Theoretical morphospace reveals mixed optimisation of the avian wing planform for flight style

Domain: biology
Published: 2026-03-31
Editorial outcome: major_revision

Abstract
Bird wings exhibit a broad degree of functional and shape variation, though the exact nature of the form-function relationship is uncertain. Recent analysis suggests that functional variability is explained by linear non-shape-based traits and that shape variation is largely explained by phylogeny. We assay the relationship between wing planform shape and functional performance using a theoretical morphospace approach that eschews assumptions of the functional optimality of empirical morphologies. Hypothesised empirical properties are considered post hoc relative to their positions in the functional performance landscapes. We produce a theoretical morphospace of wing planform shapes and compare the hypothesised functional performance and optimality of theoretical shapes with 1139 extant taxa. These tests cover flight metrics and combinations linked with 7 flight niches. Metrics pertaining to agile flight strongly constrain shape, with hovering, diving and hawking birds developing optimal planforms. Marine soarers are suboptimal for metrics linked with low cost of transport and manoeuvrable flight. Many taxa, principally passerines, remain suboptimal for all studied metrics and combinations. This suggests flight performance constrains planforms unevenly across birds. Phylomorphospace analysis suggests planform shape is only weakly influenced by phylogeny and functional optimality correlates closely with flight styles. This suggests wing shape remains a determining factor in how birds fly.

Introduction
The physical demands of becoming and staying airborne place immense pressures on avian biology which constrain phenotypic variation (1, 2). Despite this, modern birds have adopted a diverse array of flight styles and high wing shape variability (3). This makes wings, the structures underpinning flight, ideal for investigating the relationship between form and function. Wing morphology has long been associated with differing flight styles (4-13) and this relationship has been well documented from linear measurement studies (3, 8, 12, 14), as well as studies of both 2D planform shape, principally focusing on individual avian groups (15-17) and wing shape in 3-dimentions (18, 76). These demonstrate a link between shape (both in linear measurements and in planform) and performance, with distinct wing shapes linked to specific flight modes.

Recent studies of flight dynamics (18, 19) have proposed that range of motion, rather than wing shape, is the principal driver of wing diversity. Furthermore, both linear measurement and planform-based studies of shape suggest that variation in wing shape is mediated by the phylogenetic effect of shared history rather than functional pressures (12, 15, 17). To address whether motion is a primary driver of variation or if function drives wing shape diversity, here we sample across seven flight styles and one-tenth of avian diversity to study the intrinsic functional properties of the wing planform. Previo us shape-based wing studies provide valuable groundwork, establishing performance proxies and outlining the interaction between forces that affect the wing during flight, though often on small taxon sets. Tree spanning datasets of wing form have been created, though seminal datasets of linear measurements like that of Rayner (3) were never published.

A theoretical morphospace approach is used to produce a matrix of theoretical wing planform shape variation, from which optimal theoretical shapes for specific flight styles are identified through functional testing. By testing theoretical shapes rather than empirical wings, theoretical morphospaces allow direct investigation of performance within a global shape environment (20). This both permits the identification of optimal forms (shapes that perform best in a global landscape for a given trait) and avoids the assumption that any empirical shape is optimal. We produced a theoretical morphospace (Fig. 1) of avian wing planform shape variation that encompasses and expands upon the range of variation in nature. Theoretical wing planform shapes were then sampled densely and evenly within this theoretical space and subjected to functional analysis. Functional performance surfaces for the theoretical morphospace were then derived. These surfaces were created for four proposed relationships between morphology and function, which act as proxies for performance, and a series of Pareto-rank-optimised metric combinations.

An originally collected dataset of 1139 extant avian wing planforms (36 of 41 orders) was then superimposed over this analysis of theoretical shape to determine whether extant empirical wings map to the hypothesised flight optima established through testing of theoretical morphology. The optimal peaks produced by these metrics and combinations are hypothesised to be optimising factors for flight specific styles found within birds, allowing for direct predictions of which bird groups should have optimal planforms for which metrics (Table 1). If shape is a driver of functional diversity, we expect empirical wing planforms to map to optimal theoretical shapes for specific flight styles or combinations of functions. Alternatively, if empirical shapes are functionally suboptimal, the influence of function on wing planform diversity must not be as overwhelming as it is often perceived.

We also test for the degree to which phylogeny explains shape variation using ancestral state estimation and a phylomorphospace approach. Our results indicate that phylogeny does not explain much of avian wing shape variation but for more biomechanically intensive flight styles, wing shape correlates closely with hypothesised functional optimality.

Results
Theoretical Shape
The theoretical morphospace generates two principal components of variation (Fig. 2a) that represent a combined 75% of total disparity. Over half of all disparity is represented on PC1 (53.75%), which describes the breadth of the wing chord, because all planforms are scaled to identical length. Low PC1 values represent more slender theoretical shapes, with higher values representing broader forms. PC2 (21.96% of total disparity) principally describes the tip-base weighting of the planform, with low PC2 values characterised by broader tips and high PC2 values by broader bases. PC2 also characterises primary feather emargination, which is manifest in theoretical shapes as a bifurcation of the planform tip. Primary feather splay is most pronounced in shapes with low PC2 values, though less noticeable in shapes with low PC1 values. This is because a slenderer shape causes disruption of the tip and self-intersection during the theoretical shape generation, resulting in impossible forms (grey areas in Figs. 1-3). PC3 characterises only 9.14% of variation, pertaining to the anterior-posterior position of the tip. Shapes at the extremes of the theoretical space point anteriorly in a U shape or posteriorly in an N shape for low and high values of PC3 respectively (Supplementary Fig. 1). When projected into the theoretical morphospace (Fig. 2), empirical shapes occupy a large proportion of potential variation, though regions of the lower left and of the righthand quadrants remain unoccupied, with most taxa clustering around two peaks in morphological disparity (Fig. 2b).

Hypothesised Functional Performance
The performance surface (Fig. 3a) for planform aspect ratio illustrates a single optimal peak with minimum values on PC1 and median values on PC2. Optimality for aspect ratio drops downslope to higher values of PC1. The area on the extreme left of the graph is characterised by very thin, highly pointed theoretical shapes, where interference from the emarginated primaries creates impossible space (grey regions, see Methods).

The performance surface for planform second moment of area exhibits two optimal peaks (Fig. 3b). The primary peak resides in space with low PC1 and high PC2 scores, characterised by slender, broad-tipped theoretical shapes. A second, locally optimal, peak exists with PC2 values at the median and PC1 values slightly above the median. This peak is characterised by broadly rectangular theoretical planforms.

The performance surface for planform pitch agility (Fig. 3c) is contoured with an oblong optimal peak projecting parallel to PC2 originating from approximately PC1=-0.3. This peak comprises subovate theoretical wing planform shapes with rounded tips and slight tapering from root to tip. Some planforms in lower PC2 optimal space exhibit slight division in the tip but forms with more pronounced primary feather divisions fall outside of optimal space.

The optimal region for the tip angle performance surface (Fig. 3d) mirrors that of aspect ratio, characterised by long slender forms with optimality increasing with lower PC1 values. No sampled taxa occupy the optimal peak, though shapes with emarginated tip morphologies reside farther upslope than non-slotted forms.

Functional trade off and Pareto optimality
We examine combinations of performance metrics reflecting trade-offs between antagonistic functions. Trait combinations were calculated using a Pareto ranking system (28) and Goldberg (29) ranking algorithm to optimise for trade-off between multiple traits (see Methodology). The combination of planform second moment of area and tip angle (Fig. 4a, 5a), hypothesised as optimal for marine soarers, produces a Pareto surface broadly mirroring that of the aspect ratio metric. The plot of aspect ratio and tip angle (Fig. 4b, 5f), proposed as an optimal combination for migratory taxa, also presents optimal shapes at low PC1 values. This graph most closely resembles aspect ratio, with only a slight expansion of more optimal space downslope for the extremes of PC1.

The Pareto optimality surface for second moment of area and agility (Fig. 4c, 5d, e) serves as a proxy for acrobatic flight, such as hovering and diving, and features a large ridge of optimal space in negative PC1 values, decreasing downslope to both the left and right of the graph. A second moment of area, agility and broad tip angle combination (Fig. 4d, 5b), which we suggest is optimal for aerial predation, resembles that of the second moment of area:agility space, with the addition of a second branching area of optimal space for higher PC1 and median PC2 values. Several empirical planforms are optimal for this combination of traits including those with both acute and obtuse tip angles (Fig 5b). The mean performance distance from the optimal peak for aerial predators is 0.0952, indicating over 90% similarity with optimal planform shape.

