Ontogenetic and behavioral studies using birds currently do not document the early evolution of flight because birds (including juveniles) used in such studies employ forelimb oscillation frequencies over 10 Hz, forelimb stroke-angles in excess of 130°, and possess uniquely avian flight musculatures. Living birds are an advanced morphological stage in the development of flapping flight. To gain insight into the early stages of flight evolution (i.e., prebird), in the absence of a living analogue, a new approach using Strouhal number inline image was used. Strouhal number is a nondimensional number that describes the relationship between wing-stroke amplitude (A), wing-beat frequency (f), and flight speed (U). Calculations indicated that even moderate wing movements are enough to generate rudimentary thrust and that a propulsive flapping flight-stroke could have evolved via gradual incremental changes in wing movement and wing morphology. More fundamental to the origin of the avian flapping flight-stroke is the question of how a symmetrical forelimb posture—required for gliding and flapping flight—evolved from an alternating forelimb motion, evident in all extant bipeds when running except birds.

The evolution of flapping flight in birds has been intensely debated by biologists and paleontologists since Huxley (1868) first proposed an evolutionary relationship between Archaeopteryx and theropod dinosaurs. Two ecological scenarios (arboreal “trees-down” or cursorial “ground-up”) for the appearance of flight per se (Nopcsa 1907, 1923; Ostrom 1974; Bock 1986; Garner et al. 1999), and several models describing the appearance of the avian “flapping flight stroke” (Norberg 1985b; Rayner 1988, 1991a; Burgers and Chiappe 1999; Rayner 2001; Dial 2003; Padian 2003) have been proposed. Yet exactly how birds evolved their symmetrical fast-flapping thrust generating wing-beat movements has remained an enigma. To address this evolutionary scenario the flight capabilities of fossils, or the hypothetical “proto-bird,” are usually interpreted with reference to extant “analogue” species; their ability to undertake powered flight assessed assuming the same morphological constraints (Ostrom 1974; Bock 1986; Burgers and Chiappe 1999; Garner et al. 1999; Padian 2001; Dial 2003; Padian 2003). One recent example of this approach is a series of studies based on an experimental system (wing-assisted incline running, WAIR) using ontogenetic stages of the Chukar Partridge (Alectoris chukar) that claim to have identified the likely evolutionary pathway that led to the avian flapping flight-stroke (Bundle and Dial 2003; Dial 2003; Tobalske and Dial 2007; Dial et al. 2008). Alectoris, however, is capable of powered flight; both adults and juveniles have the necessary morphology (not yet seen in the antecedents of birds) and complex wing-movement capabilities required for moving in this way. Therefore, if the forelimb flapping capabilities of ontogenetic stages of Alectoris are representative of a stage in flapping flight evolution, a large gap still remains between the nonavian nonflapping ancestor and the development of a 10 (baby Alectoris) to 17 (adults and juvenile Alectoris) Hz wing-beat (forelimb oscillation) frequency, 130° dorsoventral stroke-angle kinematics (Tobalske and Dial 2007; Dial et al. 2008), and fully evolved bird flight musculature and physiology. If not, the instantaneous appearance of a fully flapping bird must be invoked.

Thus an alternative approach is required to elucidate the likely aerodynamic stages “intermediate” to the modern avian flapping flight-stroke. Using flight aerodynamics theory, Norberg (1985b) showed that Archaeopteryx only required rudimentary wing kinematics to generate lift and thrust, and consequently make the transition from gliding to flapping flight. One workable method for defining the earliest flapping stroke (in the absence of a complete fossil record), is to use physical laws to calculate how much arm- or wing-movement would be required to produce thrust and by doing so pinpoint the starting point for the evolution of forelimb flapping. By identifying likely starting conditions, what type of morphology was required to produce the first useful flapping flight-stroke, and whether the evolution of flapping was indeed a gradual process or involved saltative stages, may be determined.

