Allometry problem... A study of skeletal mass (M skel , kg) as a function of bod

Question

Allometry problem...

A study of skeletal mass (Mskel, kg) as a function of body mass (Mb, kg) for mammals and birds reported the following allometric equations:

Birds Mskel= 0.0649Mb1.068

Mammals Mskel= 0.0608Mb1.083

Calculate the skeletal mass for a bird and a mammal of body mass 0.5kg. Express the skeletal mass for each animal as a percentage of total body mass. Do these values support the popular notion that the hollow, air filled boned of boirds give them a lighter skeleton than a mammal of the same size?

Explanation / Answer

Based on your data,

Equation for the calculation is:

log (f) = log c + log (sd)

For birds:   

log (Mskel) = log (0.0649) + 1.068 log (Mb)    

By means of the allometric equation with Mb = 0.5, we have the following,

Mskel = 0.0649 × 0.5^1.068

Mskel = 0.030 kg.

Therefore, a bird with a body mass of 0.5 Kg (500 grams) must have an approximate skeletal mass of 0.03 kg (30 grams). The skeletal mass for birds as a percentage of total body mass is: 0.03 ÷ 0.5 × 100 = 6%.

For mammals:

log (Mskel) = log (0.0608) + 1.083 log (Mb)    

By means of the allometric equation with Mb = 0.5, we have the following,

Mskel = 0.0608 × 0.51.083

Mskel = 0.028 kg.

Therefore, a mammal with a body mass of 0.5 Kg (500 grams) must have an approximate skeletal mass of 0.02 kg (28 grams). The skeletal mass for birds as a percentage of total body mass is: 0.02 ÷ 0.5 × 100 = 4%.

Based on these values birds have more skeletal mass than mammals, even though their body weight is same. Thus, these values support the popular notion that the hollow, air filled boned of birds give them a lighter skeleton than a mammal of the same size.

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