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Scaling and biophysics

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From Math Bench Biology Modules:

Scaling examines how form and function change as organisms get larger – in other words, how do biological features scale across size? Do they change in meaningful ways as organisms get bigger or smaller? Of course, you can’t even ask these types of questions without having a way of measuring how relationships change mathematically.

Why study these relationships? Well, if you understand how form or functions change as organisms get bigger or smaller, it is possible to learn something fundamental about what underlies the processes or learn about what factors place evolutionary limits on organism growth and adaptations. For instance, determining at what size arthropods can no longer support the weight of their exoskeleton gives us clues about the limits of their growth.

Let’s use a concrete example so you’ll know what we mean. Here is some data on body size and metabolic rate for mammals….


  • metabolic rate increases as animals get bigger. That’s because we are specifically interested in total energy consumed (here measured through oxygen consumption). Of course, bigger animals will use more oxygen than smaller ones (think about how big a breath a lion takes compared to a mouse).
  • But look at the values adjusted for body size (the last value listed for each species). Mice use a lot more oxygen per gram than a lion. This means that lions use oxygen more efficiently than mice.
  • As mammals get bigger, this increase in efficiency is not linear (notice how the steepness of the slope decreases as size increases).
  • This means that metabolism does not scale linearly with body size.

“Who cares?” Well, it turns out that how metabolism (and other factors) scales with body size can give important information about which factors are most important in limiting these biological functions. If we can understand that, we understand a lot more about biology!

Math Bench Biology Modules, University of Maryland: Scaling and Power laws

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How scaling affects biology

There are species of animals such as the deer and the elk that are closely related but of different size. Galileo took notice that the bones of the elk are not just proportionally thicker to the bones of the deer – but instead the elk’s bones are even much thicker.

The elk’s bone has to be much thicker to lower the stress in the bone below the breaking point of the bone. Even so, elk and all the other large vertebrates are still more likely of breaking their bones than the more active smaller animals.

Elk Deer bones scaling


Turkey pizza cooking times scaling

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Mouse and Elephant surface area scaling


External links


The Principle of Scale: A fundamental lesson they failed to teach us at school

The Biology of B-Movie Monsters, Michael C. LaBarbera

Scaling: Why Giants Don’t Exist, Michael Fowler, UVa 10/12/06




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