Empirical Occupation of Shape Space
At order-level (Fig. 6), there is substantial overlap between the different bird lineages when projecting the empirical shapes onto the theoretical morphospace. Plotted as a heatmap (Fig. 2b), two broad groupings emerge. Waterbirds and Apodiformes comprise the majority of the lefthand group, with low PC1 values, while the righthand group, with median PC1 values, is dominated by members of Passeriformes as well as taxa from Cuculiformes and Galliformes. Overall, this distribution closely resembles the quadrant morphospace created by Rayner (3), derived from aspect ratio and wing loading values. Projecting phylogeny into the morphospace (Fig. 7a) further develops this evidence of homoplasy, with substantial overlap in morphology between taxa from disparate lineages. Ancestral state planforms group tightly within the same region of shape space as modern taxa. A very weak but significant phylogenetic signal was found in the shape data (K = 0.1751, p = 0.001) using a multivariate K statistic (27). Two additional tests of phylogenetic signal were conducted using the taxa sets employed by Wang and Clarke (15) and Baumgart et al. (17) (Supplementary Data 3). These were performed using the same methods employed in the above analysis with the aim of testing whether the method used is consistent across datasets. Reproduction of the Wang and Clarke dataset produced a large phylogenetic signal (K = 0.9293, p = 0.001) while reproduction of the Baumgart et al. dataset produced a signal of K = 0.088 (p = 0.002). When projected into morphospace (Fig. 7b), flight style groups exhibit considerable overlap, though some patterns are visible. Most dynamic soaring, hovering, diving and long-distance migrating birds group with the lefthand waterbird-dominated cluster, while burst-flapping poor flyers plot mostly on the right, overlapping considerably with the passeriforms.

Methods
Data Collection
All data collected for this work is freely available for download and use without permissions. 1139 images of bird wings spread to their maximum extent were sourced digitally and captured directly from museum ornithology collections, principally from the Burke Museum of Natural History and Culture (UWBM) Seattle, United States, the Puget Sound Museum of Natural History (PSM) online Wing and Tail Collection and the Natural History Museum at Tring (NHMUK), UK. Additional wing images were sourced from the online collections of:
• The Auckland War Memorial Museum (AK), Auckland, New Zealand
• The Field Museum of Natural History (FMNH), Chicago, United States
• The Musée des Civilisations de Cote d′Ivoire (MCCI), Abidjan, Ivory Coast
• The Museum of New Zealand Te Papa Tongarewa (NMNZ), Wellington, New Zealand
• The Slovenian Museum of Natural History (PMSL), Ljubljana, Slovenia
• The Naturalis Biodiversity Center (RMNH), Leiden, Netherlands
• The Smithsonian National Museum of Natural History (USNM), Washington DC, United States
as well as from online wing and feather resource collections and the published literature. A complete taxa list is provided in Supplementary Information (Data 1). For data collected directly from museum specimens, individual wings were photographed from above on a plain background. Righthand wings were selected where possible, and where needed, lefthand wings were mirrored to ensure data consistency. This resulted in a planform image, the external edge of which was then defined using the outline selection tool in Fiji (version 1.54) (75) (Supplementary Data 4). Henceforth planform refers to the outline of the outermost silhouette of the wing. 2D planform wings, characterised as outline shapes, were chosen due to the online availability of images and high degree of variability in the preservation of 3D wing reference collections. Furthermore, previous large-dataset studies of wing shape and flight performance have employed 2D shape, demonstrating its efficacy for disparity analysis (15). 2D shape can be easily defined using Elliptical Fourier Analysis (EFA) (43, 44), permitting accurate silhouette generation. EFA was completed in MATLAB following the protocol established by Deakin et al. (28). In addition to the wing planforms, the unpublished dataset produced by Rayner (3) has been reconstructed, with its original measurements (Supplementary Data 5).

The data was split at order level and includes 36 of 41 extant bird orders, with additional subsets created to characterise six niches derived from Rayner (3) and Taylor and Thomas (12): marine soaring, aerial predation, thermal soaring, wing-assisted diving, long-distance migration, and burst flapping. An additional class of hoverers was added to encompass hummingbirds. The taxa in these convex hulls do not represent a comprehensive list of all taxa with a particular flight niche in the dataset, but were chosen from the literature to encompass the approximate maximum area of occupied morphospace in which animals employing this niche may reside. This research considered flight niches individually, though many taxa may be optimised for a combination of multiple niches.

For phylomorphospace analysis, a strict consensus time-scaled supertree was generated from the all-taxa supertree on birdtree.org (45, 46) using the Hackett (47) backbone. Consensus was achieved using the consensus edges tool in phytools (48) with the least squares method (Supplementary Data 2). Two taxa, the Mexican Hermit Hummingbird (Phaethornis mexicanus) and Wilson’s Phalarope (Phalaropus tricolor), were excluded from phylomorphospace analysis as they are absent from the birdtree.org taxa list. Phylogenetic signal was assessed using the physignal command in the R package geomorph, which returns a multivariate K statistic (kmult) of the relationship between phylogeny and shape. Ancestral shapes were then computed using the command gm.prcomp for maximum likelihood ancestral state reconstruction (49, 50). This method was chosen due to the applicability of these functions for working with coordinate data, matching with the outputs of EFA. All R analyses were performed in R version 4.2.2 and Rstudio version 2022.12.0 (51, 52). The code and algorithms for computing performance characters were written in MATLAB version R2022B by Deakin (28) and modified to work with the constraints of planform shape. The code and all datasets are available in Supplementary Information (Code 1)

Theoretical Morphospace
The morphospace constructed here follows the approach utilised by Raup (53) and outlined in previous studies (28, 54-61), producing theoretical shapes using constructor variables derived from measurements of empirical taxa. While some suggest that this method does not yield truly theoretical shapes (20), it remains the prevailing method of constructing theoretical space. Using Fourier Shape Analysis via the method established in Deakin et al. (28), we characterised each planform with 1200 outline landmarks and 5 shape harmonics. This number of landmarks is well beyond the threshold of convergence and was the maximum number possible given the resolution of each outline. Plotting the formula for the elliptical harmonics produced a 2D representation of empirical shapes, the morphological disparity of which was characterised through Principal Components Analysis (PCA). Since altering formula parameters for shape proportionally changes the resulting outline, changes in the formula were used to generate an even grid of theoretical shapes encompassing the entire range of shape variation in the empirical taxa (43). This theoretical shape grid was then expanded 20% (28) resulting in 23 x 22 grid of 506 theoretical wing planform shapes plotted evenly across the principal components space (Fig. 1). Expansion of the theoretical grid ensures that a larger area of theoretical morphology is functionally tested than exists in nature, allowing for the potential identification of optimal morphologies that are not realised in living animals. Expansion of this theoretical morphology space was constrained at 120% of observed empirical variation focus on possible (i.e. non self-intersecting) shape, and forms which resemble the planforms of wings, as well as the practical limitations of computational analysis. The low number of shape harmonics used allowed for maximisation of possible landscape space, as higher harmonic levels introduced greater regions of space with self-intersecting forms due to overlap from generation of forms with emarginated primary feather. Self-intersecting shapes are theoretically impossible for 3D objects presented two dimensionally (62, 63), so 75 self-intersecting forms were removed from functional analysis, represented by the grey region in the performance space plots. All theoretical planforms are identically size scaled by standardising the parameter of the first elliptic to isolate the shape element of variation and remove any length-based effects which would obscure analysis of a dataset with a high degree of size variation.

Extrapolating theoretical planform shapes with emarginated primaries results in a split point morphology in the theoretical shapes, which is unlike the splay of primary feathers found in birds. Since the distal-most primary feathers are decoupled from the ligaments that spread the rest of the wing primaries (64), this morphology may represent underlying trends in the placement of feathers during conservation, but this is unlikely as the taxa sampled derive from multiple independent museum collections and are of varying age. It is more likely an emergent feature of characterising emargination by EFA, as it is preserved at higher harmonic values.

Performance Proxies
From previous flight studies (3, 4, 12, 13, 25) we selected four functional metrics to test planform functional optimality (Aspect Ratio (AR), Second Moment of Area (2MA), Pitch Agility (PA), and Tip Angle (TA)). These metrics incorporate traditional analytical elements of flight such as lift and drag, while providing a more direct link to specific flight behaviours (Table 1). While body size is a critical element of flying animals and is linked to flight ability through metrics like wing loading (3), relative size is not computable for theoretical shapes. As a result, only functional metrics divorced from body size were included. We then linked a single metric or combination of these metrics to wing planforms associated with a given flight style niche (Table 1b), hypothesising that birds with distinct flight styles would optimise for these performance traits. For example, aspect ratio is closely linked with cost of transport, with higher-aspect (longer and thinner) planforms reducing the energy cost of flight (3, 12). For this reason, high aspect ratio is considered optimal, particularly for birds with soaring and long-distance migratory niches such as albatrosses and other procellariiforms, where energy conservation is essential. Second moment of area describes the distribution of the aerodynamic surface relative to the root of the planform, a factor which correlates with generation of rotational moment (4). This serves as a proxy for manoeuvrability, defined by Norberg and Rayner as the ability to turn with a tight radius around the yaw axis (3, 8). We therefore hypothesise high second moment of area to be optimal for multiple flight styles including marine soaring and aerial predation, and part of the combination of metrics which drive optimisation in bird groups such as swifts, hummingbirds and procellariaforms. The relationship between the breadth of the wingtip and the trade-off between lift production and drag reduction is well established (13, 21-23). Planforms with broader rounder tips produce greater lift and conversely more pointed tip forms produce less lift but benefit by correspondingly reducing induced drag. For these reasons, we consider broad tip angles to be optimal for birds which require high lift for short periods, such as burst flappers and hypothesise that optimally shaped wings for this metric should be found within Galliformes and other predominantly terrestrial taxa (Table 1b). Pointed tip morphologies, conversely, are optimal for birds with flight niches prioritise energy saving, such as migrants (14, 24) and acute tip angle is hypothesised to be an optimising metric for members of Accipitriformes. Agility refers to the ability to rapidly instigate change in direction, particularly at high speeds. This is linked to the ability of wings to transition from stable to unstable flight modes through change of the pitch of the wing (25, 26). We consider planforms which can more easily achieve instability as more optimal, particularly for niches that involve acrobatic flying such as aerial hawking and hovering. Thus agility is hypothesised to be an optimising factor on the planform shapes of taxa including hummingbirds and other apodiforms (table1b).

