organism’s growth must depend on the speed at which it gets and uses resources from the outside world. Bertalanffy thought there were several different metabolic types, some matching the surface law, others not, that created several different growth trajectories. Since then other measurements have shown that—with the usual caveats about variation—the range of metabolic types that Bertalanffy saw was an illusion and that growth rates, like metabolic rates, are in general proportional to body mass raised to the power of 3/4. Small animals grow relatively quickly, big ones relatively slowly.
Bertalanffy believed that the link between metabolism and metabolic rate could explain why growth took the form it did and why it eventually stopped. He suggested that the net rate of growth was a simple balance between income and expenditure, reflecting the difference between the energy needed to build and expand bodies and the energy needed to maintain, repair, and replace existing parts. Because big animals metabolize relatively slowly, their maximum growth rate is also slower than that of small animals. But, he argued, this isn’t true for the costs of upkeep: The amount of energy needed to keep what you’ve already got in working order grows linearly with body mass.
So growth becomes a function of size, rather than time. Growth slows with age because as an animal grows, it comes to spend all its resources on maintenance, leaving nothing for further expansion. Bertalanffy came up with a simple equation expressing this balance between growth and decay, which fits the s-shaped curve very nicely. It has since been used in fisheries and forestry to calculate the best stage at which to catch fish or cut down trees. Roughly, this is the point at which growth has slowed so much that it is no longer economical to leave a pine in the ground or a cod in the sea, but rather is more profitable to harvest it and start over with a smaller, and so faster growing, plant or animal. If a tree is adding wood, or a fish flesh, at high speed, it is becoming more valuable, and it pays to leave it be. If it is growing only slowly, it pays to asset strip, and invest the money in something more profitable. This is why industries based around harvesting slow-growing animals, such as whales or old-growth forest, or hunting large primates for meat, are hard, if not impossible, to sustain—from a coldly economic viewpoint, the best strategy would