Modeling the physiology of the aquatic temnospondyl Archegosaurus decheni from the early Permian of Germany

Physiological aspects like heat balance, gas exchange, osmoregulation, and digestion of the early Permian aquatic temnospondyl Archegosaurus decheni, which lived in a tropical freshwater lake, are assessed based on osteological correlates of physiologically relevant soft-tissue organs and by physiological estimations analogous to airbreathing fishes. Body mass (M) of an adult Archegosaurus with an overall body length of more than 1 m is estimated as 7 kg using graphic double integration. Standard metabolic rate (SMR) at 20 C (12 kJ h−1) and active metabolic rate (AMR) at 25 C (47 kJ h−1) were estimated according to the interspecific allometry of metabolic rate (measured as oxygen consumption) of all fish (VO2 = 4.8 M0.88) and form the basis for most of the subsequent estimations. Archegosaurus is interpreted as a facultative air breather that got O2 from the internal gills at rest in wellaerated water but relied on its lungs for O2 uptake in times of activity and hypoxia. The bulk of CO2 was always eliminated via the gills. Our estimations suggest that if Archegosaurus did not have gills and released 100 % CO2 from its lungs, it would have to breathe much more frequently to release enough CO2 relative to the lung ventilation required for just O2 uptake. Estimations of absorption and assimilation in the digestive tract of Archegosaurus suggest that an adult had to eat about six middle-sized specimens of the acanthodian fish Acanthodes (ca. 8 cm body length) per day to meet its energy demands. Archegosaurus is regarded as an ammonotelic animal that excreted ammonia (NH3) directly to the water through the gills and the skin, and these diffusional routes dominated nitrogen excretion by the kidneys as urine. Osmotic influx of water through the gills had to be compensated for by production of dilute, hypoosmotic urine by the kidneys. Whereas Archegosaurus has long been regarded as a salamander-like animal, there is evidence that its physiology was more fishthan tetrapod-like in many respects.


Introduction
Quantitative modeling of an extinct animal's physiology may lead to a better understanding of its mode of life, including activity, breathing, feeding, or habitat preferences.However, this is not an easy task since crucial soft-tissue organs like gills, lungs, intestines, or other internal organs are usually not preserved in fossils.Therefore, studies on the paleophysiology of vertebrates have to rely on osteological correlates of the skeleton (e.g., Janis and Keller, 2001;Wedel, 2003;Schoch and Witzmann, 2011;Benson et al., 2012).Complementary to osteological correlates, the extant phylogenetic bracket can be applied and the fossil animal is compared with its closest living relatives (Bryant and Russell, 1992;Witmer, 1995Witmer, , 1998)).The present study deals with the physiology of the long-extinct tetrapod Archegosaurus decheni, a Paleozoic temnospondyl.Temnospondyls are basal tetrapods and range from the late early Carboniferous to the early Cretaceous (Schoch, 2014).Most researchers regard temnospondyls as stem amphibians, a group of which, the dissorophoids, gave rise to lissamphibians, i.e., frogs, salamanders, and caecilians (Ruta and Coates, 2007;Sigurdsen and Green, 2011;Schoch, 2014; but see Marjanović and Laurin, 2013, for an alternative view).Whereas dissorophoid temnospondyls usually resemble extant salamanders in body size and proportions, the majority of non-dissorophoid temnospondyls were much larger (1 m or more; some Mesozoic forms even grew up to 6 m in Published by Copernicus Publications on behalf of the Museum für Naturkunde Berlin.length) and often had a superficially crocodilian-like habitus.The physiology of such comparatively large temnospondyls is of interest because although they belong to the crowngroup Tetrapoda, they have neither closely related extant relatives nor an extant physiological analog: large, crocodilianlike non-amniotic tetrapods have been extinct since the early Cretaceous and were ecologically replaced by the superficially similar archosaurs, especially crocodilians.The skeletal morphology of non-dissorophoid temnospondyls differs from that of lissamphibians, not only in size and proportions but also in the much larger degree of ossification of the skeleton and the presence of an extensive cover of bony dermal scales.How can we imagine such animals breathing and feeding, and what was their metabolic rate?Were they merely "giant toads", as can sometimes be read in the popular literature?
This study is an attempt to assess certain aspects of the physiology of the large (more than 1 m adult size) Permian non-dissorophoid temnospondyl Archegosaurus decheni, including heat balance, gas exchange, osmoregulation, feeding, and digestion, based on a survey of osteological correlates in this temnospondyl and by virtue of theoretical calculations based on the physiology of extant vertebrates (Withers, 1992).In doing so, we are aware of the limitations of such an attempt: there are numerous sources of error, ranging from wrong prerequisites like inaccurate estimation of body mass to the choice of inappropriate extant animals for comparison.The older the geological age of the animal is, and the more distantly related it is to extant forms, the more difficult the evaluation of its physiology is.Therefore, we regard this study as an assessment of the physiology of Archegosaurus, rather than a reconstruction (which is not possible).Our aim is to show how its physiology could have been, not how it definitively was.Consequently, we replace the term "calculation" with "estimation" throughout this study.The term calculation would imply that the results were based on exact physiological measurements and represented the only true scenario, which is not possible for a fossilized animal.All estimations can be found in Appendix A.
Archegosaurus decheni was chosen for this study for the following reasons.First, it is one of the most intensively studied temnospondyls with numerous well-preserved specimens showing the cranial and postcranial skeleton and even some soft parts of the skin and the larval external gills, and its ontogeny from small larvae to large adults is also well documented (von Meyer, 1858;Hofker, 1926;Gubin, 1997;Witzmann, 2006a, b;Witzmann and Schoch, 2006).Second, some aspects of the skeleton, such as the morphology, the ribs, and the hyobranchial apparatus, are quite generalized in Archegosaurus (Witzmann and Schoch, 2006;Witzmann, 2013), and therefore the results of this study may also be valid for many other temnospondyls.Third, the paleoenvironment of Archegosaurus and its ecological role in the food web has been studied in detail based on sedimentological data, the accompanying fauna, and intestine fillings (Boy, 1993(Boy, , 1994;;Witzmann, 2004a;Kriwet et al., 2008).Fourth, Archegosaurus is a phylogenetically highly relevant taxon that is an early-diverging member of the Stereospondylomorpha (Fig. 1), a diverse clade of large-growing, crocodilianlike temnospondyls of the late Permian and the Triassic (Schoch, 2013;Eltink and Langer, 2014).Better knowledge of the paleophysiology of Archegosaurus may shed light on the ancestral lifestyle of stereospondylomorphs as well as the evolution of this large extinct clade that dominated the Triassic fluvio-lacustrine ecosystems (Schoch and Milner, 2000;Fortuny et al., 2011Fortuny et al., , 2016)).
Archegosaurus decheni is an early Permian temnospondyl that superficially resembled a long-snouted crocodilian or gharial.Its occurrence is restricted to the large Lake Humberg in the Permo-Carboniferous Saar-Nahe Basin in southwestern Germany (see Sect. 2) (Boy, 1994;Witzmann, 2006a).Archegosaurus is known from hundreds of specimens, some of which are almost complete articulated skeletons.Specimen size ranges from about 15 cm long larvae with external gills to adults that measure more than 1.5 m in length.The long, deep-swimming tail, the presence of lateral line sulci on the skull, the poorly ossified and comparatively weak fore-and hind limbs, and the retention of branchial teeth on the gill arches indicate that the large adults were also primarily aquatic animals and were capable of only short sojourns on land (Witzmann, 2006a;Witzmann and Schoch, 2006).Adults breathed via their lungs, whose presence is indicated by the extant phylogenetic bracket (Schoch and Witzmann, 2011).However, although neither ossified gill arches nor a postbranchial lamina of the shoulder girdle are preserved, adult Archegosaurus probably also breathed via fishlike internal gills and therefore was a bimodal breather.This assumption is based on the presence of the aforementioned branchial teeth that also indicate open gill clefts in large specimens (Witzmann, 2013) and on the fact that more derived stereospondylomorphs, the stereospondyls, possessed internal gills (e.g., trematosauroids, plagiosaurids, brachyopoids; Schoch and Witzmann, 2011;Witzmann, 2013).Furthermore, it is highly improbable that internal gills reappeared after they had been lost in the ancestral group.Thus, its mainly aquatic mode of life and the fact that both more basal (e.g., Trimerorhachis, Sclerocephalus) and more derived temnospondyls than Archegosaurus possessed internal gills strongly suggest that it possessed internal gills as an adult.Otherwise, if adult Archegosaurus had lost its gills completely, it should be secondarily aquatic and derived from a terrestrial ancestor (see discussion of the loss of gills in aquatic and terrestrial tetrapods in Janis and Farmer, 1999), but there is no existing evidence for this.Therefore, Archegosaurus is regarded here as a primarily aquatic tetrapod that breathed via internal gills and lungs as an adult and possessed external gills as a larva, analogous to extant lepidosirenid lungfishes and polypterid actinopterygians (Graham, 1997).Eltink and Langer, 2014) showing the phylogenetic relationships of Archegosaurus decheni.The Dissorophoidea are the putative stem group of lissamphibians (Schoch, 2014, and references therein).The skulls are redrawn after Schoch andMilner (2000, 2014) with the exception of Archegosaurus, which is redrawn after Witzmann (2006a).

