The Density Dilemma
Every fish farmer faces the same optimization problem: stock more fish to increase total production, or stock fewer to improve individual growth and survival. This tradeoff is governed by carrying capacity — the maximum biomass a system can sustain without environmental degradation. Exceed it, and the biological system collapses: ammonia spikes, oxygen crashes, diseases explode through the stressed population.
Logistic Growth in Confined Systems
Fish populations in aquaculture follow logistic growth curves. Growth is nearly exponential when biomass is far below carrying capacity, but decelerates sharply as biomass approaches the system limit. At carrying capacity, growth effectively stops — all metabolic energy goes to maintenance rather than tissue accretion. Skilled farmers harvest before this plateau, maximizing the period of rapid, efficient growth.
Mortality Cascades
Overcrowding does not cause gradual, predictable losses. Instead, it triggers cascading failures: elevated ammonia weakens immune systems, opportunistic bacteria proliferate in the organic-rich water, and one sick fish infects hundreds of crowded neighbors. A single disease event in an overstocked pond can kill 50–80% of fish within days — erasing months of investment overnight.
Finding the Sweet Spot
This simulation models biomass accumulation using density-dependent logistic growth with a survival function that degrades as biomass approaches carrying capacity. Adjust stocking density and system capacity to find the configuration that maximizes total production. Notice that maximum biomass does not equal maximum profit — the best economic result often comes at 60–80% of maximum achievable density.