Book Notes: Scaling, Why is Animal Size so Important?

by ketchupduck10 min read7th Mar 20215 comments

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TL;DR: Movie!Ant-Man is unrealistic. Also, the Internet Archive has an ebook library! 

Movie!Ant-Man can be the size of an ant… 

…and the size of an airplane…

…but throughout it all, his own body’s shape and structure doesn’t change. Without background objects (e.g., ants and airplanes), you wouldn’t be able to guess what size Ant-Man is because his own body remains unchanged. This is, to put it mildly, unrealistic. Scaling, Why is Animal Size so Important (1984) by Knut Schmidt-Nielsen discusses principles that explain why. The five-year old in me who likes fun animal facts (did you know giraffes and humans have the same number of neck bones?) really enjoyed this book. 

I, a biology novice, usually think of biology as applied chemistry (I’m not alone): it is the study of things like cell reactions and ion pumps. This book takes a different approach and talks about biology as applied physics. For example, in the chapter on eggs, Scaling doesn’t discuss applied-chemistry-y topics like what proteins exist in an egg and what their functions are. Instead, it talks about applied-physics-y topics like how large egg pores must be to allow carbon dioxide to escape while minimizing water loss through evaporation and how thick an egg shell must be to protect a developing chick while still allowing a grown chick to break its way out. In keeping with its title, it focuses on how characteristics like egg pore size and egg shell thickness change for different sizes of eggs. 

The author, Schmidt-Nielsen, was “one of the all-time greats of animal physiology”. Just as importantly, he really liked camels, going as far as to make Duke University build a basement “camel room” with “a 10-foot-high door and stainless steel walls,” despite the dearth of camels to study in North Carolina (sadly, but perhaps predictably, the room was never used for camel research). 

Framework

There are a few possible relationships between animals’ sizes and animals’ characteristics. (Animals’ characteristics, here, cover everything from their body temperatures to their heart rates.)

1. No change. A characteristic may not vary with animals’ sizes at all. 

For example, think about an ordinary person, Bob Smith, moving into homes of different sizes. As a college student, Bob lives in a dorm room. As a recent graduate, Bob lives in an apartment. As a middle-aged adult, Bob lives in a single-family home. As a retiree, Bob lives in a condo.

Even though the size of Bob’s home changes many times, Bob’s own size does not change and remains constant. 

2. Proportional change. A characteristic may vary in proportion to animals’ sizes. 

For example, think about how Ant-Man changes size. When Ant-Man becomes 200% taller, all parts of him become 200% taller. His legs, his arms, his head – all of them become 200% longer.   

The change in the Ant-Man’s length is proportional to the change in all of his body parts’ length. 

3. Disproportional change. A characteristic may vary out of proportion to animals’ sizes. This could happen 

A. because the characteristic changes faster than the animals’ sizes,

B. because the characteristic changes slower than the animals’ sizes, or

C. because the characteristic decreases when the animals’ sizes increase.

For example, think about what happens when an infant becomes an adult. Infants’ heads make up about one-fourth of their height. As they grow up, their heads become proportionally smaller and their bodies become proportionally bigger until, in adulthood, their heads make up about one-eighth of their height. 

As the infants get bigger, their head grows relatively slower than their entire body (B) while their torso and limbs grow relatively faster than their entire body (A). 

Examples

In the interest of keeping these notes to a reasonable length, I only discuss mammalian examples, although the book does discuss other animals like birds, insects, fishes, and reptiles. Like the book, I will use body mass as the measure of size. 

I’ll discuss the following examples. If you are interested in a guessing exercise, you could predict, before reading on, what relationship each of these characteristics has to increasing mammal mass. Your options are: 1. constant, 2. proportional change, 3A. disproportional change faster than mammal mass, 3B. disproportional change slower than mammal mass, 3C. inverse relationship, where the characteristic decreases as mammal mass increases. 