Under certain conditions thrust is produced behind an oscillating foil, wing, or plate, moving forward through a fluid. Thrust is produced by the formation of a jet wake behind the wing and these jets produce thrust via the generation of a reverse Karman street containing eddies of opposite circulation to those observed in the drag wake of any bluff body (Triantafyllou et al. 1993; Taylor et al. 2003; Nudds et al. 2004) (Fig. 1). The conditions corresponding to the production of thrust behind a birds' wing can thus be defined using the Strouhal number (St):


where A is wing-stroke amplitude (m), equivalent to the maximum excursion of the wing-tip, f is wing-beat frequency (Hz), and U is flight or running speed (ms−1). Previous work (Nudds and Thomas 2002; Nudds 2003; Taylor et al. 2003; Nudds et al. 2004) has shown that in cruising flight at speeds close to minimum power speed or maximum range speed (Pennycuick 1975), birds fly at St numbers close to 0.22: a value associated with high propulsive efficiency in terms of maximum thrust per unit input energy (Triantafyllou et al. 1993; Nudds et al. 2004). Insects, fish, and bats also seem to use these favorable St values (Triantafyllou et al. 1993; Taylor et al. 2003; Norberg and Winter 2006). St also rigidly defines three characteristic wake regions. At low St's (< 0.10) a drag wake is present (Fig. 1A); at St's between 0.10 and 0.50 a jet wake producing thrust predominates (Fig. 1B); and at St's > 0.50 a “piston-like” mode dominates. This latter region requires a large amount of input energy, but generates no thrust. Although an St of 0.22 might equate to the most efficient flight mode in birds and measured efficiency may plummet from 80% at St= 0.27 to 10% at St= 0.10 (Anderson et al. 1998), as long as a bird (indeed any animal) is oscillating its forelimbs at an St between 0.10 and 0.50 some thrust will be produced. This “envelope of St” defining a region of thrust generation is central to the arguments presented in this article.

Figure 1.

Schematic of drag (A) and jet wakes (B). The birds' wings are shown fixed in mid-wing-stroke for simplicity, but in reality would be flapping. At Strouhal numbers (St) below 0.10 a drag wake persists with eddies (black circles—arrows on circles depict circulation sense) of circulation separating from the leading edge of the wing (from the dorsal surface) and trailing-edge (from the ventral surface) alternately. Eddies from the dorsal surface are aligned above those from the ventral surface. To illustrate the differences between the wakes more clearly the eddies are shown almost parallel and as discrete vortices, but in reality no discrete vortex is formed and the drag wake is less uniform, because the eddies are not shed at regular points of the wing-beat cycle (Taylor et al. 2003). At St greater than 0.10 a thrust-producing jet wake is generated in the form of a reverse Karman street, containing discrete vortices of opposite circulation to the circulation observed in the drag wake. At the most efficient St (≈ 0.27) the vortex from the leading edge and dorsal surface remains attached to the top of the wing during the down-stroke of a wing-beat and is shed at the bottom of the down-stroke (Taylor et al. 2003; Nudds et al. 2004). The trailing edge vortex from the ventral surface is shed at the top of the upstroke. Hence, the line of vortices from the dorsal surface is now aligned below those from the ventral surface. See also Figure 1 of Taylor et al. (2003). The gray dashed lines show the path of the vortices as they leave the wing. The thick gray lines show the force imparted on the air by the vortices after interaction with the wing. The force upon the wing itself is, of course, in the opposite direction.

The frequency at which vortex roll-up and therefore transition to a thrust profile occurs decreases with increasing oscillation amplitude; this transition nevertheless occurs consistently in the region of St= 0.10 and a jet wake persists until St≈ 0.50 (Read et al. 2003; Taylor et al. 2003). Wake regimes are similar for both “heaving” foils and “root-flapping” foils (Taylor et al. 2003) and a simple plunging/heaving brass plate produces a similar jet wake to that of a dragonfly flying at a comparable St (Thomas et al. 2004). These results generally relate to symmetric down-and-upstrokes generating thrust with no lift, but instantaneous force coefficients depend similarly on St when a net lift is produced with asymmetric down-and-upstrokes, involving folding of the wing on the upstroke (Read et al. 2003). Thus St shows that it would be futile to oscillate a wing, or a feathered “proto-wing,” outside of the range 0.10 < St < 0.50, because to do so would produce drag and no thrust. Therefore, to benefit an animal in terms of forward locomotion (thrust generation) the earliest flapping propulsive wing-stroke must be defined by an St of at least 0.10. St defines a physical relationship between kinematics and wake, and has not varied over the last 200 million years, unlike the morphology and musculature of nonavian theropod dinosaurs and early birds.