Performance Surfaces and Pareto Ranking
Aspect Ratio was calculated as the square of span divided by area using the formula (65):
AR = R^2 / S (1)
Where R is the span length of each theoretical shape and S is the corresponding shape area.
Second moment of area was used as a proxy for manoeuvrability, as the ability to fly at low speeds and perform tight turns is correlated with large second moments of area (4). Thus, high second moment of area is considered an optimising characteristic. For each theoretical shape, second moment of area was calculated following the method in Liu et al. (54) using the formula (66):
r = 1/2 * sum(i=1 to n) (x_i * y_{i+1} - x_{i+1} * y_i) * (x_i^2 + x_i * x_{i+1} + x_{i+1}^2) (2)
Under this formula, each theoretical planform is represented as a polygon with an equal number of sides as landmarks i, and where x and y represent coordinates of the i-th landmark. This was further non-dimensionalised to remove the impact of size, producing the non-dimensionalised second moment of area r^ (65).
r^ = sqrt(r) / (S * R^2) (3)
Agility is inversely related to stability (25, 26). High agility is critical where sudden flight changes are necessary in high-speed flight (3, 26). In many birds, these sudden changes have been linked to the ability to temporarily switch from stable to unstable flight. Harvey (25) established a metric for pitch agility which relates to the ability for shapes to become unstable at higher angles of attack. This instability is key for birds to accomplish complex acrobatic feats (25). This pitch agility metric was used in this analysis, expressed as:
Delta q_dot / Delta alpha proportional to [((x_c / c_rmax) - x_CG) * (m * c_rmax^2)] / I_yy (4)
Where Delta q_dot represents the rate of change of angular acceleration relative to the y-axis (25). Since all theoretical planforms were tested equally at a single angle, Delta alpha remained static, allowing for output of relative values that could be plotted onto morphospace. Since all theoretical shapes are scaled, the maximum root chord (c_rmax) and the quarter chord of the mean chord (x_c) were calculated by dividing each planform into a uniform number of equidistant strips. Maximum planform area (S_max) was calculated from centroid area and, as the shapes tested are theoretical, mass (m) was held constant. For centre of gravity (x_CG) the farthest left point on the x axis was substituted for the position of the femoral head. As the shapes tested are theoretical rather than measurable shapes, both mass and area are reduced to standardised values. The point of rotation for each theoretical shape was chosen as the minimum x coordinate in line with the calculation for rotational efficiency. A dimensionalised variant of the second moment of inertia (I_yy) was utilised.

The angle of the planform tip and its relative pointedness is directly related to the generation of tip vortices and thus the production or reduction of induced drag (13). Pointed tips minimise weight and reduce drag in flight while broader tips produce greater thrust and lift at the expense of increased induced drag (13, 21-23). A more pointed tip is considered optimal for long duration flight behaviours while broad tips are more optimal for behaviours involving quick bursts of speed.

Tip angle was calculated from the internal angle of the tip of each planform shape, using the rightmost point as the tip and calculating the angle from it 500 points away from the tip in either direction. For shapes with a bifurcated tip, the leading-edge point was chosen.

The relative values of these characteristics were then plotted onto the two-dimensional morphospace to produce a three-dimensional performance surface (following Deakin et al. (28); Fig. 1). High points on this performance surface are considered to represent more optimal theoretical shapes for the given performance metric.

No individual design is optimal for a single trait and thus all biological forms are functionally bound by a combination of multiple functional characters as well as external influences (3, 12). To examine how different competing trait-based morphological drivers interact, a method of combining functional metrics by ranking was implemented, following the method developed by Deakin et al. (28). This method is developed from Pareto ranking algorithms (29, 67) and has been demonstrated as an effective means of analysing optimality with morphospaces (28, 54). Pareto optimisation identifies optimal subsets of data for multiple interacting factors where the scaling between variables is uneven and there is no given ranking for the relevance of a given performance metric (28). This allows for ease of comparison between large datasets where taxa are differentially preferenced for a given combination. To develop a landscape from the binary Pareto grouping, we instituted an iterative Goldberg (29) ranking algorithm which produced successive Pareto fronts and further developed into a Pareto Rank Ratio (PRR), reducing the bias introduced from the occupation density of performance space. The resulting rank ratio measures proportional optimality of a solution given optimal and sub optimal ranking (28):
PRR = { 1, R_o = 0; R_o / (R_o + R_s), R_s > 0 } (5)
Where R_o represents optimal rank under Goldberg and R_s the suboptimal rank. Where both values equal 0, the PRR is 1. The result is a Pareto rank from 0 to 1 for each theoretical shape, which can then be mapped as a single performance surface (Fig. 1).