Paleoenvironment and habitat of Archegosaurus
The Saar-Nahe Basin in southwestern Germany contains a series of late Carboniferous to early Permian sediments of successive, usually short-lived (10-1000 years), intermontane lakes within the Variscan mountain belt and yielded a large number of fossil vertebrates like bony and cartilaginous fishes and aquatic tetrapods (Boy, 1994;Schoch, 2014).Whereas Schultze and Soler-Gijón (2004) proposed that the lakes of the Saar-Nahe Basin were subject to marine influences, recent geochemical analyses indicate that these lakes were nonmarine in origin (Fischer et al., 2013).Archegosaurus decheni has only been described so far from sediments of the final stage of the deep, 80 km long Lake Humberg, which was one of the largest and longest-lasting lakes of the Saar-Nahe Basin.Its sediments are Sakmarian, lowermost Permian, in age (Meisenheim Formation, uppermost Odernheim Subformation;Schindler, 2007;Boy and Schindler, 2012).By far the most specimens of Archegosaurus have been found in layers and siderite concretions (or geodes) of the clay ironstone facies (tonsteinlager) of the Humberg black shale layers of Lebach near Saarbrücken.The fish fauna of the clay ironstone facies encompasses the plankton-feeding acanthodian Acanthodes and, among paleoniscoids, the plankton-feeding Paramblypterus and the piscivorous or benthivorous Rhabdolepis and Elonichthys (Boy, 1994;Boy and Schindler, 2012).Xenacanthid sharks are represented by Triodus, Xenacanthus, and Lebachacanthus (Boy, 1994), whereas the lungfish Conchopoma is the only known sarcopterygian fish in Lake Humberg (Schultze, 1975).A second temnospondyl that is contemporary with Archegosaurus but much less frequent in number, Glanochthon latirostris, occurred in Lake Humberg (Boy, 1993;Schoch and Witzmann, 2009).Intestine fillings show that Glanochthon also fed mainly on Acanthodes, similar to Archegosaurus (Boy, 1994;Witzmann, 2004a).In turn, at least the larvae of both temnospondyls were fed by the xenacanthid sharks in Lake Humberg, as shown by intestine fillings (Boy, 1993(Boy, , 1994;;Kriwet et al., 2008).
During the Permo-Carboniferous, the Saar-Nahe Basin was located in the tropical region, about 10 • north of the Equator (Boy and Sues, 2000;Schindler, 2007), with a monsoonal climate (Patzowsky et al., 1991).The lakes were probably situated about 2000 m above sea level (Becq-Giraudon et al., 1996).The water temperature of a lake is critical for the metabolism of its inhabitants (especially fishes and amphibians as ectothermic vertebrates).Unfortunately, no reliable data concerning water temperature in Lake Humberg and the other known lakes of the Saar-Nahe Basin exist.Therefore, the water temperature is estimated based on extant large tropical lakes with a similar high altitude.Baxter et al. (1965) reported the water temperature of different African tropical lakes.One of them, Lake Bunyonyi, is comparable to the presumed altitude of Lake Humberg: it is located 1973 m above sea level and the temperature to a depth of 10 m is about  Witzmann (2004a) and Witzmann and Schoch (2006).20 • C in June.Analogously, the temperature of Lake Humberg close to the water surface is set here at 20 • C.
The early Permian atmosphere differed from today's atmosphere especially by its significantly higher O 2 level, which probably accounted for about 29 % by volume according to recent models (Berner, 2006;Glasspool and Scott, 2010), in contrast to today's 20.95 % (Heldmaier and Neuweiler, 2004).Today's CO 2 level in the atmosphere is 0.043 % (Earth System Research Laboratory, Global Monitoring Division, June 2015, http://www.esrl.noaa.gov/gmd/ccgg/trends/).According to Berner and Kothavala (2001) the CO 2 content in the early Permian was probably only slightly higher than today and is set here as 0.047 %.

Archegosaurus model
To make an estimate of the metabolism of an animal, it is indispensable to know its body mass.The relationship between body mass and metabolic rate is described by the power curve (Withers, 1992;Heldmaier and Neuweiler, 2004): in which E metab is the rate of metabolic energy use (kJ h −1 ), M is body mass in grams, b is the mass exponent, and a is the intercept of the y axis, i.e., metabolic rate of mass = 1 g (Withers, 1992;Heldmaier and Neuweiler, 2004).
In this study, we use a volumetric model called graphic double integration (GDI) to estimate the body mass of an adult Archegosaurus specimen.This method was developed by Jerison (1973), who estimated endocast volumes of the brain of fossil vertebrates.Hurlburt (1999) was the first to apply GDI to estimate the body mass of complete specimens, including the synapsid Edaphosaurus as well as extant squamates and crocodilians.In GDI, the body (or a part of it) is described as an elliptical cylinder to calculate its volume (Jerison, 1973;Hurlburt, 1999).Multiplication of the calculated volume by the (assumed) specific gravity (SG) of the animal yields the estimated body mass.
Since no mounted skeleton of Archegosaurus is available, we used the graphic skeletal reconstruction of an adult specimen of Archegosaurus with a total length of the skeleton (from the anterior end of the premaxillae to the tip of the tail) of 125 cm (Fig. 2).The drawings show the skeleton in left lateral and dorsal view and are based on the skeletal descriptions and drawings of Archegosaurus by Witzmann (2004a) and Witzmann and Schoch (2006).The presumed body outline was drawn around the skeleton in both views, based on comparison with extant salamanders (like the giant salamanders Andrias and Cryptobranchus) and crocodilians (like the false gharial Tomistoma).The reconstruction with body outline is 126 cm long, i.e., adding 1 cm to the length of the reconstructed skeleton.Archegosaurus is reconstructed here with a deep fin, similar to aquatic salamanders and salamander larvae.The outline of the axial body (consisting of skull, trunk, and the muscular part of the tail, but not the fin, which is too thin and can therefore be neglected) and the fore-and hind limbs were treated separately in GDI.
The estimation of body mass for the Archegosaurus model based on GDI (see estimation in Appendix A1 and Fig. 3) A recent analog for Archegosaurus decheni among extant ectothermic vertebrates could be selected from among extant fishes or lissamphibians.Frogs and caecilians are not appropriate analogs since they are too small and the body mass of even their largest representatives is far below the estimated body mass of Archegosaurus.Although giant salamanders of the genus Andrias may reach body sizes similar to adult Archegosaurus (Ultsch, 2012), salamanders are derived as having a very low metabolic rate (Licht and Lowcock, 1991) and are therefore problematic as extant analogs.For these reasons, and because most non-dissorophoid temnospondyls differ conspicuously from lissamphibians in many respects and are more similar to fishes in the possession of fish-like internal gills, we have chosen the interspecific allometry of metabolic rate of all fish provided by Withers (1992, tables 4-5): Measured scaling exponents for fishes vary widely, with differences due both to methodology and true variation among species, lifestyles, and habitats (Killen et al., 2010).The scaling relationship we have chosen here produces metabolic rates that are on the high end for fishes, which may be justified by the finding that benthic fishes tend to show higher scaling exponents (Killen et al., 2010), and we presume that Archegosaurus lived a primarily benthic existence.However, an alternative interspecific scaling relationship for all fishes, E metab = 2.5 M 0.70 (Withers, 1992), yields metabolic rates that are nearly 10 times lower.The uncertainty produced by the variation in scaling relationships is much greater than that from uncertainty in body mass.Variation from the two allometric equations above produces resting metabolic rates in the range of 1.2-12 kJ h −1 for a 7 kg specimen, and variation in mass from 6 to 8 kg yields a range of just 10-13 kJ h −1 for the higher scaling relationship and 1.1-1.3 for the lower one (Appendix A1).Hence, precise estimates of body mass are valuable for reconstructing many aspects of extinct physiology but do not matter as much as the scaling relationship selected for estimates of metabolic rate.

