Hi Dr. Baudry,
Thank you for your question! Figure 6 shows my own results using all of the data I’ve collected so far on beak shape.

I use the stereo camera setup shown in Figure 3 to obtain 3D curves describing beak shape (the upper ridge of the beak, the culmen, and biting edge, the tomium). An algorithm is used to place a consistent number of evenly-spaced points on each curve. There are three curves with 30 points in three dimensions for a total of 270 variables. I then scale all of the beaks to centroid size (removing the effect of size differences) and use Procrustes superposition to minimize the differences among beaks due to translation and rotation (by sum squared distances). These new 3D Procrustes coordinates (superimposed coordinates) are then the variables with which I perform PCA. In the literature, this is sometimes called Procrustes PCA (Zelditch et al. 2004) or an unweighted Relative Warps Analysis (Figueirido et al. 2011).

Although having evenly-spaced points along 3D curves creates a large number of variables (270 in this case), they are highly correlated with one another. So the PCA can produce a large reduction in dimensionality. In Figure 6, the first principal component (PC) explains 53% of the variance and the second PC explains 35% of the variance. I’ve looked at the third and fourth PCs but haven’t tested whether these additional PCs explain more variance than one would expect by chance.

Your question about the comparison of “beak shape-space” to the phylogenetic tree is especially what got us interested in pursuing this group of birds further. When you apply a phylogenetic tree (based on molecular data) to the beak shape-space you find that for several independent goose lineages, their ancestor likely had a beak shaped more like a duck than a goose. For instance, even though Canada geese, Orinoco geese (found in South America), and blue-winged geese (found in Africa) all have similarly shaped beaks, each represents an independent lineage of geese evolved from a duck-like ancestor. Figure 6 shows this in schematic form. I used a schematic instead of overlaying the actual phylogeny because with all of the internal nodes and branches it is hard to see the path that each branch follows in a static image. In my most recent conference presentation I showed this as an animation with branches extending through beak shape-space over time so you can see lines extending independently from ducks to geese.

We are currently writing up these results for publication and for that we will be testing this against many different evolutionary trees (since they are not fully resolved) to make sure that our result is not sensitive to any one particular topology. Also, I will be collecting data from several more species to have greater coverage of the group. We are comparing our beak shape data against behavior and diet data in the ecological literature (for all species of anseriforms) and finding that these data also support our conclusion! You can trace filter-feeding behavior to near the root of Anseriformes and since geese either rarely or never filter-feed this also supports a duck-like ancestor for all geese.

I would be happy to answer any additional questions you might have!
Thanks,
Aaron

Hi Dr. Seeliger,
Thanks for your questions! Figures 8 and 9 are both lever ratios of the bones in bird skulls. They are measurements taken from specimens that predict how much bite force live birds will produce. A good analogy would be measuring the gearing ratios of a bicycle to predict how much force you would expect to apply for a particular gear. So figures 8 and 9 also represent the “gearing” of bird jaws.
The Beak Effective Mechanical Advantage (EMA) in Figure 8 is how much force will be created at the tip of the beak given the same input force to the beak. By making beaks shorter and taller, the EMA is increased, meaning you can get a greater force at the tip of the beak for the same input force. And this is what we observed in geese.
The Kinematic Inlever-Outlever ratio in Figure 9 is analogous to EMA except that this ratio measures the gearing for a joined series of links rather than a single link. That is, for a linkage as shown in Figure 2 and as animated in the video. Here the ratio terms are flipped so a low ratio corresponds to a linkage that outputs a greater force given the same input force. What’s cool is that geese also have a linkage ratio that creates a greater output force given the same input force (significantly lower ratio). So beak dimensions and the geometry of the bones in the skull are consistent with the prediction that geese have a higher bite force than ducks – in addition to differences in muscle mass (only known for a few species) which also tends to be higher in geese.
For me one of the most exciting aspects of this work for future research (and something I plan to continue working on for the rest of my dissertation) is the prospect of using detailed beak shape data as an indicator of beak behavior across birds. Traditionally people have measured beak shape with a just few simple metrics (height, depth, width). This has worked great for finding differences between species or general aspects of behavior. But having 3D curves to describe beak shape allows us to test structure-function relationships with much more precision across the vast diversity of bird feeding systems. This will make bird beaks a more amenable model system for asking detailed questions about how musculoskeletal systems function.
I’d be happy to answer any additional questions you might have! Thanks,
Aaron

Hi Dr. Ramesh,

Thank you for your questions. One trend that is emerging from the study of primate feeding is that jaw skeletal elements appear to evolve more under selection for force production rather than fracture avoidance. Our results from the jaw bones of ducks and geese appear to be showing a similar trend, however it is difficult to separate these two effects.

