• “Bird Bones and Living Habits”; sourced from Kaggle
• 420 observations (skeletons) and 12 variables
• Continuous: length and diameter measurements (in mm) of 5 key bones
• Categorical: ecological group

• The goal is to analyze the robusticity (a measure of relative thickness) of the bones in the data set to assess trends across ecological groups.

• Primarily, we’re interested in differences between wing and leg robusticity across groups.

• One possibility to keep in mind: “Flightless birds generally have robust hindlimbs and reduced forelimbs, whereas hyperaerial birds locomote almost exclusively by wing and typically have robust forelimbs and reduced hindlimbs. Bimodal birds fall between these extremes and include more hindlimb-dominated and more forelimb-dominated species” (Heers et al).

• That’s from a paper that covers a wide range of morphological variables that contribute to flight. This remark may also be taking mass into consideration. All the same, it’s something we can keep in mind.

Data manipulation

1. Add individual bone measurements to attain limb measurements

2. For each limb, Robusticity Index (RI) = diameter / length

3. For each group, we’ll asses the difference between the two indices: wing RI - leg RI

Let’s take a bird’s eye view at our initial quartet of variables we’ll be expanding on:

• Wing length
• Wing diameter
• Leg Length
• Leg diameter

Vertical lines are means.

• One way to start getting a sense of robusticity is to plot diameter (y) and length (x) via scatter plots.

• Essentially, the slope of the linear regressions (m in y = m * x) will represent our RI.

• Diameter = RI * length.

Before we jump into graphing, let’s use a Pearson correlation test and a linear regression model to get a general sense of the relationship between the diameter and length of the wing and leg bones in this data set.

Wing:
Pearson’s r: 0.91.
Adjusted R-Squared: 0.829.

Leg:
Pearson’s r: 0.889.
Adjusted R-Squared: 0.79.

Linear models makes sense for these data.

Trends at a glance:

• Terrestrial birds and singing birds have relatively robust wings.
• Swimming birds and wading birds have relatively “gracile” (non-robust) wings.

Trends at a glance:

• Raptors and swimming birds have relatively robust legs.
• Wading birds and scansorial birds have relatively gracile legs.

Already, we’re getting a sense that, for any given group, wing robusticity doesn’t necessarily correlate with leg robusticity. Let’s look at the two sets of regressions side by side.

• Another way to analyze robusticity is to calculate RI for each limb of each observation.
  
• Two new variables: Wing RI and Leg RI.
  
• This makes it easier to assess the robusticity of the limbs in relation to one another.

We already guessed that there isn’t a strong correlation between wing robusticity and leg robusticity. A correlation test and linear regression model bear that out:

• Pearson’s r of Wing RI and Leg RI: 0.158.
  
• Adjusted R-Squared: 0.022.

Linear regression lines don’t make sense here, given that the adjusted R-squared is 0.022.

• Let’s take those mean values of wing RI and leg RI and calculate the differences.
• The results will give us one possible answer to our initial question.

• Return to hypothesis: “Flightless birds generally have robust hindlimbs and reduced forelimbs, whereas hyperaerial birds locomote almost exclusively by wing and typically have robust forelimbs and reduced hindlimbs. Bimodal birds fall between these extremes and include more hindlimb-dominated and more forelimb-dominated species.” (Heers et al).

• Curiously, the two ecological groups that best seem to correspond to flightless and hyperaerial birds (terrestrial birds and songbirds, respectively) both land squarely on the “robust forelimbs” end of the spectrum.

• That said, the general expected distribution holds up: some groups have notably more robust wings than legs, some have notably more robust legs than wings, and others land in between.

A somewhat simpler question that comes to mind (and one whose answer we can already intuit) is: across the entire data set, do wings or legs tend to be more robust?

Wing RI distribution appears to be somewhat bimodal, with more variation.

Variations in Wing RI seem to account for more of the differences across groups.

• The six ecological groups listed in this data set aren’t standard taxa and don’t map onto the scientific literature.
• The data set lacks information about species, and we know there can be immense variation among species within a taxon. Such group-level data can be skewed significantly as a result.

Figure from “Scaling and functional morphology in strigiform hind limbs” by Madan et al.

Data

https://www.kaggle.com/datasets/zhangjuefei/birds-bones-and-living-habits

Research Cited

“New Perspectives on the Ontogeny and Evolution of Avian Locomotion” by Ashley M. Heers. Integrative and Comparative Biology, volume 56, number 3.

“Scaling and functional morphology in strigiform hind limbs” by Meena A. Madan, Emily J. Rayfield & Jen A. Bright. Nature.com Scientific Reports, 2017.

“Functional Morphology of Raptor Hindlimbs: Implications for Resource Partitioning” by Andrea B. Ward, Peter D. Weigl, and Rachael M. Conroy. The Auk, volume 119.

Thanks for looking!