Standard and active metabolic rate at 20 • C
As a stem group amphibian, Archegosaurus decheni was undoubtedly ectothermic.Because of the high thermal conductivity of water and the presence of gills that bring blood in close contact with the ambient water, Archegosaurus probably possessed a body temperature that coincided closely with the ambient temperature of the surrounding water (estimated here as mean 20 • C in Lake Humberg), as in most extant fishes (Heldmaier and Neuweiler, 2004).Thus, the standard metabolic rate at 20 • C (SMR 20 • C) can be estimated as 12 kJ h −1 and the active metabolic rate at 20 • C (AMR 20 • C) as 30 kJ h −1 (see estimation in Appendix A3).
4.2 Increasing active metabolic rate at higher temperature All physiological functions in an animal are temperature dependent, and each organism has its species-specific thermal optimum at which it attains its maximum efficiency (Heldmaier and Neuweiler, 2004).In analogy with aquatic amphibians, Archegosaurus was certainly capable of behavioral www.foss-rec.net/20/105/2017/Foss.Rec., 20, 105-127, 2017 thermoregulation, i.e., by changing locations in the water according to the available water temperature in the environment (Hillman et al., 2009).Archegosaurus could have raised its body temperature by staying in extremely shallow inshore water that was warmed up by the radiant heat of the sun.In turn, body temperature could be lowered by visiting deeper water layers or those parts of the shore that were covered by dense vegetation.Basking on land similar to squamates (Drane and Webb, 1980), crocodilians (Grigg and Seebacher, 2001), or specialized anurans (Hillman et al., 2009), and as assumed by Carroll et al. (2005) for Devonian tetrapods, was performed for a rather short time, if at all, by Archegosaurus because of the danger of desiccation via the gills and the skin that was probably similar to that of bony fishes (Witzmann, 2011).Resting in warm inshore water enabled Archegosaurus to raise its metabolic rate and to search more actively for fishes in the open water.For example, 25 • C is the preferred body temperature for salamander larvae (Withers, 1992, p. 134), and a water temperature T a of 25 • C can certainly be expected in shallow water at the shore of Lake Humberg.Furthermore, it can be assumed that T a was subject to seasonal fluctuations in the monsoonal tropical climate.Therefore, AMR at 25 • C is estimated as 47 kJ h −1 (see estimation in Appendix A4).Consequently, in the model, Archegosaurus was able to raise its metabolic rate by a factor of more than 1.5 in water with

Average daily metabolic rate (ADMR)
For estimation of the average daily metabolic rate (ADMR), the diel activity of the Archegosaurus model has to be estimated; i.e., how many hours was the animal active per day?
The northern pike (Esox lucius) is active for 4.8 h per day (Diana, 1980), and a similar value of 3.9 h per day was reported by Nifong et al. (2014) for the American alligator (Alligator mississippiensis).Bracketed by these data of a bony fish and an alligator, we guess that Archegosaurus may have been active for 4.5 h per day when it was swimming and foraging in the open water of the lake.With this assumption, and assuming an active body temperature of 25 • C, the average daily metabolic rate can be estimated for the Archegosaurus model as 19 kJ h −1 (see estimation in Appendix A5).
As outlined above, the extant phylogenetic bracket indicates that Archegosaurus decheni possessed lungs for air breathing, and apart from larval external gills (Fig. 4), there is direct and indirect evidence that adults possessed fish-like internal gills (Fig. 5).Unlike in lissamphibians, the skin of Archegosaurus can be ruled out as a major site of gas exchange for the following reasons: (1) the soft-tissue skin of temnospondyls has been shown to have been thicker, denser, and more keratinized than in lissamphibians, whose permeable skin appears to be derived (Maddin et al., 2007;Witzmann et al., 2010); (2) the complete postcranial body of Archegosaurus was covered by bony dermal scales (Witzmann, 2007); and (3) Archegosaurus was distinctly larger than lissamphibians (with the exception of the highly derived giant salamander Andrias) and thus had an unfavorable ratio of surface area to volume.This indicates that the skin of Archegosaurus was probably at best an accessory breathing organ as in certain fishes that supplied the skin (but not other organs) with oxygen (Graham, 1997).Therefore, the skin will not be considered as a breathing organ in the following, and we will concentrate on lung and gill breathing.

Evidence of the mode of lung ventilation in Archegosaurus
Extant amphibians and lung-breathing fishes fill their lungs by vertical movements of the buccal floor that press air from the buccal cavity into the lungs without involvement of trunk musculature (buccal pump mechanism; Brainerd, 1999).In contrast, extant amphibians (but not fishes) use contraction of the transverse abdominal musculature for exhalation (Brainerd et al., 1993;Brainerd, 1998;Brainerd and Monroy, 1998;Brainerd and Simons, 2000;Simons et al., 2000;Brainerd and Owerkowicz, 2006).The straight, short ribs of extant amphibians play no functional role in lung breathing.In contrast, the lungs of amniotes are ventilated by movements of the rib cage (aspiration pump): action of the trunk muscles expands the thorax, generates negative pressure in the lungs, and air is drawn in (Brainerd, 1999;Brainerd and Owerkowicz, 2006;Brainerd et al., 2016).
The ribs of small and middle-sized Archegosaurus are flattened, short, and straight and resemble those of extant salamanders (Fig. 4).In large specimens, the rib shafts are still flattened, but most presacral ribs (with the exception of cervical and lumbar ribs) are proportionally longer and slightly curved.The ribs of the thoracic region bear hook-or blade-like, posterodistal expansions (Fig. 2) (Witzmann and Schoch, 2006).The distal ends of the ribs are covered by periosteal bone, suggesting that no cartilaginous extensions connected the ribs to a ventral sternum.These morphological observations match the criteria of Janis and Keller (2001) for a rather rigid rib cage in basal tetrapods that could not be employed in costal aspiration.Therefore, it is assumed here that Archegosaurus drew air into its lungs by buccal pumping like extant amphibians or lungfishes.The extant phylogenetic bracket suggests that Archegosaurus used its ventral trunk musculature, the m.transversus abdominis, for forcing air out of the lungs because this muscle is employed in exhalation in both amniotes and extant amphibians (Brainerd et al., 1993;Brainerd and Owerkowicz, 2006).