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The authors explore the range of existing avian wing shape relative to theoretical possibilities, a very fun question for the functional morphology community, and not often done. This is an important framework to think about how things have evolved the way they do and what may be guiding or constraining their direction of evolution. I made some comments below which I think could improve the manuscript, but I think it is going to be a good addition to the journal after revisions.\nLine 80 – would this be better described as the wing aspect ratio? Based on the description in the next sentence, it sounds like PC1 is breadth of the wing chord relative to the wing length, not breadth of wing chord in isolation. Or is this a raw measurement of wing chord?\nLine 138 – no suppl. fig number given\nLines 144-146 – dominant by passerines or by non-waterbirds? I see passeriforms, but also cuculiforms, and galliforms on the far right. With all the other clades in that region that are hidden due to density of data points, I’d recommend being more inclusive with taxa listed in this contrasting statement, especially if non-passerine passeriforms are included in the analysis.\nLine 156 – extra “/” included\nLine 157 – “Wang” instead of “Wange”\nLine 162-163 – “burst flapping” should be hyphenated when used as an adjective\nLine 164 – passerines or passeriforms? Taxonomic categories here are of the order level, so it may make more sense to refer to the group as passeriforms instead of passerines, which is a subset of Passeriformes.\nThoughts on section at 166 – What about the idea of many-to-one mapping? (See Wainwright et al. 2005: https://academic.oup.com/icb/article/45/2/256/778330) Or the related idea of “this shape is sufficient for the task; taking the whole organism and its collection of needs and behaviors, it’s good enough.” Wings are not in isolation of the rest of the body, which would be a source for further constraints on empirical wing shape that could limit the amount of theoretical wing shape space that is achieved in reality.\nThoughts on sections at 185 – This is very interesting. Might differences in data collection protocols affect the differences found between the authors’ phylogenetic signal and that of Wang and Clarke 2015? They also captured the covert outline too. But it’s true that scale of analysis would also play a large effect.\nLine 217 (and throughout discussion) – Thinking about terms like “cost-efficient” and “optimal/non-optimal,” clear biological context matters with these sorts of statements. An albatross wing has a high aspect ratio and therefore optimal for soaring in an open marine environment, but it is not optimal for maneuvering in a forest. Relative to an albatross, a robin wing has a low aspect ratio and is therefore optimal for maneuvering the forest, but not optimal over the ocean. An albatross’s flight in a forest would be much less cost-efficient than it would be over the ocean, as it would expend significantly more energy struggling to get through the forest. So a high aspect ratio wing would be cost-efficient for certain behaviors in certain habitats, a low aspect ratio wing would be cost-efficient for other behaviors and other habitats, etc. And if they do wing-propelled diving, there could be a third “most cost-efficient/optimal shape” for that behavior, accounting for flapping through the water, as discussed later. Each plot shows optimum shape space for very specific traits or behaviors, so authors should make sure the discussion text always reflects that sort of precise articulation of the context of things like “optimal.”\nLine 232 – Good for including Pelagornis! I had written a thought that it should be mentioned somewhere, but deleted that thought, since I found it here.\nParagraph starting at line 298 – be very precise about what optimal means in this context; there are many different biological adverbs that could be added to change the meaning of the “optimals” throughout the paragraph – optimal for which aspect of a bird’s biology or behavior?\nLine 567 – What does “characterized as outline shapes” entail? Wang and Clarke 2015 and Baumgart et al. 2021 use 2d landmarks to capture an outline. Which software was used to generate an outline of the wing? How was wing shape data collected from the outline?\nLine 576 – “characterize seven six niches” – should pick a number", "reviewer_2": "In the manuscript “Bird wing planform shape is highly optimised for flight style”, the authors test the link between wing shape and flight style in birds using a new dataset and a creative morphometric approach. The authors created a theoretical morphospace onto which they have mapped flight “performance” metrics to create hypothetical performance spaces, which they paired with empirical shape measurements from a large number of avian taxa to test for functional optimization of wing morphology. The authors report some evidence for shape optimization, which is independent of phylogenetic effects. The manuscript is clear and well-written, and the subject will be of broad interest to the flight community. The figures, also, are very nice and well-presented. However, some aspects of the predictions and results remain unclear, and I do not believe that the authors have conducted the requisite tests to support their main claim. As such, I believe that some revision is necessary prior to publication. Below, I detail my major concerns with the study, as presented, followed by minor issues that should be addressed prior to publication.\nMajor concerns:\n1) My first major concern with the study is that I do not find tests that adequately supports the main assertion of the manuscript, that “Wing planform shape is highly optimized for flight style”. My concern here is two-fold. First, I find the evidence for optimization to be mixed. The results seem to support high pitch agility across most of the studied species, and the species also cluster on a plateau of high second moment of area. Aspect ratio and tip angle show gradients, with one end approaching the putative “optima”, but the other end being far from it. In the composite performance surfaces, however, the species actually appear to sit within pareto valleys rather than being on peaks or ridges. I was rather hoping that the authors would discuss that, but they did not. My second concern is that while the authors did make an effort to quantify the proximity to the “optima” (through Euclidean distances between group means and the performance optima), I found no test that would discriminate between groups in their degree of optimization. Perhaps it would be worth calculating the optimization distance for each species and then doing a phylogenetic ANOVA (or similar) to show whether different groups (either taxonomic groups or behavioral/functional groups) share similar optimization ranges. The Euclidean distance metrics and any subsequent tests do need to be included in the methods (they are not at present) and presented in the results (not in the discussion as they are now).\n2) My second major concern stems from the construction of the morphospaces and performance surfaces. The authors should be careful to note that they are, in most cases, using morphological proxies for performance rather than estimates of performance output (the exception here being the pitch agility metric – the rest of the “performance” surfaces are simply morphological traits). While the relationships between these morphological traits and their influence on flight performance are well-documented, it is unclear whether it is safe to assume a linear association between morphology and performance. I don’t have a problem with the use of these shape traits as proxies, but the authors should probably note this as a caveat of the study. Additionally, it is unclear how the authors arrived at the 20% figure to expand their theoretical grid space. This is an important consideration, because many performance traits do scale continuously (though not necessarily linearly) with shape – for example, the authors use aspect ratio as a proxy for flight efficiency. Indeed, wing aspect ratio is related to flight performance metrics like drag coefficient and lift-to-drag ratio, but the morphospace that the authors present appears to covary strongly with aspect ratio, so using it as a performance surface superimposed over the morphospace seems circular. It would be better to choose a true measure of flight performance (see Rader et al. 2020; Waldrop et al. 2020) rather than using the proxy.\n3)I think that it would be helpful for the authors to set up more explicit predictions about how wing morphology is expected to vary with flight style / performance in the introduction, and then to follow a more rigorous hypothesis testing framework throughout the analyses. As the manuscript is currently presented, I struggled to understand what the authors were predicting, which made it difficult to ascertain whether the methodological approach was appropriate for the questions.\n4) How was phylogenetic signal calculated for the dataset? In the methods, the authors list the gm.prcomp command, but in the results they talk about the kmult statistic (which does not appear in the methods).\nMinor concerns:\n1) Line 109: I’m not sure about “tongue-shaped” as a descriptor.\n2) Double check spelling of references throughout.\n- Line 157: “Wang and Clarke” is misspelled\n- Line 389: “Rader and Hedrick” is misspelled\n3) Some discussion of how the present results compare to 3-dimensional analyses (e.g., Rader and Hedrick 2023 and Rader et. al 2020) might be welcome.\n4) Line 571: Define EFA.\n5) Line 576: Typographic error; was it six or seven niches?\n6) Line 638: Perhaps the authors could elaborate on how their performance metrics provide any “direct link to specific flight behaviors”. This comment is probably best addressed by setting up some discrete predictions (see major concern #3).\n7) Line 661: How are these planforms defined?\n8) Line 688: I know that this equation is well-presented in the supplement of Harvey et al., but it would be helpful to define the terms here, especially as they pertain to the present data and methods.\nReferences:\nRader JA, Hedrick TL, He Y, Waldrop LD. 2020. Functional Morphology of Gliding Flight II. Morphology Follows Predictions of Gliding Performance. Integrative and Comparative Biology 60:1297–1308.\nWaldrop LD, He Y, Hedrick TL, Rader JA. 2020. Functional morphology of gliding flight I. Modeling reveals distinct performance landscapes based on soaring strategies. Integrative and Comparative Biology 60:1283–96."}, "author_response": "Reviewer #1 (Remarks to the Author):\nThe authors explore the range of existing avian wing shape relative to theoretical possibilities, a very fun question for the functional morphology community, and not often done. This is an important framework to think about how things have evolved the way they do and what may be guiding or constraining their direction of evolution. I made some comments below which I think could improve the manuscript, but I think it is going to be a good addition to the journal after revisions.\nLine 80 – would this be better described as the wing aspect ratio? Based on the description in the next sentence, it sounds like PC1 is breadth of the wing chord relative to the wing length, not breadth of wing chord in isolation. Or is this a raw measurement of wing chord?\nA phrase has been added here clarifying that all planforms, both theoretical and empirical are scaled to identical length. Due to this scaling the breadth of the chord, while functionally equal to aspect ratio, is better described as a raw measurement of the chord itself.\nLine 138 – no suppl. fig number given\nA supplementary figure number has been provided to fix this oversight.\nLines 144-146 – dominant by passerines or by non-waterbirds? I see passeriforms, but also cuculiforms, and galliforms on the far right. With all the other clades in that region that are hidden due to density of data points, I’d recommend being more inclusive with taxa listed in this contrasting statement, especially if non-passerine passeriforms are included in the analysis.