  • Metabolic characteristics
    • Body temperature
    • Hemoglobin concentration in blood
    • Lung volume
    • Heart mass
    • Blood mass
    • Specific metabolic rate (rate of oxygen consumption per kg of mammal mass)
  • Other characteristics
    • Bone mass
    • Brain mass
    • Maximum muscle strength exerted by a given cross-sectional area of muscle
    • Cost of running (amount of oxygen required per kg of mammal mass per km moved)

Body temperature. Body temperature for placental mammals is constant, between 36 and 40 degrees Celsius. Body temperature for marsupials (which I vaguely thought meant “cute Australian mammals” but I now realize means mammals that don’t grow placentas) is a couple degrees lower. 

Hemoglobin concentration in blood. Hemoglobin concentration in mammals is constant, around 150g hemoglobin per liter of blood. At this concentration, there is enough hemoglobin to help red blood cells carry sufficient oxygen, but not so much that blood becomes too viscous for the heart to pump easily. 

Lung volume. The total lung volume for mammals scales proportionally, at about 50mL of lung volume per kilogram of mass. If you assume mammals have the same density as water (roughly true), that means lungs occupy ~5% of total body volume. While breathing normally, mammals only use about one-seventh of their lung volume. 

Heart mass. Hearts are about 0.6% of total mass, and so scale proportionally. 

Blood mass. Blood is about 6-7% of total mass, and so scales proportionally. 

Specific metabolic rate (rate of oxygen consumption per kg of mammal mass). The specific metabolic rate (SMR) decreases as mammal size increases. In other words, larger mammals are more oxygen-efficient than smaller mammals. Each kilogram of a larger mammal’s body requires less oxygen to run than a kilogram of a smaller mammal’s body. Humans, who are about ten thousand times heavier than mice, have a SMR that is only a tenth of that of mice. (In absolute terms, however, a human still consumes more oxygen than a mouse.) 

Many characteristics related to the metabolic rate, such as frequency of breathing and heart rate, also follow the same trend of decreasing with increasing mammal mass. In other words, larger mammals breathe more slowly and have lower heart rates. 

Brain mass. Brain mass scales slower than total mass. A mammal that is a hundred times larger will have a brain that is only twenty-five times larger. 

Scaling mentions two fun facts about brains offhandedly. One, the human brain consumes about 15W of power (newer sources give figures closer to 20W, which is still in the same ballpark). Two, brain size seems to be correlated with lifespan, although the author doesn’t provide guesses for why this would be. 

Bone mass. Bone mass scales faster than total mammal mass. A mammal that is a hundred times larger will have bones that are about 150 times larger. 

A simplified explanation why follows. A bone’s strength under static gravitational loads (in plain english, when an animal is standing) depends on its cross-sectional area. If an animal doubles in length, width, and height, its bones’ cross-sectional area will increase four-fold, but its weight will increase eight-fold. Thus, proportionally changing bones will not be strong enough to support the increase in mass. The bones’ cross-sectional area must increase faster than proportional change would allow, because they must support the increasing weight of the animal. This leads to the bones’ mass also increasing disproportionately faster than the mammals’ total mass. (The actual math is more complicated because real bones have loads other than static gravitational loads, because real animals do more than just stand all day.) 

Maximum muscle strength exerted by a given cross-sectional area of muscle. This is constant for mammals. The maximum muscle strength that can be exerted by a given cross-sectional area of muscle is dependent on the size of thick and thin filaments in muscle, and those are the same across all mammals. 

Cost of running (amount of oxygen required per kg of mammal mass per km moved). I know “something oxygen something kg something km” is kind of a mouthful, but this is roughly analogous to car mileage. An animal with a lower cost of running is more fuel-efficient than one with a higher cost of running. Just like SMR, larger animals have a much lower cost of running (are more fuel-efficient) than smaller animals. An animal that is a hundred times larger has a cost of running that is only one-fifth as high. 

