Into Thinner Air: The Pliocene Demise of the Giant Volant Birds

Simple Summary: All very large flying birds with a mass greater than 20 kg became extinct about 3 million years ago. One possible reason for this is bio-mechanical stress during takeoff in less dense air. This possibility is examined using a bird flight simulation model and a paleo-air density value derived from two different proxies. Takeoff airspeed and power requirements for the three known species at this value are found to be similar to those of large extant birds, but at present air density, takeoff speed is significantly higher. The escape of lighter isotopes of nitrogen during long periods of weak geomagnetic fields could be a possible explanation for this loss in atmospheric mass and how this would appear in the geological record and how it would affect the climate in terms of cooling is discussed. Abstract: Three genera of very large volant birds existed for most of the Pliocene: the Pelagornithidae seabirds; the large North American Teratornithidae and the stork Leptoptilos falconeri in Africa and Asia. All became extinct around 3 Ma. The reasons for their demise are puzzling, as the Pelagornithidae had a world-wide evolutionary history of more than 50 Ma, smaller teratorns were still extant in the Holocene and smaller stork species are still globally extant. Extant large birds have a common critical takeoff airspeed suggesting a biomechanical limit in terms of power, risk and launch speed, and simulations of the flight of these extinct species suggest that at 1 bar they would have exceeded this value. Estimates for the Late Pliocene atmospheric density are derived from marine and terrestrial isotopes as well as resin chemistry, both approaches suggesting a value of about 1.2 bar, which drops to present levels during the period 3.3 to 2.6 Ma, thus a loss in atmospheric density may have caused biomechanical and ecological stress contributing to their extinction and/or development of smaller forms. This hypothesis is examined in terms of a possible mechanism of atmospheric mass loss and how this would be seen in the geological record. At 1.2 bar all the extinct species present takeoff airspeeds similar to large extant volant birds and which match the expected power and kinetic energy levels

Mass estimates based on femur and tibiotarsus circumferences range from 21.9 to 40.1 kg for P. sandersi (Ksepka 2014) [4] and from 15.6 to 28.6 kg for P. chilensis (Mayr & Rubilar-Rogers, 2010) [5]. However, Field et al. (2013) [8] have shown that methods of estimating the mass of fossil volant birds in species with relatively short legs do not correlate as well as other dimensions, such as maximum coracoid lateral length, which when applied to the specimen MNHN SGO.PV 1061 (Mayr & Rubilar-Rogers 2010) [5] gave a value of over 40 kg (Cannell 2020) [9]. The linear dimensions of the tarsometatarsus of Ephippiorhynchus tchoufour (saddlebill stork), were about 50% larger than extant species and may have stood at up to 2.20 m in height. (Louchart et al 2008) [10]. Based on extant species (Elliott et al 2020) [11] this implies a wingspan of 4 m and mass of up to 25 kg for a male; or with a full crop, a takeoff mass of about 28 kg.
These three giant bird orders were still represented in the Late Pliocene and the last known specimens were: the teratorns, T. incredibelis with an estimated mass of 25 kg; the pelagornithid, P. mauretanicus with a mass of about 24 kg and the stork, Leptoptilos falconeri with a mass of around 20 kg. However, all these species became extinct at the end of the Pliocene for reasons that are not understood. A change in air density may have affected their flight bio-mechanics and this hypothesis is investigated using simulations with the Flight 1.25 program (Pennycuick 2008) [12], which allow flapping cruising speeds and takeoff stall airspeeds to be estimated at different air densities and compared with the maximum takeoff airspeeds of extant large birds. The results are examined in terms of the Pliocene climatic conditions and estimates of paleo atmospheric mass (considered as paleo-Patm in bar) derived from two independent proxies: pCO2 as derived from marine boron isotopes and terrestrial sources, and the property of amber (resin) to preserve the biochemistry of the atmosphere when it was produced.
Atmosphere can be lost due to impacts, massive erosion and the preferential loss of lighter isotopes in solar wind events (Xiang et al 2016) [13]. The latter may be of particular importance during periods with weak geomagnetic fields (Wei et [14][15][16]. Measurements from bubbles trapped in ice cores, for example, have shown that pO2 has dropped over the past 800 ka (Stolper et al 2016) [17], which also implies that pN2 has increased; although it is not possible to establish which gas has kept the most stable atmospheric mass. Rimmer et al (2019) [18] conclude that in view of the variable nature of atmospheric nitrogen it could also be expected that Patm has both increased and decreased many times in the geological past. As stated by Johnson & Goldblatt (2018) [19]: the assumption that atmospheric mass should be constant over Earth's history is not an inherent property of the planet.
The last geomagnetic multiple reversal events (in particular the Mammoth and Kaena Reversals) took place at the end of the Pliocene and timing of the low magnetic intensity of this period is compared to the paleo-Patm proxies, the extinction of the large birds and climatic effects. The hypothesis presented is that the very large birds possibly flourished in an environment with a higher air density, part of which may have been lost during periods of low geomagnetic intensity leading to bio-mechanical and ecological stress. The larger species then became extinct and either new species of smaller birds evolved that were adapted to modern atmospheric densities, or the bird clade became extinct.

