Why Aren’t There Any Horse-Sized Dogs?

Why don’t dogs grow to be as large as horses? As we’ll see, the answer to the question is pertinent to more than just pet lovers and eccentrics. It has relevance for entrepreneurs, corporate strategists, social scientists, epidemiologists, and others interested in understanding how things grow — and why they stop growing.

In a recent post, we discussed Geoffrey West and his insights into universal scaling laws. West found that larger cities, companies, and organisms operate more efficiently than their smaller equivalents, and their relative ratios are remarkably predictable. Larger animals need less food per pound of body mass, their hearts beat less frequently, they live longer, and sleep less than smaller animals. Larger cities require less infrastructure per capita, such as roads, sewers, and water lines, though they generate more social interactions, more innovation, and more economic productivity than smaller cities. The size premium also applies to larger companies, which produce more assets, more net income, and more profits per employee than smaller companies.

So, if there are significant advantages to being larger, then why do organisms stop growing?  

As it turns out, the answer is related to resource availability. This includes both external resources, such as consumable calories for animals, and internal resources, such as the body’s ability to transport nutrients throughout the body.

It’s easy to see how external resource availability would constrain growth. You see this all the time in the natural world. Animals that live in harsh conditions with scarce food supplies tend to be smaller, on average, than their cousins who live in more prosperous areas.

And yet, if you took your adorable Shar Pei puppy and placed her in the most resource-rich environment with unlimited healthy meals, tasty snacks, toys, and cuddles, she would only grow to the size dictated by her species (dog) and breed (Shar Pei). Her growth would be limited by her biology, not her environment.

So what is it about biology that limits size? In the grand scheme of things, dogs and horses are mostly similar. They are warm-blooded mammals with similar bone structures, four legs, hearts that pump blood, and lungs that pump oxygen. Yet despite their similarities, you won’t see cowboys saddled up on dogs riding across the prairies or plane passengers carrying tiny horses in their carry-on luggage.

It helps to look at metabolic processes, or metabolic rates, which govern the amount of energy needed to keep the organism alive. For the average 60-pound dog, that’s about 800 calories a day, and for a 1,000-pound horse, that’s about 15,000 calories. (For the average human, it’s about 2,000 calories, but as we all know, some humans wolf down several times that amount.) Dogs, horses, and humans all digest their food and use their circulatory system to carry nutrients, oxygen, and hormones to all parts of their bodies and remove waste products like carbon dioxide.

Now here’s the kicker: although the horse and dog need different amounts of calories, pump different volumes of blood through their systems, and have different sized hearts, the size of their capillaries is almost exactly the same. In fact, the capillaries of most animals, including humans, range between five and 10 micrometers in diameter, just large enough for blood cells to pass through in single file. The giant elephant is two-to-three million times heavier than the tiny shrew, but they both have capillaries of roughly the same size.

So how do larger animals with larger hearts pump more blood to their capillaries than smaller animals and do so more efficiently? They accomplish this with marvelously efficient fractal geometry, a tree-like pattern that exhibits self-similarity from the macro to the micro. As animals grow, their circulatory systems add more branch levels, with each branch itself adding more sub-branches, all the while ensuring that the tiniest branch is just large enough to allow the passage of blood cells. The circulatory system maintains maximum efficiency by keeping the ratio of diameter-to-branching-angle constant. This is nature’s Six Sigma.

Looking at it another way, for an animal to grow larger, it must find a way to use energy more efficiently than it does when smaller. It does so by using the fractal patterns of its circulatory system. If the efficiency of its energy usage stops improving, the animal stops growing.

This is an important lesson for corporate strategists because the same rules apply. If you’re trying to double the size of your company, you have to find a way to operate more efficiently. To become twice as large, you have to operate with less than twice as many resources. The good news is, if you can do so successfully, you should be able to also more than double your profits. And you can potentially keep growing.

It’s the same with cities. If you are a city planner and you anticipate that your city will double in population over the next ten years, for instance, you have to find ways to grow while using less than twice as many resources. Again, if you can do this successfully, you can expect to more than double your GDP, the amount of innovation your city produces, and other metrics that West tracked, on average. And you can potentially keep growing.

Companies and cities that can successfully make that size-resource tradeoff have a tremendous amount of growth potential. Those that cannot make that tradeoff successfully — when their inputs outpace their outputs — will soon reach a ceiling on their growth potential. For companies, that means limited profitability, limited market share, staff burnout, and turnover. For cities, that means more traffic, longer commutes, more crime, and strained infrastructure.  

West found that animals are somewhat more efficient in their scaling activities than cities or companies. Animals achieve an efficiency ratio of roughly 25 percent. In other words, they require 75 percent more calories to achieve each 100 percent size increase. Companies and cities achieve an efficiency ratio of about 15 percent, meaning they need 85 percent more resources for each doubling of size.

Regardless of the specific ratios, the important benchmark is whether these entities can more than double their size with each doubling of resources (called super-linear scaling) or fall short of doubling their size for each doubling of resources (sub-linear scaling).

In the corporate world, the key metric is the marginal cost of growth. That is, it’s the cost of adding each new unit of growth. If the cost of growth is less than one, the company can keep growing; if the cost of growth is greater than one, the company will be constrained by its natural size limits.

To answer the question about the dog, it will not grow to be the size of a horse because it reaches the limits of its ability to distribute resources efficiently throughout its body.

So what’s the lesson? The lesson is, most companies have to be willing to change their processes in order to grow. They can’t just hire more employees, add more office space, and continue doing what they have done historically, only doing it on a larger scale. That would be like feeding the dog more food, expecting it to keep growing. Well, companies could try that — and many companies do — but they soon hit their growth ceiling.

After a certain point, adding more resources to the company without improving efficiencies results in deteriorating profitability. They have to find ways to become more efficient. What gets them from zero-percent market share to one percent may not be what gets them to two to three to four percent.

In a future post, we’ll explore the fractal geometry of scaling as it relates to organisms, cities, and companies. Stay tuned!