For those keeping score at home: 

  • Metabolic characteristics
    • Body temperature [1. constant] 
    • Hemoglobin concentration in blood [1. constant]
    • Lung volume [2. proportional]
    • Heart mass [2. proportional]
    • Blood mass [2. proportional]
    • Specific metabolic rate (rate of oxygen consumption per kg of mammal mass) [3C. inverse relationship]
  • Other characteristics
    • Brain mass [3B. disproportional, slower]
    • Bone mass [3A. disproportional, faster]
    • Maximum muscle strength exerted by a given cross-sectional area of muscle [1. constant]
    • Cost of running (amount of oxygen required per kg of mammal mass per km moved) [3C. inverse relationship]

Going back to Ant-Man then, if he scaled the way other mammals do, his brain and bones should change out of proportion to the rest of his body. Giant Ant-Man should have a small brain and huge bones, instead of still being human-shaped. His metabolic rate should also change; small Ant-Man should be massively fuel-inefficient and spend most of his time eating and breathing fast in order to provide sufficient fuel to his body, like a hummingbird-human hybrid. 

Takeaways

First, and most importantly, the Internet Archive has a library feature that lets people borrow entire ebooks! I know my local library has this feature too, but the Internet Archive’s version is broader because it works for patrons all across the world. The collection is sparse, but I’m just impressed it exists at all. Scaling, if you would like to read it, is available here. (If you want to learn more about animal scaling but don't want to read an entire book, this article has a good overview of popular misconceptions about scaling.) 

Second, humans really are mammals. I knew this intellectually, but I never quite fully believed it. We don’t walk like other mammals and we don’t talk like other mammals, so are we really mammals in any meaningful way? “Humans are mammals” always struck me as a statement more akin to “photons are waves” than to “the sun is a star”: I know it’s true but I couldn’t really feel it in my bones. After reading this book, I feel much more connected to my fellow mammals. We have more in common than just being hairy and nursing our young. My heart-and-lungs are scaled-up versions of mice heart-and-lungs and scaled-down versions of elephant heart-and-lungs. We all have similar muscle strength and body temperature and hemoglobin concentrations. Even human brains, which are eight to twelve times larger than mammalian trends would predict, are not off-the-chart outliers. 

Source: https://community.wolfram.com/groups/-/m/t/946991

Third, when it comes to biology, I should make very tentative predictions. I made guesses about which way trends were likely to go while reading this book and I was almost always wrong. Worse, I was able to come up with convincing-sounding reasons for completely incorrect hypotheses. Take, for example, body temperature. Just so I don’t implant fake knowledge into your mind, remember that body temperature is roughly constant for mammals, regardless of their size. I can come up with convincing just-so-stories for why body temperature rises with mammal size (large mammals have smaller surface-area-to-volume ratios, so they must retain more heat and be warmer) and why body temperature falls with increasing mammal size (cats and dogs I pet are always warm to my touch, so small mammals must be warmer than me). Again, both of these hypotheses are incorrect; body temperature is roughly constant for mammals, regardless of their size. The experience of reading this book hammered home for me that I should be very tentative when thinking about things I know little about, like biology. Unless I’m developing a new superhero, in which case I can just go hog-wild. 

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5 comments, sorted by Highlighting new comments since Today at 8:30 PM
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Tentitive hypothesis:

Temperature is a strongly conserved trait by evolution. Run 5 degrees hotter or colder and a lot of proteins act differently. So evolution has to keep the temperature basically fixed, and pay the performance costs of temperature regulation.

brain size seems to be correlated with lifespan, although the author doesn’t provide guesses for why this would be.

Since so many things including brain size are all correlated (as listed in this post), any two of them (such as brain size and lifespan) are unlikely to be directly (causally) linked.

I think I expressed this unclearly. Lifespan is more tightly correlated to brain size than body size (brain size scales disproportionately with body size). The author gives the example that if lifespan was correlated with our body size, humans would live 20-25 years, but since lifespan is correlated to our brain size, our expected lifespan is longer. 

I agree that the correlation doesn't necessarily point to a causal linkage. 

Guess: animals that live longer get more value from learning over their lifespans and so they benefit more from (expensive) large brains.

I'm familiar with similar points about scaling, made by JBS Haldane in the essay On Being the Right Size - which is well worth a read if you haven't already.

https://webcache.googleusercontent.com/search?q=cache:WMM8Q8K7zTgJ:https://www.damtp.cam.ac.uk/user/gold/pdfs/teaching/Haldane.pdf