In Figure \(7.16,\) why does mass-specific metabolic rate (metabolic rate per unit weight) of mammals increase with decreasing body mass?

Mass-specific metabolic rate refers to the energy consumed per unit weight (e.g., per gram) of an organism. It is usually measured in joules per gram per hour (J/g/hr) or in calories per gram per day (cal/g/day). In simpler terms, it's a measure of how much energy an animal needs to function for a given body mass.

It has been observed that there is an allometric scaling relationship between metabolic rate and body mass in animals. Allometric scaling is a measure of how a certain biological trait or parameter changes with the size of the organism. In mammals, metabolic rate scales approximately to the power of 3/4 in relation to the body mass ( \(Metabolic\,Rate \propto M^{3/4}\)), where M is body mass. This means that as the mass of a mammal increases, its metabolic rate also increases but at a slower rate than body mass.

When we compare the metabolic rate per unit weight, we can observe an inverse relationship with body mass. If we divide the metabolic rate equation by body mass, we get the mass-specific metabolic rate equation: \(Mass\,Specific\,Metabolic\,Rate \propto \frac{M^{3/4}}{M} = M^{-1/4}\) As body mass (M) increases, the mass-specific metabolic rate decreases, following a power of -1/4 relationship.

There are several reasons for this inverse relationship between mass-specific metabolic rate and body mass: 1. Surface Area-to-Volume Ratio: Smaller mammals have a higher surface area-to-volume ratio compared to larger mammals. As a result, they lose heat more quickly and need to consume more energy per unit mass to maintain their body temperature. 2. Cellular Metabolic Rates: Smaller mammals often have higher cellular metabolic rates compared to larger mammals. This means that their cells require more energy to function, leading to a higher mass-specific metabolic rate. 3. Organ System Efficiency: In larger mammals, the relative sizes of organs like the heart, lungs, and kidneys are smaller compared to smaller mammals. This improved efficiency reduces the overall metabolic rate per unit mass in larger mammals. In conclusion, mass-specific metabolic rate increases with decreasing body mass in mammals due to factors such as surface area-to-volume ratio, cellular metabolic rates, and organ system efficiency.