In terms of applying our results to human musculoskeletal systems it would be premature to make any direct links. However, this research highlights how the bird feeding system presents variation in a number of musculoskeletal elements, each of which could be studied in greater detail with potential application to human health.

For instance, the joint between the upper beak and the neurocranium in birds is highly variable in its torsional resistance. In some birds the joint is pretty much fused while in ducks and geese, for example, it allows for movement. Another chapter of my dissertation will examine how this joint stiffness varies across many different species of birds. Once we know that, we can test how the tissue properties of the joint changes with increasing or decreasing stiffness or how joints with different properties develop differently. These findings could then be applied to arthrology or surgical medicine.

For our understanding of skeletal movement the bird feeding system has one aspect which is particularly ideal. Since the mobile bones of the skull form a closed loop we can more easily predict the motion of the bones (as opposed to a free limb with many more degrees of freedom). This makes it easier to test hypotheses on skeletal movements.

For another chapter of my dissertation I will apply the linkage modeling I featured in the video across a large sample of birds. One possible hypothesis I would like to test is that birds use elastic energy storage (at the joint I mentioned previously, for example) to increase the speed of skeletal movements. The interplay between passive and active mechanisms of skeletal movements is a particularly active area of research in biomechanics currently.

I would be happy to answer any additional questions you might have. Thanks,

Aaron

Hi Dr. Yang,

Thanks for your question. Figures 8 and 9 are histograms comparing the EMA and linkage kinematic ratio, respectively, of geese and ducks. So, the Y axis is just frequency and the X axis are the EMA and kinematic ratio values. The histograms convey graphically the fact that geese and ducks differ significantly in how their beak and cranial bones amplify force – with some overlap in their distributions, of course. In both cases, geese have evolved beaks and skulls that more efficiently transmit force from muscles in the back of the skull to the tip of the beak (for cutting vegetation such as grasses and stems).

I’d be happy to answer any additional questions you might have! Thanks,
Aaron

Hi Dr. Hager,

Thanks for you question! I should mention that the tree in the poster is actually a supertree combining a number of different molecular phylogenies that have been published over the past 10 years. There is some genetic data on GenBank that has yet to be incorporated into published phylogenies so I did go through and collect most of the genetic data available for this order of birds and run some of the analyses myself. But my results largely confirmed already published phylogenies so I’ve gone with them so far.

With the Hackett et al. (2008) phylogeny as a backbone there’s actually quite a few nodes deep in the anseriform phylogeny with greater than 70% bootstrap values (for Maximum Likelihood). Right now we’re preparing a draft for publication and what I think we’ll end up doing is using the supertree published last year by Jetz et al. What is particularly great about that tree is the authors have published the 10,000 most likely trees from the Bayesian posterior probability distribution (at birdtree.org). So our current plan is to run our analyses over at least 1000 different trees and make sure that our analyses are not sensitive to unresolved nodes.

Where I’ll be looking next is a great question. Since convergence is really what allows for rigorously testing associations between structure and function I am particularly interested in groups of birds that show morphological convergence. And of course, you can only identify convergence when you understand the evolutionary history of a group.

One candidate group are pursuit divers. A friend and colleague of mine, Nate Smith, has done some great work looking at the suite of morphological characters associated with the independent acquisition of pursuit diving, including body mass and osteological pneumaticity (Smith 2011). I think it would be great to look at skull and beak shape. Even anseriforms have gotten in the pursuit diving game with Mergansers and Smews!

I’d be happy to answer any additional questions you might have.

Thanks,
Aaron

Thank you Dr. Falk! All but one of the live bird photos were taken by a friend of mine, Arlene Koziol, who is an excellent wildlife photographer and who was kind enough to allow me to use her photos in my video.

Thanks Tie Bo, glad you enjoyed it!

Thanks Arlene!

Thank you Dr. Torres, it was a lot of fun to make!

Thank you Dr. Bhanu,

So far I’ve had some really interesting results applying these methods to the bird order Anseriformes, which includes ducks, geese, swans and mergansers. Since the 3D beak shape data I’m collecting gives a much more detailed indication of how birds are feeding in the wild, I am getting better resolution among different feeding behaviors than with simple caliper measurements (the current standard).

With this enhanced resolution of beak shape I’ve been able to model the ancestral beak shapes from which ducks and geese most likely evolved (the subject of my poster). I’ve found consistently that goose shaped beaks have evolved at least four times from ancestors with duck-shaped beaks – and ecological data generally support this finding. Additionally, I’ve used the data I’m collecting to produce quantitative predictions of how the different geometries of cranial bones among these birds affect movement and force output of the beak. I’ve found that for the same muscle force geese have beak and skull shapes that more efficiently transmit force in feeding.

I’d be happy to answer any additional questions you might have! Thanks,
Aaron