figure 1 .

 1 Figure 1. Expected variation of the standardized PDAR given (1.A) different tree shapes and (1.B) different eco-evolutionary processes (A) The three standardized PDARs correspond to the three trees depicted above the graph.Note that the red PDAR also corresponds to the observed SAR as the red tree is a star phylogeny. (B) Different eco-evolutionary processes may change the PDAR if they act differently among spatial scales. We expect that competition and/or allopatric speciation may relatively increase the PD at small scale while environmental filtering and/or geographic isolation of biotas may relatively decrease the PD at small scale.

Figure 2 .

 2 Figure 2. Hypothetical example to quantify the relative robustness of PD (compared to SR) to habitat loss (AUC r ) using PDAR and SAR

Figure 3 .

 3 Figure 3. Observed rescaled median SARs and median PDARs

Figure 4 .

 4 Figure 4. Median PDARs obtained from the continental null model

Figure 5 .

 5 Figure 5. Median PDARs obtained from the Eurasian biogeographical null models

Ecology. Author manuscript; available in PMC 2015 December 15.

Ecology. Author manuscript; available in PMC 2015 December 15.Europe PMC Funders Author Manuscripts

Acknowledgements FM would like to thank Loïc Chalmandrier for helpful discussions on null models and Petr Keil for discussions on the PDARs. The research leading to these results had received funding from the European Research Council under the European Community's Seven Framework Programme FP7/2007-2013 Grant Agreement no. 281422 (TEEMBIO). FM, WT & JR belong to the Laboratoire d'Écologie Alpine, which is part of Labex OSUG@2020 (ANR10 LABX56).

Supplementary Material

Refer to Web version on PubMed Central for supplementary material.


David Poirier-Quinot
email: david.poirier-quinot@dalembert.upmc.fr.

Martin S Lawless

Brian F G Katz

WHEN HRTF TRAINING DOESN'T WORK

Keywords: binaural, HRTF, training, localization

Previous studies have established the efficiency of training programs to help users improve on binaural auditory localization when using a non-individual head-related transfer function. This paper reports the results of an experiment where participants trained with such a program, though they failed to improve. Interestingly, the same training program had successfully been used in a previous study. After a brief description of the program and the experiment protocol, a comparative analysis of the results of both studies is provided. The discussion then focuses on the differences between these studies in an attempt to better understand what caused the training to fail.

INTRODUCTION

Most wearable Augmented Reality (AR) and Virtual Reality (VR) systems today use binaural synthesis to simulate 3-dimensional environments over headphones. The objective of this technique is to render spatial auditory scenes by applying direction-dependent audio cues to monophonic signals to alter the timing and frequency content and makes it appear to the listener that the sound originates externally from a location in the virtual space [START_REF] Blauert | Spatial Hearing: The Psychophysics of Human Sound Localization[END_REF][START_REF] Begault | 3-D Sound for Virtual Reality and Multimedia[END_REF]. The set of direction-dependent audio cues, including timing and level differences between the left and right ears caused by the location of the source as well as distortions in the signal due to reflections from the head, torso, and pinna, are all contained within the head-related transfer function (HRTF), which represents the propagation of an acoustic wave from a set of specific source positions to the listener's ears. Therefore, an individual HRTF 1 tends to be unique to each listener and is not as effective for rendering spatial audio scenes for other listeners, often causing a degradation in the externalization or localization accuracy of the virtual sources [START_REF] Wenzel | Localization using nonindividualized head-related transfer functions[END_REF][START_REF] Bronkhorst | Localization of real and virtual sound sources[END_REF].

AR and VR systems commonly use non-individual HRTFs because measuring each consumer's HRTF is currently impractical. Past studies have shown that users can adapt to non-individual HRTFs, exhibiting improved localization performance approaching that of listeners using individual HRTFs [START_REF] Carlile | Accommodating to new ears: the effects of sensory and sensorymotor feedback[END_REF][START_REF] Parseihian | Rapid head-related transfer function adaptation using a virtual auditory environment[END_REF][START_REF] Stitt | Auditory accommodation to poorly matched non-individual spectral localization cues through active learning[END_REF]. However, modern literature on this "rapid" HRTF adaptation via training has been limited to studies conducted in the lab (in contrast to studies such as [START_REF] Young | Auditory localization with acoustical transposition of the ears[END_REF][START_REF] Hofman | Relearning sound localization with new ears[END_REF][START_REF] Trapeau | Adaptation to shifted interaural time differences changes encoding of sound location in human auditory cortex[END_REF] using long-term passive adaptation) in controlled environments with high-end computing and proaudio hardware. These limitations would be prohibitive for everyday consumers of AR and VR devices.

The objective of the present study was initially to determine if an HRTF training program could be conducted effectively at home using an off-the-shelf head mounted display (HMD). Participants completed a threeday HRTF training using an established learning program [START_REF] Poirier-Quinot | On the improvement of accommodation to non-individual HRTFs via VR active learning and inclusion of a 3D room response[END_REF] at home with an HMD, and their localization accuracy performance was evaluated over the course of three training sessions to assess how their performance changed with time. The results of this experiment were compared to a previous study [START_REF] Poirier-Quinot | On the improvement of accommodation to non-individual HRTFs via VR active learning and inclusion of a 3D room response[END_REF], which used the same training program in the lab, to ascertain whether the participants exhibited similar levels of localization performance improvement over the course of the training.

MATERIALS AND METHODS

Fourteen participants trained on HRTF adaptation for auditory localization, all using the same non-individual HRTF. They trained at home, for 12 minutes per day over three consecutive days. They were equipped with a Quest 2 HMD, using the built-in headphones, running a training program designed to adapt auditory cue interpretation using feedback and proprioception. The training timeline is depicted in Figure 1. The HRTF, or more precisely the binaural room impulse response (BRIR), participants trained with was that of the KU100 dummy-head, recorded with a 5 • resolution on a 0.8 m radius sphere in a dry room (T 30,1000 Hz of 0.12 s). This 4.2 × 3.8 × 3.2 m 3 room was selected as it is very similar to the one simulated in [START_REF] Poirier-Quinot | On the improvement of accommodation to non-individual HRTFs via VR active learning and inclusion of a 3D room response[END_REF] that helped accelerate training compared to anechoic conditions.

