Scaling and functional morphology in strigiform hind limbs

Strigiformes are an order of raptorial birds consisting exclusively of owls: the Tytonidae (barn owls) and the Strigidae (true owls), united by a suite of adaptations aiding a keen predatory lifestyle, including robust hind limb elements modified for grip strength. To assess variation in hind limb morphology, we analysed how the dimensions of the major hind limb elements in subfossil and modern species scaled with body mass. Comparing hind limb element length, midshaft width, and robusticity index (RI: ratio of midshaft width to maximum length) to body mass revealed that femoral and tibiotarsal width scale with isometry, whilst length scales with negative allometry, and close to elastic similarity in the tibiotarsus. In contrast, tarsometatarsus width shows strong positive allometry with body mass, whilst length shows strong negative allometry. Furthermore, the tarsometatarsi RI scales allometrically to mass0.028, whilst a weak relationship exists in femora (mass0.004) and tibiotarsi (mass0.004). Our results suggest that tarsometatarsi play a more substantial functional role than tibiotarsi and femora. Given the scaling relationship between tarsometatarsal width and robusticity to body mass, it may be possible to infer the body mass of prehistoric owls by analysing tarsometatarsi, an element that is frequently preserved in the fossil record of owls.

toes, all of which have distinctly curved, nearly uniform raptorial claws used to strike and grip prey items 1,4,11,14 . In the Tytonidae, digit II and digit III are approximately equal in length with serrations on the underside of the talon on the central toe, but in the Strigidae, digit II is distinctly shorter than digit III 4 . Strigiformes have a digit II claw that is larger than digit III and can be distinguished as birds of prey from this character alone 11,[15][16][17][18] ; they have shorter, more robust toes relative to other raptors, particularly on digits III and IV, in addition to a slightly lower inner claw curvature; they can also rotate digit IV in order for digits II and III to oppose digit I and digit IV, creating a functionally zygodactyl foot 11,12 .
The hind limbs of birds must support their body mass and withstand the forces associated with locomotion and hunting. As body mass increases, the strength of support structures must therefore increase correspondingly. Geometric similarity, or isometric scaling, occurs when proportionate dimensions are preserved as size changes. Isometrically, areas, such as the cross-sectional area of the hind limb, scale to length squared, whereas body mass scales to length cubed. Non-isometric, or allometric, scaling occurs when certain proportions change in a regular fashion. In a log-log plot of mass x against length y where y = bx a , isometry is found when the scaling exponent a = 0.33. An exponent greater than 0.33 represents positive allometry, where a linear morphological variable increases at a faster rate than body mass. An exponent less than 0.33 represents negative allometry, where a linear morphological variable decreases relative to an increase in body mass. For long columns such as hind limb elements, whose critical morphological variables are length and diameter, a scaling exponent of 0.25 indicates elastic similarity, where structures maintain a constant value of elastic deflection with changing body mass 19,20 . In the case of a ratio between two measurements of the limb, such as the ratio of width to length, isometry is represented by a scaling exponent of a = 0, with positive allometry represented at a > 0 and negative allometry at a < 0 (refs 19 and 20).
Recent studies have found that total avian limb length scales with positive allometry 21,22 . Studies of the individual bones comprising the limb have shown varying results across the different elements and across phylogenetic groups and locomotor categories. In general, the lengths of the tarsometatarsus and in some cases the tibiotarsus scale with positive allometry, whereas femur lengths scale close to isometry 23,24 . There is some evidence to suggest that the lengths of the horizontal bones of the hind limb, the femur and phalanges, scale closer to elastic similarity (a = 0.25) (refs 23,24).
The aim of this study is to focus on a single clade and quantify hind limb scaling across a range of owl species with varying adult body mass. Our null hypothesis states that as owls increase in body mass, the length of their hind limb bones (femur, tibiotarsus, and tarsometatarsus) and the robusticity of these bones (ratio of width to length) will scale in order to maintain isometry.

Results
Among the three hind limb elements, tarsometatarsi present the greatest morphological disparity across species while femora and tibiotarsi display far less variability (Fig. 1). To highlight synapomorphies of each family, morphologies of the hind limb elements of T. alba and B. virginianus are described here (Figs 2, 3 and 4).