\nThis passage has been rephrased to include Cuculiformes and Galliformes and to use the broader clade level designation Passeriformes rather than passerines, which previously suggested a more restricted class.\nLine 156 – extra “/” included\nThe extra / has been removed\nLine 157 – “Wang” instead of “Wange”\nThe spelling of Wang has been corrected\nLine 162-163 – “burst flapping” should be hyphenated when used as an adjective\nA hyphen has been added between burst and flapping\nLine 164 – passerines or passeriforms? Taxonomic categories here are of the order level, so it may make more sense to refer to the group as passeriforms instead of passerines, which is a subset of Passeriformes.\nPasseriforms has been substituted for passerines to in order to better clarify that we are referring to the entirety of the clade.\nThoughts on section at 166 – What about the idea of many-to-one mapping? (See Wainwright et al. 2005: https://academic.oup.com/icb/article/45/2/256/778330) Or the related idea of “this shape is sufficient for the task; taking the whole organism and its collection of needs and behaviors, it’s good enough.” Wings are not in isolation of the rest of the body, which would be a source for further constraints on empirical wing shape that could limit the amount of theoretical wing shape space that is achieved in reality.\nThis is an excellent point, that the rest of the animal is a likely source of constraint on the shape of the wing planform. While this will not affect the performance of the theoretical shapes, the elements tested by the analysis, it does warrant comment in reference to discrepancies in empirical wings. An acknowledgement of this and of many-to-one mapping has been added to the end of section a of the discussion.\nThoughts on sections at 185 – This is very interesting. Might differences in data collection protocols affect the differences found between the authors’ phylogenetic signal and that of Wang and Clarke 2015? They also captured the covert outline too. But it’s true that scale of analysis would also play a large effect.\nA sentence has been added here acknowledging that the addition of covert feathering data by Wang and Clarke may also be a factor contributing to the discrepancy in phylogenetic signal between the datasets.\nLine 217 (and throughout discussion) – Thinking about terms like “cost-efficient” and “optimal/non-optimal,” clear biological context matters with these sorts of statements. An albatross wing has a high aspect ratio and therefore optimal for soaring in an open marine environment, but it is not optimal for maneuvering in a forest. Relative to an albatross, a robin wing has a low aspect ratio and is therefore optimal for maneuvering the forest, but not optimal over the ocean. An albatross’s flight in a forest would be much less cost-efficient than it would be over the ocean, as it would expend significantly more energy struggling to get through the forest. So a high aspect ratio wing would be cost-efficient for certain behaviors in certain habitats, a low aspect ratio wing would be cost-efficient for other behaviors and other habitats, etc. And if they do wing-propelled diving, there could be a third “most cost-efficient/optimal shape” for that behavior, accounting for flapping through the water, as discussed later. Each plot shows optimum shape space for very specific traits or behaviors, so authors should make sure the discussion text always reflects that sort of precise articulation of the context of things like “optimal.”\nWe agree that what is optimal in wings varies across bird groups and have made adjustments to the discussion to highlight that different groups of birds are hypothesised as optimal for specific flight styles. These hypotheses are made in reference to table 1 and are expanded upon in methods section c. additions have been made to methods section c to state which bird groups are hypothesised to be optimised for each flight style, linking table 1 into the text. We have also more explicitly outlined in the introduction that this is what underpins our analysis. We hope that this additional context improves the clarity of the underlying hypothesis that specific bird groups should experience functional pressure toward the development of optimally shaped wings for specific flight styles.\nLine 232 – Good for including Pelagornis! I had written a thought that it should be mentioned somewhere, but deleted that thought, since I found it here.\nWe are glad to see that Pelagornis is a welcome addition, no change is necessary in response to this comment.\nParagraph starting at line 298 – be very precise about what optimal means in this context; there are many different biological adverbs that could be added to change the meaning of the “optimals” throughout the paragraph – optimal for which aspect of a bird’s biology or behavior?\nThe use of optimal to refer to both areas in morphospace and planform shape created some confusion., the paragraph has been restructured to clear up this confusion and specify when optimality refers to either the planforms or the areas of highest performance.\nLine 567 – What does “characterized as outline shapes” entail? Wang and Clarke 2015 and Baumgart et al. 2021 use 2d landmarks to capture an outline. Which software was used to generate an outline of the wing? How was wing shape data collected from the outline?\nAdditional information about the initial capture of outline data and its digitisation has been added to methods section 2a including which programs were used for generating outline data from wing images.\nLine 576 – “characterize seven six niches” – should pick a number\nThe number 7 has been removed to correct this oversight.\nReviewer #2 (Remarks to the Author):\nIn the manuscript “Bird wing planform shape is highly optimised for flight style”, the authors test the link between wing shape and flight style in birds using a new dataset and a creative morphometric approach. The authors created a theoretical morphospace onto which they have mapped flight “performance” metrics to create hypothetical performance spaces, which they paired with empirical shape measurements from a large number of avian taxa to test for functional optimization of wing morphology. The authors report some evidence for shape optimization, which is independent of phylogenetic effects. The manuscript is clear and well-written, and the subject will be of broad interest to the flight community. The figures, also, are very nice and well-presented. However, some aspects of the predictions and results remain unclear, and I do not believe that the authors have conducted the requisite tests to support their main claim. As such, I believe that some revision is necessary prior to publication. Below, I detail my major concerns with the study, as presented, followed by minor issues that should be addressed prior to publication.\nMajor concerns:\n1) My first major concern with the study is that I do not find tests that adequately supports the main assertion of the manuscript, that “Wing planform shape is highly optimized for flight style”. My concern here is two-fold. First, I find the evidence for optimization to be mixed. The results seem to support high pitch agility across most of the studied species, and the species also cluster on a plateau of high second moment of area. Aspect ratio and tip angle show gradients, with one end approaching the putative “optima”, but the other end being far from it. In the composite performance surfaces, however, the species actually appear to sit within pareto valleys rather than being on peaks or ridges. I was rather hoping that the authors would discuss that, but they did not. My second concern is that while the authors did make an effort to quantify the proximity to the “optima” (through Euclidean distances between group means and the performance optima), I found no test that would discriminate between groups in their degree of optimization. Perhaps it would be worth calculating the optimization distance for each species and then doing a phylogenetic ANOVA (or similar) to show whether different groups (either taxonomic groups or behavioral/functional groups) share similar optimization ranges. The Euclidean distance metrics and any subsequent tests do need to be included in the methods (they are not at present) and presented in the results (not in the discussion as they are now).\nTo address the concern that the main finding of the paper, as expressed in the title, does not adequately match the findings, we have changed the title to more clearly state that the optimisation of avian wings for flight style is variable and not all groups exhibit wings with functionally optimal planform shapes. Since our analysis only tests the functional performance of theoretical shapes relative to each other, and not empirical shapes, there exists no discrete performance data for theoretical shapes which could form the basis of between-group testing. We have emphasised the nature of this divide between theoretical and empirical forms to clarify this case.\n2) My second major concern stems from the construction of the morphospaces and performance surfaces. The authors should be careful to note that they are, in most cases, using morphological proxies for performance rather than estimates of performance output (the exception here being the pitch agility metric – the rest of the “performance” surfaces are simply morphological traits). While the relationships between these morphological traits and their influence on flight performance are well-documented, it is unclear whether it is safe to assume a linear association between morphology and performance. I don’t have a problem with the use of these shape traits as proxies, but the authors should probably note this as a caveat of the study. Additionally, it is unclear how the authors arrived at the 20% figure to expand their theoretical grid space. This is an important consideration, because many performance traits do scale continuously (though not necessarily linearly) with shape – for example, the authors use aspect ratio as a proxy for flight efficiency. Indeed, wing aspect ratio is related to flight performance metrics like drag coefficient and lift-to-drag ratio, but the morphospace that the authors present appears to covary strongly with aspect ratio, so using it as a performance surface superimposed over the morphospace seems circular. It would be better to choose a true measure of flight performance (see Rader et al. 2020; Waldrop et al. 2020) rather than using the proxy.\nThe introduction has been modified to express that the performance metrics tested represent proxies for performance based on established understanding of the relationship between morphology and function. These proxies do not represent a true measure of performance output, and this is why we only test theoretical chapes, rather than the empirical planforms. This is the benefit of theoretical morphology as it allows us to produce analyses of relative functional performance independent of attempting to ascertain the discrete performance of individual taxa. To avoid confusion, we have adjusted the phrasing of the introduction to better emphasise this divide and that only theoretical shapes are tested with the functional proxies.\nAdditionally, the 20% figure for expanding morphospace is determined by the limits of theoretical shape generation, producing theoretical shapes what are possible and not too far from winglike shapes. It would hypothetically be possible to expand this space indefinitely to include winglike shapes as well as simple polygons etc. though in practice this would be unnecessarily computationally expensive and include a vast number of self-intersecting forms which are impossible and therefore untestable. We have added clarification of this point to section b of the methods to clarify this point.