The training program, detailed and evaluated in [START_REF] Poirier-Quinot | On the improvement of accommodation to non-individual HRTFs via VR active learning and inclusion of a 3D room response[END_REF], was developed in Unity. It is divided into 14 difficulty levels where participants faced the various challenges of auditory localization with non-individual binaural rendering: front-back confusions, localization blur, etc.. Each level is composed of trials; for each trial, participants indicate which of the visual targets surrounding them is the one emitting a sound. The number of visual targets (i.e. of potential decoys) displayed depends on the current level's focus and difficulty grading. To further help with the task, participants are equipped with a virtual auditory source, a "probe" attached to each of their hands, to allow them to listen to how the HRTF sounds at any given position.

Before the first training, to establish a baseline reference, and after each training session, participants performed an auditory localization task in the same virtual environment as the training. This evaluation task, identical to that used in [START_REF] Parseihian | Rapid head-related transfer function adaptation using a virtual auditory environment[END_REF][START_REF] Stitt | Auditory accommodation to poorly matched non-individual spectral localization cues through active learning[END_REF][START_REF] Poirier-Quinot | On the improvement of accommodation to non-individual HRTFs via VR active learning and inclusion of a 3D room response[END_REF][START_REF] Poirier-Quinot | Impact of wearing a head-mounted display on localization accuracy of real sound sources[END_REF] consisted in a series of trials during which participants pointed towards the perceived location of the sound source. Participants could no longer use the probe during the localization task. Participants were tested on twenty different source locations distributed around them on the sphere, each repeated three times for each localization session.

The audio stimulus used during both the training and localization task consisted of a sequence of three white noise bursts, lasting a total of 180 ms to limit the use of head movement and dynamic localization cues. Played as a loop during the training, so that participants had time to estimate its position using their probes, it was only played once during the localization task. During the training, participants would only hear the stimulus when their head was at rest position [START_REF] Poirier-Quinot | On the improvement of accommodation to non-individual HRTFs via VR active learning and inclusion of a 3D room response[END_REF]), preventing them from relying on, and thus learning, dynamic cues via head movement despite the looping stimulus. The binaural rendering was generated off-line, prior to the experiment, with a different audio file created for each potential position on the sphere by convolving the input bursts with each of the KU100 BRIRs. As in [START_REF] Poirier-Quinot | On the improvement of accommodation to non-individual HRTFs via VR active learning and inclusion of a 3D room response[END_REF], eight different versions of the stimulus were created for each position, using different noise seeds and applying a ±3 dB level roving to ensure participants did not rely on synthesis artifacts to identify auditory source positions.

Along with the HMD, participants were given instructions to set up the experiment at home. They were instructed to use the HMD built-in headphones, to train while standing up in a clutter-free 2 m wide zone to encourage full auditory sphere exploration, and to disable WiFi during training to avoid distracting notifications.

Data analysis

Localization accuracy was assessed based on the methodology presented in [START_REF] Poirier-Quinot | HRTF Performance Evaluation: Methodology and Metrics for Localisation Accuracy and Learning Assessment[END_REF]. The global extent of the localization error is first assessed using the great-circle error. Critical localization confusions are then evaluated using the response classification scheme proposed in [13, c.f. Fig- ure 4] with a 45 • threshold, illustrated in Figure 2. Finally, the local extent of localization error is evaluated using the local great-circle, local lateral, and local polar weighted error. These "local" metrics are computed by considering only responses classified as "precision" responses, i.e. that fell within a 45 • cone around the source location, to avoid localization reversals inflating angular metric values [START_REF] Poirier-Quinot | Impact of wearing a head-mounted display on localization accuracy of real sound sources[END_REF].

Analyses of variances (ANOVAs) [START_REF] Faraway | Extending Linear Models with R: Generalized Linear, Mixed Effects and Nonparametric Regression Models[END_REF] were conducted for each of the dependent variables of mean global and local great circle angle, lateral, and polar errors (using R [START_REF] Core | R: A Language and Environment for Statistical Computing[END_REF]), to assess the evolution of participant performance within and across sessions. The factors included in the analysis were source location repetition (1, 2, or 3) and session number (L0-L3), as well as the first-order interaction between these two factors. Likewise, generalized linear mixed models (GLMMs), constructed as repeated measures logistic regressions [START_REF] Faraway | Extending Linear Models with R: Generalized Linear, Mixed Effects and Nonparametric Regression Models[END_REF], were used to evaluate the evolution of the percentage of reversal errors based on the same factors of the ANOVAs. For the GLMMs, the significance of each factor was determined by performing goodness of fit comparisons between the full models and models with single-term deletions.

Similar statistical models were used to compare the localization performance of the participants in the present study to those in [START_REF] Poirier-Quinot | On the improvement of accommodation to non-individual HRTFs via VR active learning and inclusion of a 3D room response[END_REF] in Section 3.2. The models were adjusted to include the factor of group: participants in the present study are referred to as the G current group, those in the previous study [START_REF] Poirier-Quinot | On the improvement of accommodation to non-individual HRTFs via VR active learning and inclusion of a 3D room response[END_REF] as the G previous group. The firstorder interaction terms between groups and the other factors were also included in the models.

For all tests, statistical significance was determined for p-values below a 0.05 threshold. The notation p < ε is adopted to indicate p-values below 10 -3 . Post-hoc pair-wise comparisons for significant factors were made with Tukey-Kramer adjusted p-values.

RESULTS AND DISCUSSION

Training assessment in the current study

The evolution of the four angular metrics for G current is illustrated in Figure 3. ANOVA indicated that training had a significant impact on the global great-circle error (p < ε). Post-hoc comparison showed that it significantly decreased only between L0 and L1 (50.4 ± 2.1 • vs. 44.4 ± 2.1 • , p < ε), not evolving after L1 (p = 1.00 for each L1 through L3 comparison). Further analysis showed that training had no significant impact on local great-circle error, lateral error, and weighted-polar (p > 0.05).

The evolution of precision responses rate and confusion rates for G current is illustrated in Figure 4. ANOVA indicated that training had a significant impact on the percentage of in-cone and off-cone confusions (p < ε for both). Post-hoc comparisons showed that between L0 and L1, the in-cone confusion rate dropped from 21.0% to 16.9%, and the off-cone confusion rate from 1.8% to 0.7%. Neither confusion rate evolved after L1. No significant effect was observed for training on the front-back confusion rate.

