Raw Data and Detailed Analytical Methods The tree topology and branch lengths The tree includes 72 extinct, worldwide distributed species, belonging to the Laurasiatheria and Proboscidea clades within the crown group Mammalia. Most intrafamilial relationships are not known and are therefore left as polytomies. This is known to have minor impact on variance-covariance matrix estimation (Finarelli and Flynn 2006, Meloro et al. 2008, Raia et al. 2010). Species first appearance records in the NOW and Paleodb databases were used to calculate branch lengths (Finarelli and Flynn 2006, Meloro et al. 2008, Raia et al. 2010). Ages for internal nodes, corresponding to genera, families, orders, and other inclusive nodes were taken directly from the fossil record. For further details see Meloro et al. (2008), Meloro et al. (2010), Carotenuto et al. (2010), Raia et al. (2010), Raia (2010), and Raia et al. (2011). Ungulates fall within the clade Laurasiatheria, which includes hedgehogs + shrews + moles, bats, whales + artiodactyls, carnivorans, pangolins and perissodactyls (Waddell et al. 1999). The tree was produced in Mesquite (Maddison and Maddison 2010). As for ruminants, we used the phylogenetic topology in Hernandez-Fernandez and Vrba (2005) and Decker et al. (2009) for living species and interfamilial relationships, and the works of specialists for placing extinct species. The higher-level relationships between ruminants are now reaching a consensus and support a (camels,(chevrotains,(pronghorns,(giraffes,(deer,bovids))))) topology (Decker et al. 2009, Spaulding et al. 2009). Within Pecorans, the phylogeny of antilocapridae follows Semprebon and Rivals (2007). Paleomerycids were allied to cervoids (Gentry et al. 1999). Within bovinae, tragelaphini and bovini are sister groups, with nilgai and its fossil relatives (boselaphini) sister to both. Pliocervini were allied to Cervini (Petronio et al. 2007). The phylogeny of rhinos follows the comprehensive cladistic analysis in Cerdeño (1995), and taxonomic attributions in Lacombat (2003), for some of the species. Phylogeny and taxonomy of tapiromorph perissodactyls was depicted after Holbrook (1999). The phylogeny and taxonomy of equids follows Strömberg (2006), and Maguire and Stigall (2008). Higher-level tree topology and split ages within Carnivora follows Wesley-Hunt and Flynn (2005) and Finarelli and Flynn [2006, see also Finarelli (2008), Meloro and Raia 2010]. Canid subfamilies ages and relationships were taken from Wang (1994), Wang et al. (1999), Finarelli and Flynn (2006), and Tedford et al. (2010). The phylogeny of machairodont felids follows Slater and Van Valkenburgh (2008). The current phylogeny of Felidae is robust but molecular estimates of time of divergence are not (Johnson et al. 2006), and were thence taken directly from the fossil record. Taxonomy and phylogeny of hyenas follow Werdelin and Solounias (1991) and Turner et al. (2008). For proboscideans, we followed the phylogenetic descriptions and age estimates in Shoshani and Tassy (2005), and Thomas et al. (2000). Literature cited 1. Carotenuto F., Barbera C., and Raia P., (2010). Occupancy, range size and phylogeny in Eurasian Pliocene to Recent large mammals. Paleobiology 36, 399-414. 2. Cerdeño, E. (1995) Cladistic analysis of the family Rhinocerotidae (Perissodactyla). Am. Mus. Novit., 1–25. 3. Decker JE et al. (2009) Resolving the evolution of extant and extinct ruminants with high throughput phylogenomics. PNAS 106: 18644–18649. 4. Finarelli JA, Flynn JJ (2006) Ancestral state reconstruction of body size in the Caniformia Carnivora, Mammalia: the effects of incorporating data from the fossil record. Syst. Biol. 55:301–313. 5. Finarelli, J. A. (2008). A Total Evidence Phylogeny of the Arctoidea (Carnivora: Mammalia): Relationships Among Basal Taxa. J Mammal Evol 15, 231–259. 6. Flynn JJ, Finarelli JA, Zehr S, Hsu J, Nedbal MA. Molecular phylogeny of the carnivora (mammalia): assessing the impact of increased sampling on resolving enigmatic relationships. Syst. Biol. 2005, 317-337. 7. Fortelius, M. (coordinator) [2010]. Neogene of the Old World Database of Fossil Mammals (NOW). University of Helsinki. http://www.helsinki.fi/science/now/. 8. Gentry AW, Rössner GE, Heizmann, EPJ (1999): Suborder Ruminantia. – In: Rössner GE, Heissig K (editors): The Miocene Land Mammals of Europe: pp. 225-258. München (Verlag Dr. Friedrich Pfeil). 9. Hernandez-Fernandez, M., and Vrba, E.S., (2005) A complete estimate of the phylogenetic relationships in Ruminantia, a dated species-level supertree of the extant ruminants: Biological Reviews, v. 80, p. :269–302. 10. Holbrook, L. T. (1999) The Phylogeny and Classification of Tapiromorph Perissodactyls (Mammalia). Cladistics 15, 331–350. 11. Johnson WE, Eizirik E, Pecon-Slattery J, Murphy WJ, Antunes A, Teeling E, O’Brien SJ. 2006. The late Miocene radiation of modern Felidae: a genetic assessment. Science 311, 73-77. 12. Maddison, W. P. and D.R. Maddison. 2010. Mesquite: a modular system for evolutionary analysis. Version 2.73 http://mesquiteproject.org 13. Maguire, K. C., and A. L. Stigall. (2008). Paleobiogeography of Miocene Equinae of North America: a phylogenetic biogeographic analysis of the relative roles of climate, vicariance, and dispersal. Palaeogeography, Palaeoclimatology, Palaeoecology 267:175–184 14. Meloro C., Raia P. (2010). Cats and dogs down the tree: the tempo and mode of evolution in the lower carnassial of fossil and living Carnivora. Evolutionary Biology 37, 177-186. 