\n3)I think that it would be helpful for the authors to set up more explicit predictions about how wing morphology is expected to vary with flight style / performance in the introduction, and then to follow a more rigorous hypothesis testing framework throughout the analyses. As the manuscript is currently presented, I struggled to understand what the authors were predicting, which made it difficult to ascertain whether the methodological approach was appropriate for the questions.\nThe introduction has been expanded to include reference to the underlying hypothesis that specific bird groups should possess optimal planforms for specific metric combinations, with reference to table 1 which outlines the flight style groups analysed and their link to specific metric combinations. This was previously underemphasised within the introduction and hopefully has now been reinforced.\n4) How was phylogenetic signal calculated for the dataset? In the methods, the authors list the gm.prcomp command, but in the results they talk about the kmult statistic (which does not appear in the methods).\nThe section of methods addressing the calculation of phylogenetic signal has been amended to draw distinction between he commands used for phylogenetic signal, which generate a multivariate k statistic (kmult) and the command used for ancestral shape reconstruction, gm.prcomp.\nMinor concerns:\n1) Line 109: I’m not sure about “tongue-shaped” as a descriptor.\nThe term tongue-shaped has been replaced with “a rectangular region of optimality” to improve specificity in description of the shape of the optimal peak.\n2) Double check spelling of references throughout.\n- Line 157: “Wang and Clarke” is misspelled\n- Line 389: “Rader and Hedrick” is misspelled\nThese misspellings have been corrected\n3) Some discussion of how the present results compare to 3-dimensional analyses (e.g., Rader and Hedrick 2023 and Rader et. al 2020) might be welcome.\nReference has been added to the existence of these 3-dimentioanl studies in the introduction and comparison of our results to those of Rader et al. 2020 has been added to section c of the discussion.\n4) Line 571: Define EFA.\nThis acronym has been expanded to Elliptical Fourier Analysis.\n5) Line 576: Typographic error; was it six or seven niches?\nThe extra number has been removed.\n6) Line 638: Perhaps the authors could elaborate on how their performance metrics provide any “direct link to specific flight behaviors”. This comment is probably best addressed by setting up some discrete predictions (see major concern #3).\nAlong with modifications to the discussion and introduction, the discussion section c had been modified to make more explicit which bird groups each of the four functional metrics are hypothesised to be optimising for, with reference made to table 1. We hope that the addition of these predictions into the main text further clarifies what we mean when we say that a bird group should be optimal a particular metric or combination of metrics.\n7) Line 661: How are these planforms defined?\nAdditional clarification of what we mean by planform and how the information was captured has been added to section 2a of the methodology. This should hopefully explain that planform here represents the outline of the righthand wing when viewed from directly above.\n8) Line 688: I know that this equation is well-presented in the supplement of Harvey et al., but it would be helpful to define the terms here, especially as they pertain to the present data and methods.\nTo better explain how the formula derived by Harvey et al. relates to out theoretical planforms, additional clarification of terms has been added to section d of methods, with explanation of how these parts were calculated for theoretical outline shapes.\nReferences:\nRader JA, Hedrick TL, He Y, Waldrop LD. 2020. Functional Morphology of Gliding Flight II. Morphology Follows Predictions of Gliding Performance. Integrative and Comparative Biology 60:1297–1308.\nWaldrop LD, He Y, Hedrick TL, Rader JA. 2020. Functional morphology of gliding flight I. Modeling reveals distinct performance landscapes based on soaring strategies. Integrative and Comparative Biology 60:1283–96."}, {"round": 2, "reviewer_comments": {"reviewer_1": "I reviewed an earlier iteration of this paper before, and this version is stronger and does address concerns from reviewers. I think this is an acceptable version for publication.\nOne minor comment:\nLine 85-86 – awkward phrasing, I’d suggest rearranging: “...represented on PC1 (53.75%) which describes the breadth of the wing chord, because all planforms are scaled to identical length.” (“since” is a time word, “because” is causal.)", "reviewer_3": "Your innovative study of the planform of avian wings is fascinating and worthwhile. With one exception which I describe below, in general, I perceive that you revised your earlier manuscript in agreement with the recommendations of two reviewers. Specific to the major concerns of reviewer 2, your revisions effectively addressed concern 1 (Optimization is mixed), 3 (specific predictions and testing framework) and 4 (calculation of phylogenetic signal).\nOn the issue of using morphological proxies for performance (Reviewer 2 concern 2), I suggest that it is still not clear that your proxies are generally untested hypotheses about relationships between form and flight performance. You describe empirical properties and functional performance in ways that give the incorrect impression that there is strong evidence from prior studies when such evidence is lacking, particularly for your proxies of maneuverabilty and agility. Thus, I encourage you to add language throughout the manuscript that clarifies that your proxies are hypotheses that merit future empirical tests. Here are specific locations:\nLine 11: Instead of “Empirical properties” use “Hypothesized empirical properties”\nLine 13: Insert “hypothesized” before “functional performance and optimality”\nLine 17: Insert “hypothesized to be” before “linked with efficient”\nLine 62: Change wording for “established” Perhaps aspect ratio is adequately established as a proxy for cost of transport given various empirical studies, but the other proxies (2nd moment of area, agility index and tip anglehave not been adequately tested empirically as proxies for maneuverability, agility and induced power requirements, respectively.\nLine 66: Insert “hypothesized” before “flight optima”\nLine 78: Insert “hypothesized” before “functional optimality”\nLine 103: Change header by inserting “Hypothesized” before “Functional Performance” This information is lacking on Line 17,\nAdditional Comments:\nIn most cases when you use the word efficiency, it would be helpful to define the numerator and denominator, at least at first use. This might be lift:drag ratio, cost of transport (Joules per meter) or rotational efficiency (perhaps rotational energy per unit aerodynamic work). Specific instances include Line 17, Line 212, Line 232, Line 703, Line 747, Table 1 (first row below headers).\nManeuverability versus Agility: It would be helpful to define the difference between maneuverability and agility and clarify if there is any redundancy between Savile’s and Harvey’s predictions for the relationship between planform and the ability to vary body pitch. If the 2nd moment of area is large, the Savile (and later Rayner and Norberg) hypothesis seems to be that the aerodynamic surfaces are distributed relatively far from the axes of the body originating at the center of mass, so the wings can establish large rotational moments, presumably about the roll, pitch and yaw axes. The agility index of Harvey et al is specific to the ability to modulate pitch stability. Perhaps these proxies are not redundant if Savile's predictions are more for roll rather than pitch.\nMany-to-One versus Pleiotropy (One-to-Many). I feel you or perhaps Reviewer 1 may have misinterpreted “many to one” being a potential explanation for why the planforms of birds occupy a subset of the potential morphospace. Many to one is a form of phenotypic redundancy, where many traits accomplish one performance. In the case of the Wainwright et al study you cite, the multibar linkage systems in the jaws of fish have many components that contribute to feeding. Redundancy is hypothesized to increase evolvability, because directional selection can act on one phenotypic trait while the necessary performance (e.g. feeding) is accomplished by other traits. I think the wings of birds are the reverse, where for many species one pair of wings must accomplish a variety of tasks (takeoff, cruising, gliding, maneuvering or even things like shading young from the sun or producing feather sounds (sonations) during sexually-selected displays or to alert conspecifics about danger from predators). This is therefore an example of one-to-many or pleiotropy, and it is hypothesized that one phenotype accomplishing many functions tends to constrain evolvability. A discussion of these ideas is available in:\nBergmann, P. J., & McElroy, E. J. (2014). Many-to-many mapping of phenotype to performance: an extension of the F-matrix for studying functional complexity. Evolutionary Biology, 41(4), 546-560.\nalso see:\nGhalambor, C. K., Walker, J. A., & Reznick, D. N. (2003). Multi-trait selection, adaptation, and constraints on the evolution of burst swimming performance. Integrative and comparative biology, 43(3), 431-438.\nFigure 4: Consider using a different marker (e.g red dots) for the species in the performance groups you highlight at the top of each panel. For example, in panel 1, make all the marine soarer dots a different color than black so that it is easier to understand which species are near the optima.\nBody Size: You mention that body size is a critical element not included in your metrics (Line 679). I suggest slightly more information would be helpful, and you might move some of this to the discussion. Yes, wing loading increases with increasing mass as you hint at on line 679, but also maximum mass-specific power available from the flight muscles is understood to decline as a function of increasing body mass, which is thought to explain why the smallest birds can easily out maneuver larger birds (e.g. mobbing behavior, aerial combat in hummingbirds, hawking in small passerines). Stated another way, most small birds are highly maneuverable and agile because they have marginal power to spare, and this may help explain why passerines, which are mostly on the small end of the range of body masses in birds, do not emerge from your study as having optimal planforms.\nSigned: Bret Tobalske"}, "author_response": "REVIEWER COMMENTS\nReviewer #1 (Remarks to the Author):\nThe authors explore the range of existing avian wing shape relative to theoretical\npossibilities, a very fun question for the functional morphology community, and not\noften done. This is an important framework to think about how things have evolved\nthe way they do and what may be guiding or constraining their direction of evolution.\nI made some comments below which I think could improve the manuscript, but I think\nit is going to be a good addition to the journal after revisions.\nLine 80 – would this be better described as the wing aspect ratio? Based on the\ndescription in the next sentence, it sounds like PC1 is breadth of the wing chord\nrelative to the wing length, not breadth of wing chord in isolation. Or is this a raw\nmeasurement of wing chord?\nA phrase has been added here clarifying that all planforms, both theoretical and\nempirical are scaled to identical length. Due to this scaling the breadth of the chord,\nwhile functionally equal to aspect ratio, is better described as a raw measurement of\nthe chord itself.\nLine 138 – no suppl. fig number given\nA supplementary figure number has been provided to fix this oversight.\nLines 144-146 – dominant by passerines or by non-waterbirds? I see passeriforms,\nbut also cuculiforms, and galliforms on the far right. With all the other clades in that\nregion that are hidden due to density of data points, I’d recommend being more\ninclusive with taxa listed in this contrasting statement, especially if non-passerine\npasseriforms are included in the analysis.