Training comparison with the previous study

The training protocol used in the current study was nearly identical to that used in [START_REF] Poirier-Quinot | On the improvement of accommodation to non-individual HRTFs via VR active learning and inclusion of a 3D room response[END_REF]. As such, the results of G current participants are compared to those reported in [START_REF] Poirier-Quinot | On the improvement of accommodation to non-individual HRTFs via VR active learning and inclusion of a 3D room response[END_REF] in this section. Only the results of participants of the "G-reverb" group in [START_REF] Poirier-Quinot | On the improvement of accommodation to non-individual HRTFs via VR active learning and inclusion of a 3D room response[END_REF], training with a room acoustic condition comparable to that of the present study, will be considered in this analysis. This group is referred to here as G previous . G current and G previous trained during the same amount of time, with what appears to be the same dedication, as they completed a comparable average and standard deviation of 103 ± 46 and 109 ± 47 "training trials", respectively, over the 3 days of their training. To better appreciate the comparison, an exhaustive list of the differences between the current training protocol and that used in [START_REF] Poirier-Quinot | On the improvement of accommodation to non-individual HRTFs via VR active learning and inclusion of a 3D room response[END_REF] is provided in Table 1.

The factors of session and group as well as the interaction between them significantly affected the global great-circle angle error (p < ε, p < 0.002, and p < ε, respectively). Post-hoc means comparisons showed that Table 1: Differences between the protocols of the present study vs. that used in [START_REF] Poirier-Quinot | On the improvement of accommodation to non-individual HRTFs via VR active learning and inclusion of a 3D room response[END_REF]. ITD stands for Interaural Time Difference and HOA for High Order Ambisonic.

Previous study [START_REF] Poirier-Quinot | On the improvement of accommodation to non-individual HRTFs via VR active learning and inclusion of a 3D room response[END_REF] ANOVA of the absolute local lateral error indicated that both group and session factors were significant (p < ε for both treatments), as well as the interaction between them (p < 0.02). As for local great-circle error, post-hoc analysis did not show any difference between both groups in L0 (p = 0.54). G previous showed a marked improvement in absolute local lateral error between L0 and L2 (p < ε) and between L0 and L3 (p < ε), but there were no significant differences between L1, L2, and L3 (p > 0.05 for all comparisons). On the other hand, G current showed no improvement at all during training, having similar absolute local lateral errors across all four sessions (p > 0.05 for all comparisons). This result is illustrated in Figure 3(c).

For absolute local weighted-polar error, only the main factors of session (p < 0.003) and group (p < ε) were significant, the interaction term was not (p = 0.08). On average between the two groups, the participants showed improvement between L0 and L2 (p < 0.03), and between L0 and L3 (p < 0.003), for a total improvement of 2.2 ± 0.6 • , showed in Figure 3(d). There was no difference between L1-L3 (p > 0.05 for all comparisons). Across the four sessions, the participants in G previous had a better absolute local weighted-polar error than G current by 3.4 ± 0.9 • .

The interaction effect between the factors of session and group was also significant for front-back, in-cone, and off-cone confusion rates (p < ε, p < 0.003, and p < 0.04, respectively). Both G previous and G current had similar amounts of front-back confusion rates in L0 (17.4% and 16.6%, respectively; p = 1.00). G previous participants front-back confusion decreased to 11.8% in L1 (p < 0.04), to then stagnate from L1 to L3 (p > 0.05 for all comparisons between sessions). By comparison, G current stagnated during the whole training, and still had a front-back confusion rate of 16.3% in their last session L3 (p > 0.05 for all comparisons), illustrated Figure 4(b). G previous had fewer in-cone confusions overall, starting at 11.8% in L0 and significantly improving to 4.1% in L2 (p < ε). While the in-cone confusion rate in L3 was lower for G previous , it was not significant different from L2 (p = 0.87). In comparison, G current had 21.0% incone confusions in L0, significantly more than G previous (p < 0.05), and only improved to 15.2% in the final session (p < 0.02), illustrated in Figure 4(c). Lastly, while both groups initially had similar off-cone confusions rates in L0 (1.3% for G previous and 1.8% for G current , p = 1.00) and demonstrated improvement over time, G previous ended the sessions with a slightly better rate of 0.1% compared to 0.9% for G current , though these are not significantly different from each other (p = 0.23). Off-cone confusion rate evolution across sessions for both groups is illustrated Figure 4(d).

The impact of training on individual performance of G current and G previous is illustrated in Figure 5. This figure depicts an individual's change in "precision" response rate (i.e. 1-confusion rate) on the Y-axis and change in local accuracy on the X-axis between L1 and L3. Improvement in precision rate is indicated by a greater precision rate in L3 (higher on the Y-axis), while improvement in local accuracy is shown by lower great-circle angle error (left on the X-axis). The majority of the participants in G previous demonstrate improvement in one or both categories. G current , however, is more centered about the middle of the graph with only some individuals exhibiting improvement, primarily in local accuracy. The figure also suggests that there is no obvious cluster of "good" vs. "bad" learners in G current , as has been seen in previous studies [START_REF] Parseihian | Rapid head-related transfer function adaptation using a virtual auditory environment[END_REF][START_REF] Stitt | Auditory accommodation to poorly matched non-individual spectral localization cues through active learning[END_REF].

Discussion: why so little improvement for G current compared to G previous ?

The first interesting result reported in Section 3.2 is the difference between the performance of both groups before the training in L0. It might be that the lack of HRTF selection in G current compared to G previous is responsible for this difference. For comparison, results of reported in [START_REF] Parseihian | Rapid head-related transfer function adaptation using a virtual auditory environment[END_REF][START_REF] Stitt | Auditory accommodation to poorly matched non-individual spectral localization cues through active learning[END_REF] indicate that participants using a worst-match HRTF with individualized ITD had an initial great-circle error above 60 • , and a precision response rate below 50%. Additionally, the results of G current are very close to those obtained by participants using a random HRTF without ITD individualization in [START_REF] Steadman | Short-term effects of sound localization training in virtual reality[END_REF], reporting an initial great-circle error of 51 • and a precision response rate of 55%. This initial difference could also be attributed in part to the absence of ITD adjustment for G current compared to G previous . The similitude between their initial lateral local angle errors however argues against this hypothesis.