15. Meloro, C., P. Raia P, P. Piras P, C. Barbera C, and P. O’Higgins. P (2008. ) The shape of the mandibular corpus in large fissiped carnivores: allometry, function and phylogeny. Zool. J. Linn. Soc. 154:832–845. 16. Petronio C, Krakhmalnaya T, Bellucci L, Di Stefano G (2007) Remarks on some Eurasian pliocervines: Characteristics, evolution, and relationships with the tribe Cervini. Geobios 40:113–130. 17. Raia P., (2010) Phylogenetic community assembly over time in Eurasian Plio-Pleistocene mammals. Palaios 25, 327–338. 18. Raia P., Carotenuto F., Eronen J.T., Fortelius M. (in press) Longer in the tooth, shorter in the record? The evolutionary correlates of hypsodonty in Neogene ruminants. Proc. Royal Soc Lon B 19. Raia P., Carotenuto F., Meloro C., Piras P., and D. Pushkina (2010). The shape of contention. Adaptation, history and contingency in ungulate mandibles. Evolution 64 (5), 1489 -1503. 20. Semprebon, G. M. and Rivals, F. (2007) Was grass more prevalent in the pronghorn past? An assessment of the dietary adaptations of Miocene to Recent Antilocapridae (Mammalia: Artiodactyla). Palaeogeography, Palaeoclimatology, Palaeoecology 253, 332–347. 21. Shoshani, J., And Tassy, P., (2005), Advances in proboscidean taxonomy and classification, anatomy and physiology, and ecology and behaviour: Quaternary International, v. 126–128, p. 5–20. 22. Slater, G.J., And Van Valkenburgh, B. (2008) Long in the tooth: Evolution of sabertooth cat cranial shape: Paleobiology, v. 34, p. 403–419. 23. Spaulding M., O’Leary M.A., Gatesy J. (2009). Relationships of Cetacea (Artiodactyla) Among Mammals: Increased Taxon Sampling Alters Interpretations of Key Fossils and Character Evolution. PLoS ONE 4: e7062. 24. Strömberg, C. A. E. (2006). The evolution of hypsodonty in equids: testing a hypothesis of adaptation. Paleobiology 32, 236–258. 25. Tedford RH, Wang X, Taylor BE. 2010. Phylogenetic systematics of the North American fossil Caninae (Carnivora: Canidae). Bullettin of the American Museum of Natural History n. 325. 26. The Paleobiology Database. (http://www.paleodb.org/cgi-bin/bridge.pl). Occurrence data were retrieved for Proboscideans and Laurasiatherians on December 2010. 27. Thomas, M.G., Hagelberg, E., Jones, H.B., Yang, Z., And Lister, A.M., (2000) Molecular and morphological evidence on the phylogeny of the Elephantidae: Proceedings of the Royal Society London B, v. 267, p. 2493–2500. 28. Turner A, Antón M, Werdelin L. (2008) Taxonomy and evolutionary patterns in the fossil Hyaenidae of Europe. Geobios 41, 677–687. 29. Waddell, P. J., Okada, N., and M. Hasegawa. 1999. Towards resolving the interordinal relationships of placental mammals. Systematic Biology 48: 1-5. 30. Wang X. (1994). Phylogenetic systematics of the Hesperocyoninae (Carnivora: Canidae). Bullettin of the American Museum of Natural History n. 221. 31. Wang, X., R. H. Tedford, and B. E. Taylor. 1999. Phylogenetic systematics of the Borophaginae (Carnivora: Canidae). Bulletin of the American Museum of Natural History 243, 1–391. 32. Werdelin, L., Solounias, N., 1991. The Hyaenidae: taxonomy, systematics and evolution. Fossils and Strata 30, 1–104. 33. Wesley-Hunt GD, Flynn JJ. (2005). Phylogeny of the Carnivora: basal relationships among the carnivoramorphans, and assessment of the position of ‘Miacoidea’ relative to Carnivora. Journal of Systematic Palaeontology 3, 1–28. The tree in Newick format ((((((Listriodon_splendens:13.3,Bunolistriodon_lockharti:8.8):7.8,(Hyotherium_soemmeringi:11.28,(Chleuastochoerus _stehlini:16.39,(Microstonyx_major:11.61,(Metridiochoerus_andrewsi:13.37,Propotamochoerus_palaeochoerus:5.74) :2.87):5.59):3.88):4.32):32.45,((Dorcatherium_guntianum:11.45,Dorcatherium_naui:16.95):26.97,(((Helladotherium_d uvernoyi:14.34,Bohlinia_attica:13.54)Sivatheriinae:5.67,Palaeotragus_coelophrys:19.22):24.84,((Walangania_africanu s:29.92,(Micromeryx_flourensianus:27.09,(((Lagomeryx_parvulus:7.5,Procervulus_dichotomus:6.5):2,Euprox_furcatus :14)Muntiacinae:1.5,(Cervavitus_novorossiae:15.4,Croizetoceros_ramosus:19.1)Cervinae:5.5):11.59):6.73)Cervoids:3. 36,(((Tragoportax_amalthea:6.8,Tragoportax_gaudryi:6.8,Tragoportax_rugosifrons:6.8):7.95,(Leptobos_etruscus:14.1 5,Protragelaphus_skouzesi:10.46):3.49)Bovinae:2.45,((Kobus_sigmoidalis:16.06,(Antidorcas_recki:8.22,((Gazella_borb onica:5.19,Gazella_capricornis:2.29,Gazella_deperdita:0.99,Gazella_dorcadoides:3.39,Gazella_sinensis:3.34):0.61,Gaz ellospira_torticornis:8.5):0.61):7.91):2.31,Palaeoryx_pallasi:13.73):3.48)Bovidae:24.29):3.36):3.36):9.62):6.42,((((((Ste phanorhinus_etruscus:17.7,(Ceratotherium_neumayri:6.45,Ceratotherium_praecox:10.85):6.45):6.61,Lartetotherium_ sansaniensis:12.51):1.93,Dihoplus_schleiermacheri:18.44):9.2,(Aceratherium_incisivum:22.7,(Acerorhinus_zernowi:22 .66,(Alicornops_simorrensis:18.03,((Chilotherium_habereri:7.4,Chilotherium_schlosseri:8.7):11.4,Brachypotherium_br achypus:15.78):2.24):1.12):2.24)Aceratheriinae:4.95):20.37,(Ancylotherium_pentelicum:38.24,Chalicotherium_grande :31.24):12.77):3.81,((Cremohipparion_matthewi:10.89,Cremohipparion_mediterraneum:10.89):10.09,Hippotherium_ primigenium:17.98,(Hipparion_dietrichi:8.14,Hipparion_platyodus:9.24):12.85)Hipparionini:33.83)Perissodactyla:9.43) :21.99,((Ursus_etruscus:45.86,(Canis_etruscus:22.6,Vulpes_alopecoides:22.6):23.28):4.54,((((Pachycrocuta_brevirostri