The femur of T. alba has a strong, moderately developed trochanter and a straight shaft; distally, the rotular groove is deep and wide and the popliteal area is shallow; the fibular condyle is also strongly developed. The femur of B. virginianus presents with a stout trochanter with a heavily sculpted base and a stout, straight shaft; the rotular groove is deep and wide, as is the popliteal area; the fibular condyle is very prominent (Fig. 2).
In the tibiotarsus, T. alba has moderately developed cnemial crests, and a slight fibular crest; the fibula is free of the shaft and the distal condyles are of nearly equal size. In the tibiotarsus of B. virginianus, the cnemial and fibular crests are also moderately developed, though the fibula is fused distally to the shaft and the distal condyles are also of nearly equal size (Fig. 3).
Tyto alba tarsometatarsi generally present with a pronounced calcaneal ridge, a hypotarsus with a wide, open tendinal canal, a deep groove on the anterior proximal end, and closely crowded trochleae where the second and fourth trochleae are deflected backward and the fourth is shorter. The tarsometatarsus of B. virginianus also presents with a prominent calcaneal ridge, wide, deep tendinal grooves on the anterior and posterior, a wide, flat shaft, an arched canal on the anterior face of the shaft at the proximal end, and an elevated fourth trochlea (Fig. 4).
Maximum length of the femur, tibiotarsus, and tarsometatarsus all show a significant relationship with body mass (p < 0.0001; Fig. 5; Table 2). Femora scale close to isometry, however isometry can be rejected in favour of slight negative allometry (a = 0.3067 ± 0.0209; R 2 = 0.9066). In contrast, tibiotarsi scale with negative allometry and closer to elastic similarity (a = 0.2587 ± 0.0294; R 2 = 0.8106). Tarsometatarsi maximum lengths scale against body mass with strong negative allometry (a = 0.1529 ± 0.0608), indicating a much shorter length relative to body mass, although this element does display a great deal of variability across species (R 2 = 0.2748) ( Fig. 5; Table 2). Following pgls, the direction of allometry does not change in the femur or the tarsometatarsus, but while the slope (a) remains similar, the increased size of the confidence intervals means that isometry cannot be rejected for the tibiotarsus. All results remain significant, although the p-value for the tarsometatarsus is much higher than before, at 0.03773 (Table 3).
Robusticity indices on a semi-log plot for femora (a = 0.0038 ± 0.0022; R 2 = 0.1086) and tibiotarsi (a = 0.0036 ± 0.0012; R 2 = 0.3281) show weak positive allometry (p < 0.001) close to an exponent of 0, as expected for isometry. In contrast, the tarsometatarsi robusticity index scales with strong (p < 0.0001) positive allometry (a = 0.0279 ± 0.0059; R 2 = 0.5778) ( Fig. 5; Table 2). Note that RI R 2 values are generally less than limb length Scientific RepoRts | 7:44920 | DOI: 10.1038/srep44920 regression R 2 values, although tarsometatarsi RI scales to body mass with R 2 = 0.5778 (Table 2). Following pgls, while the slopes (a) of the regressions remain similar for both the femur and the tibiotarsus, the increased size of the confidence intervals means that weak positive allometry cannot be rejected, although both elements scale close to isometry. Furthermore, the result for the femur is no longer significant (p = 0.05671). Allometry for the tarsometatarsus remains positive and significant (Table 3).

Discussion
In birds, the hind limbs serve as the principal support structure for the body mass. In animals of broadly similar overall morphology but different sizes, as in the owls studied here, a proportional relationship between body mass and the dimensions of the supporting skeletal structure would seem obvious. One would expect that as the birds become larger, stress in the hind limb elements would increase proportionately and the corresponding dimensional adjustments would be evident in those elements. Previous large scale studies of bird hind limb scaling have shown that tarsometatarsus length and frequently tibiotarsus length scale against body mass with strong positive allometry, while femur length scales with isometry [21][22][23] .
