Optimal population density: trading off the quality and quantity of welfare
Figure 1. Left: Hypothetical curves depict how average (per-individual) welfare expectancy might decline with increasing population density, depending on whether the most aversive effects of density develop at low densities (“early” in population growth), at a constant rate (“continuous”), or only at high population densities (“late”). Right: Average welfare under each of these three scenarios is multiplied by population density to give total welfare. Total welfare below the level achieved at the maximum sustainable size (K) is shaded. Despite average welfare always being positive, the welfare-optimal population size (O) is less than the maximum sustainable population size under the “late” (O=0.75) and “continuous” (O=0.81) scenarios. Total welfare continues to increase up to K under the “early” model (O=1.00), where higher population densities have a smaller effect on average welfare.
Figure 2. Left: As the population grows from 0 to K average welfare declines from net-positive to net-negative (red shading). A population of wild animals might appear to have very poor welfare at their natural population density, yet have the potential for good welfare at lower population density. Right: In such a case, their total welfare would be maximized by sustaining a medium-sized population, with “Late” density effects increasing the population’s optimal size and potential welfare.