The size of the Haast's eagle

[blaze]

Some weeks I noticed something weird in Brathwaite (1992), the publication that estimates the weight of Harpagornis at 11.5kg for males and 14.5kg for females. Quote:

The longest ulna of Haast's Eagle in Canterbury Museum (AV36405; 279 mm) was 17% longer than that of the Otago Museum skeleton (C40.8). Weight is proportional to the cube root of linear dimensions but the square root of areas. As ulna length is a measure of wing area rather than of body size, body weight should be proportional to the linear measurement cubed divided by the measurement squared. Therefore, the female weight was calculated as male weight x 1.17^3/2 which gave 11.5 x 1.27 = 14.46 kg for the female.

How true is the bolded part? I suppose larger animals need longer/larger wings but are the male and female so far apart in size that the female already needs proportionally longer wing bones to support a weight increase of 27% rather the 60% suggested by isometric scaling? He didn't provide evidence that the ulna was only proportionally longer so in lack of more data I don't think isometric scaling or something close to it can be ruled out thus the female could have actually weighted 18.4kg.

But there's more:

His weight estimate was based on comparing an skeleton of an Harpagornis mounted in the Otago Museum with those of two other eagles, he found that it had a torso 1.05 * 1.36 * 1.32 the dimensions of that of a white-bellied sea eagle and 1.26 * 1.73 * 1.58 those of a wedge-tailed eagle. Harpagornis seems to have had a proportionally much deeper and wider torso, being not much greater in length... or did it?



This is the skeleton he measured, let's compare it with other eagle skeletons: 1, 2, 3, 4, 5. IMO it's clear that is badly mounted, with the shoulder girdle too far back in the torso, in the other eagle skeletons measured by Bratwaite (1992) the length of the torso is exactly 2.25 times the width and between 3.3 and 3.5 times the depth if we apply those proportions to the Harpagornis skeleton we get a torso length between ~428mm and ~460mm

Let's take 428mm so now the skeleton is 1.59 * 1.73 * 1.58 times the dimension of the wedge-tailed eagle skeleton, which suggests a volume 4.35 times greater (compared to 3.44 previously), according to the sources given by Brathwaite (1992) the average weight of the wedge-tailed eagle is 3.4kg (Brown and Amadon, 1968), thus the Harpagornis could have weighted 14.8kg meaning that the largest female could have weighted 23.7kg.

Does it seem too heavy? while not necessarily accurate in this case, Campione et al. (2014) equation for theropd body mass gives a mass of 18-19kg to the type specimen of Harpagornis based on its femur circumference of 63.5mm (greater than a dire wolf's) and guess what? the type specimen is only ~1.5% bigger than the average, on average the largest known bones of Harpagornis are 7.4% bigger than those of the type specimen (Holdaway, 1990) which scaled up from the femur circumference estimate results in masses of 22-24kg.

This is certainly not definitive but it gives food for thought.

[Infinity Blade]

Nice!

I think you also stated that Harpagornis had a femur circumference as great as that of the humeri of 40-50kg cougars, leopards, and jaguars, and I assume this is the type specimen in particular being referred to (I heard a figure of 63.5mm on Carnivora). Such an impressive animal.

[blaze]

Yes it's the type specimen.

I just compared the lengths of bones that Holdaway (1990) gives for harpy eagles and Harpagornis, excluding the measurements of the wing bones*, Harpagornis is 34-35% bigger both at average and at max size, which again suggests that the largest known females could have reached 20kg in mass (assuming 6.5 and 9kg for average and max weight of harpies and assuming Holdaway's sample is representative of that weight range).


*the wing bones reduce the average which suggests Harpagornis had proportionally shorter wings than the harpy, probably further adaptation to living in the forest.

[coherentsheaf]

"How true is the bolded part?"

To my knowledge not at all. this paper observed the quadratic entity ulnar length multiplied by secondary length to explain 98% of the variance in wing area, strongly suggesting that Ulnar length is not n a linear relationship with wingarea.

If you want we ca use the tables in the peper to construct a regression equation for predicting body mass from ulnar length.

[coherentsheaf]

Ok I have gone trhough the data now, from: www.raison.com.na/raptor%20wing%20areas,%20weights%20and%20loading.pdf

The first thing that catches the eye is that the martial eagle has an ulna almost as long as that of the largest Harpagornis. After making a regression equation (log transformed) I got a predicted mass of about 4kg for the largest Harpagornis so Harpagornis has a punly short ulna or s maybe smaller than often claimed.