In this study St was used to determine the wing-beat frequencies (f) required at different forward running speeds by an early “flapper” to produce thrust and an estimate of how much thrust is produced is presented. This St approach is very different from the aerodynamics model of Norberg (1985b), but nonetheless complementary in its aim and in what it determines (i.e., the generation of favorable vorticity). The morphology of the earliest flapper is not known, so a likely range of relevant morphologies is bracketed here by three illustrative fossil “morphs” based upon the morphologies of the avian Archaeopteryx and the nonavian theropods Protarchaeopteryx and Caudipteryx.

Material and Methods


To calculate the f required by the earliest flapper to produce thrust at different speeds (U), the St equation is rearranged to


Three estimates for wing-stroke amplitude (A) were used. The first was derived from a relationship determined by Nudds et al. (2004):


where b is wingspan and θ is dorsoventral (wing) stroke-angle. θ can be estimated from an equation derived from extant bird data (Nudds et al. 2004)


To avoid contradicting the suggestion in the Introduction that extant birds may provide a bad model for proto-birds, two further fixed estimates for θ of 30° and 100° were also used. The former represents a conservative estimate, that most tetrapods are capable of achieving, at least in a craniocaudal plane—e.g., Varanus exanthematicus (Jenkins and Goslow 1983), Sceloporus malachiticus (Kohlsdorf and Biewener 2006), Monodelphis domestica (Lammers et al. 2006), and Wistar rats (Garnier et al. 2008)—and the latter an extreme value only achievable by modern birds. The true proto-bird value should lie between these and maybe close to estimates derived from equation (4). An estimate of A and f gives an indication of how complex and physiologically demanding a bird's flight-stroke or proto-bird's thrust producing flap is.

To deduce b, the likely morphology of the earliest “flapper” must be estimated. In the absence of the definitive fossil find, three taxa examples from the literature were selected, which arguably bracket the earliest “flapper” (Table 1): Protarchaeopteryx, Caudipteryx, and Archaeopteryx. Numerous cladistic analyses have placed the first two of these fossil taxa very close to the phylogenetic divergence of Aves (Turner et al. 2007), within nonavian theropods, whereas Archaeopteryx likely had morphology associated with the earliest flapping bird, at least in terms of its wingspan and body size (Mayr et al. 2007). Although this taxon is uncontroversially considered to be the earliest diverging lineage within Aves, some have suggested Archaeopteryx was not capable of flapping flight (Vazquez 1992; Speakman and Thomson 1994; Longrich 2006) whereas others have concurred on the opposite position (Norberg 1985a; Rayner 1991a; Burgers and Chiappe 1999; Chatterjee and Templin 2003). Whichever hypothesis is correct, it is clear that this Jurassic (ca. 140 – 150 Ma) bird sits close to the transition to flapping flight. Archaeopteryx is estimated to have a b of around 0.58 m and a wing area (S) of 0.0479 m2 (Yalden 1971).

Table 1.  Estimated biometrics for the three morphs.
MorphMb (kg)b (m)S (m2)θ (°)1
  1. 1Calculated from equations (3) and (4).


Although there is no definitive evidence for the presence of feathers on its forelimbs, Protarchaeopteryx was otherwise covered in feathers (Ji et al. 1998). Here, Protarchaeopteryx is assumed to have a b of 0.59 m (from Table 1 of Ji et al. 1998) and a 0.03-m chord (estimated from the length of the feathers associated with the femur of Protarchaeopteryx); therefore an S of 0.0178 m2. RLN has already shown previously that a flat-plate with a chord of only 0.025 m can generate a thrust wake in airspeeds of 1.5–2 ms−1 (Taylor et al. 2003; Nudds et al. 2004; Thomas et al. 2004) and it is possible that smaller chords would also work.

The forelimb morphology (in terms of S) of Caudipteryx was considered intermediate between, Protarchaeopteryx and Archaeopteryx. To reiterate and to preempt criticism from paleobiologists, the assumption was that the “forelimb morphology” was intermediate not the organism itself. Furthermore, we are not arguing that our estimates of the morphology of these dinosaurs are definitive, but rather that they provide realistic “morphs” bracketing the likely morphology of the first “flapper.”Caudipteryx was taken to have a b of 0.43 m (from Table 1 of Ji et al. 1998) and an average chord of 0.06 m (S= 0.0276 m2) was assumed based upon the length of the second remex (forelimb quill feather). A more exact estimate was not possible, because the other remiges are damaged (Ji et al. 1998).

