Maximum Sustainable Yield Calculator

Under the Schaefer logistic-growth model this calculator uses, the population's growth rate is fastest at the midpoint between zero and carrying capacity and slows down as it approaches either extreme, producing a symmetric growth curve whose single peak sits mathematically at exactly half the carrying capacity — that's the biomass level that supports the largest sustainable harvest.

Yes — MSY is calculated as the intrinsic growth rate multiplied by the carrying capacity and divided by four, so with the growth rate held fixed, a larger carrying capacity produces a proportionally larger MSY every time, since carrying capacity enters the formula as a direct multiplier with no other term working against it.

A ratio below 1 means the current stock biomass is below the level that would produce the maximum sustainable yield, so continued harvesting at the same rate risks further decline. Fisheries science generally treats a ratio below 0.5 as an overfished stock requiring active rebuilding rather than routine management.

The Schaefer model is deliberately simplified to isolate population size as the only driver of surplus production, which makes it tractable with just three inputs. Real fish populations respond to predator-prey dynamics, environmental variability, and age-structure effects that this symmetric-curve model does not capture.

The Schaefer surplus-production model is a genuine, widely taught foundation of fisheries science -- published by Milner B. Schaefer in 1954 in the Inter-American Tropical Tuna Commission Bulletin -- and has informed real management decisions historically, but modern stock assessments typically supplement or replace it with age-structured and multi-species models that account for factors this simplified version leaves out.