Insights from the Lotka-Volterra Model

In science, there’s an inherent trade off between comprehensibility and realism. Realistic models tend to be intricate … even convoluted. But to be comprehensible, a model must be simple. [***] For a good example of this trade off, look to high-school physics. In the real world, we know that projectiles are affected by aerodynamics. (That’s why frisbees fly differently than baseballs.) But since aerodynamics are complicated, high school teachers ignore them. Instead, they teach students that earthbound projectiles behave as they would on the moon — blissfully unaffected by air drag. This simplification is a lie, of course. But it’s useful for teaching students about the essence of Newton’s equations. [***] Science is filled with this sort of simplification. We learn about the world by developing toy models — models which simplify reality, yet retain (we hope) an element of truth. [***] In economics, there’s no shortage of toy models. But most of these playthings belong in the landfill; they’re models that assume away the most pertinent features of the real world. (For example, neoclassical economic models capitalism by assuming ‘perfect competition’, whereas the real world is marked by pernicious oligarchy.) [***] In short, if we want simple models that capture key elements of human behavior, it’s best to leave mainstream economics behind. Instead, a good place to start is with population biology — specifically the Lotka-Volterra model of predator-prey dynamics. Like projectile motion that neglects aerodynamics, the Lotka-Volterra equations are a toy model of how predator and prey populations respond to each other. In a sense, it’s the simplest ‘systems model’ that still provides useful insights about the real world. [***] In what follows, we’ll take a tour of the Lotka-Volterra model, and see how it gives insights into human behavior.