Teratornithidae
The giant teratorn, Argentavis magnificens is only known from Argentinian fossils from the Miocene. Smaller teratorns such as teratornis merriami, with an estimated wingspan of 3.2 and mass of about 14 kg became extinct at the end of Pleistocene. A large teratorn (T. incredibelis) was found in late Pliocene deposits in California, linear dimensions suggesting it was about 30% smaller than argentavis and 30% larger than merriami. A premaxillary was also found from the late Pliocene (3.5 to 3.2 Ma), a partial proximal shaft was dated to 1.8 to 0.9 Ma, but is severely crushed and thus difficult to scale, however, it differs from known teratorns and is slightly larger. A large fragment of a right carpometacarpus from Florida was dated at between 1.66 and 1.4 Ma, but in the same deposits were found fossils of an early and smaller T merriami (Campbell & Tonni 1983) [20]. Campbell et al (1999) [21] conclude that the carpometacarpi cannot be used for scaling due to poor preservation; nevertheless, a reasonable estimate for the size of T. incredibelis would be of a bird of a size between A magnificens and T merriami.
Based on a 30% linear increase of T merriami and the relationship between wing area and mass for raptors (Cannell 2020) [9], its wingspan would be about 4.2 m, with Aspect Ratio (AR) of around 8.5 and mass of about 25 kg. Flight muscle mass in teratorns may have been higher than the usual bird standard of 17% adopted in Flight 1.25 and a value of 19% was adopted, as discussed in Cannell (2020) [9].

Pelagornithidae
Fragments of a pelagornithid classed as P. mauretanicus from Ahl al Oughlam, Casablanca, Morocco were dated 2.5 Ma (Mourer-Chauviré and Geraads, 2008) [22]. At the time of deposition, the site consisted of a network of fissures and interconnected galleries in a jumble of calcarenite blocks at the foot of what was then a cliff on the shore (Louchart et al 2013) [23]. This dating was based on the faunal assemblage and the possibility thus exists that these deposits are secondary and some of the creatures may have flourished at an earlier or later dates. This is noted by Mourer-Chauviré and Geraads (2010) [24], as the marine avifauna shows many similarities with that of the older Yorktown Formation in North Carolina, dated to 4.5 to 5 Ma, however, the authors state that pseudodontorns were present in North America, New Zealand, Japan, and Peru during the Pliocene, the Ahl al Oughlam form, dated from 2.5 Ma, is the most recent form known to date.
Discovery of a proximal Pelagornis humerus (UCMP 219007; University of California Museum of Paleontology, Berkeley, California, U.S.A.) from the Middle-Upper Pliocene (~3.35-2.5 Ma) Purisima Formation of northern California represents the youngest record of Pelagornithidae from the Pacific Ocean basin and demonstrates that pelagornithids survived in both the Atlantic and Pacific Oceans until the late Pliocene. This fossil from Santo Gregorio Beach California, is a proximal portion of a left humerus with a long, dorsoventrally-compressed shaft, measuring 385 mm. A prominent protuberance occurs near the ventral margin of the anterior surface of the shaft ventral to the deltopectoral crest, 113 mm from the proximal end. Compared with the biostratigraphically dated Pelagornis mauretanicus from Morocco, the more precise dating makes it the youngest reliably dated pelagornithid fossil worldwide with an estimated age of between 3.35-2.6 Ma (Boessenecker and Smith 2011) [25]. This upper limit of 2.6 Ma (late Pliocene tephra) is much younger than expected from lithologic correlations that assign these strata to the late Miocene Tahana Member, however, the age of this tephra cannot be older than about 3.3 Ma, the age of the disseminated ash horizon found stratigraphically lower in the Purisima Formation and to the south (Powell et al 2007) [26].
The latest dates for pelagornithids are: Peru -about 3 to 3.9 Ma (Chavéz et al. 2007) [27], Japan and New Zealand -3.1 to 3.6 Ma (Ono 1989) [28], California -2.6 to 3.4 Ma and Morocco -2.5 Ma (with the reservations covered above). Thus around 3 Ma these birds, an avian clade with a temporal span of more than 55 million years and a worldwide geo-graphic distribution became extinct. Boessenecker and Smith (2011) [25], among many others, find it puzzling that such a long-lived, cosmopolitan, and presumably adaptable taxon such as the Pelagornithidae did not survive whereas many other sea birds continued to thrive.
The wingspan of this specimen was estimated by Boessenecker and Smith [25] at between 4.3 to 5.37 m, slightly smaller than the Miocene P chilensis, yet still one of the largest volant birds ever reported. The "teeth" spacing from Ahl al Oughlam fossil, although similar to P chilensis, is about 85% smaller, suggesting a wingspan of about 5.5 m (based on simple linear beak dimensions) with AR of 18 (Campbell & Tonni, 1983, Cannell 2020 [20,9]. If the P chilensis had a mass of up to 40 kg these recent specimens would possibly have been about 20 to 24 kg (full crop) and wingspan of ~5.1 m (average of the three estimates).