The second striking result is the difference in learning from L1 to L3 between the two groups, illustrated in Figure 5. We examine this evolution from L1 to reduce the contribution of procedural learning which appears most prevalent between L0 and L1. Previous studies results suggest that a certain percentage of non-proficient learners should be expected in every HRTF learning experiment [START_REF] Parseihian | Rapid head-related transfer function adaptation using a virtual auditory environment[END_REF][START_REF] Stitt | Auditory accommodation to poorly matched non-individual spectral localization cues through active learning[END_REF][START_REF] Poirier-Quinot | HRTF Performance Evaluation: Methodology and Metrics for Localisation Accuracy and Learning Assessment[END_REF]. This percentage is well above zero however, even in non-favorable conditions as when par- ticipants train with a worst-match HRTFs (e.g. 5 nonlearners out of 8 participants in the W10 group in [START_REF] Stitt | Auditory accommodation to poorly matched non-individual spectral localization cues through active learning[END_REF]). As such, it is unlikely that the observed difference is due to an unlucky participant selection in the current experiment. The next obvious factor might be the HRTF. Looking at the results of participants training on their worstmatch HRTF in [START_REF] Parseihian | Rapid head-related transfer function adaptation using a virtual auditory environment[END_REF][START_REF] Stitt | Auditory accommodation to poorly matched non-individual spectral localization cues through active learning[END_REF], some participants still show a significant improvement between evaluations L1 and L3 in these studies. Still, it might be that the KU100 HRTF used in the present study was very different from every G current participants' individual HRTF, thereby presenting a significantly lower potential for improvement as argued in [START_REF] Stitt | Auditory accommodation to poorly matched non-individual spectral localization cues through active learning[END_REF]. As a reminder, G previous participants used their best-match HRTF, selected before L0 based on subjec-Figure 6: Frequency response (1 channel) of the Quest 2 integrated headphones, measured with a KU100 dummy-head. The logarithmic sine-sweep used as a stimulus was uploaded to the Quest Unity using the PCM (lossless) decompression algorithm. For comparison, the response of the Quest 2 connected (3.5 mm jack output) to a HD 600 headset has been added ("Quest 2 with HD 600"), as well as that of the HD 600 alone, using the same unity application, not running on the Quest 2 but on a computer. tive affinity among a 7-elements subset from the LISTEN database [START_REF] Katz | Perceptually based head-related transfer function database optimization[END_REF]. This is a serious claim, however, and requires further tests to be evaluated.

Another potential factor might be that G current trained with the Quest 2 integrated headphones, whereas G previous trained with a Sennheiser HD 600. The frequency responses of both devices were measured on a KU100 dummy head, reported in Figure 6. The usable (± 5 dB) frequency range for the Quest 2 appears to be 300 to 8000 Hz, with a steep drop off after 7500 Hz. Notably, the reduction in energy in the a critical localization spectral cue high-frequency region also could have significantly affected participants' poor training performance in the current study. Comparatively, the measured frequency range for the HD 600 headphones was 40 to 12 000 Hz.

There remain two principal additional factors that could be the reason for G current participant's poor performance improvement during the training compared to G previous : the use of different room acoustics, and the fact that participants trained at home in an uncontrolled environment. Additional tests are required and are being conducted to investigate the role of each element.

If there is a silver lining to the absence of perceptual HRTF adaptation reported after L1, it is that the evolu-tion of localization metrics observed between L0 and L1 might then used as a measure of expected procedural learning improvement in those metrics. Based on the existing literature [START_REF] Poirier-Quinot | HRTF Performance Evaluation: Methodology and Metrics for Localisation Accuracy and Learning Assessment[END_REF], the L0-L1 evolution leading to the L1-L3 performance plateau seems indeed both too fast and not large enough to be attributed to perceptual learning. If so, typical procedural learning evolution of those metrics are notably 5 • improvement in overall great-circle angle error, 7 % improvement in precision response rate, 4 % in in-cone error rate, and 2 % in off-cone error rates. The remaining metrics showed no marked improvements.

SUMMARY AND CONCLUSION

This paper reported the performance evolution of participants training on auditory localization with a nonindividual HRTF-BRIR. Surprisingly, said evolution was minimal: performance metrics show a slight improvement after the first training session and none after the second and third (12 min each), suggesting only procedural learning but not perceptual HRTF adaptation. These results were compared to those of a previous study where participants trained with the same program, this time very obviously improving after each session. The comparison suggests that the limited learning could be a result of the headphones/audio-hardware used (Quest 2 integrated headphones), of a lack of affinity between participants and the HRTF used (KU100), or of the uncontrolled nature of the training environment. A complementary study is underway to understand better what happened here. The results of this study, and the follow-up work, should help to design more robust HRTF training programs.

Figure 1 :

 1 Figure 1: Schematic timeline of the experiment sequence. Li are localization tasks used to evaluate participant performance, Ti are training tasks.

Figure 2 :

 2 Figure 2: Response classification scheme proposed in [13], defining the response type as a function of the response position on the sphere. The white circle indicates the considered target position, at spherical coordinates (35 • , 10 • ). The listener is facing X with his left ear pointing towards Y . The angle threshold used in the figure is of 20 • compared to the 45 • used in the analysis to better illustrate the various response type regions.

4 •

 4 and 42.7 ± 2.1 • , respectively. After L1 however, G current did not improve in their global great-circle angle performance in L2 or L3 (p = 1.00 for all three comparisons), while G previous demonstrated clear localization improvement (p < ε for all three comparisons). This result is illustrated in Figure3(a).Once again, the global great-circle error was decomposed into local angular metrics and confusion error rates. The factors of session and the interaction term between session and group were significant in the ANOVA model for local great-circle angle error (p < ε). Both groups of participants had the same initial local great-circle errors in L0 (p = 0.97), illustrated in Figure3(b). G current did not demonstrate any performance improvement across the four sessions (p > 0.96). On the other hand, G previous local great-circle error significantly improved from 25.1 ± 0.8 • in L0 to 20.4 ± 0.8 • in L3 (p < ε).

Figure 3 :

 3 Figure 3: Evolution of mean and 95% Confidence Interval (CI) of angular errors across sessions for G current and G previous .

Figure 4 :

 4 Figure 4: Evolution of mean and 95% Confidence Interval (CI) of response category rates across sessions for G current and G previous . The four category rates sum to 100%.