An implicit assumption in the calculations is that the organisms modeled are capable of moving their forelimbs in a dorsoventral orientation (like birds). Many authors (e.g., Yalden 1971; Norberg 1985a,b; Rayner 1991a; Burgers and Chiappe 1999) concur that Archaeopteryx could flap, but the forelimb movement capabilities of Protarchaeopteryx and Caudipteryx have not been determined (Kurochkin and Bogdanovich 2008). The nonavian theropod Deinonychus may have had forelimb motion capabilities only trivially different from the flight-stroke of birds (Gauthier and Padian 1985) or, at least, intermediate between that of crocodilians and birds (Jenkins 1993; Gatesy and Baier 2005): between an antero-posterior and dorsoventral orientation.


It is difficult to calculate thrust theoretically with accuracy for any flapping wing, particularly with the limited parameters that can be estimated from fossil taxa. It is possible, however, to obtain a reasonable estimate of the aerodynamic force vector (R) using the models of Pennycuick (1975), with the addition of a force duration factor (Burgers and Chiappe 1999)


where ρ is air density (here taken as 1.23 kg m−3), CL is the lift coefficient, S is wing area, and p is a factor defining the duration of force generation during a wing-stroke. Here a value for p of 0.5 was used, which assumes that force is generated during the down-stroke only. A passive upstroke is a reasonable assumption to make for primitive flappers. CL was taken as 1, a value approximating that calculated for Passer domesticus and Turdus merula (Nachtigall and Kempf 1971). By adopting a CL of 1 R for the earliest flappers maybe over estimated because an early feathered forelimb is unlikely to produce a CL approaching that of modern birds. UW is the average speed of the wings relative to the air, calculated as the resultant (sum vector) of the forward speed of the body relative to the air (U) and the average flapping speed of the wings relative to the body (UF) (see fig. 6 of Norberg and Norberg 1971). UF is calculated from


where y is the point along the wing-span where the vectorial calculations are performed (0.7 = a point 70% of semi-span proximal-distally, Norberg 1985b). While running, residual lift is a lift force that does not act as a net force, because residual lift is unable to exert any work upon the animal until it exceeds body weight at which point lift-off would occur (Norberg and Norberg 1971; Pennycuick 1975).


Figure 2 shows that to obtain an St of 0.10 or 0.22 at low speeds does not require very high wing-beat frequencies. At the theoretical maximum running speed for the Archaeopteryx morph of 2 ms−1 (Burgers and Chiappe 1999) the frequency required to produce a jet wake (St= 0.10) is < 1 Hz and gliding from a tree at 8 ms−1 (Rayner 2001) would still only require a frequency of ≈ 2 Hz at a θ estimated from equations (3) and (4) and 100° (Fig. 2A). Even at a restricted θ of 30° the frequency required to obtain St= 0.10 is only 1.3 Hz at 2 ms−1 and 5.3 Hz at 8 ms−1. All these frequencies of forelimb oscillation are within the scope of terrestrial animals that lack wings—≈7 Hz is produced by Cavia porcellus and S. malachiticus (Gasc 2001; Kohlsdorf and Biewener 2006). For the Archaeopteryx morph to achieve St= 0.22 requires an increase in f, but for all three values of θ the required hertz is < 3 at 2 ms−1 and only at the very low amplitude estimate (30°) does the required frequency at 8 ms−1 exceed 5 Hz (11.7 Hz). The relationship between f and U for the different St's is similar for the Protarchaeopteryx morph (Fig. 2B) because its b is very similar to that of the Archaeopteryx morph (Table 1) and therefore, the estimate of A for a given θ for both morphs is similar.

Figure 2.

Graphs of wing-beat frequency (f) against flight speed (U) for (A) Archaeopteryx–morph, (B) Protarchaeopteryx–morph, and (C) Caudipteryx–morph. Solid lines represent a wing-stroke angle of 30°, dotted lines that calculated from equation (4) and dot-dash lines a wing-stroke angle of 100°. Strouhal numbers of 0.10 are gray lines and 0.22 black lines. The estimated maximum running speed (Runmax) (Burgers and Chiappe 1999) and a gliding speed estimate (Glide) (Rayner 2001) for the Archaeopteryx morph are also shown.

