Question

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

Short answer

Mass-specific metabolic rate refers to the energy consumed per unit weight of an organism and is influenced by factors such as surface area-to-volume ratio, cellular metabolic rates, and organ system efficiency. In mammals, an inverse relationship exists between mass-specific metabolic rate and body mass. As body mass increases, the mass-specific metabolic rate decreases due to the allometric scaling relationship and larger mammals having improved efficiency and heat retention, leading to a lower overall metabolic rate per unit mass. Smaller mammals have a higher surface area-to-volume ratio and higher cellular metabolic rates, resulting in a higher mass-specific metabolic rate as they need more energy to maintain body temperature and cellular function.

Step-by-step solution

Definition of Mass-specific Metabolic Rate

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.

Allometric Scaling

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.

Inverse Relationship between Mass-specific Metabolic Rate and 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.

Reasons for the Inverse 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.

Key concepts

Allometric Scaling

Allometric scaling is a fascinating concept in biology that describes how the characteristics of living organisms change with size. This scaling relationship often follows a power-law, where the trait of interest, such as metabolic rate, scales disproportionately with the mass or size of the organism. In mammals, this is commonly expressed as the metabolic rate scaling to the 3/4 power of the body mass, noted mathematically as \(Metabolic\,Rate \propto M^{3/4}\).

What this means is that as the size of a mammal increases, its metabolic rate also increases, but it does not do so at the same rate as the increase in body size. The metabolic rate increases at a slower pace compared to the body mass. For example, a larger mammal like an elephant will have a higher overall metabolic rate than a smaller one like a mouse, but when we look at metabolic rate per unit of body mass, smaller animals often have a higher rate.

This concept of allometric scaling helps us understand the energetic needs and efficiencies within different sized organisms, offering insight into why smaller mammals tend to have higher energy needs on a per mass basis compared to their larger counterparts.

Surface Area-to-Volume Ratio

The surface area-to-volume ratio is a crucial concept when discussing the mass-specific metabolic rate, particularly in mammals. It essentially describes how much surface area an object has relative to its volume. For smaller mammals, this ratio is higher, meaning that they have relatively more surface area compared to their volume than larger mammals do.

This large surface area means that smaller animals lose heat to their environment more rapidly than larger ones. Heat loss is a major factor in determining an animal's energy requirements. Since small mammals lose heat quickly, they must produce a significant amount of energy per unit of body mass to maintain a stable internal temperature. This often leads to higher metabolic rates per unit mass.

The impact of the surface area-to-volume ratio on energy consumption is a prime reason why such ratios are fundamentally linked to an organism's overall energy budget and are considered a key factor in the observed allometric scaling in metabolism.

Cellular Metabolic Rates

Cellular metabolic rates refer to the energy turnover that occurs at the cellular level within living organisms. In smaller mammals, these rates tend to be higher than in larger ones, meaning that the cells of smaller mammals process energy more quickly and require more energy to perform their functions compared to larger mammals.

This elevated cellular activity can be attributed to several factors, including higher organ surface areas relative to body size, and possibly more dense or more active cellular components. As a result, smaller mammals generally exhibit elevated metabolic rates per unit of body mass, as their cellular machines work harder to support their life processes.

Importantly, these high cellular metabolic rates contribute to the higher overall mass-specific metabolic rate seen in small mammals. This characteristic underscores the fact that smaller organisms often have energetic demands that are quite distinct from those of larger organisms, aligning closely with the principles observed in allometric scaling and the surface area-to-volume ratio.