The Science
The larger the animal, the slower its pulse rate. Blood has to move more slowly in a very large aorta to keep from choking in tiny capillaries. While any animal's surface area varies as the square of its length, its volume varies as the cube. That means large animals have less surface area for cooling blood, and their metabolic rates have to be slower.
Mysteriously, these and a large variety of other phenomena change with body size according to a precise mathematical principle called quarter-power scaling. A cat, 100 times more massive than a mouse, lives about 100 to the one-quarter power, or about three times, longer. (To calculate this number take the square root of 100, which is 10 and then take the square root of 10, which is 3.2.) Heartbeat scales to mass to the minus one-quarter power. The cat's heart thus beats a third as fast as a mouse's.
Scaling emerges as a direct result of the geometrical and statistical properties of the internal networks animals (and plants) use to distribute nutrients and to discard waste products.
To return to the mouse and cat example, it might seem that because a cat is a hundred times more massive than a mouse, its metabolic rate (the intensity with which it burns energy) would also be a hundred times greater - what mathematicians call a linear relationship. After all, the cat has a hundred times more cells to feed.
But if this were so, the cat would quickly overheat. The reason: the surface area a creature uses to dissipate the heat of the metabolic fires does not grow as fast as its body mass. To see this, consider a mouse as an approximation of a small sphere. As the sphere grows larger, to cat size, the surface area increases along two dimensions but the volume increases along three dimensions. The size of the biological radiator cannot possibly keep up with the size of the metabolic engine.
If this was the only factor involved, metabolic rate would scale to body mass to the two-thirds power, more slowly than in a simple one-to-one relationship. The cat's metabolic rate would be not 100 times greater than the mouse's but 100 to the power of two-thirds, or about 21.5 times greater.
But biologists, beginning with Max Kleiber in the early 1930s, found that the situation was much more complex. For an amazing range of creatures, spanning in size from bacteria to blue whales, metabolic rate scales with body mass not to the two-thirds power but slightly faster -- to the three-quarter power.
Evolution seems to have found a way to overcome in part the limitations imposed by pure geometric scaling, the fact that surface area grows more slowly than size.
Kleiber's law means that a cat's metabolic rate is not a hundred or 21.5 times greater than a mouse's, but about 31.6 -- 100 to the three-quarter power. This relationship seems to hold across the animal kingdom, from shrew to blue whale, and it has since been extended all the way down to single-celled organisms, and possibly within the cells themselves to the internal structures called mitochondria that turn nutrients into energy.
There are of course very few large species, like elephants and whales, and a huge number of the smaller species. Regardless of this, if a graph is drawn showing the size of animals on one axis and the number of species on the other axis, the slope of the resulting line would reveal another quarter-power scaling law? Population density, the average number of offspring, the time until reproduction - all are dependent on body size scaled to quarter-powers.
Initial work on Scaling assumed that the nutrient supply networks in all animals and plants work according to three basic principles:
- the networks branched to reach every part of the organism
- the ends of the branches (the capillaries and their botanical equivalent) were all about the same size. After all, whatever the species, the sizes of cells being fed were all roughly equivalent
- evolution would have tuned the systems to work in the most efficient possible manner
What emerged closely approximated a so-called fractal network, in which each tiny part is a replica of the whole. Magnify the network of blood vessels in a hand and the image resembles one of an entire circulatory system.
To be as efficient as possible, it was assumed that the network would also be "area-preserving." i.e. if a branch split into three daughter branches, their cross-sectional areas had to add up to that of the parent branch. This would insure that blood or sap would continue to move at the same speed throughout the organism.
Such a model produces three-quarter-power scaling between metabolic rate and body mass, but only for plants. Predictions based on this model for mammals were all wrong, so some extra factor was still missing.
In making the model as simple as possible, the scientists had hoped they could ignore the fact that blood is pumped by the heart in pulses and treat mammals as though they were trees. After studying hydrodynamics (the nature of liquid flow) they realized they needed a way to slow the pulsing blood as the vessels got tinier and tinier.
These finer parts of the network would not be area-preserving but area-increasing, i.e. the cross sections of the daughter branches would add up to a sum greater than the parent branch, spreading the blood over a larger area.
After adding these and other complications, scientsts found that the improved model also predicted three-quarter-power scaling in mammals. Other quarter-power scaling laws also emerged naturally from the equations. Evolution, it seemed, has overcome the natural limitations of simple geometric scaling by developing these very efficient fractal-like webs.
One implication of the scaling law is that all mammals will have approximately the same blood pressure. Although tis seems on the face of it unlikely, this is in fact the case.
The content on this site has been drawn from a wide range of Web & printed resources and edited/summarised to form a single point of reference and overview of the Billion Heart Beats.