Ciconiidae (Leptoptilini)
The very large extinct species of stork, Leptoptilos falconeri, was represented during the Pliocene in the Northern half of Africa, South Asia (Siwalik Hills, India, late Pliocene) and probably also in the Ukraine. In the latest Pliocene fossils have been found in Omo, Ethiopia and Koro Toro, Chad   [29]. According to Louchart et al (2005) [29], the diversity of the Leptoptilini has been overestimated, and L. falconeri appears to remain the only valid extinct species of this tribe in the Pliocene.
L. falconeri weighed about 20 kg and probably stood up to 2 m tall and had relatively slightly reduced forelimbs, allometrically congruent with a slight limitation in flight abilities for a bird of large size and mainly terrestrial habits; it became extinct by the end of the Pliocene and the reasons for its extinction remain enigmatic  [29]. These dimensions suggest a linear scaling increase over the extant Marabou stork (Leptoptilos crumenifer) of about 33%, giving a wingspan of 3.72 m, or with the slightly reduced forelimbs, around 3.6 m -as compared to the value of 2.8 m for a 9 kg extant Marabou stork. Aspect Ratio (AR) would thus be slightly less than extant large storks, at about 9.

Materials and Methods
To test the effect of any change in the density of the flight medium, simulations were carried out with the widely used flapping model Flight 1.25 (Pennycuick 2008) [12]. The input data used the above mass, wingspan and wing shape (AR) values. Flight muscle percentage was the program standard of 17%, except for the teratorns simulations, which adopted a slightly higher value of 19%. The output of these simulations gives cruising airspeed at minimum power; climb rate at maximum power and myofibril work. Takeoff airspeed is taken as 70% of level cruising speed at minimum power based on ultra-light aircraft designs and which agree with the running and flapping takeoff speeds of large extant birds (Cannell 2020) [9].
A problem of bird flight aerodynamic models (such as Flight 1.25) is that when applied to flight with an acceleration component (for example, takeoff) their predictions are at best an indication of relative power values (Nudds & Bryant 2002) [30]. However, many birds start takeoff from an initial jump, and a frame by frame analysis of multiple videos of storks taking flight shows that they follow the pattern described in the literature of rapid leg extension, together with a strong wing upstroke to gain both forward and upward acceleration (Askew et al 2001, Earls 2000, Provini et al 2014) [31][32][33].
Borelli, in De Motu Animalium (1680) suggested that vertical takeoff speed should be the same regardless of animal size (Bobbert 2013) [34], and this "Borelli's Rule" was confirmed by Newton who reasoned that to jump to a given height (h) in a gravitational filed (g), an animal must achieve a vertical takeoff velocity (v), which corresponds to kinetic energy, such that: h= v 2 /2g, and is independent of mass. Bobbert (2013) [34] found that size does affect jump height, but the vertical velocities reached were remarkably constant over a wide range of linear scaling. Thus, although for the critical takeoff phase of the teratorns and pelagornithid a flapping and running simulation approach can be used, for the stork a different method is adopted based on the kinetic energy needed to reach minimum airspeed.
To determine the air densities -or paleo air pressure -to be tested, two independent proxies were adopted: resin/amber and the difference between marine and terrestrial derived pCO2.

Resin/Amber d13C isotope
Amber occurs worldwide as 'bursts' in the geological record: the early Late Triassic (Carnian, 237-228.4 Mya), the Early to mid-Cretaceous (145-96 Mya), the Eocene (56-33.94 Mya) and the late Oligocene to the Miocene (28-5.8 Mya) (Seyfullah 2018) [35]. Warm, humid and higher air density conditions favour photosynthesis (Takeishi et al 2013) [36] and thus resin production and general biodiversity. It is noteworthy that these periods also coincide with the development of flight: pterosaurs (Kellner 2015) [37] and 'flying fish' (Xu et al 2013) [38] in the Mid to Late Triassic; the well-known emergence of gliding mammals, birds and several unusual gliding or flying therapods in the Late Jurassic -Early Cretaceous; birds and the iconic large pterosaurs in the Cretaceous; Giant Pelagornithids (Cenizo et al 2015) [6], the Bat 'Big Bang' (Simmons 2005) [40] in the Eocene; and the Giant Birds of the Miocene [9].
Tappert et al (2013) [41] note that resins have chemical properties that have not changed significantly with plant evolution and that make them particularly suitable as proxies of environmental changes over geological time. For copious resin producers it was therefore assumed that the metabolized CO2 was sourced from isotopically undisturbed air that had a δ13C composition approximating a global atmospheric average. The authors also remark that several definite trends appear in the data, yet the known observation that 13C fractionation in plants increases with increasing pCO2 cannot account for the δ13C shifts in the resin record and therefore some other process must be responsible. Diagenesis is dismissed as, if this were the case, fossil resins from different localities should show an erratic distribution of the δ13C resin mean, which is not observed in the data nor considered in the chemistry of amber by Nissenbaum &Yakir (1995) [42]. Insect attack has been shown to affect resin composition by enriching δ13C levels (McKellar et al 2011) [43], but leaving the resin turbid; clear samples should thus be less affected.
Similar data for the Miocene was found by Kocsis et al (2019)[44} in the amber from Brunei, in which modern resin yielded on an average 3‰ lower δ13C values, with a decreasing trend in average δ13C of about 1‰ from the late middle Miocene to late Miocene. The authors mention that this could be explained by gradual changes in local environmental conditions or an increased amount of less mature specimens among the younger samples; however, Tappert et al (2013) [41] found this same trend in Mexican, Dominican and Malaysian samples, suggesting a more global explanation.
An evaluation of the effect of a variable pO2 on amber isotopes, using experimental work on the isotopic fractionation in C3 plants and partial pressure of oxygen, revealed that the fractionation of carbon during photosynthesis was found to increase when the pO2 in the ambient air is significantly higher than modern values, resulting in depleted 13C plant mass (Berner et al 2000) [45]. The opposite effect has also been observed under lower than modern pO2 in ambient air (Beerling et al 2002) [46]. From these observations, Tappert et al (2013) [41] considered that a direct relationship is a reasonable assumption for moderate pO2 levels, provided that major physiological adaptations of plants are not involved.
In this empirical model, paleo-pO2 at the time of resin formation may have been as low as 13% in the Eocene and 18% in the Mid-Miocene. This is starkly at variance with all versions of the standard Geocarbsulf and Geoacarbsulfor models and fire activity in pure sphagnum moss peat -a highly flammable and easily ignitable material that burns in modern natural fires -is effectively "switched off" at pO2 < 16% (Belcher et al 2010) [47]. Possibly for these anomalies in relation to established geological models and wildfires, this link of resin chemistry to paleo pO2 has not received the attention it deserves.
The possibility that the Patm of these periods may have been higher, however, has yet to be considered. At higher pressure, low levels of pO2 not only sustain biological processes, but are essential to avoid oxygen poisoning. A modern example of this is deep sea diving: in order to work at 130 m depth in the northern sector of the North Sea oil field, for example, the breathing mixture used only contains 10% oxygen (Wilmshurst 1998) [48].
Thus the mass estimates of O2 based on the Geocarbsulf model data (Berner 2006; Royner et al 2014) [49][50] and on the pO2 derived from resin/amber data can be reconciled by varying the Patm values (air density) of the resin model such that the mol m -3 are similar, essentially by increasing the atmospheric mass by the relevant factor:

Paleo Patm = (pO2 gcs /pO2 amb) bar
where pO2 gcs is the values estimated from the geocarbsulf model and pO2 amb is from amber data. Carbon isotope data from more recent "Borneo Amber" (Kocsis et al 2020) [44] suggests that, unlike the gradual change in pO2 from Tappert et al (2013) [41] from the Miocene to the present, d13C levels remain enriched up to around 3 Ma. As there is no evidence that pO2 has radically changed since the Miocene, the derived pO2 value for the Late Pliocene would be slightly less than 18%, which to reach the Geocarbsulf model value of 21%, would require an increase in Patm of around 1.2 bar, the Borneo amber isotope data suggesting that any loss in Patm would have been about 3 Ma.

Marine and Terrestrial Derived pCO2
The ability of boron isotopes in foraminifera to record seawater pH stems from the acid-base equilibrium between boric acid and borate ion. Marine carbonates have boron isotopic compositions of 15-25‰, substantially lower than that of seawater (39.61‰). This is due to the dominant incorporation of borate ion into growing carbonate, so as the boron isotopic composition of borate varies with pH, so does δ11B of marine carbonate (Rae et al 2001(Rae et al , 2018 [51][52]. The main interest in this technology stems from the ability to reconstruct past CO2 from paleo-pH, as these are closely coupled in seawater, both being governed by the primary carbonate system variables. rom knowledge of aqueous [CO2], along with estimates of temperature and salinity, Henry's Law allows calculation to be made of the partial pressure of atmospheric CO22 in equilibrium with this water. Curiously, the pCO2 values derived from marine (benthic) carbonates are higher than the values derived from stomata or C3 data and this difference in sea water derived CO2 and terrestrial based data has long been something of a paradox and similar to the "enigmatic" conditions of the Oligocene (O'Brien et al 2020) [53]. However, a possibly overlooked factor in this process is air pressure. The oceans absorbs a large amount of CO2 due to the relatively high solubility of this gas in seawater, with the dissolved CO2 participating in chemical and biological processes while being circulated around the global ocean; this results in generally negative partial pressure (pCO2) gradients at the air-sea interface which drive CO2 uptake by the ocean. The solubility of CO2 in seawater is often measured as the Henry's Law Constant (KH) and expressed as [mol (kg H2O) −1 atm−1]; this varies with temperature, but is approximately linear over the range 0 C to 50 C and directly proportional to partial pressure (Bailey et al 2018) [54]. What is often ignored, however, is that KH is also expressed in terms of [atm], as the solubility CO2 is highly responsive to air pressure -about 55 times greater than that of N2 at 20 C. Although this can be seen almost on a daily basis when opening a can of soda (~1.25 bar at 20 C), surprisingly few studies on this property have been carried out.
Al-Anezi et al (2008) [55] examined the solubility of CO2 in a solution of 35,000 ppm NaCl + MgCl2 + Na2SO4 (similar to real seawater) at 1 and 2 bar and over several constant temperatures. At 25 C and 1 bar the solubility was 70 (CO2 concentration in ppm), at 2 bar it rose to 550 ppm (their figures 6 and 7, note that Fig. 6 appears to have squares and diamonds inverted). Assuming a linear difference -reasonable as CO2 solubility in water from 0.1 bar to 0.9 bar is almost linear (their figure 18) -this gives a gradient of about 48 ppm per 0.1 bar. Thus for derived values from marine and terrestrial sources:

Marine pCO2 = Terrestrial pCO2 + Component from any Difference in Patm
Marine derived pCO2 from the mixed layer dwelling planktic species Globigerinoides ruber shows a sharp dip at the start of the Mammoth Reversal and a more permanent reduction at the start of the Kaena Reversal from about 370 ppm to 320 ppm. By the mid-Pleistocene these are similar to pre-industrial values (de la Vega et al 2020) [56].  [62][63] and, in particular, plant based C3 data (Cui et al 2020) [64] indicate more constant pCO2 values of below 300 ppm for the Pliocene, Both the stomata and C3 plant data also give very consistent values in relation to other sources -including ice core and blue ice data -for the Pleistocene {64], strongly suggesting that overall atmospheric pCO2 has been correctly assessed for the Pliocene.
Taking the marine data (average of 50 ka bins) from Martínez-Boti et al (2015) [60] and de la Vega et al (2020) [56] and comparing these values with the pCO2 derived from terrestrial C3 plants [64] and metasequoia stomata values [62], the difference between marine and terrestrial derived CO2 is seen to drop over the period from 3 to 2.

Teratornithidae
At 1 bar, the Flight 1.25 cruising speed for the large teratorn is simulated at 18.8 m/s, climb rate 50 cm/s and aerobic muscle power within the myofibril stress limits. Stall airspeed would be about 13.2 m/s -almost 50 kmh. Even with strong and robust legs this precludes any form of 'jump' based takeoff which could only contribute to a vector of about 4 m/s (discussed below). An option could be to run into a headwind similar to the Andean Condor (Vultur gryphus) which has a stall (takeoff) speed of about 11m/s at a flap rate of about 3 Hz (McGahan 1972) [65]. However, the experimental placement of food has shown that condors will not land in certain locations where the costs of flapping flight are extremely high (Williams et al 2020) [66].
With no headwind and on flat ground, a takeoff at over 13 m/s could be a stressful and high risk action. As discussed below, this value is higher than the limit for all extant large birds and any change in wind could drop airspeed to below stall. At 1.2 bar the simulations show that cruise speed drops to 17.1 m/s, giving a stall estimate of 11.97 m/s and within the extant biological limit for large birds.

Pelagornithidae
At 1 bar the simulation data shows that cruising speed would be 16.8 m/s resulting in a stall speed about 11.8 m/s. Aerobic muscle power is within the limits given by Pennycuick (2008) [12] and climb a comfortable 64 cm/s for a wingbeat of 1.69 Hz. Swans 'run' over the water surface with wings beating in at a low angle and feet 'slapping' the water to get extra traction and support. Albatross perform a similar takeoff, whereas large pelicans use both feet to 'hop' and effectively 'row' the water surface to gain forward and upward momentum on the wing upstroke. Therefore on open water and with some form of paddle gait, getting airborne would appear to have been feasible and similar to large the takeoff of the large swan Cygnus olor, with a cruising speed of 16.1 m/s and thus a stall of about 11.3 m/s (Alerstam et al 2007) [67].
However, on land (necessary for nesting and chick feeding), the short legs of pelagornithidae may have been problematic: measurements of the leg bones of the Miocene P chilenens (bone wingspan 4.6 m) and a Wandering Albatross (Diomedea exulans) skeleton (with a bone wing span of 2 m) show that the much larger and heavier Pelagornithidae had leg bones only about 20% longer than the extant albatross: Femur (15, 12.5); Tibiotarsus (23,19) and Tarsometatarsus (11, 7.5) -all values in cm and taken from digital images: P chilensis [5] and D exulans (N. Jones, Museum of Zoology, Cambridge 2016,). Gaining airspeed by running may therefore have been difficult.
At 1.2 bar, cruise speed drops to 15.3 m/s and stall to 10.7 m/s -10% less and similar to that of the wandering albatross (Pennycuick 2008) [12] for a wingbeat of 1.57 Hz. As discussed in Cannell (2020) [9], the bone stress on the lightweight, but very long wing bones, of pelagornithids could have been critical during takeoff, and as stress is proportional to the square of the wingbeat, at 1.2 bar this reduction in frequency would be equivalent to a stress reduction of (1.69/1.57) 2 or 16%.

Ciconiidae (Leptoptilini)
For the large 20 kg stork L falconeri, the simulation setup for 1 bar (present air density) indicates that this bird with relatively shorter wings had enough power to fly at a fast cruise speed of 18.9 m/s, thus stall airspeed at 1 bar would be about 13.23 m/s. The question remains, however, on how these birds attained takeoff airspeed? Most birds start takeoff from an initial jump, and storks follow the pattern described in the literature of rapid leg extension, together with a strong wing upstroke to gain both forward and upward acceleration ( [31][32][33]. A problem of bird flight aerodynamic models (such as Flight 1.25) is that when applied to flight with an acceleration component (for example, takeoff) their predictions are at best an indication of relative power values and may bear little relation to reality (Nudds & Bryant 2002) [30]. Thus for a "jump" takeoff a different approach is required that takes into account the initial jump energy, the required airspeed kinetic energy and available power. Birds jump speeds range between 1.5 m/s for finches and doves, (Provini et al 2014) [33] [31] and these values do not scale with bird size. This property was first mentioned by Borelli, in De Motu Animalium (1680), who noted that takeoff jump speed should be the same regardless of animal size (Bobbert 2013) [34]. This became known as Borelli's Rule and Newton later reasoned that to jump to a given height (h) in a gravitational filed (g), an animal must achieve a vertical takeoff velocity (v), which corresponds to kinetic energy, such that: h= v 2 /2g and is independent of mass. Bobbert [34] found that size does affect jump height, but the vertical velocities reached were remarkably constant over a wide range of linear scaling. Thus scaling up the linear dimension of a bird such as a stork results in the animal having a higher mass (m), a higher stall speed (v) and needing greater energy (m/2 v 2 ) to reach stall airspeed, whereas initial launch (vertical jump) speed tends to be constant. Askew et al (2001) [31] examined many species of birds (and bees) and found that over a broad range of body size (0.0002-5 kg) and contractile frequency (5-186 Hz), the myofibrillar power output of flight muscles during short maximal bursts is very high and of similar magnitude at 360-460 W kg−1, with the caveat that the power outputs are all short-term efforts that are not sustainable.
The At the higher air density equivalent to 1.2 bar, stall speed drops to 12.04 m/s thus an energy requirement of 1449 J. Burst muscle power to energy ratio over 1 second would thus be (1392/1449-90) or 1.02. Power and energy are matched and the takeoff speed is constrained within the apparent maximum limits.