Figure 5 :

 5 Figure 5: (L3 -L1) difference in individual participant performance for (a) G current and (b) G previous . The Y-axis represents the evolution of precision type response rate, while the X-axis shows the evolution of participants local great-circle angle error. Points in the top-left corner represent participants with the best relative performance improvement between L1 and L3.

  (G previous ) Current study (G current ) HRTF usedBest-match HRTF issued from a 2 min subjective selection from LISTEN[START_REF] Warusfel | IRCAM Listen HRTF database[END_REF] subset[START_REF] Katz | Perceptually based head-related transfer function database optimization[END_REF]

			KU100 dummy-head
	Virtual acoustic environment Simulated test room HOA [18]	Actual test room BRIR
	ITD individualization	ITD based on head circumference	No ITD adjustment
	Headphones	Sennheiser HD 600	Quest 2 integrated headphones
	Location	In the lab	At participant's home

both G previous and G current started with statistically similar performance levels in L0 (p = 1.00), with errors of 47.2 ± 2.4 • and 48.7 ± 2.1 • respectively. Both groups exhibited significantly lower global great-circle angle errors in L1 (p < ε), statistically similar to one another (p = 0.46) at 37.4 ± 2.

We use the term individual to identify the HRTF of the user, individualized or personalized to indicate an HRTF modified or selected to accommodate the user best, and non-individual or non-individualized to indicate an HRTF that has not been tailored to the user. A so-called generic or dummy-head HRTF is a specific instance of a non-individual HRTF.

th Convention of the European Acoustics Association Turin, Italy •

th -15 th September 2023 • Politecnico di Torino

Turin, Italy • 11 th -15 th September 2023 • Politecnico di Torino

ACKNOWLEDGMENTS

This work was funded in part through a fundamental research collaboration partnership between Sorbonne Université, CNRS, Institut ∂'Alembert and Meta Reality Labs.


Youseph Ibrahim

Patrice F Rey

Donna L Whitney

Christian Teyssier

Françoise Roger

Valérie Bosse

Bénédicte Cenki

From dome to duplex: convergent gravitational collapse explains coeval intracratonic doming and nappe tectonics, central Australia

In central Australia, an apparently coeval gneiss dome (Entia Dome) developed adjacent to a thrust belt (Arltunga Nappe Complex) within an intracratonic setting. Here we employ a combination of fieldwork, geochronology, and numerical modeling to investigate the structure and tectonic evolution of these features. We present a structural model linking an extensional domain comprising the Entia Dome, across a transitional zone containing the Bruna décollement zone and the Illogwa shear zone, into a contractional zone comprising thrusts and duplexes of the Arltunga Nappe Complex. Supported by numerical modeling, we propose a tectonic model in which the dome and nappe complex formed synchronously because of the convergent gravitational collapse of the 30-40 km deep Paleozoic Harts Range rift.

INTRODUCTION

Defying traditional plate tectonics, the Alice Springs Orogeny (ASO) developed between 450 to 300 Ma deep within the interior of the Australian continent (Fig. 1), at significant distances from any plate boundaries. It spans ~600 km, following a WNW-ESE striking corridor amidst the weaker regions between the North, South, and West Australian cratons [START_REF] Nixon | Intracontinental fault reactivation in high heat production areas of central Australia: Insights from apatite fission track thermochronology: Geochemistry[END_REF]. Before the ASO, a large portion of the Australian Paleoproterozoic interior remained buried beneath the Neoproterozoic to Devonian Centralian Superbasin, remnants of which include the Amadeus Basin (Fig. 1). During much of the Palaeozoic Era, Australia existed as a Gondwana promontory bordered by active margins to the NW [START_REF] Metcalfe | Multiple Tethyan ocean basins and orogenic belts in Asia[END_REF], N [START_REF] Jost | The Mesozoic and Palaeozoic granitoids of northwestern New Guinea[END_REF] and Pacific margins [START_REF] Rosenbaum | The Tasmanides: Phanerozoic tectonic evolution of eastern Australia[END_REF]. Consequently, the intracratonic ASO has been attributed to a combination of mantle dynamics [START_REF] Houseman | Mechanisms of lithospheric rejuvenation associated with continental orogeny[END_REF][START_REF] Roberts | Geodynamics of central Australia during the intraplate Alice Springs Orogeny: Thin viscous sheet models[END_REF] and far-field stresses [START_REF] Klootwijk | Middle-Late Paleozoic Australia-Asia convergence and tectonic extrusion of Australia[END_REF][START_REF] Silva | Intracontinental orogeny enhanced by far-field extension and local weak crust[END_REF].

The region NE of the Amadeus basin presents an intriguing geological association of the Entia gneiss dome, in which Paleoproterozoic upper amphibolite facies gneisses were exhumed alongside a series of nappes (Fig. 1). The nappe complex comprises the amphibolite to granulite facies rocks (10 kbar, 850ºC;[START_REF] Hand | U-Pb ages from the Harts Range, central Australia: Evidence for early Ordovician extension and constraints on Carboniferous metamorphism[END_REF][START_REF] Mawby | Sm-Nd evidence for high-grade Ordovician metamorphism in the Arunta Block, central Australia[END_REF] of the Harts Range Metamorphic Complex (HRMC), the Paradise Nappes, and their lower-grade Neoproterozoic covers [START_REF] Forman | The Arltunga Nappe Complex, Macdonnell Ranges[END_REF]. These isoclinal fold nappes were thrust onto the greenschist facies Ruby Gap duplex and White Range duplex, which consist of Amadeus basin sequences, overlapping the Amadeus basin [START_REF] Dunlap | Thermal and structural evolution of the intracratonic Arltunga Nappe Complex[END_REF]. Collectively, these nappes constitute the Arltunga Nappe Complex.

