Of Dwarfs and Giants: The Goldilocks Effect in Animal Speed

Human folklore abounds with tales of giants and dwarfs. From the giant cyclops in the Odyssey, to the six inch tall, ‘little people’ encountered by Gulliver in his travels. But what is the limit to human size, and what sized human would have been the fastest?
Of Dwarfs and Giants: The Goldilocks Effect in Animal Speed
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In the animal kingdom, it’s not the largest creatures like elephants, nor the smallest like mice, that hold the title of the fastest movers. Instead, it's often the animals of intermediate size—those that occupy the middle ground between tiny and massive—that tend to be the quickest. This counterintuitive pattern, observed consistently in nature, has puzzled scientists for decades. While intuition may suggest that larger animals should be faster due to their longer strides, the reality is far more complex.

In our recent study, Taylor Dick (University of Queensland), Friedl De Groote (KU Leuven) and I sought to shed light on this mystery by using cutting-edge musculoskeletal simulations. By creating digital models of human locomotion and scaling them from the size of a mouse to the size of an elephant, we were able to explore the biomechanics of speed across a wide range of body sizes. This innovative approach has helped clarify the mechanisms behind the unusual scaling of speed and revealed generalized rules that can predict how animals of various sizes move.

Background: The Puzzle of Speed and Size

The relationship between an animal's size and its maximum speed has long fascinated biologists. Small animals, like mice and shrews, often seem quick in short bursts but can't sustain high speeds for long. On the other end of the spectrum, large animals like elephants and hippos are lumbering in comparison to their body size. In contrast, animals like cheetahs, antelopes, and ostriches, which are of intermediate size, are some of the fastest on the planet.

This phenomenon is not limited to land animals. In the water, creatures like dolphins and seals also follow this pattern, and similarly, in the sky, birds such as falcons and hawks exhibit higher flight speeds than both larger birds like albatrosses and smaller ones like sparrows.

Understanding why intermediate-sized animals are the fastest has been a major question in evolutionary biology, biomechanics, and ecology. Several theories have been proposed, including the role of metabolic constraints, muscle power, and the biomechanics of limb movement. However, the diversity of animal shapes, gaits, and environments has made it difficult to pinpoint the exact factors responsible for this pattern.

Study Method: Human Musculoskeletal Simulations

To address these challenges, we created predictive musculoskeletal simulations based on human locomotion. These simulations were designed to mimic the way muscles, bones, and tendons work together to produce movement, allowing the models to replicate real-world physical constraints and biomechanical processes.

We scaled these models across a wide range of body masses, from the size of a mouse (~ 100 grams) to the size of an elephant (up to 2,000 kilograms). While the models were based on human anatomy, they were generalized to mimic basic principles of locomotion found in many animals, such as the use of legs for support and propulsion.

The goal of the study was to push each model to move as fast as possible and observe how speed, posture, and energy costs changed with size. The simulations allowed us to control for factors like muscle force and limb structure, which vary widely across species, and focus on the general principles that govern movement across different body sizes.

Key Findings: Speed and Posture changes

The simulations produced three key findings that mirrored real-world observations of animals:

  1. Intermediate Sizes are the Fastest: Only models from 100g to 900kg were capable of moving; the 1000kg and 2000kg models could not move. This suggests an upper limit on human body size. Among the models that did move, and consistent with observations in nature, the simulations showed that the fastest speeds were achieved by models of intermediate size. As body mass increased from small to large, maximum speed followed a hump-shaped curve, peaking at ~60kg. This suggests that there are fundamental biomechanical constraints that limit the speed of both very small and very large animals.
  2. Crouched to Upright Postures: Another significant finding was the transition from crouched postures in smaller models to more upright postures in larger ones. This change in posture is commonly seen across animals as they change in size. Smaller animals like rodents tend to move with a crouched posture, while larger animals like horses and elephants adopt more upright postures. This suggests that this transition is linked to the need for larger animals to support more weight with their limbs.
  3. Decreased Cost of Transport: The simulations also showed that as body size increased, the cost of transport (the energy required to move a certain distance) decreased. This aligns with real-world data, where larger animals tend to be more energy-efficient movers compared to smaller animals and this finding highlights the importance of energetics in determining movement strategies and speeds in animals of different sizes.

Implications: A New Framework for Predicting Animal Movement

The study's findings have important implications for understanding animal locomotion and evolution. By revealing generalized rules that apply across a wide range of body sizes, we have created a framework that can predict how animals of different sizes will move. This has potential applications in fields ranging from ecology and conservation to robotics and clinical biomechanics.

For example, understanding how body size affects speed and energy use could help conservationists predict how animals might respond to changes in their environment, such as habitat loss or climate change. Similarly, the principles uncovered in this study could be used to design more efficient robots and exoskeletons that mimic the biomechanics of natural movement.

Conclusion: Intermediate-Sized Animals Hold the Key to Fast Movement

The results of this study suggest that when it comes to speed, there is a "Goldilocks effect" at play: animals that are neither too small nor too large tend to be the fastest. This is due to a combination of biomechanical factors, including muscle force, limb length, and posture. While small animals are limited by their need for rapid leg movement and large animals are constrained by their weight, intermediate-sized animals seem to strike a balance. By using innovative predictive musculoskeletal simulations, we have provided new insights into the factors that determine how fast animals can move. Our findings offer a unifying explanation for the widespread pattern of intermediate-sized animals being the fastest and open the door to further research on the biomechanics of movement across species.

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Biomechanics
Life Sciences > Biological Sciences > Zoology > Biomechanics
Scaling Laws
Mathematics and Computing > Statistics > Statistical Theory and Methods > Scaling Laws
Muscle Physiology
Life Sciences > Biological Sciences > Physiology > Muscle Physiology
Skeletal Muscle
Life Sciences > Biological Sciences > Anatomy > Musculoskeletal System > Muscle > Skeletal Muscle

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