s:8.88,Adcrocuta_eximia:3.27):8.76,Ictitherium_viverrinum:12.02):2.58,Dinocrocuta_gigantea:12.45)Hyaenidae:20.53, (((Homotherium_crenatidens:8.76,Machairodus_aphanistus:1.74):2.32,(Paramachairodus_orientalis:5.72,Megantereo n_cultridens:9.48):1.36):19.73,((Acinonyx_pardinensis:18.12,Lynx_issiodorensis:16.52):9.52,Panthera_gombaszoegens is:26.44)Felini:4.76)Felidae:8.34):9.67)Carnivora:41.44):15.57,((Mammut_borsoni:50.33,(Mammuthus_meridionalis:4 7.36,(Gomphotherium_angustidens:13.09,(Anancus_arvernensis:26.06,Tetralophodon_longirostris:18.86):6.83):13.08 ):4.36):4.36,(Deinotherium_giganteum:21.75,Prodeinotherium_bavaricum:21.75):21.75)Proboscidea:51.3):10; Species data We compiled a database of fossil occurrences of mammals as provided by Paleodb (www.paledb.org) and NOW (http://www.helsinki.fi/science/now/) databases. Our data span phylogenetically over western Palearctic Laurasiatherians and Proboscideans, exclusive of small mammals. The reason for excluding small species is that they have lower preservation potential by a sheer size effect (Damuth 1982), they are much less diverse as fossils, and there is very little consensus about the higher-level phylogenies of many small mammals fossil groups. Our body mass data span from 4kg to 11.2 metric tons. The smallest living ungulate is the lesser mouse-deer Tragulus kanchil at some 2Kg in body weight, the largest “large land mammal” alive is the African elephant Loxodonta africana, at some 5 metric tons. Thus, our data are entirely comparable, hence truly representative, of the mammalian size spectrum. We concentrated on Western Palearctic mammal faunas that we are more familiar with, both in terms of taxonomy and phylogeny. The Neogene mammalian record in the Western Palearctic is continuous and intensively studied (Bernor et al. 2006). The age span of the dataset covers the entire Neogene (i.e. ca. 23 Ma). Species are distributed between continents and epochs as follows: 58 Miocene species (42 European (E), 14 Asian (As), and 2 African (Af)), 38 Pliocene species (24E, 10As, 4Af), and 23 Pleistocene species (18E, 1As, 4Af). Given the Miocene is much longer (some 17.7 Ma) than the other two epochs (Pliocene: ca. 2.8 Ma, Pleistocene: ca. 2.6 Ma), and given that living species were excluded (they should belong to Pleistocene otherwise), our sampling intensity is quite even. The record was divided in 1 My long time bins according to the fossil localities age estimates, as they appear in the reference databases. To perform the geostatistic analyses we had to restrict our investigation to those species with more than 2 occurrences for each time bin. This limits the number of species suitable for analyses but allows using high-quality, continuous data. In order to determine the movement of a species during its life span we had to identify its position in successive, equal-time intervals. As we partitioned the record according to localities age estimates, some fossil sites were probably put in the wrong bin because age estimates are themselves uncertain to a degree, and they are necessarily imprecise even when estimates are obtained from absolute dating methods (which give an age with confidence interval). Although this introduce some inaccuracy in our partitioning, it must be minor when age estimates are direct. Furthermore, since misplacement errors are random, they could not provide any systematic trajectory in habitat tracking. Finally, we removed from the record all of the localities with uncertain aging a priori. The use of artificial, equal time intervals can be misleading when computing time series (Kirchner and Weil 1998). Yet, it is appropriate to standardize the data when dealing with sampling issues. In the particular case of our study, unequal time intervals could have misestimate the extent of species movement from one long stratigraphic interval to a short, successive one, and the other way around because of biased sampling. Whereas wrong estimation also applies when computing movements between a poor-sampled and a well-sampled time bin, at least one potential bias (unequal duration) is reduced by using artificial, equal time intervals. We nonetheless performed a specific test for the influence of sampling inequality between time bins (see below). To compute species movements between successive intervals, we first detected the actual position of all localities by using their paleocoordinates. Paleodb database provides the correct position of a specific fossil locality related to its measured age (hence its paleocoordinates). For the remaining localities we computed the paleolatitude and the paleolongitude by using the PointTracker software (www.scotese.com). The position a species occupied on the Earth in a given time bin was identified by the Central Feature (CF) of its geographical distribution (Carotenuto et al. 2010). We computed the CF by using Esri ArcGis 9.3. The CF identifies the weighted center of the geographic distribution of fossil localities where a species is present. It represents that single fossil locality that minimizes the summed distance to all other localities. As such, it is bound to correspond to a locality placed in the highest fossil sites’ density territory for a species. Identifying the movement of a species in different time bins via the crude computation of distances between the CFs of successive time bins is not advisable because the distribution of the fossil localities is itself uneven in time and space (Raia et al. 