The Caudipteryx morph has a shorter b and therefore the estimates of f at a given U and St (Fig. 2C) are higher than that for the Archaeopteryx and Protarchaeopteryx morphs (Fig. 2A,B). Nonetheless, only at an St of 0.22 in combination with the low θ (30°) does the required f begin to move into the realms of what is likely only achievable by birds (> 8 Hz) and then only at speeds in excess of about 4 ms−1 (Fig. 2C).

By selecting three different values of A and two estimates of St corresponding to the minimum required for thrust generation (0.10 most relevant in terms of the first flight-stroke) and the optimum for thrust generation (0.22), together with three different “morphs” (in effect three values of b) and plotting f against U for each combination we have demonstrated the sensitivity of St to changes in these parameters. Equation (1) shows that to maintain a given St at a constant U, increases in A must be accompanied by decreases in f and vice versa (because f is inversely related to A): thus larger A equals a lower f. Yet even at a very low estimated θ of 30°, the required frequency to enter the thrust producing St regime—0.10 (Nudds et al. 2004)—is surprisingly low for all three morphs. Even at speeds of up to 3 ms−1, an optimum St for birds of 0.22, using θ= 30°, is achieved at < 5 Hz for all morphs (Fig. 2).

Unlike the relationship between f and U at different St, R for Archaeopteryx and Protarchaeopteryx morphs differs greatly (Table 2). This is because all other things being equal in equation (5), R is dependent upon S (a doubling of S doubles R) and that of the Archaeopteryx morph is 2.7 times that of the Protarchaeopteryx morph. The Caudipteryx morph has an S intermediate between the other two morphs and consequently produces thrust at a given forward speed also intermediate between the other two. With the exception of the Archaeopteryx morph and its fully developed wing, the amount of aerodynamic force produced is small, and the net thrust in all cases is much less than residual lift (Table 2). Nonetheless, at a low St (corresponding to very low f) some thrust is still produced.

Table 2.  Aerodynamic force production (R = net thrust + residual lift) at two different forward speeds and at the two different Strouhal numbers (St). The range of net thrust and residual lift values encompassed using the three different stroke-angles (θ) is shown for each speed and Strouhal combination.
MorphU (m s−1)Weight (N)St=0.10St=0.22
Net thrust (N)Residual lift (N)Net thrust (N)Residual lift (N)
Archaeopteryx2 1.960.011–0.0120.107–0.1080.022–0.0240.099–0.101
 8 1.960.107–0.1211.081–1.0900.220–0.2501.024–1.034


Calculations based upon the St–wake relationship demonstrate that the evolutionary transition to a “flapping flyer” does not need to be viewed as a great “step change” and thus need not involve complicated preadaptive scenarios for the refinement of the avian wing-stroke (for example, swimming Ebel 1996; Pfretzschner 2000), because the generation of a useful jet wake does not require a great amount of wing-movement (Fig. 2). Results concur with those of Norberg (1985b), but this St analysis shows that thrust could be produced with a more rudimentary feathered limb than that of Archaeopteryx and in doing so supports an appearance of a flapping stroke prior to a forelimb recognizable as a modern bird wing. It is important to note, however, that an St just greater than 0.10 does not necessarily predict generation of a thrust force capable of propelling the animal forward (Table 2) on its own, nor does it predict lift generation. Instead, the creation of a thrust producing jet wake simply adds to the forward momentum of an organism (or body) already being propelled forward. For a terrestrial organism this propulsion is generated by the legs in a run (Burgers and Chiappe 1999) whereas in a gliding animal forward momentum is generated by gravity acting upon the body. It is worth iterating that the calculations of R were governed by Sts of 0.10 (minimum requirement) and 0.22 (optimum requirement), with the aim of determining whether low oscillation frequencies can produce thrust. If f is increased at any given speed, the proportion of R manifest as thrust also increases, because the wing-path angle is increased (arctangent of UF/U). Increasing f alone will also increase St, but as long as it remains below 0.50, thrust is still produced and the absolute value may increase, although the efficiency in terms of the thrust/energy input ratio decreases (Triantafyllou et al. 1993; Taylor et al. 2003). So there is potential for more thrust to be produced than modeled here, although with less efficiency.