Evidence of gill types in Archegosaurus
As outlined above, it can be assumed that fish-like internal gills were present in adult Archegosaurus because of phylogenetic reasoning and the presence of open gill clefts in adults, although the cartilaginous gill arches proper are not preserved.Internal gills do not occur in any living tetrapod and are restricted among extant vertebrates to fish-like vertebrates (Coates and Clack, 1991;Schoch and Witzmann, 2011).How can we assess whether the internal gills of Archegosaurus were used for uptake of most of the necessary O 2 and for CO 2 elimination, as in most extant fishes, or if they mainly had the function of eliminating CO 2 , as in most air-breathing fishes (Graham, 1997)?Cru-cial in this point might be the fact that small and middlesized growth stages of Archegosaurus possessed three pairs of external gills (Fig. 4), which were completely lost in large specimens.The morphology of their gill rami and filaments is well preserved as carbonaceous imprints (Witzmann, 2004b).Similarly, larvae of lepidosirenid lungfishes (i.e., the African lungfish Protopterus and the South American lungfish Lepidosiren) possess four pairs of external gills, which can also be retained in large specimens of Protopterus annectens (Graham, 1997) and whose morphology is very similar to those of Archegosaurus.The internal gills of lepidosirenids are reduced to two holobranchs and one hemibranch (Burggren and Johansen, 1986).In lepidosirenids, external gills are accessory organs for the aquatic uptake of O 2 in larvae and juveniles, which, in contrast to adults, are not obligate air breathers and get most of their O 2 aquatically (Graham, 1997).This recalls the situation of polypterid actinopterygians (Polypterus and Erpetoichthys), which have paired lungs and breathe air as adults in O 2 -poor water and in phases of increased activity (Magid et al., 1970;Babiker, 1984;Pettit and Beitinger, 1985;Graham, 1997).In turn, polypterids possess only four gill arches (instead of five), and the internal gills are reduced to three holobranchs and one hemibranch (Britz and Johnson, 2003;Bartsch, 2004).However, air breathing starts quite late in ontogeny (Babiker, 1984); larvae and juveniles have one pair of external gills whose pinnate morphology is similar to that of the external gills of lepidosirenids and Archegosaurus but are attached to the hyoid arch rather than to the gill arches (Bartsch, 2004).Polypterids are capable of excursions on land and can be exposed to air for up to 6-8 h (Sacca and Burggren, 1982;Pettit and Beitinger, 1985;Pace and Gibb, 2011;Standen et al., 2014;Du et al., 2016).External gills also occur in larvae of lissamphibians (Duellman and Trueb, 1994), and especially the morphology of the three pairs of external gills in salamanders corresponds to that of lepidosirenids and Archegosaurus.However, whereas the external gills of temnospondyls and salamanders can be regarded as homologous structures, the external gills of larval lepidosirenids evolved convergently, and the external gills of polypterids also developed independently (Witzmann, 2004b).These extant examples show that external gills occur in larvae of bimodalbreathing vertebrates that have reduced their internal gills to a certain degree (lepidosirenids, polypterids) or have completely reduced them (lissamphibians) and use external gills for aquatic breathing until the lungs are fully functional.
Considering these facts, the presence of larval external gills in Archegosaurus may suggest that the internal gills were not completely developed and that the lungs may have played an important role in O 2 intake in phases of hypoxia and during increased activity.However, the question is whether Archegosaurus had reduced its internal gills to such a large degree that it was an obligate air breather like adult lepidosirenid lungfishes or whether it was a facultative air breather like Polypterus and Erpetoichthys.In spite of the outer morphological similarities between Archegosaurus and lepidosirenids, like larval external gills on the branchial arches, we did not choose lepidosirenids as an extant analog of Archegosaurus for breathing.This is because lepidosirenids -analogous to amniotes -are highly derived in possessing a high buffering capacity and low pH of the blood, and they therefore have the ability to release substantial amounts of CO 2 via the lungs (Bassi et al., 2005).Lepidosirenids experience limited water availability or spend time estivating in dry burrows; thus, they have reduced gills to a large degree, to the point of not being able to use them sufficiently for O 2 or CO 2 exchange (de Moraes et al., 2005).Furthermore, lepidosirenids have reduced their internal gills to such a degree that they are obligate air breathers even in well-aerated water.The only reason to substantially reduce or eliminate gills is if a large amount of time is spent on land since gills would soon dry out.If a vertebrate is aquatic, there is no selective pressure to reduce the gills substantially, and it makes sense to always release CO 2 and usually get O 2 from the gills, except during aquatic hypoxia and times of activity (Brainerd, 2015).No estivation burrows of Archegosaurus are known, and it was probably less terrestrial than lepidosirenids.Therefore, and because its breathing physiology has been intensively studied (e.g., Magid et al., 1970;Babiker, 1984), we took Polypterus as an extant analog of Archegosaurus for estimation of the breathing rates.
Polypterids (or Cladistia) attain a maximum body length of 40-90 cm and are regarded as the sister group of all other extant actinopterygians (Graham, 1997;Bartsch, 2004).Similar to lepidosirenid lungfishes and tetrapods, polypterids possess paired lungs that originate ventrally from the pharynx (Lechleuthner et al., 1989;Graham, 1997;Brainerd, 2015).Dependency on air breathing increases with on-togenetic size in polypterids but never becomes obligatory in well-aerated water (Babiker, 1984;Graham, 1997).Polypterid lungs are very efficient and enable these fishes to rely completely on air breathing for O 2 uptake when water is virtually devoid of oxygen (Babiker, 1984).However, the gills are always the principal site for CO 2 release (Graham, 1997).
In summation, Archegosaurus is regarded here as a facultative air breather similar to polypterid fishes, meaning it got O 2 from the gills when it was in well-aerated water but relied on its lungs for O 2 uptake in times of activity and in oxygendepleted water.The bulk of CO 2 was always eliminated via the gills.

Ventilation of gills
Oxygen is about 30 times less soluble in water than in air, and thus its availability for respiration is limited for animals that breathe water (Heldmaier and Neuweiler, 2004).To extract a sufficient quantity of O 2 , water-breathing animals have to pump a large amount of water continuously through their gills.In the majority of bony fishes, ventilation of the gills occurs through the action of two pumps, the relative size of which may vary between taxa (Hughes, 1960): (1) a positive pressure buccal force pump anterior to the gills, which is generated by movements of the lower jaw and buccal floor, and (2) an opercular suction pump that is generated by mediolateral movements of the opercular and branchiostegal apparatus posterolateral to the gills.Both pumps are usually also present in air-breathing fishes like extant lungfishes (Burggren and Johansen, 1986) and actinopterygians (Brainerd and Ferry-Graham, 2006).How did Archegosaurus ventilate its gills?Its larval external gills were probably periodi-Foss.Rec., 20, 105-127, 2017 cally moved back and forth to generate convective movement of water across the gill filaments so that CO 2 -rich water was dispersed and replaced by fresh, oxygenated water, similar to extant salamander larvae (Hillman et al., 2009).It is more difficult to imagine how Archegosaurus ventilated its internal gills because no tetrapod possesses an opercular apparatus, which was already reduced in tetrapodomorph fishes from Tiktaalik onwards (Daeschler et al., 2006).This means that Archegosaurus was not able to use an opercular pump, and therefore the buccal pump must have increased its importance for gill ventilation: vertical movements of the buccal floor pumped water in a posterior direction towards the gills, and this might have been associated with regular opening and closure of the mouth.This view is supported by the fact that the only ossified element of the hyobranchium in Archegosaurus (and many other aquatic temnospondyls) is the robust basibranchial (Witzmann, 2013) that was located on the buccal floor (Fig. 5).The basibranchial, especially its broadened, downturned anterior portion, was the insertion site of the rectus cervicis muscle, which aids in lowering the mandible when it is pulled posteroventrally, a mechanism that is probably plesiomorphic for gnathostomes (Lauder and Reilly, 1994).Among extant bony fishes, moray eels have lost the opercular apparatus and ventilate their gills solely by action of the buccal pump (Hughes, 1960;Farina et al., 2015); therefore, they have to move the lower jaw continuously (observations of moray eels ventilating their gills at rest in a public aquarium by F. Witzmann suggest 30 depressions of the mandible per minute).In Archegosaurus, the opercular pump might have been functionally replaced to a certain degree by the flexibility of the cartilaginous gill arches.Similar to sharks (Hildebrand and Goslow, 1998) and larvae of lampreys (ammocoetes) (Brainerd and Ferry-Graham, 2006), contraction of the cartilaginous gill arches may have pressed water out of the pharynx and over the gills during exhalation, and their elastic recoil during inhalation might have served as a suction pump and have drawn water from the mouth cavity towards the gills.In spite of this, the ventilation of internal gills in Archegosaurus and other basal tetrapods was certainly less effective than in bony fishes with a functional opercular and branchiostegal apparatus.

Breathing rate in the Archegosaurus model
The assumption of the following estimations of O 2 uptake is that Archegosaurus was required to meet 100 % of its oxygen needs from gas exchange in the lungs in times of hypoxia in water or during increased activity.The assumption of the following estimations for CO 2 release is that the internal gills of Archegosaurus were the primary site of CO 2 -gas exchange and Archegosaurus maintained low bicarbonate buffer activity in the blood and high blood pH (Witzmann, 2016).If Archegosaurus did not have gills and released 100 % of the CO 2 from its lungs, and maintained a low CO 2 buffering capacity, it would have to breathe much more frequently to re-lease enough CO 2 , relative to the lung ventilation required for just O 2 uptake.That scenario is also modeled below.Assumptions in the following estimations are based on the gas exchange strategy of Polypterus senegalus, which is taken as the extant analog of the Archegosaurus model, which involves O 2 uptake in the lungs and CO 2 release from the gills as assumed for Archegosaurus.

Lung morphometric data of the Archegosaurus model based on Polypterus senegalus
Lung morphometric data (lung volume, tidal volume, etc.) are available for Polypterus senegalus (Magid et al., 1970;Babiker, 1984;Brainerd, 1994).Consequently, the lung volume V L in the Archegosaurus model can be estimated as 1400 mL and the tidal volume V t (i.e., the inspired volume of air; Withers 1992) as 840 mL (see estimation in Appendix A6).et al., 1971).Although these values refer to O 2 uptake of Lepisosteus (CO 2 is always eliminated via the gills), they show that the values estimated for the Archegosaurus model without gills would imply that it had to break through the water surface unusually often for an aquatic animal.Among several fish species that breathe with lungs or a gas bladder, no breathing rate higher than 20 breaths per hour has been www.foss-rec.net/20/105/2017/Foss.Rec., 20, 105-127, 2017

Lung
observed (Graham, 1997, table 5.2).Therefore, it is unlikely that Archegosaurus took 120 breaths per hour and much more probable that Archegosaurus eliminated the bulk of metabolic CO 2 via gills rather than via the lungs.