2009, Carotenuto et al 2010). To overcome this problem, for each time bin we took the geometric centre (GC) of all the fossil localities occurring in that time bin (regardless of which set of species is present in each locality) as to represent the centre of a virtual reference system, according to which the CFGC distance was computed for each species (Figure 1). The successive step was to geometrically translate all of the GC-‐CF vectors of the same species to a single GC (Figure 1) (any GC could be used as a common reference since translation would be geometrically equivalent) and then to compute the distances between the translated CFs (Figure 1) . For geodesic distance computation we used the Vincenty Inverse Formula (Vincenty 1975) by using the package SDMTools in R. Distances were obtained to an accuracy of 0.5 mm, and were calculated considering the WGS-84 ellipsoid model for the Earth, according to the original reference system of localities coordinates of our database. These distances were explicitly considered the outcome of habitat tracking by species. We urge the reader to consider that the “distance” could not be zero even if the species’ occupied habitat did not change in location, since the GCs are calculated on the distribution of fossil localities, which is clearly uneven. In addition, some bias in the distribution of fossil localities occupied by a species in a given time interval could be, in principle, introduced by purely taphonomic factors. Rather than focusing on the distance magnitude per se, we were interested in the distances for comparative purposes. The species stratigraphic duration was computed as the difference in million years between the species first and last occurrence in the fossil record. Extinct species body sizes in the collected database were either taken from literature or estimated regressing remains’ measures vs known body size (Damuth and MacFadden 1990). We regressed the total distance covered by each species over its existence versus its stratigraphic duration, both using raw data and under a phylogenetic correction. Regression was performed under phylogenetic generalized least square (PGLS), assuming the Brownian motion model of evolution, and then correcting branch lengths by using Pagel’s transform. The Brownian motion model assumes a phenotypic trait to evolve according to a constantvariance random walk. Differences in trait values are thus expected to be proportional to the variance/covariance matrix derived from the tree, which includes the divergence times among species as off-diagonal elements, and their distance to the tree root on the diagonal. Pagel’s is a multiplier of the off-diagonal elements of the variancecovariance matrix that provides the best fit of the Brownian motion model to the trait data by means of a maximum likelihood approach (Freckleton et al. 2002). Pagel’s is appropriate to use if a given trait evolves under a nonBrownian motion. Stratigraphic duration (the Y variable) is not a phenotypic trait in the strict sense. Yet, a phylogenetic correction is advisable if closely related species tend to inherit similar durations, which is clearly the case in our data. We calculated the phylogenetic signal in duration to be significant (K = 0.308, p = 0.003; see Blomberg et al. 2003 for a description of the K metric). This means that closely related species inherit a phenotypic trait (or a suite of traits) having a shared effect on stratigraphic duration. PGLS regressions were performed by using the R package ape (Paradis et al. 2004). One potential problem with these regression models is that the relationship between duration and total distance might be inflated by chance: the longer a species lives, the greater the distance it could move over. To this aim, we also tested whether the maximum distance covered by a species over a single interval (that is between two successive time bins) does correspond to the last time bin when the species lived. For each species we computed the prior probability that the last interval would correspond to the longest distance traveled as 1/# of intervals covered. Then, we calculated the combined probability over all of the species, and assessed if the total number of instances where the last interval corresponds to the longest distance covered departs significantly from chance by means of the binomial distribution. The rationale is that if habitat tracking really prolongs survival, species may have actively tried to cover larger distances under the worst conditions, which presumably occur just before they went extinct. This is expected assuming that extinction is not fast enough that species cannot track their preferred habitat, whether or not they are doomed, or if environmental variables change gradually (Brett et al. 2007). On potential problem with this procedure is that unequal sampling between successive time bins may artificially increase the distance between CFs. This is particularly relevant before species extinction, since in the last interval the commonness (hence the number of localities where a species occur) is expected to be low. If sampling affects distance calculation, one could argue that distances computed between evenly sampled intervals should be smaller or less variable than between unevenly sampled intervals. We know that distances are more variable between any two successive intervals than between the two latest, which tend to be uniformly