\nThis passage has been rephrased to include Cuculiformes and Galliformes and to\nuse the broader clade level designation Passeriformes rather than passerines, which\npreviously suggested a more restricted class.\nLine 156 – extra “/” included\nThe extra / has been removed\nLine 157 – “Wang” instead of “Wange”\nThe spelling of Wang has been corrected\nLine 162-163 – “burst flapping” should be hyphenated when used as an adjective\nA hyphen has been added between burst and flapping\nLine 164 – passerines or passeriforms? Taxonomic categories here are of the order\nlevel, so it may make more sense to refer to the group as passeriforms instead of\npasserines, which is a subset of Passeriformes.\nPasseriforms has been substituted for passerines to in order to better clarify that we\nare referring to the entirety of the clade.\nThoughts on section at 166 – What about the idea of many-to-one mapping? (See\nWainwright et al. 2005: https://academic.oup.com/icb/article/45/2/256/778330) Or the\nrelated idea of “this shape is sufficient for the task; taking the whole organism and its\ncollection of needs and behaviors, it’s good enough.” Wings are not in isolation of the\nrest of the body, which would be a source for further constraints on empirical wing\nshape that could limit the amount of theoretical wing shape space that is achieved in\nreality.\nThis is an excellent point, that the rest of the animal is a likely source of constraint on\nthe shape of the wing planform. While this will not affect the performance of the\ntheoretical shapes, the elements tested by the analysis, it does warrant comment in\nreference to discrepancies in empirical wings. An acknowledgement of this and of\nmany-to-one mapping has been added to the end of section a of the discussion.\nThoughts on sections at 185 – This is very interesting. Might differences in data\ncollection protocols affect the differences found between the authors’ phylogenetic\nsignal and that of Wang and Clarke 2015? They also captured the covert outline too.\nBut it’s true that scale of analysis would also play a large effect.\nA sentence has been added here acknowledging that the addition of covert\nfeathering data by Wang and Clarke may also be a factor contributing to the\ndiscrepancy in phylogenetic signal between the datasets.\nLine 217 (and throughout discussion) – Thinking about terms like “cost-efficient” and\n“optimal/non-optimal,” clear biological context matters with these sorts of statements.\nAn albatross wing has a high aspect ratio and therefore optimal for soaring in an\nopen marine environment, but it is not optimal for maneuvering in a forest. Relative\nto an albatross, a robin wing has a low aspect ratio and is therefore optimal for\nmaneuvering the forest, but not optimal over the ocean. An albatross’s flight in a\nforest would be much less cost-efficient than it would be over the ocean, as it would\nexpend significantly more energy struggling to get through the forest. So a high\naspect ratio wing would be cost-efficient for certain behaviors in certain habitats, a\nlow aspect ratio wing would be cost-efficient for other behaviors and other habitats,\netc. And if they do wing-propelled diving, there could be a third “most cost-\nefficient/optimal shape” for that behavior, accounting for flapping through the water,\nas discussed later. Each plot shows optimum shape space for very specific traits or\nbehaviors, so authors should make sure the discussion text always reflects that sort\nof precise articulation of the context of things like “optimal.”\nWe agree that what is optimal in wings varies across bird groups and have made\nadjustments to the discussion to highlight that different groups of birds are\nhypothesised as optimal for specific flight styles. These hypotheses are made in\nreference to table 1 and are expanded upon in methods section c. additions have\nbeen made to methods section c to state which bird groups are hypothesised to be\noptimised for each flight style, linking table 1 into the text. We have also more\nexplicitly outlined in the introduction that this is what underpins our analysis. We\nhope that this additional context improves the clarity of the underlying hypothesis\nthat specific bird groups should experience functional pressure toward the\ndevelopment of optimally shaped wings for specific flight styles.\nLine 232 – Good for including Pelagornis! I had written a thought that it should be\nmentioned somewhere, but deleted that thought, since I found it here.\nWe are glad to see that Pelagornis is a welcome addition, no change is necessary in\nresponse to this comment.\nParagraph starting at line 298 – be very precise about what optimal means in this\ncontext; there are many different biological adverbs that could be added to change\nthe meaning of the “optimals” throughout the paragraph – optimal for which aspect of\na bird’s biology or behavior?\nThe use of optimal to refer to both areas in morphospace and planform shape\ncreated some confusion., the paragraph has been restructured to clear up this\nconfusion and specify when optimality refers to either the planforms or the areas of\nhighest performance.\nLine 567 – What does “characterized as outline shapes” entail? Wang and Clarke\n2015 and Baumgart et al. 2021 use 2d landmarks to capture an outline. Which\nsoftware was used to generate an outline of the wing? How was wing shape data\ncollected from the outline?\nAdditional information about the initial capture of outline data and its digitisation has\nbeen added to methods section 2a including which programs were used for\ngenerating outline data from wing images.\nLine 576 – “characterize seven six niches” – should pick a number\nThe number 7 has been removed to correct this oversight.\nReviewer #2 (Remarks to the Author):\nIn the manuscript “Bird wing planform shape is highly optimised for flight style”, the\nauthors test the link between wing shape and flight style in birds using a new dataset\nand a creative morphometric approach. The authors created a theoretical\nmorphospace onto which they have mapped flight “performance” metrics to create\nhypothetical performance spaces, which they paired with empirical shape measurements from a large number of avian taxa to test for functional optimization of\nwing morphology. The authors report some evidence for shape optimization, which is\nindependent of phylogenetic effects. The manuscript is clear and well-written, and\nthe subject will be of broad interest to the flight community. The figures, also, are\nvery nice and well-presented. However, some aspects of the predictions and results\nremain unclear, and I do not believe that the authors have conducted the requisite\ntests to support their main claim. As such, I believe that some revision is necessary\nprior to publication. Below, I detail my major concerns with the study, as presented,\nfollowed by minor issues that should be addressed prior to publication.\nMajor concerns:\n1) My first major concern with the study is that I do not find tests that adequately\nsupports the main assertion of the manuscript, that “Wing planform shape is highly\noptimized for flight style”. My concern here is two-fold. First, I find the evidence for\noptimization to be mixed. The results seem to support high pitch agility across most\nof the studied species, and the species also cluster on a plateau of high second\nmoment of area. Aspect ratio and tip angle show gradients, with one end\napproaching the putative “optima”, but the other end being far from it. In the\ncomposite performance surfaces, however, the species actually appear to sit within\npareto valleys rather than being on peaks or ridges. I was rather hoping that the\nauthors would discuss that, but they did not. My second concern is that while the\nauthors did make an effort to quantify the proximity to the “optima” (through\nEuclidean distances between group means and the performance optima), I found no\ntest that would discriminate between groups in their degree of optimization. Perhaps\nit would be worth calculating the optimization distance for each species and then\ndoing a phylogenetic ANOVA (or similar) to show whether different groups (either\ntaxonomic groups or behavioral/functional groups) share similar optimization ranges.\nThe Euclidean distance metrics and any subsequent tests do need to be included in\nthe methods (they are not at present) and presented in the results (not in the\ndiscussion as they are now).\nTo address the concern that the main finding of the paper, as expressed in the title,\ndoes not adequately match the findings, we have changed the title to more clearly\nstate that the optimisation of avian wings for flight style is variable and not all groups\nexhibit wings with functionally optimal planform shapes. Since our analysis only tests\nthe functional performance of theoretical shapes relative to each other, and not\nempirical shapes, there exists no discrete performance data for theoretical shapes\nwhich could form the basis of between-group testing. We have emphasised the\nnature of this divide between theoretical and empirical forms to clarify this case.\n2) My second major concern stems from the construction of the morphospaces and\nperformance surfaces. The authors should be careful to note that they are, in most\ncases, using morphological proxies for performance rather than estimates of\nperformance output (the exception here being the pitch agility metric – the rest of the\n“performance” surfaces are simply morphological traits). While the relationships\nbetween these morphological traits and their influence on flight performance are\nwell-documented, it is unclear whether it is safe to assume a linear association\nbetween morphology and performance. I don’t have a problem with the use of these\nshape traits as proxies, but the authors should probably note this as a caveat of the\nstudy. Additionally, it is unclear how the authors arrived at the 20% figure to expand\ntheir theoretical grid space. This is an important consideration, because many\nperformance traits do scale continuously (though not necessarily linearly) with shape\n– for example, the authors use aspect ratio as a proxy for flight efficiency. Indeed,\nwing aspect ratio is related to flight performance metrics like drag coefficient and lift-\nto-drag ratio, but the morphospace that the authors present appears to covary\nstrongly with aspect ratio, so using it as a performance surface superimposed over\nthe morphospace seems circular. It would be better to choose a true measure of\nflight performance (see Rader et al. 2020; Waldrop et al. 2020) rather than using the\nproxy.\nThe introduction has been modified to express that the performance metrics tested\nrepresent proxies for performance based on established understanding of the\nrelationship between morphology and function. These proxies do not represent a\ntrue measure of performance output, and this is why we only test theoretical chapes,\nrather than the empirical planforms. This is the benefit of theoretical morphology as it\nallows us to produce analyses of relative functional performance independent of\nattempting to ascertain the discrete performance of individual taxa. To avoid\nconfusion, we have adjusted the phrasing of the introduction to better emphasise this\ndivide and that only theoretical shapes are tested with the functional proxies.\nAdditionally, the 20% figure for expanding morphospace is determined by the limits\nof theoretical shape generation, producing theoretical shapes what are possible and\nnot too far from winglike shapes. It would hypothetically be possible to expand this\nspace indefinitely to include winglike shapes as well as simple polygons etc. though\nin practice this would be unnecessarily computationally expensive and include a vast\nnumber of self-intersecting forms which are impossible and therefore untestable. We\nhave added clarification of this point to section b of the methods to clarify this point.