Table of Contents

• Prequiz...
• The Power Function
• 1: Introduction
• 2: What are scaling relationships?
• 3: The power function
• 4: The shape of the power function
• 5: The conversion factor "a"
• 6: The power factor "b"
• Log Transformations
• 7: Introduction
• 8: What are logarithms again?
• 9: Graphing on a log scale
• 10: Visualizing the data
• 11: Getting to a straight line
• 12: The key parameter is "b"
• The value of "b"
• 13: Introduction
• 14: A geometric approach
• 15: Scaling surface area of cubes
• 16: Scaling surface area of cubes
• 17: A "2/3 scaling law"?
• Confronting ideas with data
• 18: Introduction
• 19: An unexpected result
• 20: A "3/4 scaling law"?
• 21: Internal transport systems
• 22: Branching and supply networks
• 23: Deriving the "3/4 scaling law"
• 24: So what's the real value of "b"?
• Review
• 25: Review of Concepts

What should the value of "b" be?

What is the real, underlying purpose for these kinds of scaling studies? The main driver is to learn something about the underlying biology of organisms. Any factor that scales across a whole group or several groups of organisms in a consistent way is likely to teach us something pretty fundamental about biology! Therefore, the specific value of "b" could potentially lead us to uncover some general truths about the critical factors that drive metabolism across all species. Wow! So much potential information, just by figuring out the value of a parameter in a model!

The best way to do this is to think about what processes would lead to certain values of key parameters - and then if we measure that value using real data, we can test which hypothesis is most likely to be true. All the way back to the 1800s, people thought that body size should scale with metabolism to the ⅔ power. We will describe the rationale, which is based on heat loss and geometry. Then, in the following section, we'll see what happened when people started empirically testing this prediction.