Gill surface area in the Archegosaurus model
Archegosaurus is considered here as a facultative air breather whose adult internal gills were able to supply the animal with the necessary amount of oxygen in well-aerated water at rest.Therefore, the surface area of the internal gills in the Archegosaurus model can be estimated based on the oxygen consumption rate at SMR estimated above as 5280 cm 2 or 0.75 cm 2 g −1 (see estimation in Appendix A9).
To our knowledge, no data concerning the surface area of polypterid fishes are available, but they can be compared to other extant air-breathing fishes.The value for the Archegosaurus model is smaller than that of the facultative air breather Amia with 1.95 cm 2 g −1 (Daxboeck et al., 1981) but slightly larger than that of Lepisosteus osseus with 0.59 cm 2 g −1 (Landolt and Hill, 1975), which is also a facultative air breather.The value is much larger than that for obligatory air-breathing teleosts like Anabas testudineus with 0.39 cm 2 g −1 and Clarias mossambicus with 0.17 cm 2 g −1 (Graham, 1997, p. 116), and especially the lepidosirenid lungfish Lepidosiren with only 0.00065 cm 2 g −1 (de Moraes et al., 2005).
6 Feeding and digestion 6.1 Food capture Archegosaurus was a piscivorous temnospondyl with a gharial-like "fish-eater snout".Intestine fillings of numerous specimens clearly show that it preyed preferentially on the acanthodian Acanthodes, whereas remains of the actinopterygian Paramblypterus within the stomach are exceptional (Boy, 1994;Witzmann, 2004a).
Most fishes and aquatic extant amphibians use suction during aquatic feeding.However, suction feeding was likely not possible in adult Archegosaurus with its elongate, narrow rostrum.Rather, it may have performed a lateral strike towards its prey, as performed by long-snouted crocodilians, gharials, and the actinopterygian Lepisosteus, for instance (Lauder and Norton, 1980;Cleuren and De Vree, 2000).The ossified basibranchial probably supported the buccal floor with the presumably simple tongue pad; therefore, it had to be a robust element because it was elevated during feeding to press the prey item against the toothed palate to fix and kill the prey.After killing, the prey had to be repositioned before swallowing, analogous to Lepisosteus (Lauder and Norton, 1980) and extant crocodilians (Cleuren and De Vree, 2000).A unidirectional flow of water in the buccal cavity and pharynx, from the mouth opening towards the gill slits, may have aided in transport of the prey.Furthermore, the large interpterygoid vacuities (Fig. 5) that were covered by small, dentigerous bony platelets in Archegosaurus indicate that the eyeballs were involved in the intrabuccal transport and swallowing by retraction into the mouth cavity, as reported in extant anurans (Levine et al., 2004) and salamanders (Deban and Wake, 2000).The branchial teeth on the ceratobranchials precluded the escape of prey through the gill slits (Witzmann, 2004b).Prey was probably swallowed whole, as in extant amphibians and Lepisosteus (Lauder and Norton, 1980).

Food content
The content of the food of Archegosaurus -mainly the acanthodian Acanthodes -can only very roughly be estimated because acanthodians are a long-extinct group of fishes whose phylogenetic position is still a matter of controversy (Brazeau and Friedman, 2015, and references therein).Initially regarded as the sister group of osteichthyans or their stem forms, acanthodians turned out to be a paraphyletic group of stem chondrichthyans in a recent phylogenetic analysis (Zhu et al., 2013).Therefore, the nutrition data of raw shark meat are taken as a rough approximation for the food content of Acanthodes to estimate the overall energy density of the food of the Archegosaurus model as 5.5 kJ g −1 (see estimation in Appendix A10).

Digestion
Absorption in the Archegosaurus model can be estimated based on the average daily metabolic rate estimated above (see estimation in Appendix A11).Per day, 0.08 kg of food has to be assimilated, with 0.006 mol of protein per day and 0.02 mol of fat per day.The kilograms of food per day that the Archegosaurus model had to consume to assimilate 0.08 kg can be estimated as 0.1 kg of food per day, meaning that more than six middle-sized acanthodians had to be consumed per day (see estimation in Appendix A12).

Osmoregulation and excretion
As described above, the paleoenvironment of Archegosaurus is interpreted as a large freshwater lake (Fischer et al., 2013;Schoch, 2014).Therefore, it can be assumed that Archegosaurus was hyperosmotic and hyperionic with respect to the ambient water.The osmolarity of the body fluids of Archegosaurus may have been similar to the polypterid Erpetoichthys with a value of 200 mOsm L −1 (Lutz, 1975) and anurans with a value of 210 mOsm L −1 (Mayer, 1969); therefore, a value of 205 mOsm L −1 is set for the Archegosaurus model, and the osmolarity of the ambient freshwater is set as 50 mOsm L −1 (Martinez- Palacios et al., 2008).Similar to most freshwater fishes, Archegosaurus can be regarded as an osmoregulator and ionoregulator because osmolarity and ionic composition of body fluids were different from the osmolarity of the ambient water.Because Archegosaurus was probably hyperosmotic to the surrounding water, it gained water by diffusion through the skin and the gills (Fig. 6).Similar to extant freshwater fishes and extant aquatic amphibians, it can be assumed that the kidneys produced dilute, hypoosmotic urine (Withers, 1992).In this way, the osmotic influx of water through the gills and the skin was compensated.

Water balance of Archegosaurus model
In the Archegosaurus model, which is regarded here as hyperosmotic, 173 g of water per day were gained by osmosis through skin and gills (see estimation in Appendix A13).

Ammonia and urine excretion
Most fishes (including basal actinopterygians like polypterids) and amphibian larvae are ammonotelic animals, i.e., ammonia (NH 3 or NH + 4 ) is the main end product of their nitrogen metabolism (Withers, 1992;Hillman et al., 2009).Exceptions are elasmobranchs, coelacanths, and estivating lepidosirenid lungfishes that excrete urea, similar to terrestrial amphibians and mammals (Wright, 2007).Ammonia is formed by the liver and kidney and is excreted down along the blood-to-water partial pressure gradient through the gills, which are usually the dominant excretion site of nitrogenous waste products in actinopterygians; this diffusional route dominates nitrogen excretion by the kidneys (as urine) and via the skin (Wright, 2007).In aquatic amphibians like Necturus or Typhlonectes, nitrogen excretion via the kidneys is also normally low (Hillman et al., 2009).Thus, it can be assumed that the main nitrogen excretory form in the largely aquatic Archegosaurus was ammonia, and the major excretion site was the internal gills.
No data concerning the relative amount of ammonia and urea in nitrogen excretion of polypterids are available.However, in other basal actinopterygians like Acipenser (in freshwater) and Amia, 7-12 % of nitrogen is eliminated as urea (Wright, 2007, table 6.1).For the Archegosaurus model, we take a value of 10 %, and thus 90 % of the ammonia nitrogen is eliminated by the gills.The amount of urea that was ex-creted per day in the Archegosaurus model can be estimated as 0.018 mol (see estimation in Appendix 14).

Solute balance of the Archegosaurus model
Because Archegosaurus was hyperosmotic and hyperionic to the ambient water like extant freshwater fishes, it must have lost ions by diffusion through the skin and the gills (Fig. 7).To retain a constant osmolarity of its body fluids, ions (mainly Na + and Cl − ) were probably actively taken up from the surrounding water via chloride cells in the gills.It can be assumed that a loss of potassium ions (K + ) occurred via the gills, as was demonstrated in extant freshwater teleosts (Gardaire and Isaia, 1992), and via the kidneys (Fig. 7); this loss was compensated for by absorption of potassium from the food.
The loss and uptake of Na + and Cl − in the Archegosaurus model are estimated (see estimation in Appendix 15).According to these estimations, the Archegosaurus model is able to compensate for the loss of these ions via gills, skin, and urine (198 mmol day −1 ) by their active uptake through the gills and via ingestion of food (218 mmol day −1 ).