Understanding of the regional geology took a transformative turn when detrital zircon data revealed that the HRMC, into which the Entia dome was emplaced, did not belong to the Paleoproterozoic basement. Instead, these gneisses are the metamorphic equivalent of Neoproterozoic to Palaeozoic marine siliciclastic and limestone sediments of the Amadeus Basin with interlayered metavolcanics [START_REF] Maidment | High grade metamorphism of sedimentary rocks during Palaeozoic rift basin formation in central Australia[END_REF][START_REF] Tucker | A rift-related origin for regional mediumpressure, high-temperature metamorphism[END_REF]. Amphibolite to granulite facies metamorphism between 470 to 450 Ma is associated with bedding-parallel fabrics, suggesting syn-rift high-T metamorphism within the Harts Range Rift, a 30 to 40 km deep sub-basin adjacent to the Amadeus Basin [START_REF] Hand | U-Pb ages from the Harts Range, central Australia: Evidence for early Ordovician extension and constraints on Carboniferous metamorphism[END_REF][START_REF] Mawby | Sm-Nd evidence for high-grade Ordovician metamorphism in the Arunta Block, central Australia[END_REF][START_REF] Maidment | Tectonic cycles in the Strangways Metamorphic Complex, Arunta Inlier, central Australia: Geochronological evidence for exhumation and basin formation between two high-grade metamorphic events[END_REF][START_REF] Tucker | A rift-related origin for regional mediumpressure, high-temperature metamorphism[END_REF]. Granulite facies conditions seem to have been confined to deeper parts of the Harts Range Rift, with little effect on the adjacent Paleoproterozoic basement [START_REF] Mawby | Sm-Nd evidence for high-grade Ordovician metamorphism in the Arunta Block, central Australia[END_REF].

Episodic pegmatite emplacement between 450 and 300 Ma within the Entia Dome and the HRMC suggests the maintenance of high-T conditions in the deeper crust during most of the Paleozoic [START_REF] Buick | Timing relationships between pegmatite emplacement, metamorphism and deformation during the intra-plate Alice Springs Orogeny[END_REF]. Hence, the Entia Dome is a post-460 Ma structure that ascended through the HRMC during the ASO. The driver for protracted partial melting following an episode of high-grade metamorphism in this intracontinental setting remains enigmatic [START_REF] Buick | Timing relationships between pegmatite emplacement, metamorphism and deformation during the intra-plate Alice Springs Orogeny[END_REF][START_REF] Asimus | Melt-present deformation at the Entia Dome, Central Australia: A metamorphic core complex formed during lower crustal tectonic extrusion[END_REF]. This paper focuses on the structure and tectonic history of the region between the Entia Dome and the Ruby Gap Duplex (RGD) across the intervening Illogwa Shear Zone (ISZ; Fig. 1).

We document a structural continuity from the Entia Dome to the RGD and argue that the dome and duplex, active between 340 and 310 Ma, represent an extensional and contractional domain, respectively, linked by a translational domain that consists of the Bruna Décollement Zone (BDZ) and the ISZ. We propose that the deep Harts Range rift basin led to a significant gravitational potential anomaly that relaxed via inward convergent gravitational collapse.

A TRANSECT FROM DOME TO DUPLEX Entia Dome

The Entia Dome comprises migmatitic quartzofeldspathic gneisses and layered amphibolites and calc-silicates. A composite layer-parallel compositional banding fabric defines an internal architecture involving two subdomes separated by a planar high-strain zone (Fig. 1,2A). The subdome cores host the Huckitta and Inkamulla granodiorites dated (U-Pb zircon) at 1762 Ma and 1773 Ma, respectively [START_REF] Maidment | Tectonic cycles in the Strangways Metamorphic Complex, Arunta Inlier, central Australia: Geochronological evidence for exhumation and basin formation between two high-grade metamorphic events[END_REF]. Both granodiorites display a magmatic to solid-state fabric concordant with overlying migmatitic gneisses. On average, lineations within the dome trend to the NE (Fig. 1) and plunge 20-30° to the NE. Polyphase structures in the migmatites show evidence of at least three fabric-forming events (Fig 2D -E), with a clear regional partitioning. In the dome, the metatexite compositional layering and layer parallel foliation is folded into tight to isoclinal recumbent folds, ranging from centimeter to 10's of meters in amplitude (Fig. S1A-B). The sub-horizontal migmatitic layering displays locally sub-horizontal asymmetric boudinage and low-angle extensional shear bands with melt segregation that points to a strong extensional tectonic regime above the solidus (Fig. S1C). The magmatic fabric in the granodiorites preserves remnants of older structures (Fig. S2). At the margin of the dome, the recumbent folds are refolded by cascading recumbent folds (Fig. S3).

Granite-bearing extensional fractures, some axial planar to these second-generation folds, show that these folds also developed at temperatures above the solidus (Fig. 2D-E). In between the subdomes, the high-strain zone records a strong horizontal NW-SE shortening, with tight to isoclinal upright folds (Fig. S4). The strain distribution is consistent with that expected during the exhumation of a migmatitic-cored dome, with vertical shortening and horizontal extension on top of the dome, gravity folding along its margin [START_REF] Cruden | Flow and fabric development during the diapiric rise of magma[END_REF], and horizontal shortening between the subdomes [START_REF] Rey | The origin of contractional structures in extensional gneiss domes[END_REF].

U-Pb ages of metamorphic monazite from Entia gneisses between 365 and 308 Ma (Wade et al., 2008 and references therein;[START_REF] Varga | Pressuretemperature-time constraints on gneiss dome formation in an intracontinental orogen[END_REF], as well as U-Pb ages of metamorphic zircon growth in the Huckitta Granodiorite at ~332 ± 3 Ma [START_REF] Maidment | Tectonic cycles in the Strangways Metamorphic Complex, Arunta Inlier, central Australia: Geochronological evidence for exhumation and basin formation between two high-grade metamorphic events[END_REF] and ~330 ± 6 Ma [START_REF] Hand | U-Pb ages from the Harts Range, central Australia: Evidence for early Ordovician extension and constraints on Carboniferous metamorphism[END_REF] point to a protracted metamorphism from 360 to 310 Ma, peaking at 7-9 kbar and 680-720ºC (Varga et al., 2021 and references therein) and melt present conditions [START_REF] Asimus | Melt-present deformation at the Entia Dome, Central Australia: A metamorphic core complex formed during lower crustal tectonic extrusion[END_REF]. To better constrain the age of deformation, we conducted U-Th-Pb LA-ICPMS geochronology (Fig. S8) on monazite from a folded leucocratic vein within a metatexite between the subdomes (Figs. 1, 2D, S4). Two distinct date populations identified at 339 ± 4 Ma and 314 ± 4 Ma, as well as a concordant date at 365 ± 8 Ma, are interpreted as two pulses of doming and melt extraction during a ~365 Ma to 310 Ma period of protracted metamorphism, melting and deformation.