The relationship between ulnar length and area is nonlinear but only weekly so.

[creature386]

I would go with the former idea (puny ulna), since I strongly doubt that all the weight estimates for the smaller specimens that are all well above 4 kg are based only on ulnar length. Hence, other bones have to be larger. The femur for example is extremely large, according to Ausar. blaze's argument of proportionally short wings for flying through forests appears convincing.

[blaze]

I suppose that is the case, the longest Harpy eagle ulna out the ones measured by Holdaway was only 229mm, much less than the average of the martial eagle. According to the book Raptors of the world, martial eagles have wingspans up to 240cm while harpies only get up to 200cm despite being twice as heavy.

[creature386]

I just found that the paper cited in the OP even included comments on the puny ulna:

A relatively short ulna is characteristic of broad-winged forms, such as the large forest eagles, and not of open-country species (pers. obs.).

Who do I always forget to read the damn papers before commenting?

BTW, for anyone who is interested in Harpagornis' overall measurements, I recommend →this paper. The tables 2 and 3 nicely demonstrate that Harpagornis has a notably greater humerus:ulna ratio than the harpy eagle which would support the notion of the broad-wing adaptations being more pronounced in it.

[blaze]

I had not noticed that either lol

[theropod]

Shouldn’t an ulna that’s 17% longer imply a wing area 37% greater ((1.17²-1)×100%), assuming the wing proportions remain the same? So given weight is proportional to wing area (is it?), the ulna’s owner would have been about that much more massive. That’s much more cautious than isometric scaling, and yet it still gives us a body mass of roughly 20kg using blaze’s
assumptions about the animal’s volume.

[blaze]

I suppose it could go that way too, there's also some other things to consider, while Haast originally gave the length of the ulna of the male at 238mm and this is the measurement Brathwaite used, the specimen actually preserves both one is 231mm and the other 236mm, for an average of roughly 234mm (Holdaway, 1990), which makes a 279mm ulna roughly 19% bigger not 17%, still, it would be nice to know the allometry of Harpagornis, comparing the measurements of the Otago male and the type specimen we find that the type is bigger by this amount:

Ulna L: 9.0%
Femur L: 8.4%
Femur C: 12.6%
Tibiotarsus L: 6.6%
Tibiotarsus C: 16.3%
Tarsometatarsus L: 4.1%
Tarsometatarsus C: 6.9%

Comparing the various measurements, when it comes to length it appears that the ulna is proportionally longer, being 9% longer compared to 6.4% the mean of the femur/tibiotarsus/tarsometatarsus but ll of these bones are proportionally much thicker than suggested by isometric scaling based on their length so which is it, the ulna is elongated or are the lower limb elements foreshortened?

[coherentsheaf]

I dd a log transformed regression equation of body mass over wing area from the data above. Summary table:

Residuals:
Min 1Q Median 3Q Max
-0.216280 -0.067163 0.001967 0.092204 0.172484

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -1.21220 0.12355 -9.812 1.2e-12 ***
log10(Wing_area) 1.24877 0.03889 32.113 < 2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.09992 on 44 degrees of freedom
Multiple R-squared: 0.9591, Adjusted R-squared: 0.9581
F-statistic: 1031 on 1 and 44 DF, p-value: < 2.2e-16

The resulting mass of the large eagle restored by Brathwaite would be 10.06 kg and the logarithmic confidence interval transformations 8267.286g 12250.53g.

[blaze]

As in the largest one?

[coherentsheaf]

Sept 28, 2014 9:30:04 GMT 5 blaze said:

As in the largest one?

Yes. I set the wing area as 15 000 cm^2

[coherentsheaf]

Ok I redid the analysis only using birds of prey with a body mass of more than 1kg and adding several measurements of vultures I had excluded due to them lacking Ulnar length, the measurement I was looking for when creating the data base. It seems like this has considerable influence on the regression line:

Residuals:
Min 1Q Median 3Q Max
-0.131077 -0.037283 0.000823 0.039854 0.126369

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -2.0485 0.3836 -5.34 5.41e-05 ***
log10(Wing_area) 1.4982 0.1047 14.31 6.55e-11 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.07412 on 17 degrees of freedom
Multiple R-squared: 0.9233, Adjusted R-squared: 0.9188
F-statistic: 204.7 on 1 and 17 DF, p-value: 6.552e-11

Note that the predictive accuracy decreased due to smaller sample size.

Predction: 16144.61g

95% confdence:
12255.04 - 21268.67