Discussion
Many factors could have either contributed to the direct extinction of these large birds or led to stress factors that reduced population sizes to unsustainable levels, such as: ecological stress, an impact event or biomechanical stress due to atmospheric loss.

Ecological
The marine mega fauna extinction event at the end of the Pliocene (Pimiento et al 2017) [68] is one of several studies that examine the very high levels of extinction of large marine creatures towards the end of the Pliocene, mentioning that seabirds lost 35% of their generic diversity. However, Figure 4 in their supplementary notes shows that the extinction rate for birds in the Pliocene was in fact similar to that of the other Cenozoic periods, such as the Oligocene. The authors also state that the global neritic zones area dropped from about 30 to 21 million km2 at the end of the Pliocene, or by 9 million km2. However, neritic zone area has varied even more during the Pleistocene, with sea-level changes of far greater amplitude during ice-age cycles and over much shorter time periods, but without major extinction events.
The assemblage of fossil birds in the coastal locality of Horcon in central Chile reveals the changes in seabird fauna in the area of influence of the Humboldt Current over the last 5 Ma and Chávez Hoffmeister et al (2014) [69] note that the Pliocene record consists exclusively of extant families. In comparison with the Late Miocene, the only suprageneric taxon absent from the Pliocene record in Chile is the Pelagornithidae, but other large birds such albatross and petrels are also rare, a possible indication that they had similar feeding habits to the Pelagornithidae. Hence the Pacific coast, at least, does not seem to have experienced a major seabird extinction event at the end of the Pliocene.

Extraterrestrial
The most commonly known example of an extraterrestrial extinction event is the Chicxulub KT impact, yet other events may influence life forms, such as a near supernova event. Melott et al (2019) [70] make the case for such an intense radiation period, in particular the effect of muons on the ozone layer as high energy photons and cosmic rays can ionize and dissociate molecules in the atmosphere, notably N2, resulting in a series of chemical reactions which deplete ozone and result in an increase in UVB radiation.
However, if this were the case, this radiation should affect pollen grains as has been found at the end of the Devonian (Marshall et al 2020) [71] and proposed for the end of the Permian (Benca et al 2018) [72], based on the description of malformed pollen from coeval formations over a period of about 1 Ma (Foster and Afonin 2005) [73]. As far as can be determined, no such pollen deformations have been observed for the end of the Pliocene. It should be mentioned, though, that any process that increased UVB radiation from supernovas, lower atmospheric mass or ozone depletion due to low geomagnetic fields causes feather damage and would affect larger birds, as their primary feathers take longer to grow (Sullivan et al 2019) [74].  [75][76][77]. Thus the Earth's atmosphere was dangerously exposed to solar winds and solar events for tens of thousands of years. The earlier Gilbert-Gauss reversal (3.58 Ma) also resulted in a weak field before the transition, but which rapidly gained in intensity (Goguitchaichvili et al 2009, Valet et al 2020) [78,75] If atmospheric mass were lost (in particular the lighter isotope 14N) during a period of weakened geomagnetic field this would appear as a marked temporary rise in 15N in the geological record. According to McKay et al (2012) [79] during the warmest intervals of the Pliocene from 4.5-3.0 Ma, Earth's average surface temperature was 2-3°C warmer than present and equator to pole temperature gradients were weaker. There was, however, a major phase of ice sheet expansion and cooling in coastal Antarctic waters at ∼3.3 Ma and, as can be seen in their Figure 1, there was a large shift in 15N at the end of the Mammoth Event from less than zero to 8‰ (standard definition) and again at the end of the Kaena transition. Similar shifts can also be seen at the Matuyama Gauss transition at about 2.58 Ma and at the Reunion Excursion -as well as a relatively rapid large positive shift at the Gilbert-Gauss Reversal. These rapid increases in 15N could be due to a change in biological productivity from warmer waters (as indicated by the TEX derived SST) however, the surface waters are relatively shallow (ice is frequently grounded in the record) and so the recorded changes in sea-level may have affected affect these readings; certainly (their) Figure 2 shows longer ice durations for the period starting at about 3.3 Ma (from sea ice diatoms) and no relation exists between the high 15N values and the icesheet extension (Glacial proximity) [79].