South Margin of the Entia Dome

The Bruna décollement zone deforms the contact between the Paleoproterozoic Entia gneisses and the Neoproterozoic to Paleozoic Irindina Gneiss at the base of the HRMC (Fig. 1) [START_REF] James | Strain and displacement in the Harts Range detachment zone: A structural study of the Bruna Gneiss from the western margin of the Entia Dome, central Australia[END_REF]. Separating the basement and cover, the Bruna Granitic Gneiss (BGG) (Fig. S5) has been interpreted as a ~1745 Ma (U/Pb zircon) laccolith [START_REF] Ding | Structural evolution of the Harts Range Area and its implication for the development of the Arunta Block, central Australia[END_REF][START_REF] Mortimer | U-Pb and Rb-Sr geochronology and geological evolution of the Harts Range ruby mine area of the Arunta Inlier[END_REF][START_REF] Cooper | Rate of Arunta Inlier evolution at the eastern margin of the Entia Dome, central Australia[END_REF]. The BGG records heterogeneous deformation [START_REF] James | Strain and displacement in the Harts Range detachment zone: A structural study of the Bruna Gneiss from the western margin of the Entia Dome, central Australia[END_REF]. Along the S margin of the Entia Dome, the BDZ corresponds to a prominent Sdipping normal shear zone. A strong L-S fabric carries a mineral and stretching lineation plunging to the SSW (Fig. 2F). Sm/Nd whole rock-garnet-hornblende isochron dating of BGG from the sheared NW margin of the Entia Dome yielded an age of 449 ± 10 Ma, interpreted to reflect a phase of Ordovician deformation [START_REF] Mawby | Sm-Nd evidence for high-grade Ordovician metamorphism in the Arunta Block, central Australia[END_REF]. Similar ages have been reported in the Harts Range (e.g., [START_REF] Buick | Timing relationships between pegmatite emplacement, metamorphism and deformation during the intra-plate Alice Springs Orogeny[END_REF]. To constrain the age of shearing along the S margin of the dome, we have performed in situ LA-ICPMS U-Pb dating of titanite from an isoclinally folded aplite vein (Fig. 2C) hosted in sheared BGG (Fig. 1). We obtained a date of 315 ± 4 Ma (Fig. S8), interpreted as the minimum emplacement age for the vein and maximum age for shearing and folding, closely agreeing with the 314 ± 4 Ma age obtained in the high-strain zone between the subdomes.

South of the Entia Dome, the BDZ flattens into a broad synform (Fig. 2A). The L-S fabric is flat-lying, with the prominent stretching lineation gently plunging to the SSW or NNE.

In some localities, strain shadows around K-feldspar and S-C fabrics in the BGG support a topto-the-SW sense of shear (Fig. S6A-B). However, deformation was heterogeneous, varying in intensity and involving both simple and pure shear (Fig. S6C). Underlying the BGG, the Strangways gneisses are exposed in the core of a few discrete antiforms (Fig. 1). The BGG thins out above the roof thrust of the duplex (Fig. 2).

Ruby Gap duplex and the Illogwa shear zone

South of the BGG, the ISZ consists of quartzofeldspathic gneisses and schists, with mafic and calc-silicate interlayering, reminiscent of the rocks in the Entia Dome. The foliation dips 30-50° to the N and carries a down-dip stretching and muscovite lineation. We have observed S-C fabrics, δ-clasts, and σ-clasts recording clear top-to-the-SW kinematics (Fig. 2E, Fig. S7). This shear zone is in structural conformity with the overlying upper amphibolite facies BDZ to the N and the underlying greenschist facies RGD to the S. Although the ISZ is often presented as a retrograde shear zone [START_REF] Foden | Metamorphic events in the eastern Arunta Inlier, Part 2. Nd-Sr-Ar isotopic constraints[END_REF], it is part of an inverted metamorphic gradient linking the upper-amphibolite facies at the Entia Dome's S margin to the greenschist facies fabric of the RGD [START_REF] Collins | Crustal scale ductile fault systems in the Arunta Inlier[END_REF][START_REF] Dunlap | Thermal and structural evolution of the intracratonic Arltunga Nappe Complex[END_REF]. We speculate that the ISZ fabric is the axial planar fabric of an anticlinal fold nappe made mainly of Paleoproterozoic gneisses, which could be structurally underneath the Paradise Nappes (Figs. 2,3). 207 Pb/ 206 Pb zircon ages of 1794 ± 6 Ma and 1769 ± 3 Ma are interpreted as crystallization ages and later alteration, respectively. In contrast, the 327 ± 2 Ma 40 Ar-39 Ar age obtained on muscovite [START_REF] Reno | Summary of results-Joint NTGS-GA geochronology project: Constraining cooling and deformation in the eastern Aileron Province through 40Ar/39Ar stepheating of hornblende, muscovite, and biotite: Northern Territory Geological Survey Record[END_REF] defining the lineation (Fig. S7) can be interpreted as the age of the ASO fabric.

Underneath and in structural conformity with the ISZ, the RGD is a S-directed duplex comprising Amadeus basin sequences and the underlying Paleoproterozoic basement. To the West, it occupies the lowest structural level of the Arltunga Nappe Complex, underlying the Paradise and HRMC nappes and coeval with the structurally equivalent White Range duplex [START_REF] Dunlap | Thermal and structural evolution of the intracratonic Arltunga Nappe Complex[END_REF] (Fig. 1). To the first order, what is preserved is the duplicated limb of an anticlinal fold nappe (Fig. 2A). The basement and the competent Heavitree Quartzite are attached, and the overlying incompetent Bitter Springs Fm (Fig. 2B) acts as a décollement.

Thrusting occurred between 336 and 311 Ma ( 40 Ar-39 Ar on white mica) at temperatures straddling the ductile-brittle transition (250-300 ºC; [START_REF] Dunlap | Neocrystallization or cooling? 40Ar/39Ar ages of white micas from lowgrade mylonites[END_REF]. Under these conditions, thrust sheets internally deform by stretching in the transport direction.