In this study, owl femora maintain isometry in midshaft width and fall just short of isometry when maintaining length as body mass increases, indicating that the dimensional proportions of the femur remain almost the same relative to body size. Tibiotarsi display isometry in midshaft width and negative allometry in maximum length, close to the exponent of 0.25 expected for elastic similarity, as body mass increases. Owl tibiotarsi therefore maintain their midshaft width proportions while maximum length decreases slightly across species. Robusticity indices for both femora and tibiotarsi confirm that these two elements scale with very slight positive allometry to body mass but close to the expected exponent of 0 for isometry. The most pronounced changes in shape dimensions are seen in the owl tarsometatarsus. Here, midshaft width scales with positive allometry and maximum length scales with strong negative allometry, indicating that the tarsometatarsus becomes shorter and stouter as owl species increase in body mass. As therefore expected, robusticity index scales with strong positive allometry, meaning that as the owls studied here increase in size, their tarsometatarsi become relatively more robust. These results remain significant even after accounting for the phylogenetic similarities between species,  although the large confidence intervals and the fact that Pagel's lambda is often reported as 0 or 1 suggest that these analyses suffer from issues relating to low sample size, and future analyses would benefit from considering more species from both strigiform families.
Campbell 25 noted the sheer variety of tarsometatarsus morphologies across the class Aves, and that different functions modify this element dramatically. He further acknowledged that birds with a similar tarsometatarsus morphotype, and subsequent functional similarity, would likely have a consistent relationship between their body mass and the dimensions of this element. We find this to indeed be the case in our clade-specific study of Strigiformes. Moreover, owls are most frequently represented in the fossil record by their durable tarsometatarsi 26 . Given the correlation between tarsometatarsus width and body mass, where midshaft width increases as owls become more massive, this measurement alone may allow researchers to estimate prehistoric owl body masses. Yet this conclusion contradicts Field 27 , who asserted that avian skeletal element dimensions may be influenced more by ecology than biomechanics, citing the short, robust owl tarsometatarsus as an example of adaptation for prey handling efficiency. Field concluded that such elements make poor body mass estimates and found instead that femur length was a stronger correlate to body mass in Strigiformes than other skeletal dimensions.
However, our results broadly tally with previous studies in demonstrating that avian hind limb elements may show adaptations that are clade-specific. For example, the femur lengths of palaeognaths (14 species, including tinamous, kiwis, moas, cassowaries, emus, and ostriches) and sphenisciformes (penguins, 7 species), scale with slight negative allometry 28 . In waterfowl and other species classified as non-running birds (20 taxonomically disparate taxa), all major hind limb elements scale with isometry 24 . Conversely, in a study of 8 taxonomically disparate "running birds", the horizontal bones of the limbs scale closer to elastic similarity 23 . The tendency of the owl tibiotarsi to also scale close to elastic similarity suggests a role for this element in resisting deflection during locomotion and prey capture, much as the limb bones of running birds appear to be resisting functional loading in a similar manner 23,25 .
The tarsometatarsus plays a role in skeletal support, locomotion and hunting, and prey capture. Since Strigiformes ambush their prey close to the ground, prey may not be dead or seriously injured upon seizure, leaving open the possibility for a struggle within the bird's talons. Furthermore, many owls must be able to restrain their squirming prey while operating under darkness. They have also been shown to strike at prey with far more force than is necessary to kill it, a behaviour which is attributed to the need to penetrate snow or leaf litter to capture hidden prey 29 , and may necessitate proportionally stronger foot bones. In a study comparing the hind limbs of equivalently sized nocturnal owls and diurnal hawks, which tend to predate on similarly-sized mammals, owls demonstrated greater grip force 30 . Sesamoids, or ossified tendons in areas of high stress, were virtually absent in hawks but well-developed in owls, spanning the length of each hind limb muscle studied. The greater force output of owl hind limbs may be a result of the presence of sesamoids in the muscles in combination with a short, robust tarsometatarsus, in contrast to the long, gracile hawk tarsometatarsus which is well adapted for high-velocity movements 30 . This greater force production may be an adaptation to prevent prey escaping an owl's grip in the dark, whereas hawks do not require this level of force since as diurnal hunters they may visualise their prey should it escape from their talons.

