a, Photograph under regular light.b, Photograph under UV light that enhances the fossilized soft tissue structures such as skin membranes and fur.

a, Extant dermopteranCynocephalus: anatomical relationship of the propatagium, the manual digital webbing, and the plagiopatagium to the forelimb and hand.b, Gliding eleutherodonts: relationship of the propatagium and plagiopatagium to the forelimb and manus, based onin situ preservation of the membranes with intact forelimbs ofMaiopatagium furculiferum (BMNH2940) and BMNH2942.c,d, Eleutherodont BMNH2942 with matching outlines of the propatagium, plagiopatagium and uropatagium on both slabs, BMNH2942B (c) and BMNH2942A (d). Red arrows indicate the margins of propatagium, plagiopatagium and uropatagium for BMNH2942B and the propatagium and plagiopatagium for BMNH2942A.

a,b, Stereo pair photographs (a) and camera lucida drawing (b) of the dorsal view of the preserved skull.c,d, Stereo pair photos (c) and camera lucida outlines for structural identification (d) of the anterior part of the skull ofMaiopatagium (BMNH2940) in ventral view as prepared from the underside of the fossil slab.e, Stereo pair images obtained by computed tomography (CT) scanning of the upper dentition of the megachiropteran fruit batHypsignathus in occlusal view (University of Chicago teaching collection). The bi-serial cusp rows of upper molars are functionally analogous to the upper premolars and molars ofMaiopatagium.f, Occlusal view ofHypsignathus upper (purple) and lower (red) tooth rows. Note that lower molars are lingual (internal) to the upper molars (purple).g, Phytophagous phyllostomid batSturnira lilium (FMNH105870): upper premolars and molars with taller labial cusp row and lower lingual platform specialized for a frugivorous diet⁴⁸. We consider phytophagous megachiropteranHypsignathus and phyllostomidSturnira to be dietary analogues toMaiopatagium and possibly toShenshou.

a, Juvenile specimen that has the lower permanent premolar half-erupted to replace the deciduous premolar that is only represented by root alveoli at the ultimate premolar locus; M₁ crown present but the roots not yet formed.b, CT scan images of the scapula–coracoid complex in ventral view, virtually disarticulated to show structural details. The scapular plate (red) is a composite from complementary parts preserved on the left and right scapulae. The procoracoid (green) shows the coracoid foramen and a well defined contact surface for the coracoid (blue).c, Shoulder girdle structures imaged from CT scans in ventral view.d, Shoulder girdle structures in dorsal view. Bones are coloured as follows: humerus, yellow; scapula, red; procoracoid, green; coracoid, blue; clavicles, brown; sternal series of paired manubrium, sternebrae 1–3, and a gracile xiphoid are coloured brown; the partially rendered costal ribs, brown; thoracic (dorsal) ribs, purple; vertebral column, grey. Because this is a young specimen, the interclavicle is not fully ossified.Supplementary Video 1 shows the full extent of BMNH3258 imaged by CT scans.

a,b,Maiopatagium furculiferum (holotype, BMNH2940): details of shoulder girdle and forelimbs as preserved.c,d, A new, unnamed eleutherodont BMNH2942 (see also ref.25): preserved structures of shoulder girdle on the main slab (BMNH2942A). The interclavicle is fully ossified in BMNH2940 and BMNH2942A. The clavicles are also joined to each other and to the interclavicle in both specimens.

a, Reconstruction of shoulder girdle based on STL models of eleutherodont BMNH3258 (a juvenile, in ventral view); the interclavicle is not fully ossified and was reconstructed from the preserved interclavicles of BMNH2940, BMNH2942 and several other eleutherodonts with well preserved clavicule–interclavicles.b, Shoulder girdle of the monotremeTachyglossus (adult).c, Shoulder girdle of the monotremeOrnithorhynchus (adult).d, Procoracoid, coracoid and scapula of a juvenileOrnithorhynchus. Note that the gracile coracoid, which is a juvenile feature, is similar to that of eleutherodonts. BMNH3258 is identified as a juvenile eleutherodont because it shows the lower permanent premolar in the process of erupting, and its shoulder girdle and partial forelimb elements are 80–85% the size of those on the adult specimen ofMaiopatagium.