Summary

The structure across our transect consists of the Entia Dome with a double-dome architecture, adjacent to the Arltunga Nappe Complex to the S, comprising a stack of imbricated metamorphic fold nappes including the ISZ (Figs. 2A,3). The structural geology is conformal, with a progressive decrease in metamorphic conditions from upper amphibolite facies in the Entia Dome and the BGG, to lower amphibolite facies across the ISZ and greenschist facies in the RGD (Figs. 2A,3). Structures within the Entia Dome and the BDZ developed under extension, while the Arltunga Nappe Complex developed under contraction. Exhumation of the Entia Dome, shearing along the BDZ and ISZ, and thrusting of the Arltunga Nappe Complex are age-bracketed between ~345 and ~310 Ma. The structural continuity and geochronology indicate that these features are synchronous and interrelated.

TECTONIC MODEL

The Entia Dome was emplaced into the 30-40 km deep Harts Range Rift basin (i.e., Irindina Province), the base of which reached granulite facies metamorphism and melting at ~470 Ma [START_REF] Maidment | High grade metamorphism of sedimentary rocks during Palaeozoic rift basin formation in central Australia[END_REF][START_REF] Tucker | A rift-related origin for regional mediumpressure, high-temperature metamorphism[END_REF]. The density contrast between the Neoproterozoic to Paleozoic sedimentary basin infill and the metamorphic Paleoproterozoic basement creates a strong horizontal pressure gradient, leading to significant gravitational stresses acting laterally towards the basin [START_REF] Rey | Gravitational collapse of the continental crust: Definition, regimes and modes[END_REF]. As the geotherm in the basin reached melting conditions, these gravitational forces may have overcome viscous strength to drive centripetal flow, forcing the exhumation of the Entia Dome and the development of gravity nappes.

To test this hypothesis, we ran a set of thermal-mechanical numerical experiments using the Underworld framework [START_REF] Moresi | Computational approaches to studying non-linear dynamics of the crust and mantle[END_REF]). The model setup comprises a 34 km deep rift basin, embedded into a metamorphic basement overlying a viscous mantle (Fig. 4A). The temperature field reflects conditions at ~470 Ma and delivers partial melting in the deeper level of the basin as well as the basement. Rheology is temperature, stress, strain, strain rate and melt dependent. Detailed model information is provided in the data repository.

We have tested static, mild, and faster convergent and divergent velocity conditions. All sets of experiments lead to the exhumation of a basement-cored double-dome, pushing the basin infill upward and laterally into gravity nappes (Fig. 4B-D). This experiment (Fig. 4) suggests that the contractional collapse of the Harts Range Rift basin exhumed the Entia Dome and triggered S-SW gliding of gravity-driven fold nappes, accommodated by isoclinal folding and foliationparallel slip. At cooler conditions, limbs of the isoclinal fold nappes are imbricated forming the RGD and White Range duplex. A transitional domain links the extensional exhumation of the dome to the contractional deformation at the front of the nappe complex (Fig. 4D). The delay between granulite facies conditions at 470-450 Ma and doming at ~340-310 Ma may be due to rifting's divergent velocity balancing the convergent gravitational velocity until ~355 Ma and slow conductive heating delaying basement weakening and convergent flow.

CONCLUSIONS

We propose a tectonic model linking the Entia Dome and the RGD based on i/ the structural and metamorphic continuity between the dome and the duplex, ii/ geochronological constraints showing synchronous dome exhumation and nappe emplacement from ~340 to ~310 Ma, and iii/ coupled thermo-mechanical numerical experiments illustrating the geodynamics.

Our model invokes the contractional gravitational collapse of the Neoproterozoic to Devonian Harts Range Rift basin as the driver for exhumation of the Entia dome, associated with gravitational spreading of the basin infill. This gravity-driven deformation was superimposed on far-field stresses driven by plate tectonics and may have contributed to deformation along the N margin of the Amadeus basin. While the processes described here explain some Carboniferous features observed in the east Arunta region, it cannot explain the totality of the ASO strain field.

FIGURES

Figure 1 .

 1 Figure1. Geological map of the study area, central Australia, including location of geochronology data ( 40 Ar/ 39 Ar on muscovite from Reno and Fraser, 2021), using a combination of our own data and data from[START_REF] Forman | The Arltunga Nappe Complex, Macdonnell Ranges[END_REF],[START_REF] Shaw | Arltunga-Harts Range region[END_REF],Shaw and[START_REF] Shaw | Quartz, Northern Territory, sheet 5951[END_REF][START_REF] Dunlap | Structure, kinematics, and cooling history of the Arltunga Nappe Complex[END_REF]. HRG-Harts Range Group.

Figure 2 .

 2 Figure 2. (A) Composite cross section from Ruby Gap Duplex to Entia Dome. Major thrust faults are shown as thick black lines. Lighter shading indicates interpretation above the current topography. The Harts Range Metamorphic Complex, including the Irindina Gneiss, is shown in light blue. Section lines and legend are shown in Figure 1. (B) Folds in the Bitter Springs Group. (C) Folded aplite vein with axial planar foliation in the Bruna décollement zone (pen for scale). (D, E) Upright folds (notebook for scale) (D) refolded into cascading folds (pen for scale) (E) in the high-strain dome envelope. (F) L-S tectonite within the Bruna décollement zone. (G) Kinematic indicators in the Illogwa shear zone.

Figure 3 .

 3 Figure 3. Two schematic views of the structural architecture of Entia Dome and Arltunga Nappe Complex. Paradise Nappes are colored green. Legend and section lines are shown in Figure 1. HRG-Harts Range Group.

Figure 4 .

 4 Figure 4. Numerical experiment showing contractional gravitational collapse of a deep and hot rift basin triggering exhumation of a gneiss dome and associated gravity nappes. (A) Initial model setup showing materials distribution, density profiles, boundary conditions, and isotherms.Velocity boundary condition Vx is applied to both vertical walls. Vx is compressional at 0.05 mm yr -1 for 4 m.y. and extensional at 0.5 cm yr -1 for the following 6 m.y. Decaying heat anomaly approximates temperature conditions associated with rifting. Blue and red dashed lines

ACKNOWLEDGMENTS

We acknowledge funding by Australian Research Council grants ARC-LP190100146 and ARC-DP220100709, and support by NCI's National Computational Merit Allocation Scheme, Pawsey Supercomputing Centre, and Underworld provided by AuScope. B.C. received funding from European Horizon 2020 grant no. 793978. We thank our reviewers for their comments and insights.