Burgers and Chiappe (1999) suggested that once Archaeopteryx reached 7.83 ms−1 its wings would generate R = 2.62 N (0.66 N thrust and 1.96 N lift) and it would become airborne. These workers used a CL of 2, qualified by the assumption that unsteady aerodynamic effects would elevate the value. The current study, however, is concerned primarily with a steady state, or constant velocity (U) forward propulsion, and not necessarily lift. Nonetheless, using a CL of 1 here, Archaeopteryx would need to be traveling at 11.4 ms−1 before getting airborne. Encouragingly, according to Burgers and Chiappe's (1999) model, Archaeopteryx at take-off is operating at St= 0.29, slightly higher than the optimum determined for birds in cruising flight (Nudds 2003; Nudds et al. 2004), but within the optimum thrust producing range for oscillatory propulsion in general (Taylor et al. 2003). Similarly, for all but one (St= 0.07) of the eight different combinations of flight parameters in Table 1 of Norberg (1985b), Archaeopteryx flew within the interval 0.10 < St < 0.35, coincident with the favorable range.

Having demonstrated that the development of a thrust generating wing was possible at relatively low wing-beat frequencies, do our results favor one of the alternative “origin of flight hypotheses” (i.e., arboreal versus cursorial)? A winged precursor to birds may have benefited from thrust generation equally running along the ground (Burgers and Chiappe 1999; Dial 2003), gliding from trees (Bock 1986), pouncing from elevated ground onto its prey (Garner et al. 1999), or ground-running and using hang-gliding on steep slopes (Lindhe Norberg 2007). For a gliding animal, the development of thrust production is sufficient to evolve powered flight (Norberg 1985b), but for a runner lift is a crucial development because the animal must work against gravity to become airborne (for detailed discussion see Norberg 1985b, 1990; Rayner 1991b; Lindhe Norberg 2007). Before the issue of lift development can be tackled, however, the problem for the “cursorial” hypothesis (Burgers and Chiappe 1999; Dial 2003; Dial et al. 2008) is not thrust generation but how a symmetrical forelimb movement could have originated on the ground. The “arboreal” hypothesis can explain the development of a symmetrical forelimb posture more easily (Norberg 1985b; Rayner 1991a): holding both forelimbs out to the side is a natural stance when jumping down, parachuting, or gliding.

A wingless avian precursor (i.e., a nonavian theropod) wishing to increase its running speed can either alternate its forelimbs (as a human does) or alternatively move them in a symmetrical manner (flapping) and generate thrust. These two strategies can be viewed as two alternative “adaptive peaks” (Wright 1932) representing highest “fitness” in terms of running performance (Fig. 3). If terrestrial theropods occupied the trough between these peaks, then either strategy is of course possible. If, however, they were positioned on either side of the trough, then it would be most parsimonious to expect them to adopt the strategy of the adaptive peak they are already ascending, because to adopt the other would first require a concomitant reduction in “fitness,” not favored by natural selection (see Arnold et al. 2001 for an overview of evolution on phenotypic landscapes). So far research into the forelimb movements of nonavian theropods have focused on range of motion and shoulder morphology (Jenkins 1993; Gatesy and Baier 2005; Baier et al. 2007), but whether a symmetrical or asymmetric movement pattern characterized the antecedents of birds remains unclear. Initially, holding an early feathered limb out passively just produces drag (Rayner 1991a), whereas thrusting the shoulder and arm forward aids forward momentum. For example, the arms and trunk provide internal torques around the trunk's long axis and these angular impulses to the lower body are needed for the legs to alternate through stance and swing phases (Hinrichs 1990). Furthermore, amounts of thrust generated at low running speeds are extremely low (Table 2) and it is doubtful whether they would aid forward locomotion more than an asymmetric forelimb gait. It is possible to imagine how a strong competing function could have driven the evolution of forelimb movement onto the symmetrical peak (Fig. 3), such as a predatory stroke (Padian 2001) or the reduction of inertial forces during turning (Carrier et al. 2001). Existing “cursorial” flight origin hypotheses (including WAIR), however, do not currently provide this competing function. Because the wingspan (b) of both adults and juvenile Alectoris (Tobalske and Dial 2007) are bracketed by those of the Caudipteryx, Protarchaeopteryx, and Archaeopteryx morphs examined here, the Strouhal number (St) approach suggests that an Alectoris-like organism was capable of generating thrust with very rudimentary kinematics. In fact, any plausible size of proto-bird could theoretically attain an St of 0.10 and produce thrust as long as it was capable of the sufficient combination of A and f.