Biomechanical Stress due to Atmospheric Loss
There is the possibility that these cooling events may have been subject to precessional forcing, which has been raised by Caballero-Gill et al (2020) [80], the authors make the case for a cooling frequency of 100 ka, although it can be seen in Valet et al (2020) [75] that periods of low geomagnetic intensity also align closely with periods of cooling.
Similar sharp spikes in 15N can be seen at about 2.1 Ma 3.14 and 3.6 Ma in Ocean Drilling Program (ODP) Site 1012 (32N, 118W) in a non-glacial setting (Liu et al 2008) [81]: during the stable Mammoth chron, 15N levels are less enriched levels when the intensity of the field is higher. The same sharp steps in d15N are seen in the African coast in boreholes from the Benguela current region: at 3 Ma, 2.6 Ma and in particular at 2.05 Ma for subtropical borehole 1082 (22S), and at 3Ma, 2.6 Ma and 2.05 Ma for the sub-Antarctic borehole 1090 (43S) (Etourneau et al 2009) [82]. Thus is possible that the apparent loss in atmosphere indicated by the paleo-Patm proxies (amber and pCO2) not only resulted in the global cooling seen in the record, but also led to a reduction in species size of teratorns and storks.

Dynamic Soaring in Pelagornithids
The wind profile over relatively calm sea is often expressed as a logarithmic equation, where the velocity at a certain height is a function of friction (or shear) velocity, which in turn is a function of the inverse square root of air density. Thus the wind profile at a higher air density equivalent to 1.2 bar would be vertically extended by a factor of √1.2 (~1.1) or 10%.
Dynamic soaring is used by extant sea birds for long migrations (such as the Manx shearwater, Puffinus puffinus) or in foraging (albatross). In practice, the larger birds fly in an 'S' pattern in order to gain energy from the wind gradient. Pennycuick (2008) [12] and Richardson et al. (2018) [83] note that a two-layer model of wind speed consisting of zero wind in the lower layer and a more uniform wind in the upper layer helps in estimating the increase of airspeed and kinetic energy when a bird crosses the wind-shear layer. The strong winds of Southern Ocean create a wind gradient which for a 10 m/s wind (at standard height) the greatest wind speed differences are from the sea surface to about 10 m in height and thus where the energy harvested is greatest. This is confirmed by behavioural observations: the average flight height of Laysan (Phoebastria immutabilis) and wandering albatrosses was found to be between 3 to 8 m (Yonehara et al., 2016) [84], similar to the average flying height for albatross of 5 m observed off Bird Island (Pennycuick, 1982) [85] and the height range of highest energy gain between about 5 and 15 m found by Sachs et al. (2012) [86]. At the higher air density (1.2 bar) the extra 10% would allow better energy harvesting from 5.5 to 16.5 m and with higher lift (proportional to rho), favoring a bird with longer wingspan and better aerodynamic penetration (heavier), which would allow faster foraging. A drop in air density would remove these advantages, as noted in Cannell (2020) [9] for the Giant Pelagornithidae species of the Eocene and Miocene, which became reduced in size. At 1 bar the optimum wingspan for dynamic soaring may have been reduced to a value similar to the largest extant albatross size (from 5.1 to 3 m or linear reduction of 59%), which would reduce the mass of a pelagornithid to about 4.8 kg: a body plan possibly too light for aerodynamic penetration in strong winds. Thus unlike the teratorns and storks, downsizing may not have been an option for the Pelagornithidae.