high. Thus, our preoccupation was to verify that distances are not artificially large between unevenly sampled intervals. To this aim, we devised a statistical test. We computed the distance per million years between any pair of species CFs, regardless of the fact the intervals were successive or not. This produces a matrix of dissimilarity. Then, for the same set of paired comparison, we produced another matrix of dissimilarity in sampling intensity between intervals, by computing the ratio of the between the two intervals number of localities, standardized by the most locality-rich interval (in practice, consider two intervals, one having half the localities of the other: their dissimilarity will be 0.5, two intervals with the same number of localities will have dissimilarity = 0). These two dissimilarity matrices were tested for correlation to each other by means of a Mantel test with randomizations. The test revealed no sensible effect of sampling inequality on distance calculation. Of the 72 matrix correlations we produced, only 4 were positive and significant (meaning that sampling inequality and distance are positively related). Among them, only one regards a species which covered the largest distance just prior to extinction. More importantly, there were 7 significant negative matrix correlations. A negative correlation is expected if tracking implies a shift in the species preferred geographic location without a shift in range position, with no loss of commonness. This can be verified if and only if CFs are good representation of what we call “preferred geographic position” and sampling is good enough not to introduce artificial differences in commonness (hence the number of localities per time interval). Thus, If anything, this test confirmed the quality of the fossil record we used here. The results of the test are now presented in the ESM table S3. To test for the relationship between morphological stasis and species duration, we retrieved from the NOW database information on species molar shape, including the number and shape of molar teeth cusps, and their relative crown height (= hypsodonty) which are attributes indicative of the type of food consumed, and therefore of the habitat exploited. NOW cheek teeth data include information on crown type (i.e. whether the tooth occlusal surface is selenodont, lophodont, and so on); and crown relative height (brachydont, mesodont, or hypsodont). In particular, we used the NOW variables i molar tooth shape, which describes the general shape of the cusp pattern (e.g. whether cups are selenodont, lophodont, ectolophodont and so on, see Jernvall and Fortelius 2002); ii tooth crown type, which is a categorical variable describing the molar cusp pattern at a much finer scale than the variable i; and relative tooth crown height, which is an ordinal variable describing the degree of hypsodonty (the relative height of the molars crown). Hypsodonty is of fundamental importance to achieve teeth durability and exploit grasses (Janis and Fortelius 1988). It is important to emphasize that variable i and ii and are different from each other. For instance, although most of the rhinos here used are ectolophodont (meaning that cusps are united in forming ridges perpendicular to the jaw, of which the external one is more pronounced) the genus Ancylotherium belongs to a crown type category on his own. Data on carnivores were implemented by us. We ascribed each carnivore species to either one of the categories “generalized carnivore”, “bone-cracker”, or “hypercarnivore”, depending on their carnassials and lower premolars shape. Carnivores whose lower carnassials include a crusching area (i.e. the talonid) were considered to be “generalized carnivore”. Strict meat-eaters lost their talonid iteratively several times in carnivores’ natural history (Van Valkenburgh 1991). They were ascribed to the category “hypercarnivore”. Finally, some hyenas, percrocutids, amphicyonids, and some borophagine canids show adaptations to bone crushing, including enlarged premolars and deeper mandibles (Meloro et al. 2008), and were consequently ascribed to the category “bone cracker”. Teeth shape variables were reduced by principal component analysis, by using the function dudi.mix in the R package ade4 (Dray and Durfur 2007). dudi.mix is specifically meant to perform ordination with mixed variables (in our case we have both categorical and ordinal variable types). The two first principal components (PCs) were retained for analyses. We computed morphological disparity for all clades in the tree by using the PC scores applying the function tip.disparity in the package Geiger in R, computing the average euclidean distance among all species in the clades. These disparity values were regressed against the average of the total distances covered by all species included in the clade. A significant negative relationship would indicate that morphological disparity is lower in clades composed of long-distance travelling species. Since the tree includes polytomous clades, we resolved multichotomies at random 100 times and re-ran the correlation each time, thereby originating a family of correlation statistics to be inspected for significance. The same analysis was repeated after including body size (besides teeth shape variables) to calculate PC scores. The results are qualitatively very similar whether or not body size is considered. As such, herein we present only the results of the purely morphological analysis (that is excluding size data). Literature cited 1. Bernor, R.L., V. Fahlbuch and H.W. Mittmann, Editors, The Evolution of Western Eurasian Neogene Mammal Faunas, Wiley, New York (1996). 