Synthesizing the results
Physiology of an animal does not fossilize, and therefore our approach to reconstructing physiological aspects of Archegosaurus is based on (1) direct observations at fossil skeletons and identification of osteological correlates of physiologically relevant soft-tissue organs since these organs (e.g., gills and lungs) are only directly preserved in fossils in exceptional cases and (2) comparison with extant animals.Although Archegosaurus is phylogenetically more closely related with extant amphibians (lissamphibians) than with osteichthyan fishes, lissamphibians are not appropriate analogs for the physiology of Archegosaurus because most of them have a much smaller size and body mass, and salamanders have an unusually low metabolic rate.Furthermore, lissamphibians are highly derived in the possession of a thin, naked skin that is well vascularized and capable of large-scale cutaneous respiration (Duellman and Trueb, 1994).In contrast, Archegosaurus is more similar to osteichthyan fishes than to lissamphibians in possessing internal gills and ossified dermal scales that covered the body.For these reasons, we compared Archegosaurus mainly with airbreathing fishes (especially polypterids) and to a lesser degree with lissamphibians.This comparison may yield qualitative information (e.g., how the gills are used for O 2 uptake and CO 2 loss and how they are ventilated) as well as quantitative guesses, i.e., modeling of the physiology of the fossil animal under study dependent on the physical principles of life processes, such as the relationship between body mass and metabolic rate.It was our aim to show that the particular physiological mechanisms were interconnected with each other in the Archegosaurus model and quantitatively interdependent (Fig. 8).
The first step was the estimation of body mass based on a skeletal reconstruction and by graphic double integration (Fig. 8).This laid the foundation for almost all further theoretical estimations, and therefore special care was required in reconstructing the skeleton and the body outline.This step was based mainly on fossil evidence (the preserved skeleton) and to a lesser degree on assumptions based on extant analogs (drawing of body outline and assumption of specific gravity).
The second step was the assessment of SMR dependent on the estimated body mass.This was completely carried out by comparison with modern analogs, and there is undoubtedly a large source of error in the choice of the best metabolic rate: even when body mass is given, metabolic rate may be variable between different individuals of a group (as shown in Fig. 3 in Heusner, 1982 for different species of mammals, for example).Therefore, there are not only multiple sources of error concerning the estimation of body mass of a fossil tetrapod but also in assessment of metabolic rate when the mass and the taxon that serves as an extant analog are given.We started our physiological estimation for the Archegosaurus model with metabolic rates given for different salamanders (Withers, 1992), but the resulting metabolic values were unrealistically low.This falsified our first assumptions that temnospondyls like Archegosaurus could be best compared to salamanders in terms of their physiology.The low values can be attributed to the exceptionally low metabolism of salamanders, which is in fact the lowest of all extant tetrapods (Licht and Lowcock, 1991).It can also be attributed to the fact that maximum body size and mass in most salamanders (and all frogs and caecilians) is well below the value for temnospondyls like Archegosaurus.An exception in respect of size and mass is the giant salamanders of the genera Cryptobranchus and Andrias that reach maximum sizes of 70 to 150 cm, but these animals are highly derived in respect of their respiratory physiology (Ultsch, 2012) and like other salamanders have a low metabolic rate (Licht and Lowcock, 1991).Therefore, and because of similarities like the presence of internal gills, we chose a metabolic rate given for fishes rather than for salamanders (Withers, 1992) to estimate the SMR for the Archegosaurus model (Fig. 8).The subsequent estimation of AMR and ADMR were dependent on the ambient water temperature of Lake Humberg in which Archegosaurus lived.Therefore, the temperature in the surface layers of this fossil lake was estimated based on (1) direct geological evidence (paleolatitude of the lake close to the equator and its altitude in the early Permian) and ( 2) in analogy with an extant lake in a comparable climatic region and altitude.Estimations of SMR, AMR, and ADMR were the prerequisites for many of the subsequent estimations (Fig. 8).For reconstruction of the mode of breathing in Archegosaurus, the finding that adult specimens possessed fish-like internal gills was most important.This is derived from fossil evidence (the presence of branchial teeth) and the phylogenetic position of Archegosaurus (with closely related temnospondyls showing osteological correlates of internal gills).Direct fossil preservation of larval external gills and comparison with living vertebrates that develop larval external gills suggest that Archegosaurus had reduced its internal gills to a certain degree and relied on aerial respiration for O 2 uptake as an adult in hypoxic water and in times Figure 8. Synthesizing data and modeling from many sources.Graphic summary of the physiological reconstructions of the present study for Archegosaurus decheni considering the information provided by osteological correlates (i.e., information provided directly by the fossils) and theoretical estimations based on the physiology of extant analogs.The particular results like body mass, metabolic rate, feeding (inclusive nutrition and digestion) and respiration are mutually dependent. of activity.With these prerequisites, estimation of breathing rate for CO 2 elimination suggests that if the internal gills were not present, Archegosaurus would have had to ventilate its lungs to an extent that would have been unusual for an aquatic animal.Alternatively, it would imply a highly derived respiratory physiology, as seen in the extant lungfish Lepidosiren (see Sect. 5.2.1).The presence of internal gills in adult Archegosaurus is not only important for the attempt to reconstruct the mode of breathing in this temnospondyl, it is also crucial for our understanding of its mode of osmoregulation and excretion (Fig. 8) since gill-bearing and non-gill-bearing vertebrates differ in their water and solute balance.Like freshwater fishes, Archegosaurus had to cope with osmotic influx of water through the gills and had to compensate for this by production of dilute, hypoosmotic urine by the kidneys.Furthermore, chloride cells in the gills may have helped to retain a constant osmolarity of the body fluids by active uptake of ions from the surrounding water (Withers, 1992).In contrast to this, feeding and digestion of Archegosaurus is independent from reconstruction of this animal with or without gills as an adult.The fossils showing the fortunate combination of well-preserved snout morphology, dentition, and numerous gut contents make the reconstruction of Archegosaurus as a piscivorous animal specialized www.foss-rec.net/20/105/2017/Foss.Rec., 20, 105-127, 2017 on Acanthodes unequivocal.However, aspects of digestion that were estimated above (protein absorption) were prerequisites for the estimation of ammonia-urine excretion in the Archegosaurus model (Fig. 8).
8.2 The perception of Archegosaurus through time: from an early reptile to a salamander-like animal to a "fish with four legs" Archegosaurus decheni has been known to the scientific world since its original description by Goldfuss (1847).
In the first comprehensive monographs of this taxon, Archegosaurus was attributed to reptiles rather than to amphibians (von Meyer, 1854(von Meyer, , 1858)), and this assignment was certainly influenced by the outline of the skull that is so characteristic for gharials and long-snouted crocodilians rather than for lissamphibians.However, this view was already disputed by contemporary scientists like Vogt ( 1854), who classified Archegosaurus as an amphibian based on the structure of its vertebral column.Vogt was supported by Owen (1861, p. 202), who regarded Archegosaurus as a "transitional form between the batrachians and the ganoids".At least since the 1890s it has been universally accepted that Archegosaurus (and temnospondyls in general) are amphibians in the broader sense, i.e., anamniotic tetrapods.In analogy with extant lissamphibians, Archegosaurus had been reconstructed as a salamander-like animal that was derived from more terrestrial ancestors and was thus secondary aquatic (Schoch and Milner, 2000;Witzmann and Schoch, 2006).During its ontogeny, a phase of metamorphosis was assumed in which Archegosaurus reduced its larval external gills and relied completely on lung breathing (Boy, 1974;Boy and Sues, 2000).In our model, which is based on new results concerning the breathing modes of temnospondyls (Schoch and Witzmann, 2011;Witzmann, 2013Witzmann, , 2016)), Archegosaurus was a primarily aquatic animal throughout its life history, and in contrast to extant aquatic lissamphibians, it was not derived from a more terrestrial ancestor.Rather, Archegosaurus is reconstructed here as an animal that possessed internal gills as an adult as a direct heritage from its fish-like ancestors.Analogous to polypterid actinopterygians, we assume that the internal gills of Archegosaurus were slightly reduced, as indicated by the presence of larval external gills that served as accessory water-breathing organs until the lungs were fully functional.This hypothesized slight reduction might be connected with sporadic terrestrial sojourns of Archegosaurus, which can also be observed in polypterids (Sacca and Burggren, 1982;Pettit and Beitinger, 1985;Graham, 1997;Bartsch, 2004;Pace and Gibb, 2011;Standen et al., 2014;Du et al., 2016).The assumption of the presence of internal gills in Archegosaurus is supported by the rather unrealistically high breathing rate estimated in this study when presupposed that the Archegosaurus model had to rely solely on its lungs for CO 2 elimination.Thus, the physiology of the Archegosaurus model is much more simi-lar to that of air-breathing fishes than to that of lissamphibians, and this probably holds true for the majority of temnospondyls.The temnospondyls that can probably best be compared with lissamphibians are the mostly small-growing dissorophoids (Fig. 1) that have a salamander-like habitus and constitute the presumed stem group of lissamphibians (Schoch, 2014).Dissorophoids are derived in having completely reduced the ancestral internal gills and were clearly adapted to a terrestrial lifestyle as adults (Witzmann, 2016).
9 Data availability This is not applicable because there are no data sets/research data that could be deposited.All methods and data on which this study is based on are provided in the text and appendix.

Appendix A
All estimations mentioned in the main text are shown below.