\n3)I think that it would be helpful for the authors to set up more explicit predictions\nabout how wing morphology is expected to vary with flight style / performance in the\nintroduction, and then to follow a more rigorous hypothesis testing framework\nthroughout the analyses. As the manuscript is currently presented, I struggled to\nunderstand what the authors were predicting, which made it difficult to ascertain\nwhether the methodological approach was appropriate for the questions.\nThe introduction has been expanded to include reference to the underlying\nhypothesis that specific bird groups should possess optimal planforms for specific\nmetric combinations, with reference to table 1 which outlines the flight style groups\nanalysed and their link to specific metric combinations. This was previously\nunderemphasised within the introduction and hopefully has now been reinforced.\n4) How was phylogenetic signal calculated for the dataset? In the methods, the\nauthors list the gm.prcomp command, but in the results they talk about the kmult\nstatistic (which does not appear in the methods).\nThe section of methods addressing the calculation of phylogenetic signal has been\namended to draw distinction between he commands used for phylogenetic signal,\nwhich generate a multivariate k statistic (kmult) and the command used for ancestral\nshape reconstruction, gm.prcomp.\nMinor concerns:\n1) Line 109: I’m not sure about “tongue-shaped” as a descriptor.\nThe term tongue-shaped has been replaced with “a rectangular region of optimality”\nto improve specificity in description of the shape of the optimal peak.\n2) Double check spelling of references throughout.\n- Line 157: “Wang and Clarke” is misspelled\n- Line 389: “Rader and Hedrick” is misspelled\nThese misspellings have been corrected\n3) Some discussion of how the present results compare to 3-dimensional analyses\n(e.g., Rader and Hedrick 2023 and Rader et. al 2020) might be welcome.\nReference has been added to the existence of these 3-dimentioanl studies in the\nintroduction and comparison of our results to those of Rader et al. 2020 has been\nadded to section c of the discussion.\n4) Line 571: Define EFA.\nThis acronym has been expanded to Elliptical Fourier Analysis.\n5) Line 576: Typographic error; was it six or seven niches?\nThe extra number has been removed.\n6) Line 638: Perhaps the authors could elaborate on how their performance metrics\nprovide any “direct link to specific flight behaviors”. This comment is probably best\naddressed by setting up some discrete predictions (see major concern #3).\nAlong with modifications to the discussion and introduction, the discussion section c\nhad been modified to make more explicit which bird groups each of the four\nfunctional metrics are hypothesised to be optimising for, with reference made to table\n1. We hope that the addition of these predictions into the main text further clarifies\nwhat we mean when we say that a bird group should be optimal a particular metric or\ncombination of metrics.\n7) Line 661: How are these planforms defined?\nAdditional clarification of what we mean by planform and how the information was\ncaptured has been added to section 2a of the methodology. This should hopefully\nexplain that planform here represents the outline of the righthand wing when viewed\nfrom directly above.\n8) Line 688: I know that this equation is well-presented in the supplement of Harvey\net al., but it would be helpful to define the terms here, especially as they pertain to\nthe present data and methods.\nTo better explain how the formula derived by Harvey et al. relates to out theoretical\nplanforms, additional clarification of terms has been added to section d of methods,\nwith explanation of how these parts were calculated for theoretical outline shapes.\nReferences:\nRader JA, Hedrick TL, He Y, Waldrop LD. 2020. Functional Morphology of Gliding\nFlight II. Morphology Follows Predictions of Gliding Performance. Integrative and\nComparative Biology 60:1297–1308.\nWaldrop LD, He Y, Hedrick TL, Rader JA. 2020. Functional morphology of gliding\nflight I. Modeling reveals distinct performance landscapes based on soaring\nstrategies. Integrative and Comparative Biology 60:1283–96.\nREVIEWER COMMENTS\nReviewer #1 (Remarks to the Author):\nOne minor comment:\nLine 85-86 – awkward phrasing, I’d suggest rearranging: “...represented on PC1\n(53.75%) which describes the breadth of the wing chord, because all planforms are\nscaled to identical length.” (“since” is a time word, “because” is causal.)\nThis sentence has been rewritten to fit the reviewers improved phrasing and to\nreplace ‘since’ with ‘because’.\nReviewer #3 (Remarks to the Author):\nOn the issue of using morphological proxies for performance (Reviewer 2 concern\n2), I suggest that it is still not clear that your proxies are generally untested\nhypotheses about relationships between form and flight performance. You describe\nempirical properties and functional performance in ways that give the incorrect\nimpression that there is strong evidence from prior studies when such evidence is\nlacking, particularly for your proxies of maneuverabilty and agility. Thus, I encourage\nyou to add language throughout the manuscript that clarifies that your proxies are\nhypotheses that merit future empirical tests. Here are specific locations:\nLine 11: Instead of “Empirical properties” use “Hypothesized empirical properties”\nLine 13: Insert “hypothesized” before “functional performance and optimality”\nLine 17: Insert “hypothesized to be” before “linked with efficient”\nLine 62: Change wording for “established” Perhaps aspect ratio is adequately\nestablished as a proxy for cost of transport given various empirical studies, but the\nother proxies (2nd moment of area, agility index and tip anglehave not been\nadequately tested empirically as proxies for maneuverability, agility and induced\npower requirements, respectively.\nLine 66: Insert “hypothesized” before “flight optima”\nLine 78: Insert “hypothesized” before “functional optimality”\nLine 103: Change header by inserting “Hypothesized” before “Functional\nPerformance” This information is lacking on Line 17,\nThe suggested insertions have been made to better reflect the degree of clarity in\nthe scientific understanding of the link between the empirical properties tested in this\nanalysis and their link to flight performance. Additionally, the word ‘established’ in line\n62 has been replaced with ‘proposed’ to further emphasise this point.\nIn most cases when you use the word efficiency, it would be helpful to define the\nnumerator and denominator, at least at first use. This might be lift:drag ratio, cost of\ntransport (Joules per meter) or rotational efficiency (perhaps rotational energy per\nunit aerodynamic work). Specific instances include Line 17, Line 212, Line 232, Line\n703, Line 747, Table 1 (first row below headers).\nThe manuscript has been edited to replace the term ‘efficiency’ with the more\nrelevant descriptor of low transport cost flight. This should hopefully reduce\nconfusion about the nature of the metric used as higher aspect ratio is a proxy for\nenergy savings through drag reduction. The addition of units for efficiency is not\nrelevant to this research as efficiency is not the metric being tested.\nManeuverability versus Agility: It would be helpful to define the difference between\nmaneuverability and agility and clarify if there is any redundancy between Savile’s\nand Harvey’s predictions for the relationship between planform and the ability to vary\nbody pitch. If the 2nd moment of area is large, the Savile (and later Rayner and\nNorberg) hypothesis seems to be that the aerodynamic surfaces are distributed\nrelatively far from the axes of the body originating at the center of mass, so the\nwings can establish large rotational moments, presumably about the roll, pitch and\nyaw axes. The agility index of Harvey et al is specific to the ability to modulate pitch\nstability. Perhaps these proxies are not redundant if Savile's predictions are more for\nroll rather than pitch.\nThe methods section of the paper has been altered to better reflect the difference s\nbetween agility and manoeuvrability, emphasising that these metrics describe\nmovement on different axes with agility a function of pitch and manoeuvrability yaw.\nThis demonstrates that there is no redundancy between these metrics and, while\nboth characterise change in direction in space, they refer to different specific aspects\nof this movement.\nMany-to-One versus Pleiotropy (One-to-Many). I feel you or perhaps Reviewer 1\nmay have misinterpreted “many to one” being a potential explanation for why the\nplanforms of birds occupy a subset of the potential morphospace. Many to one is a\nform of phenotypic redundancy, where many traits accomplish one performance. In\nthe case of the Wainwright et al study you cite, the multibar linkage systems in the\njaws of fish have many components that contribute to feeding. Redundancy is\nhypothesized to increase evolvability, because directional selection can act on one\nphenotypic trait while the necessary performance (e.g. feeding) is accomplished by\nother traits. I think the wings of birds are the reverse, where for many species one\npair of wings must accomplish a variety of tasks (takeoff, cruising, gliding,\nmaneuvering or even things like shading young from the sun or producing feather\nsounds (sonations) during sexually-selected displays or to alert conspecifics about\ndanger from predators). This is therefore an example of one-to-many or pleiotropy,\nand it is hypothesized that one phenotype accomplishing many functions tends to\nconstrain evolvability. A discussion of these ideas is available in:\nBergmann, P. J., & McElroy, E. J. (2014). Many-to-many mapping of phenotype to\nperformance: an extension of the F-matrix for studying functional complexity.\nEvolutionary Biology, 41(4), 546-560.\nalso see:\nGhalambor, C. K., Walker, J. A., & Reznick, D. N. (2003). Multi-trait selection,\nadaptation, and constraints on the evolution of burst swimming performance.\nIntegrative and comparative biology, 43(3), 431-438.\nAdditional text has been added to the end of discussion section 3a address the\npossibility of pleiotropy as a constraint on bird wing shape. This form of constraint is\nlikely one of many factors which combine to drive the differential evolution of optimal\nwings across the dataset, and its inclusion makes for a more comprehensive\ndiscussion of flight constraints. Additionally the two proposed references have been\nadded to the citation list.\nFigure 4: Consider using a different marker (e.g red dots) for the species in the\nperformance groups you highlight at the top of each panel. For example, in panel 1,\nmake all the marine soarer dots a different color than black so that it is easier to\nunderstand which species are near the optima.\nBody Size: You mention that body size is a critical element not included in your\nmetrics (Line 679). I suggest slightly more information would be helpful, and you\nmight move some of this to the discussion. Yes, wing loading increases with\nincreasing mass as you hint at on line 679, but also maximum mass-specific power\navailable from the flight muscles is understood to decline as a function of increasing\nbody mass, which is thought to explain why the smallest birds can easily out\nmaneuver larger birds (e.g. mobbing behavior, aerial combat in hummingbirds,\nhawking in small passerines). Stated another way, most small birds are highly\nmaneuverable and agile because they have marginal power to spare, and this may\nhelp explain why passerines, which are mostly on the small end of the range of body\nmasses in birds, do not emerge from your study as having optimal planforms.\nThree additional sentences have been added to discussion section f to incorporate\nthis idea. The relaxation of constraint as a result of proportionally greater muscle\npower may help to explain the lack of optimality in passerine birds but critically is not\na universal trend as hummingbirds posess optimal planforms and appear to be\nhighly constrained by function despite their size. The text of the article has been\nedited to reflect this."}]

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