2. Blomberg, S. P., T. Garland, and A. R. Ives. 2003. Testing for phylogenetic signal in comparative data: behavioral traits are more labile. Evolution 57:717–745. 3. Brett, C.E., Hendy, A.W., Bartholomew, A.J., Bonelli, J., And Mclaughlin, P.I., 2007, Response of shallow marine biotas to sea-level fluctuations: A review of faunal replacement and the process of habitat tracking: PALAIOS, v. 22, p. 228–244. 4. Carotenuto F., Barbera C., and Raia P., (2010). Occupancy, range size and phylogeny in Eurasian Pliocene to Recent large mammals. Paleobiology 36, 399-414. 5. Damuth, J. & Mcfadden, B. J. 1990 Body size in mammalian paleobiology: estimation and biological implications. New York, NY: Cambridge University Press. 6. Dray, S. and Dufour, A.B. (2007): The ade4 package: implementing the duality diagram for ecologists. Journal of Statistical Software. 22(4): 1-20. 7. Freckleton, R. P., P. H. Harvey, and M. Pagel. 2002. Phylogenetic analysis and comparative data: a test and review of evidence. Am. Nat. 160:712–726. 8. Kirchner JW, and A. Weil (1998). No fractals in fossil extinction statistics. Nature 395, 337-338. 9. Meloro, C., P. Raia, P. Piras, C. Barbera, and P. O’Higgins. 2008. The shape of the mandibular corpus in large fissiped carnivores: allometry, function and phylogeny. Zool. J. Linn. Soc. 154:832–845. 10. Paradis E., Claude J. & Strimmer K. 2004. APE: analyses of phylogenetics and evolution in R language. Bioinformatics 20: 289-290. 11. Raia, P., Carotenuto, F., Meloro, C., Piras, P., Barbera, C. & Kotsakis, T. 2009 More than three million years of community evolution. The temporal and geographical resolution of the Plio-Pleistocene Western Eurasia mammal faunas. Palaeog. Palaeoclim. Palaeoecol. 276, 15–23. 12. Van Valkenburgh, B. (1991) - Iterative evolution of hypercarnivory in canids (Mammalia: Carnivora): evolutionary interactions among sympatric predators. Paleobiology, 17, 340–362. 13. Vincenty, T. (1975). "Direct and Inverse Solutions of Geodesics on the Ellipsoid with application of nested equations". Survey Review XXIII (misprinted as XXII) (176): 88–93. 14. Janis, C. M., and M. Fortelius. 1988. On the means whereby mammals achieve increased functional durability of their dentitions, with especial reference to limiting factors. Biol. Rev. 63:197–230. 15. Jernvall, J., and M. Fortelius. 2002. Common mammals drive the evolutionary increase of hypsodonty in the Neogene. Nature 417:538–540. Supplementary Figure 1 – The phylogeny used in this study. Terminal branches in green identify species which covered the largest distance over their last temporal interval. Table S1 - Raw Data and Principal Component Scores. max.dist = longest distance covered over a single time bin (in km). durations = stratigraphic duration in million years. dis.tot = total distance covered over the species existence (in km). mass = log10 of the body size in grams. FA = first appearance datum, LA = last appearance datum. Species Aceratherium incisivum Acerorhinus zernowi Acinonyx pardinensis Adcrocuta eximia Alicornops simorrensis Anancus arvernensis Ancylotherium pentelicum Antidorcas recki Bohlinia attica Brachypotherium brachypus Bunolistriodon lockharti Canis etruscus Ceratotherium neumayri Ceratotherium praecox Cervavitus novorossiae Chalicotherium grande Chilotherium habereri Chilotherium schlosseri Chleuastochoerus stehlini Cremohipparion matthewi Cremohipparion mediterraneum Croizetoceros ramosus Deinotherium giganteum Dihoplus schleiermacheri Dinocrocuta gigantea Dorcatherium guntianum Dorcatherium naui Euprox furcatus Gazella borbonica Gazella capricornis Gazella deperdita Gazella dorcadoides Gazella sinensis Gazellospira torticornis Gomphotherium angustidens Helladotherium duvernoyi Hipparion dietrichi Hipparion platyodus Hippotherium primigenium max.dist 2773.869 1234.745 1501.238 2583.009 1682.699 1811.455 1322.014 2219.4 1062.294 702.3691 3682.738 1808.274 1370.173 487.2853 1241.384 657.1003 5389.536 1424.034 1667.711 1441.874 1486.253 1649.005 2740.265 2586.474 5912.629 905.329 1306.317 1164.175 845.5416 1323.722 1511.169 1037.981 2198.733 672.9007 3187.784 1196.197 908.2502 1577.687 2112.389 dist.tot durations FA LA mass PC1 PC2 3761.87 9.14 20.42 5.30 6.041 0.336 -0.338 1934.2 6.20 11.60 1.81 5.954 0.336 -0.338 2613.38 4.30 3.59 0.78 4.699 0.311 1.408 3296.3 4.15 2.58 0.78 4.845 0.54 1.887 2366.42 8.25 3.59 0.78 5.813 -0.05 -0.344 2643.37 11.40 11.59 5.33 6.544 1.607 -1.469 1669.83 4.15 6.99 5.30 6.444 0.511 -1.057 2973.01 2.64 13.59 5.30 4.447 -0.902 -1.496 1812.79 2.95 13.64 11.61 5.813 -0.82 -0.714 1073.23 10.07 7.74 5.30 6.204 0.589 -0.516 7003.88 6.35 11.19 5.30 5.072 1.978 -0.188 4700.94 4.30 8.69 7.75 4.477 -0.153 1.637 3288.49 7.67 8.89 7.00 6.079 -0.085 1.085 810.42 10.62 8.19 7.00 6.322 -0.352 0.716 2482.77 4.80 8.99 5.33 4.903 -0.82 -0.714 1180.69 7.50 15.19 5.30 5.973 1.282 -1.044 6807.58 8.91 2.49 0.78 5.845 -0.352 0.716 2941.83 7.31 7.99 5.30 6.022 -0.167 0.303 2740.41 4.10 7.74 7.00 4.652 1.978 -0.188 1836.59 3.05 11.19 5.30 5.021 -0.484 0.184 1758.59 3.05 8.99 7.25 5.272 -0.751 -0.185 2140.78 3.06 3.19 0.13 4.903 -1.086 -1.083 9948.52 14.10 11.19 4.20 7.051 1.534 0.216 6707.59 10.35 8.99 5.30 6.079 -0.218 0.901 