Figure 3.

Diagram of two alternative adaptive peaks in an adaptive landscape (Wright 1932) representative of two ways in which the forelimbs can be used/held during terrestrial running (symmetrical, left peak; asymmetrical, right peak). From the two hypothetical starting forelimb postures for a nonavian terrestrial theropod dinosaur the development of the opposite is unlikely, because it initially requires a reduction in fitness (i.e., running performance). Only the paths indicated by the gray-dashed arrows are possible.

Calculating A and f for fossil organisms is difficult and in terms of f, complete guess work. Hence, we do not advocate St as a framework for estimating the exact flight capabilities of fossil taxa, but instead emphasize its value for demonstrating the relative ease in which thrust can be produced in a flapping animal. The amount of thrust produced by organisms without fully developed wings (i.e., the Caudipteryx and Protarchaeopteryx morphs) is small at all speeds, however, and would be insufficient to propel an organism up a slope (Table 2). This is also true for the Archaeopteryx morph running at 2 m s−1, the likely upper running speed of feathered theropods. For example, the ratio of aerodynamic force production (R) to body weight produced by Alectoris during WAIR is 60% in adults, 88% in juveniles, and 7% in babies (Tobalske and Dial 2007) compared to just 0.1% for the Caudipteryx and Protarchaeopteryx morphs at St= 0.10 and 2 ms−1 (Table 2). Only in Archaeopteryx with a wing analogous to a modern bird does the estimate of thrust production (6% of body weight) approach that of Alectoris during WAIR and then only for babies. In addition, not just thrust generation is necessary for WAIR to work, because some down-force is generated to push the bird toward the substrate to aid traction. This would require more than just a simple up-and-down wing-movement pattern, because wing-rotation during the stroke is also required. WAIR (Dial 2003; Dial et al. 2008) has not yet been demonstrated in an organism using simple kinematics (so far only a bird and then using highly developed wing-kinematics), so whether WAIR provides a plausible scenario for the early development of the flight-stroke is not yet certain. Of course, WAIR is just a special case of the already established “cursorial” hypothesis (wing used as a primary thrust generator) advocated by Burgers and Chiappe (1999) and so faces the same problems for demonstrating the evolution of a symmetrical stroke over an asymmetrical stroke, at least on a moderate slope. If steep slopes are taken as the initial selection pressure, it would need to be demonstrated that a proto-bird generating little thrust (and no down-force) would benefit from flapping its wings over placing its forelimbs upon the substrate, otherwise we would perhaps expect climbing claws to evolve. It would be interesting to compare the running performance of a baby Alectoris negotiating a range of slopes of different angles with and without flapping, to see whether flapping improves its performance. Although, wing-beat frequencies and stoke-angles would be difficult to manipulate, perhaps sufficient reduction in wing area could be achieved to reduce the thrust producing capabilities of Alectoris down to < 1% of body weight in line with that predicted for the Caudipteryx and Protarchaeopteryx morphs here. Until a locomotory advantage to rudimentary flapping over asymmetrical forelimb movement can be demonstrated, cursorial hypotheses can only be viewed as plausible mechanisms for evolving more complex wing-kinematics and morphology from an already established symmetrical posture.

In recent years much attention has been given to determining how fossil proto-birds could have moved their wings like extant birds. Proto-birds, however, were not capable of true powered flight. Instead, it is likely that after (and only after) a symmetrical forelimb posture had evolved—which may represent a stumbling block for the cursorial hypothesis (Ostrom 1974) and derivatives (Burgers and Chiappe 1999; Dial 2003; Dial et al. 2008)—could, as suggested by the St/wake-type relationship and model of Norberg (1985b), the flapping flight-stroke evolve incrementally building on very basic movements. Exactly, how avian flight evolved remains an enigma, but the evolution of a symmetrical forelimb posture was fundamental and the appearance of a fully derived avian flapping flight-stroke was subsequently a relative formality.

Associate Editor: G. Hunt


RLN was funded by a Leverhulme Early Career Research Fellowship. We thank two anonymous reviewers for their useful comments, which greatly improved an earlier version of the manuscript.