22 Questions
What is the range of body mass spanned by vertebrates?
8 orders of magnitude
Who is credited with the first treatise on scaling?
Galileo Galilei
What are the three engineering principles of scaling?
Changing dimensions, changing materials, and changing architecture
How do tetrapods change their architecture as they scale?
By changing posture or adapting novel features
What novel material did vertebrates evolve to support their bodies nearly 500 million years ago?
Bone
How do tetrapods alter their bones to convey new material properties?
By altering bone density and cross-sectional geometry
What is an example of a structure that uses compression to span a large distance?
The Danhe bridge
Why doesn't the T-Rex catch the jeep in the famous movie scene?
Due to scaling limitations, a T-Rex would not be able to catch a jeep
How does muscle strength scale with cross-sectional area?
Muscle strength increases with cross-sectional area (x2)
What happens to body mass as it increases?
Body mass increases with volume (x3)
What is the main difference between torpor and hibernation?
Torpor is a shorter period of reduced activity, while hibernation is a longer period of dormancy
How do physiological processes scale with clock time?
Physiological time scales differentially with clock time
What is the relationship between heart rate and lifespan in mice and elephants?
Mice have a much faster heart rate than elephants, but similar total heartbeats over their lifespan
How do the skeletons of birds and mammals compare at a given body mass?
Birds and mammals have identical skeletal mass, but birds have denser skeletons in some areas
What happens to metabolism as body mass increases?
Metabolism slows down with increasing body mass
Why don't small animals like hummingbirds and shrews deplete their energy reserves quickly?
They have adaptations that allow them to replenish their energy reserves quickly
What is the significant difference in biomechanics, anatomy, and materials when it comes to size in living organisms?
The physical laws governing size ranges affect biomechanics, anatomy, and materials, leading to differences in the functional, physiological, and temporal components of living organisms.
What is the prediction for the largest land mammal to have ever existed, weighing approximately 20 tons?
Paraceratherium.
What is an example of how materials change as size increases, in terms of strength and stiffness?
Birds have bone geometry that promotes stiffness and strength at small sizes.
What is an example of how size affects the design of structures, in terms of wall thickness and material choice?
A bridge example, where stone and steel are used differently due to size.
What is the range of sizes that living organisms span?
A great range of sizes.
How does size affect the functional, physiological, and temporal components of living organisms?
Size has implications for lifespan, physiology, and functional components of living organisms.
Study Notes
Vertebrates and Scaling
- Vertebrates span 8 orders of magnitude in body mass, from 1L to 100,000,000L.
- Galileo's theory of scaling (1638) deals with the structural and functional consequences of size changes.
Engineering Principles of Scaling
- To maintain performance as a structure scales, it must change dimensions, materials, or architecture.
- Changing dimensions: proportional dimensions might change, e.g., Irish stone wall vs. Great Wall of China.
- Changing architecture: architecture changes, e.g., Danhe bridge vs. Golden Gate bridge.
- Changing materials: materials and their properties directly affect scaling, e.g., stone vs. steel.
Biological Scaling
- Vertebrates evolved bone nearly 500 million years ago as a new material to support the body.
- Tetrapods alter bone density and cross-sectional geometry to convey new material properties.
- Birds have proportionally lighter skeletons than mammals, but with denser skeletons and bone geometry that promotes stiffness and strength at small sizes.
Scaling and Strength
- Muscle strength increases with cross-sectional area (x2), while body mass increases with volume (x3).
- Running requires moving body mass using muscle strength, which is affected by scaling.
Scaling, Metabolism, and Endurance
- Metabolism scales more slowly than body mass, so small animals burn through their reserve energy faster.
- Body energy storage (fat reserves) is proportionally identical across all body sizes.
- Torpor and hibernation are different strategies for energy conservation.
Scaling and Time
- Physiological time scales differentially with clock time.
- Total physiological processes may be more important than overall time.
- Heartbeat and respiration rates vary with body size, but overall physiological processes remain similar.
Scaling and the Skeleton
- At any given body mass, the skeletal mass of birds is identical to that of mammals, but birds have denser skeletons and bone geometry that promotes stiffness and strength.
- The largest land mammal ever to exist, Paraceratherium, weighed about 20 tons and had a unique skull structure.
Explore the fascinating world of vertebrates and discover how their skeletons change in proportion to their body mass. From the tiny to the gigantic, learn about the implications of scaling on structure and function.
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