Conclusion
In the case of Strigiformes, we find a differing scaling relationship for each element of the hind limb. The tarsometatarsus shows a clear allometric scaling relationship, becoming relatively stouter, shorter and more robust as species body size increases. In contrast, the femur and tibiotarsus show only a slight increase in robusticity as size increases, facilitated by slight negative allometry in length, particularly in the tibiotarsus, whilst midshaft width maintains geometric similarity. These results suggest that the tarsometatarsus plays a primary role in withstanding functional loading in owls. Tarsometatarsus robusticity (R 2 = 0.5778) scales most closely with body mass and its width is also the best indicator of body mass based on dimensional measurements alone (R 2 = 0.9324). Therefore, using measurements from tarsometatarsi, the element most commonly recovered from the fossil record of owls, body mass estimates of extinct taxa may be possible.

Materials and Methods
The collections of the George C. Page Museum at the La Brea Tar Pits in Los Angeles, California, and the Natural History Museum at Tring, Hertfordshire were utilized in order to measure dimensions and evaluate osteological features among owl species representing both the Strigidae and the Tytonidae. Exceptionally preserved Pleistocene subfossil material from the Page Museum, where at least nine species of owls are represented by over 7,500 specimens in the collections, provided an opportunity to gauge morphological variation within species. Limb bones from six species were measured from the Rancho La Brea fossil assemblage at the Page Museum: Asio flammeus (short-eared owl), Asio otus (long-eared owl), Athene cunicularia (burrowing owl), Bubo virginianus (great horned owl), Tyto alba (barn owl), and the extinct Oraristrix brea (La Brea owl). A total of seventy-nine femora, sixty-three tibiotarsi, and fifty-five tarsometatarsi were evaluated (Table 1 and  Supplementary Table S1).
From the collections in Tring, data for a single specimen representing each of ten species were acquired of the following species: As. flammeus, As. otus, At. cunicularia, B. virginianus, Ketupa ketupu (Malay fish owl), Nyctea scandiaca (snowy owl) and Strix aluco (tawny owl) representing the Strigidae; and T. alba, T. capensis (African grass owl), and T. novaehollandiae (Australian masked owl) representing the Tytonidae (Supplementary Table S2).
Unbroken adult specimens of the three major hind limb elements: femur, tibiotarsus, and tarsometatarsus were measured in millimetres with digital callipers. Digital photographs of each specimen were obtained. Right limb bones were utilized, where possible, in order to ensure each element belonged to an individual specimen. Maximum length and midshaft width were determined from each element ( Fig. 1; Supplementary Tables S1 an d S2).
The tarsometatarsi maximum length is defined as the distance between the calcaneal ridge and the tip of the trochlea (Fig. 1a). In tibiotarsi, maximum length is defined as the distance between the cnemial crests and the distal condyle (Fig. 1a'). Femoral maximum length was defined as the distance between the tip of the trochanter and the end of the distal condyle. In all, midshaft width was defined as the mediolateral width at half the total length (Fig. 1a").  In order to assess scaling patterns among hind limb elements, the robusticity of each element was obtained by calculating a robusticity index: the ratio of midshaft width to maximum length (Supplementary Tables S1  and S2). The values acquired for robusticity were plotted against body mass (taken as the average of male and female body masses; body mass for Tyto alba is of Tyto alba guttata subspecies) in grams using values obtained from Dunning 31 , and Campbell and Bochenski 32 for Oraristrix brea (which they calculated using the formula for ordinary least squares regression: log(y) = 2.548·log(x) − 0.414, where y = mass in grams and x = least shaft circumference of femur in mm; formula taken from the results of a study of the relationship of hindlimb bone dimensions to weight in birds by Campbell & Marcus 25 ), in R (v. 3.2.4) 33 on a semi-log plot, whereas midshaft width and maximum length were plotted in the same manner on log/log plots. Ordinary least squares (OLS) regression analyses were performed on the data to display the strength of the correlation (R 2 ) between the variables and the statistical significance of those correlations (p-value). Ninety-five percent confidence intervals were calculated for each regression and the scaling exponent, intercept, R 2 value, and p-value were tabulated ( Fig. 5; Table 2). To ensure that the results obtained were not merely due to the close phylogenetic relatedness of the species studies, the regressions were repeated using phylogenetic generalised least squares (pgls; Table 3) using the R package caper 34 . A maximum clade credibility tree was created in TreeAnnotator package in Beast 2.1.2 (ref. 35) from a set of 1,000 trees downloaded from birdtree.org 8 . Pagel's lambda (λ ) varies between 0 and 1, and indicates the level of phylogenetic signal in the data, where 0 represents no phylogenetic signal.