A1 Estimation of body volume and body mass by graphic double integration (GDI)
Using Adobe Photoshop CS6, 62 vertical lines were drawn across the lateral outline of the axial body (i.e., 62 slices through the body), each separated by a distance of 2 cm (Fig. 3a, b).In the same locations, 62 transverse lines were drawn across the body outline in dorsal view.The vertical and transverse lines are perpendicular to each other and represent the vertical (d v ) and transverse diameter (d t ) of each of the 62 elliptical slices.The area A e of each ellipse was calculated as Then the average of the areas of the individual ellipses Āe was calculated as 52.5 cm 2 for the axial body.Multiplication of this value by body length L yielded the volume V ab of the elliptical cylinder representing the axial body: The same method was used to estimate the volumes of the forelimbs (×2) and the hind limbs (×2).Fore-and hind limbs were drawn in lateral and dorsal view (Fig. 3c, d).In dorsal view, the individual fingers and toes were drawn as attached to each other to form a paddle.The outline of each forelimb has a length of 15.3 cm, and 15 vertical and transverse lines were drawn across the lateral and dorsal outlines, respectively, separated by a distance of 1 cm.The average area of the individual ellipses was then calculated as 4.5 cm 2 .Therefore, the volume of both forelimbs is 2 × 4.5 cm 2 × 15.3 cm = 138 cm 3 .The outline of the hind limbs has a length of 19.8 cm, and the 19 elliptical slices were set in intervals of 1 cm, as in the forelimbs.The average area of the ellipses is 5.2 cm 2 , and therefore the volume of both hind limbs is 2 × 5.2 cm 2 × 19.8 cm = 206 cm 3 .Accordingly, the total volume (V ) of the Archegosaurus reconstruction is V = 6615+138+206 cm 3 = 6959 cm 3 or approximately 7 L (V ≈ 7 L).
Body mass can be calculated from the product of volume and density ρ (or specific gravity) of the body.Only very few values of specific densities of amphibians can be found in the literature.With values between 1.007 and 1.018 (William, 1900), the specific gravity of late larval stages of Bufo and Rana is only slightly above the density of water (value of 1), and a specific gravity between 1.01 and 1.08 has been reported for the terrestrial salamander Hynobius (Hasumi and Iwasawa, 1992).The specific gravity of an aquatic animal like Archegosaurus depends on the amount of air in the lungs.In times when the animal was floating at the surface or actively swimming, it may have relied on buoyancy provided by the lungs filled with air, and the specific gravity may have been slightly less than 1.In contrast, when the animal was walking on the bottom or lurking submerged for prey, a value slightly larger than 1 would have been advantageous and most of the air was exhaled from the lungs.Therefore, we assume that the specific gravity of Archegosaurus corresponded largely with the density of water; thus, the body mass M of the Archegosaurus reconstruction is M = Vρ = 7 L × 1 kg L −1 = 7 kg.It must be emphasized here, however, that this value is an estimate with several sources of errors that can be attributed to potential mistakes in the skeletal reconstruction (due to incompleteness of the fossils, distortion of skeletal elements, incorrect reconstruction of the amount of soft tissue covering the skeleton, or inadequate specific gravity assumed), for example.We estimate that the volume calculation may be incorrect by at most 1 L either way, meaning the mass may have been 6 to 8 kg.This range requires notably thin (for 6 kg) or robust (for 8 kg) reconstructions, to the point that they look unlikely.Hence, 6-8 kg is a conservative range and will be used in the following as the basis for physiological estimations.

A2 Estimation of body surface area of the
Archegosaurus model Head, trunk, and tail (without fin) are subdivided into 63 elliptical cylinders of 2 cm length (see Appendix A1).The perimeter P of each respective ellipse was calculated using the following equation (given in Hurlburt, 1999, for example): P = 2π[(0.5)(d 2 v +d 2 t )] 0.5 , again with d v being the vertical and d t being the transverse diameter of the ellipse.Multiplication of each perimeter by the length of 2 cm yielded the respective surface area; addition of the surfaces of all cylinders yielded the surface area of head, trunk, and tail (without fin) of approximately 3001 cm 2 .
Surface areas of fore-and hind limbs were calculated in the same way; the surface area of both forelimbs is 239 cm 2 and of both hind limbs is 322 cm 2 .
The surface area of the fin was estimated by fitting 14 rectangles in the dorsal fin and 13 rectangles in the ventral fin.The area of each rectangle was calculated, the areas summated and multiplied by 2 (left and right surface of the fin).This method yielded a surface area of the fin of 389 cm 2 .

A3 Estimation of standard and active metabolic rate at 20 • C
The range of body temperatures of Archegosaurus might have been between 10 and 30  Trueb, 1994, p. 210).The extant Australian lungfish Neoceratodus has the same range of body temperatures (10-30 • C, mean 19.9 • C; Pusey et al., 2004).Thus, the assumption for the following estimations is that the body temperature T b of Archegosaurus was equal to the ambient temperature of the water T a : T b = T a .Taking the allometric formula for the metabolic rate of fishes (see Sect. 4) E metab = 4.8 M 0.88 (for 20 • C) and the estimated body mass for an adult Archegosaurus of 7000 g, the standard metabolic rate (i.e., rate of a resting animal) at 20 • C (SMR 20 • C) can be estimated as 4.8 × 7000 0.88 = 11.6 kJ h −1 ≈ 12 kJ h −1 .This estimate includes potential error in body mass and error resulting from uncertainty in the allometric curve for metabolic rate of fishes.Using 6000 and 8000 g ranges of body masses yields a range of 10.1-13.1 kJ h −1 .However, use of an alternate scaling relationship for all fishes, E metab = 2.5 M 0.70 , yields a standard metabolic rate 10 times lower for a 7 kg Archegosaurus, ≈ 1.2 kJ h −1 .
AMR in fishes is typically 1.6 to 3.8 times the costs connected with SMR (Boisclair and Sirois, 1993).Therefore, it is assumed here that the active metabolic rate at 20 • C (AMR 20 • C) was 2.5 times SMR 20 • C in Archegosaurus and can be estimated as 2.5 × 12 kJ h −1 = 30 kJ h −1 .

A5 Estimation of average daily metabolic rate (ADMR)
It is assumed here that Archegosaurus was active for 4.5 h per day (see main text).

A6 Estimation of lung morphometric data of Archegosaurus based on Polypterus senegalus
Lung volume V L .Lung volume in Polypterus senegalus is about 20 % of body volume (Brainerd, 1994).For the Archegosaurus model with a body volume of 7000 mL, the lung volume can be estimated as V L = 1400 mL.
The minute volume V E in millimeters of air per minute required to sustain this rate of oxygen consumption can be estimated as follows: V O 2 = V E (pO 2in − pO 2ex )/100 kPa 10 mL O 2 min −1 = V E (29 − 7.8 kPa)/100 kPa → V E = 47 mL air min −1 .
Thus, the resting breathing rate at SMR 20 The minute volume V E in liters of air per minute can be estimated as follows: Thus, the breathing rate at AMR 25 The respiratory quotient (RQ) is defined as the ratio of volume CO 2 produced per O 2 consumed (Withers, 1992), i.e., V CO 2 /V O 2 .For carbohydrate metabolism, RQ is 1, for lipids it is approximately 0.7, and for protein it is approximately 0.84 (Withers, 1992).In the following, we use the RQ for protein because Archegosaurus fed predominantly on fish (see main text).Therefore, we assume V CO 2 = 0.84V O 2 for the Archegosaurus model.The partial pressure of carbon dioxide in exhaled air from Polypterus senegalus is approximately pCO 2ex = 2.2 kPa (we took the mean values of left and right lungs in Magid et al., 1970, table 1).The partial pressure of carbon dioxide in inhaled air (pCO 2in ) is taken to be 0.047 kPa for the early Permian atmosphere (see Sect.V O 2 is 10 mL O 2 min −1 in the Archegosaurus model (see Appendix A7).SA is the gill surface area.X is the diffusion distance of the water-blood barrier.In fish gills, X ranges from 0.6 to 6 µm (Withers, 1992, table 12-8); therefore, the mean of these values is taken here: 3.3 µm = 3.3×10 −4 cm.D is the diffusion coefficient that is set here at about 10 × 10 −6 cm 2 s −1 ; this estimation is based on Withers (1992, table 12-6, value between human lung and eel skin).p w O 2 − p c O 2 is the difference between the partial pressure of oxygen in the ambient water and in the capillaries during the time a body of water is in contact with the lamellae of the gills.Here we assume a value of p w O 2 − p c O 2 = 0.1 kPa in the Archegosaurus model because in extant fishes the epithelium of the gill lamellae usually has a thickness of around 5 µm (Heldmaier and Neuweiler, 2004) and no significant difference in concentration between blood and water can be expected.
The gill SA required for V O 2 = 10 mL O 2 min −1 = 0.16 mL O 2 s −1 can be estimated as for a specimen of Archegosaurus with a body mass of 7000 g.
Therefore, the surface area of gills per gram in the Archegosaurus model is 5280 cm 2 /7000 g = 0.75 cm 2 g −1 .