a, An unnamed eleutherodont BMNH1133: right pes, showing that the calcar is distinct from, and coexists with, the os calcaris in this fossil.b,Maiopatagium (BMNH2940): right pes. Both specimens show a bony (calcified) calcar element that is articulated with the laterally bent calcaneal tuber by a contact of V-shaped trough and crest. This topographic relationship is identical to the calcar–calcaneus structural relationship of bats. Among a range of length and morphology of calcars in bats⁴⁰, the eleutherodont calcar bears some resemblance to the short and stubby calcar of some bats (for example,Desmodus, among phyllostomid bats)⁴¹, although the base of the calcar is more conical and massive, distinctive from that ofDesmodus⁴¹.

a, Manual digit 3 phalangeal index. Eleutherodonts have more elongated manual phalanges than extant gliders and arborealists.b, Ternary distribution of intrinsic proportions of metacarpals, proximal phalanges, and intermediate phalanges of digit 3. Eleutherodont manual proportions are closest to those of extant mammals that are both arboreal and gliding, and are very similar to the pedal proportions of bats adapted to pedal roosting.c, Functional olecranon index, which is the ratio of olecranon length to length of the remainder of the ulna^31,32. Eleutherodonts are well within the 25–75% quartiles of extant gliding mammals in having the shortest olecranon ratio, and they are below the lower 25% quartile of non-gliding arboreal mammals. The value range of this index for eleutherodonts is consistent with the interpretation that they are mostly arboreal, and some are glissant.d, Brachial index, measured as the radius length divided by humerus length³¹. By this index, eleutherodonts are similar to extant mammalian gliders in having high brachial index ratios, althoughXianshou and extant gliders partly overlap with the 25–75% quartiles of non-gliding arboreal mammals.e, Pedal length ratio (metatarsal length/femoral length) as an index for substrate preference. Eleutherodonts are most comparable to extant gliding mammals. The index supports previous inferences ofAgilodocodon,Eomaia andSinodelphys being scansorial/arboreal, although it is less supportive of the hypothesis thatVolaticotherium is a glider (seeSupplementary Table 9).

a, Ratio of dentary length to the summed lengths of forelimb and hindlimb as an index for substrate preference, as used by Menget al.²⁰ to help infer thatVolaticotherium is a glider. By this index, eleutherodonts are closest in values to extant gliders and arboreal mammals. However, we note that the eutriconodontVolaticotherium, the docodontAgilodocodon, and theriansEomaia andSinodelphys, all of which had been inferred to be arboreal by qualitative morphological analyses, cannot be differentiated from extant terrestrial and semifossorial mammals by this index alone. Results suggest thatVolaticotherium may not be a volant mammal, given our expanded reference dataset for this index. The efficacy of this index needs further study.b, Intermembral index is measured as the summed lengths of the humerus and radius divided by the summed lengths of the femur and tibia. Values for eleutherodonts overlap with both gliders and arborealists for this index.c, Femoral epicondyle index, which is measured as the epicondylar width divided by the femoral length (as in ref.31).d, Crural index, which is measured as the tibial length divided by femoral length.e, PCA of six functional indices (seeSupplementary Information), showing the first two components (PC1 and PC2). Purple points are eleutherodonts, and squares are non-eleutherodont Mesozoic mammals.Maiopatagium, BMNH2942 and BMNH1133 are either nested in or close to the morphospace region (purple and blue polygon) of extant mammalian gliders, suggesting that they are gliders.Volaticotherium is separated from gliders along PC2, suggesting that it may not be a glider.f, PCA showing PC1 and PC3.Maiopatagium, BMNH2942, 1133,Xianshou songae andVolaticotherium occupy the same morphospace regions as modern gliders and arboreal taxa. However,Shenshou and BMNH1137 are separated from gliders, especially along PC3, and are closely associated with non-gliding arboreal mammals.

This file contains Supplementary Information parts A-J.

Part 1. Shoulder girdle and forelimb of a juvenile specimen (BMNH3258). Color codes: humerus - metallic yellow; scapula – red; procoracoid – green; coracoid – blue; clavicles – brown; sternal series of paired manubrium, sternebrae 1-3 – brown, and a gracile xiphoid – brown; the partially rendered costal ribs – brown; thoracic (dorsal) ribs – purple; vertebral column – metallic grey.Part 2. Comparison of the shoulder girdle of eleutherodonts and monotreme mammals.a. Partial reconstruction of the eleutherodont shoulder girdle and sternal series, mostly based on CT scans of BMNH3258; the un-ossified interclavicle is supplemented fromMaiopatagium furculiferum type specimen (BMNH2940) and other specimens.b. AdultOrnithorhynchus anatinus (the platypus).c. JuvenileOrnithorhynchus anatinus.d. AdultTachyglossus aculeatus (the short beaked echidna). The rotation of the shoulder girdles in anatomical orientation with the sternal series is nearly horizontal.