6182.45 4.15 2.58 0.13 5.58 -0.231 1.874 1302.02 3.20 15.19 5.30 4 0.484 -1.545 2420.19 5.80 11.59 9.00 4.556 0.484 -1.545 1586.74 8.70 11.09 2.59 4.699 -0.82 -0.714 1407.82 4.71 8.99 7.00 4.38 -1.456 -0.258 2486.68 3.23 8.69 7.75 4.342 -1.508 0.34 3221.06 6.53 11.59 5.30 4.362 -0.953 -0.899 2075.96 9.90 15.96 9.00 4.362 -1.641 0.155 3997.4 5.68 11.19 4.20 4.362 -1.255 0.162 829.12 2.50 15.99 5.33 5.167 -0.516 -1.49 6467.74 15.46 12.49 4.20 6.533 1.607 -1.469 2781.58 3.23 9.49 4.20 6 -1.374 0.524 1309.7 2.40 4.89 0.78 5.279 -0.484 0.184 3155.37 6.43 3.39 0.13 5.167 -0.484 0.184 6330.47 10.61 3.19 0.78 5.438 -0.751 -0.185 Homotherium crenatidens Hyotherium soemmeringi Ictitherium viverrinum Kobus sigmoidalis Lagomeryx parvulus Lartetotherium sansaniensis Leptobos etruscus Listriodon splendens Lynx issiodorensis Machairodus aphanistus Mammut borsoni Mammuthus meridionalis Megantereon cultridens Metridiochoerus andrewsi Micromeryx flourensianus Microstonyx major Pachycrocuta brevirostris Palaeoryx pallasi Palaeotragus coelophrys Panthera gombaszoegensis Paramachairodus orientalis Procervulus dichotomus Prodeinotherium bavaricum Propotamochoerus palaeochoerus Protragelaphus skouzesi Stephanorhinus etruscus Tetralophodon longirostris Tragoportax amalthea Tragoportax gaudryi Tragoportax rugosifrons Ursus etruscus Vulpes alopecoides Walangania africanus 4444.469 901.4213 1840.515 2133.872 978.1225 1108.771 1540.787 2723.964 2675.284 1280.424 1024.645 2059.229 3819.161 2153.522 691.9995 1070.261 6750.95 1069.497 3360.689 1389.143 3060.444 2836.732 658.955 746.371 1095.906 1712.501 2549.22 1088.392 2299.561 900.3368 1829.236 1438.742 3083.018 7123.41 1615.26 2680.76 4984.69 1209.03 2878.33 3289.06 4753.22 5208.44 1999.79 1786.93 4405.17 4200.96 2862.95 1685.71 2361.12 8799.5 1632.51 4901.18 1751.78 4174.21 3023.07 1636.34 1165.11 1702.39 2665 6751.94 2156.48 4789.51 1214.92 3145.23 2259.81 5721.79 5.75 5.35 7.65 2.68 6.60 8.07 3.86 11.91 4.30 7.46 13.75 4.30 3.86 2.68 8.00 11.35 4.30 4.10 4.24 3.25 3.60 4.75 10.90 7.10 2.44 4.30 14.92 3.60 4.70 2.40 2.69 4.30 12.80 2.58 5.29 5.32 17.99 16.89 2.58 2.49 2.58 11.60 16.89 15.96 2.49 16.89 2.49 2.58 8.99 4.89 15.96 5.32 4.89 9.49 20.49 11.60 11.60 15.96 16.89 11.59 16.89 16.89 16.89 15.18 12.74 16.89 0.13 0.13 1.81 9.00 5.33 0.13 0.78 0.13 1.81 5.33 13.70 0.13 13.70 0.78 0.13 5.30 1.81 11.10 0.13 2.50 3.60 7.75 7.25 7.75 3.60 11.60 3.60 11.61 11.10 13.70 15.16 11.61 13.65 5.364 4.799 4.255 5.053 3.699 5.766 5.602 4.959 4.477 5.342 6.855 6.797 4.799 5.176 3.602 5.519 5.079 5.301 5.602 4.954 4.929 4.477 6.643 5.079 4.813 6.146 6.652 5.104 4.903 5.134 4.954 4.041 4.256 0.74 1.978 0.575 -0.902 -0.82 0.336 -1.056 1.148 -0.119 0.74 1.708 0.561 -0.032 -0.423 -0.82 1.978 0.54 -1.374 -0.953 -0.02 0.74 -0.82 1.267 1.978 -1.241 -0.05 1.607 -0.953 -0.82 -0.686 0.379 -0.153 -0.902 1.234 -0.188 1.83 -1.496 -0.714 -0.338 0.296 0.209 1.581 1.234 -0.504 -0.282 1.221 1.973 -0.714 -0.188 1.887 0.524 -0.899 0.66 1.234 -0.714 -0.154 -0.188 0.709 -0.344 -1.469 -0.899 -0.714 -0.53 0.911 1.637 -1.496 Table S2 – References for body size data. Species Reference Aceratherium incisivum NOW Database Acerorhinus zernowi NOW Database Acinonyx pardinensis NOW Database Adcrocuta eximia NOW Database Alicornops simorrensis NOW Database Anancus arvernensis Average of estimates for best equations in Christiansen (2004, Table 7) in Meloro C. et al. - Effect of predation on prey abundanceand survival in Plio-Pleistocene mammalian communities. Evolutionary Ecology Research, 9: 1–21 (2007) Ancylotherium pentelicum NOW Database Antidorcas recki Kappelman J. et al. - Bovids as indicators of Plio-Pleistocene paleoenvironments in East Africa. Journal of Human Evolution 32, 229–256 (1997) Bohlinia attica NOW Database Brachypotherium brachypus NOW Database Bunolistriodon lockharti NOW Database Canis etruscus NOW Database Ceratotherium neumayri NOW Database Ceratotherium praecox NOW Database Cervavitus novorossiae NOW Database Chalicotherium grande NOW Database Chilotherium habereri NOW Database Chilotherium schlosseri NOW Database Chleuastochoerus stehlini Deng T. - Late Cenozoic environmental changes in the Linxia Basin (Gansu, China) as indicated by cenograms of fossil mammals. Vertebrata PalAsiatica pp. 282-298 (2009) Cremohipparion matthewi NOW Database Cremohipparion mediterraneum NOW Database Croizetoceros ramosus NOW Database Deinotherium giganteum NOW Database Dihoplus schleiermacheri NOW Database Dinocrocuta gigantea Deng T. - Late Cenozoic environmental changes in the Linxia Basin (Gansu, China) as indicated by cenograms of fossil mammals. Vertebrata PalAsiatica pp. 282-298 (2009) Dorcatherium guntianum NOW Database Dorcatherium naui NOW Database Euprox furcatus NOW Database Gazella borbonica NOW Database Gazella capricornis NOW Database Gazella deperdita NOW Database Gazella dorcadoides NOW Database Gazella sinensis NOW Database Gazellospira torticornis NOW Database Gomphotherium angustidens NOW Database Helladotherium duvernoyi NOW Database Hipparion dietrichi NOW Database Hipparion platyodus NOW Database Hippotherium primigenium NOW Database Homotherium crenatidens Deng T. - Late Cenozoic environmental changes in the Linxia Basin (Gansu, China) as indicated by cenograms of fossil mammals. Vertebrata PalAsiatica pp. 282-298 (2009) Hyotherium soemmeringi NOW Database Ictitherium viverrinum NOW Database Kobus sigmoidalis Kappelman J. et al. - Bovids as indicators