Biology Project banner Biology project link Biomath link

The Biology Project > Biomath > Power Functions > Applications > Allometric Scaling

Power Function Applications

Allometric Scaling

Allometry is the study of the relative change in proportion of an attribute compared to another one during the growth of an organism. These attributes may be morphological, physiological, or otherwise.

In the exponential function module we showed how allometric equations are derived. In this section, we sill use allometric equations, which are power functions, in calculations. Our example is the relationship between insect body mass and resting metabolic rate.

 

The bee Ascosphaera apis. Photo credit: Stephen Ausmus courtesy of U.S. Department of Agriculture, Agricultural Research Service.

 

Niven and Scharlemann [1] found that insect resting metabolic rate (RMR) scaled positively with body mass (M) according to the equation,

RMR = 4.14 · M0.66,

where M is measured in mg and RMR is measured in mm3 O2 per hour.

[1] Niven, J.E., and J.P.W. Scharlemann (2005). Do insects metabolic rates at rest and during flight scale with body mass? Biol. Lett. 1: 346-349.

Use the allometric scaling equation to answer the following questions:

Find the approximate resting metabolic rate of an insect of given body mass.

Find the body mass of an insect given its resting metabolic rate.

Find the fastest possible resting metabolic rate of an insect.

Describe the graph of the function that describes allometric scaling of insect body mass and resting metabolic rate.

*****

The Biology Project > Biomath > Power Functions > Applications > Allometric Scaling


The Biology Project
Department of Biochemistry and Molecular Biophysics

The University of Arizona

March 2007
Contact the Development Team

http://www.biology.arizona.edu All contents copyright © 2007. All rights reserved.

Biochemistry