Population Cycling
Market shares oscillate among competitors over time with no permanent dominance.
The mathematical formalization of predator-prey dynamics began with Alfred Lotka and Vito Volterra in the 1920s. The Lotka-Volterra model describes how prey population grows exponentially when predators are absent but declines proportionally to predator encounters, while predator population declines exponentially without prey but grows proportionally to prey consumed.
These coupled equations produce oscillations: prey increases → predators increase (with time lag) → prey decreases → predators decrease (with time lag) → cycle repeats. The system never reaches stable equilibrium but perpetually oscillates around average values.
Real systems exhibit more complex dynamics due to prey carrying capacity, predator functional response saturation, alternative prey availability, age/size structure effects, and spatial heterogeneity creating refugia.
Business Application of Population Cycling
Market shares oscillate among competitors over time with no permanent dominance. Product development cycles of 3-10 years create delays before competitive advantages manifest. When one company gains market advantage, competitors respond with innovation, pricing, and investment - but responses lag, creating oscillatory dynamics rather than stable equilibria.
Discovery
Alfred Lotka and Vito Volterra (1926)
Independently developed equations describing population oscillations, with Volterra inspired by Adriatic fisheries data showing how reduced fishing during WWI increased predator fish populations