of Plio-Pleistocene paleoenvironments in East Africa. Journal of Human Evolution 32, 229–256 (1997) Lagomeryx parvulus NOW Database Lartetotherium sansaniensis NOW Database Leptobos etruscus Body size estimates with for bovids TLML equation in Janis (1990) by m3 lenght in Masini, F. - I bovini villafranchiani dell’Italia. PhD dissertation, Università di Firenze (1988) Listriodon splendens NOW Database Lynx issiodorensis NOW Database Machairodus aphanistus NOW Database Mammut borsoni Average of estimates for best equations in Christiansen (2004, Table 7) in Meloro C. et al. - Effect of predation on prey abundanceand survival in Plio-Pleistocene mammalian communities.Evolutionary Ecology Research, 9: 1–21 (2007) Mammuthus meridionalis Christiansen P. - Body size in proboscideans, with notes on elephant metabolism. Zoological Journal of the Linnean Society 140, 523–549, (2004) Megantereon cultridens Body size estimates with all felids M1 length equation in Van Valkenburgh (1990) by M1 length in Sardella, R. - Sistematica e distribuzione stratigrafica dei macairodontini dal Miocene superiore al Pleistocene. PhD dissertation, Università ‘La Sapienza’ Roma (1993) Metridiochoerus andrewsi Raia P. et al. - One size does not fit all: no evidence foran optimal body size on islands. Global Ecology and Biogeography 19, 475–484 (2010) Micromeryx flourensianus NOW Database Microstonyx major NOW Database Pachycrocuta brevirostris NOW Database Palaeoryx pallasi NOW Database Palaeotragus coelophrys NOW Database Panthera gombaszoegensis Body size estimates with all felids M1 lenght equation in Van Valkenburgh (1990) by M1 lenght in Schaub, S. - Revision de quelques Carnassiers villafranchiens du Niveau des Etouaires (Montagne de Perrier, Puy-de-Dôme). Eclog. Geol. Helvetiae, 42: 492– 506 (1949) Paramachairodus orientalis NOW Database Procervulus dichotomus NOW Database Prodeinotherium bavaricum NOW Database Propotamochoerus palaeochoerus NOW Database Protragelaphus skouzesi NOW Database Stephanorhinus etruscus NOW Database Tetralophodon longirostris NOW Database Tragoportax amalthea NOW Database Tragoportax gaudryi NOW Database Tragoportax rugosifrons NOW Database Ursus etruscus NOW Database Vulpes alopecoides NOW Database Walangania africanus Body size estimates with all ruminants FLML equation in Janis (1990) by m1 lenght in Barry J.C. et al. - Oligocene and early Miocene Ruminants. (Mammalia, Artiodactyla) form Pakistan and Uganda. Palaeontologia Electronica Article Number: 8.1.22A (2005) Table S3- Correlation between the inter-CF distances and the ratios between the number of localities per time bin were a species was present. The table shows the matrix correlation test results, performed by using a randomized version of Mantel’s test. § = significant correlation. * = species covering the longest distance just prior to extinction. Species R p Aceratherium incisivum -0.068 0.700 * Acerorhinus zernowi§ -0.947 1.000 * Acinonyx pardinensis -0.127 0.560 * Adcrocuta eximia -0.506 0.850 * Alicornops simorrensis 0.464 0.200 * Anancus arvernensis§ 0.803 0.020 Ancylotherium pentelicum -0.615 0.820 * Antidorcas recki -0.349 0.780 * Bohlinia attica 0.999 0.140 * Brachypotherium brachypus 0.387 0.210 Bunolistriodon lockharti 0.763 0.210 * Canis etruscus Ceratotherium neumayri -0.419 0.820 0.142 0.350 Ceratotherium praecox -0.354 0.940 * Cervavitus novorossiae -0.528 0.900 * Chalicotherium grande -0.273 0.780 * Chilotherium habereri -0.154 0.460 Chilotherium schlosseri -0.061 0.570 * Chleuastochoerus stehlini Cremohipparion matthewi§ 0.877 0.160 -0.816 1.000 * Cremohipparion mediterraneum 0.741 0.260 * Croizetoceros ramosus§ 0.999 0.010 * Deinotherium giganteum 0.110 0.230 Dihoplus schleiermacheri -0.101 0.580 Dinocrocuta gigantea§ -0.989 1.000 0.889 0.050 Dorcatherium naui -0.050 0.490 Euprox furcatus§ -0.730 0.960 * Dorcatherium guntianum Gazella borbonica§ 0.773 Gazella capricornis -0.211 0.500 * Gazella deperdita 0.674 0.240 * Gazella dorcadoides -0.370 0.630 * Gazella sinensis -0.215 0.690 Gazellospira torticornis -0.853 0.840 0.530 0.020 Helladotherium duvernoyi -0.194 0.810 Hipparion dietrichi -0.510 0.800 * Hipparion platyodus 0.513 0.160 * Hippotherium primigenium 0.320 0.110 Homotherium crenatidens§ -0.480 Gomphotherium angustidens§ Hyotherium soemmeringi Ictitherium viverrinum 0.974 0.010 1.000 * 0.080 -0.496 0.740 * Kobus sigmoidalis 0.007 0.390 * Lagomeryx parvulus 0.423 0.260 Lartetotherium sansaniensis§ -0.286 0.970 Leptobos etruscus -0.576 0.860 0.193 0.200 Listriodon splendens Lynx issiodorensis -0.254 0.830 * Machairodus aphanistus§ -0.834 1.000 * Mammut borsoni -0.162 0.540 Mammuthus meridionalis -0.020 0.320 * Megantereon cultridens -0.469 0.730 Metridiochoerus andrewsi -0.248 0.620 * Micromeryx flourensianus -0.129 0.700 * Microstonyx major -0.045 0.690 0.922 0.070 Pachycrocuta brevirostris Palaeoryx pallasi -0.535 0.820 * Palaeotragus coelophrys -0.119 0.690 * Panthera gombaszoegensis 0.136 0.310 * Paramachairodus orientalis -0.247 0.670 * Procervulus dichotomus 0.439 0.050 Prodeinotherium bavaricum 0.205 0.170 * -0.775 0.890 * Protragelaphus skouzesi 0.991 0.130 * Stephanorhinus etruscus 0.126 0.600 * Propotamochoerus palaeochoerus Tetralophodon longirostris -0.067 0.660 Tragoportax amalthea -0.077 0.530 Tragoportax gaudryi 0.371 0.290 Tragoportax rugosifrons 0.972 0.160 * -0.191 0.680 * Vulpes alopecoides 0.992 0.110 * Walangania africanus 0.645 0.330 Ursus etruscus