A10 Estimation of food content
For raw shark meat, 100 g (data from http://nutritiondata.self.com/facts/finfish-and-shellfish-products/4121/2) has the following content: 5 g total fat, 21 g protein, 0 g carbohydrate, and 74 g water.It is assumed here that 10 % of the complete fish are indigestible (cartilage, scales), again 20 % of which is water.Therefore, 1 g of shark contains 0.045 g total fat, 0.189 g protein, 0.686 g water, and 0.08 g indigestible dry material.The total dry percentage is 31.4%.

A11 Estimation of food absorption
Absorption in the Archegosaurus model can be estimated as follows.The average daily metabolic rate in Archegosaurus is ADMR = 19 kJ h −1 = 456 kJ day −1 .Therefore, the grams of food per day that have to be assimilated can be estimated as g food/day = (456 kJ day −1 )/(5.5 kJ g −1 ) = 83 g day −1 = 0.08 kg day −1 .From this, the amount of protein and fat that must be assimilated per day can be estimated: protein: (18.9 %)(83 g day −1 ) = 16 g day −1 , conversion to moles: (16 g day −1 )/(2724 g mol −1 ) = 0.006 mol day −1 ; fat: (4.5 %)(83 g day −1 ) = 3.7 day −1 , conversion to moles: (2.90 g day −1 )/(180 g mol −1 ) = 0.02 mol day The kilograms of food per day that Archegosaurus had to consume to assimilate 0.08 kg can be estimated as follows: in extant amphibians, assimilation energy ranges from 65 to 95 % (Hillman et al., 2009); therefore, 80 % assimilation energy is assumed here.To assimilate 0.08 kg, Archegosaurus had to feed 0.08/0.80= 0.1 kg of food per day.If we assume that an acanthodian of ca. 8 cm body length had a weight of around 15 g (compare living goldfish), then Archegosaurus had to eat about six fish of this size per day.
This means that about 173 g water per day was gained through skin and gills in the Archegosaurus model.

A14 Estimation of urea excretion
According to Withers (1992), 100 g of protein yields 1.14 mol ammonia.As estimated in the digestion model (see

Figure 2 .
Figure 2. Skeletal reconstruction with body outline of an adult specimen of Archegosaurus decheni from the early Permian of the Saar-Nahe Basin, Germany.(a) Dorsal view; (b) lateral view.Redrawn and modified after Witzmann (2004a) and Witzmann and Schoch (2006).

Figure 3 .
Figure 3. Graphic double integration (GDI) of Archegosaurus decheni to estimate body mass and body surface area.(a, b) Outline of the axial body (i.e., head, trunk, and tail) in (a) dorsoventral and (b) lateral view with 62 slices through the body, each separated by a distance of 2 cm; the fin of the tail is shown in grey; (c, d) outline of a forelimb in dorsoventral (c) and lateral view (d) with 15 slices, each separated by a distance of 1 cm; (e, f) outline of a hind limb in dorsoventral (e) and lateral view (f) with 19 slices, each separated by a distance of 1 cm.

Figure 4 .
Figure 4. Reconstruction of a small larva of Archegosaurus decheni showing three pairs of external gills and branchial platelets.Redrawn and modified after Witzmann (2004a).

Figure 5 .
Figure 5. Skull, mandible and hyobranchial apparatus of an adult Archegosaurus decheni in ventral view.Cartilaginous elements are shown in grey.The denticulate bony platelets that covered the interpterygoid vacuities in life are not shown.Redrawn and modified after Witzmann (2006a, 2013).

Figure 6 .
Figure 6.Water balance of the Archegosaurus model.Like extant freshwater fishes, Archegosaurus was probably hyperosmotic to its environment and gained water by diffusion through the skin and the gills; the osmotic influx of water had to be compensated for by the production of dilute, hypoosmotic urine by the kidneys.

Figure 7 .
Figure 7. Solute balance of the Archegosaurus model.Because Archegosaurus was probably hyperosmotic and hyperionic to its environment, it lost ions by diffusion through the gills similar to freshwater fishes.It can be assumed that specialized chloride cells were present in the gills that actively took up ions (mainly Na + and Cl − ) from the ambient water to retain a constant osmolarity of the body fluids.
SA/X)(p w O 2 − p c O 2 )/100 kPa SA = (V O 2 )(X)/[D(p w O 2 − p c O 2 )/100] SA = (0.16 mL O 2 s −1 )(3.3 × 10 −4 cm)/(10 × 10 −6 )(0.001) = 5280 cm 2 −1 .www.foss-rec.net/20/105/2017/Foss.Rec., 20, 105-127, 2017 F. Witzmann and E. Brainerd: Modeling the physiology of the aquatic temnospondyl A12 Estimation of assimilation 2) = 0.000079 cm s −1 = osmotic pressure in kPa = RTC osm = 2474C osm at 25 • C (R is gas constant, T is temperature, and C osm is osmotic concentration in mol L −1 ) SA total = surface area of body and gills = 4000 cm 2 (body surface) + 5280 cm 2 (gill surface) = 9280 cm 2 .In body fluids, the osmotic concentration C osm body is 205 mOsm (see Sect. 7) = 0.21 mol L −1 ; in water, it is C osm water = 50 mOsm = 0.05 mol L −1 .L hyd = (0.000079 cm s −1 )/(135 000 kPa) = 5.85 × 10 −10 cm (s −1 kPa −1 ) SA total = 9280 cm 2 in = (2479)(C osm body) = (2479)(0.21)= 521 kPa out = (2479)(C osm water) = (2479)(0.05)= 124 kPa in − out = 521 − 124 kPa = 397 kPa Then the estimation of water flux is as follows: breathing rate required to meet O 2 needs at SMR 20 • C and AMR 25 • CUsing the lung morphometric data and the partial pressure of oxygen (pO 2 ) in the early Permian atmosphere of 29 kPa, the breathing rate at SMR 20 • C in the Archegosaurus model is estimated (see estimation in Appendix A7).The Archegosaurus model took about one breath every 20 min when resting at SMR and a little more than one breath every 5 min at AMR 25 • C to meet its oxygen needs in hypoxic water.For comparison, Polypterus senegalus has a breathing rate of about one breath every 4 min when completely dependent on air breathing for O 2 uptake in hypoxic water(Babiker, 1984, fig.1).The breathing rate for CO 2 is estimated for the Archegosaurus model, with the lungs presupposed to be the only breathing organ (see estimation in Appendix A8).When only lung breathing is presupposed, it took the Archegosaurus model about one breath every 2 min to eliminate CO 2 at rest and almost two breaths per minute during activity at 25 • C. For comparison, the garfish Lepisosteus osseus, which breathes water at low temperatures via its gills and becomes an obligate air breather as metabolic rate and ambient water temperature increase, has to come to the surface only every 4 to 9 min to gulp air at 25 • C (Rahn A7 Estimation of air-breathing rate required to meet O 2 needs at SMR 20 • C and AMR 25 • C, if all oxygen is obtained from the air (as in hypoxic water) For these estimations, lung volume V L = 1400 mL and tidal volume V t = 840 mL are given.The partial pressure of oxygen in fresh air (pO 2 ) is set as 29 kPa in the early Permian atmosphere, and the partial pressure of exhaled air (pO 2ex ) is 5.7 kPa in Polypterus senegalus (based on the mean values of left and right lungs in Magid et al., 1970, table 1).According to the early Permian atmospheric conditions, we extrapolated pO 2ex in Archegosaurus as 7.8 kPa.Breathing rate at SMR 20 • C. SMR 20 • C in Archegosaurus model is 12 kJ h −1 (see above).The rate of oxygen consumption V O 2 at SMR (20 • C) in mL O 2 min −1 can be estimated as follows: (Magid et al., 1970)dal volume for Polypterus senegalus is 60 % of lung volume(Magid et al., 1970); thus, tidal volume in the Archegosaurus model is V t = 840 mL air per breath.
Breathing rate at AMR 25 • C. AMR 25 • C (R 2 ) in the Archegosaurus model is 47 kJ h −1 (see Sect. 4.2).The rate of oxygen consumption V O 2 at AMR (25 • C) in millimeter of O 2 per minute can be estimated as follows: • C is BR SMR = V E /V t = 47/840 = 0.05 breaths per minute or about one breath every 20 min.