Takeoff and Landing Airspeeds
Flight speed is expected to increase with mass and wing loading among birds (and aircraft) for fundamental aerodynamic reasons and Alerstam et al (2007) [67] tested this hypothesis with a database of multiple tracked flights for 138 bird species. The data showed that other constraints have an important influence on cruising flapping flight speed that go beyond aerodynamic scaling effects (such as phylogenetic group). However, when this data, together with level flapping cruising flight of other bird species (Pennycuick 1997) [87] is examined for large birds (mass >1 kg) another factor emerges: an overall limitation of flapping flying speed. Using a takeoff speed for all species of 70% of flapping cruise speed gives the relation shown in Figure 2. For nearly all birds above ~ 4 kg, takeoff airspeed is limited to around 11 to 12 m/s. Body mass and wingspan were derived from a review of 33610 specimens and the radar tracking of the larger birds was largely for level flight or with a slight vertical component, and include swans, pelicans, eagles, geese, storks, flamingos, cranes, cormorants, ducks, spoonbills, gulls, vultures and ravens. Data on the Andean Condor (McGahan 1972) [65] has been added in red along with observational data of level flight of 17 large species by Pennycuick 1997. [87] The data of Cygnus cygnus (blue) is based on only one tracked flight. The flight of the common crane (grus grus) is marked in green and differs in that this large bird has a low AR and long legs used to gain initial airspeed. However, data on the larger Antigone canadensis, (formerly Grus Canadensis) gives a flight speed of 12 m/s (Tacha et al 1992) [88] whereas Flight 1.25 estimates a minimum power speed of 15.5 m/s (6 kg, wingspan 2.4 m and AR of 4); takeoff airspeed is thus possibly lower than 11 m/s. Alerstam et al (2007) [67] note that functional flight adaptations and constraints have an important influence on cruising flapping flight speed and takeoff airspeed appears to be one of these constraints and a limiting factor in determining maximum volant bird size and aerodynamics. This suggests that very large extinct birds of the Cenozoic may have had a flight medium that allowed takeoff speed to be also kept within the same constraint, i.e. a higher density as proposed by Pennycuick. At the predicted air density for the Pliocene of about the equivalent of 1.2 bar, takeoff airspeeds in relation to the present lowland and sea level of about 1 bar are shown in Table 1. Although this difference appears small, in terms of impact energy (proportional to airspeed squared), this represents a reduction of almost 20% in impact energy possibly of vital importance to a 20 kg bird with lightweight bones. Landing is also a risk for large birds and is normally preceded by a slow glide with a high angle of attack to modify the wing profile (as in a flap). Simulations for all three large birds give a minimum sink glide speed of about 11 m/s at 1 bar. At 1.2 bar this drops to  In order to test the kinetic energy methodology of a standing jump launch, simulations were carried out for the even larger Miocene saddlebill stork Ephippiorhynchus tchoufour with a linear dimensions of the tars metatarsus about 50% larger than extant species, suggesting this bird may have stood at 2.20 m in height (Louchart et al 2008) [10]. Based on data from extant species this implies a wingspan of 4 m, AR of 9 and mass of up to 25 kg for a male; or with a full crop, a takeoff mass of about 28 kg. Flapping cruising speed at 1 bar is 19.9 m/s, or a simulated takeoff airspeed of 13.93 m/s. This gives a kinetic energy of 2717 J. With a muscle mass of 4.25 kg, available burst power would be about 1700 W plus launch energy of around 130 J: a ratio of power to energy of 0.66. The bird would be extremely underpowered for a jump takeoff. At 1.4 bar, airspeed is 11.9 m/s kinetic energy is further reduced and the power to energy ratio is about 1. A jump takeoff therefore becomes viable at about level of air density suggested by Cannell (2020) [9] for the Giant Teratorn and Pelagornithid species according to simulations with Flight 1.25, with all three giant Miocene species having estimated takeoff speeds of between 11 and 13m/s in agreement with the apparent limit for large extant birds.

Other possible impacts of atmospheric loss
According to Chemke & Kapsi (2017) [89], a more massive atmosphere on an earth like planet would cause adiabatic warming, changes in Hadley Cells and reduce the temperature gradient from the equator to the poles. Thus if atmospheric loss affected the flight of all large birds, these climate impacts should have resulted in a cooler world with a higher temperature gradient after ~3 Ma. This is seen in the record: Ballantyne et al (2010) [90] note that during the Pliocene warm period the Arctic was ~19 °C warmer than today, whereas Antarctica was only ~13 °C warmer (based on three independent proxies from an early Pliocene peat deposit in the Canadian High Arctic), although tropical sea surface temperatures (SST) were similar to the present. This distribution has long been a puzzle and Fedorov et al (2003) [91] found that the mechanisms currently proposed in an Earth system model could not explain Pliocene warmth and simultaneously reproduce these features. More recently, Haywood et al (2016) [92] note in a review of geological archives and climate models that although high-latitude SST reconstructions indicate substantial warming, the lack of tropical SST warming in areas outside upwelling zones has proven puzzling: along with the paradox that a reduced latitudinal SST gradient implies potentially weaker atmospheric forcing of oceanic circulation, and hence weaker oceanic heat transport.

Conclusions
Three species of very large birds with habitats that ranged from temperate to subtropical, coastal, mountain and savannah and covering the Americas, Eurasia, Africa and Antarctica disappeared from the fossil record at about 3 Ma, which strongly suggests a global phenomenon. After flourishing for more than 50 Ma the Pelagornithidae, became extinct, although other smaller species of teratorns and storks continued to exist up to the Holocene. Thus the factor that links the extinct species to this critical period is their extreme size and mass.
The very low magnetic fields encountered in the Mammoth and Kaena Reversals exposed the atmosphere to solar winds and other events atmosphere allowing for the potential loss of lighter volatiles. Two proxies of paleo Patm derived from amber (resin) and the difference between pCO2 as derived from global marine and terrestrial sources indicate a drop in paleo-Patm from about 1.2 to 1 bar over the period 3 Ma to 2.6 Ma BP.
Maximum bird size may be limited by available power, and Pennycuick (2008) indicates that this maximum all-up mass of birds that are able to fly horizontally would be around 16 kg. Another limit is the energy required for takeoff -either by jumping (in which Borelli's Rule limits launch speed) or from other airspeed constraints which limit takeoff speed for all large extant birds at around 11 to 12 m/s and are possibly related to risk of injury. These constraints, including available power, are dependent on the flight medium density and at 1 bar, the stork and teratorn with mass of 20 kg or more have estimated takeoff airspeeds higher than the extant critical level of 11 to 12 m/s. At the proxy level of 1.2 bar for the Pliocene of the period before 3 Ma, all airspeed values are within this limit and a standing jump takeoff would have been also been within the energy constraint of the large stork.
Any changes in atmospheric mass would have had impacted the climate, causing cooling and a greater temperature gradient from the equator to the poles. This is in agreement with the geological record.
Supplementary Materials: The following are available online at www.mdpi.com/xxx/s1, Figure S1: title, Table S1: title, Video S1: title. (as per the review and edit)