Enter the carrying capacity of the environment and the intrinsic rate of increase into the calculator to estimate the Maximum Sustainable Yield using a simple logistic-growth MSY approximation.

Maximum Sustainable Yield Calculator

Quick MSY
With Effort (EMSY)

Enter the population’s carrying capacity and growth rate. MSY = r × K ÷ 4.

Adds catchability to estimate the effort level (EMSY) that yields MSY.

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Maximum Sustainable Yield Formula

The following formula is commonly used to estimate Maximum Sustainable Yield (MSY) under a simple logistic population growth model.

MSY = \frac{rK}{4}

Variables:

  • MSY is the Maximum Sustainable Yield (e.g., individuals or biomass per unit time)
  • K is the carrying capacity of the environment (e.g., individuals or biomass)
  • r is the intrinsic rate of increase (per unit time)

To estimate MSY in the logistic model, multiply the carrying capacity (K) by the intrinsic rate of increase (r), then divide the result by 4. In this model, MSY occurs at a population size of K/2. Note that MSY is model- and assumption-dependent (for example, it assumes density-dependent logistic growth with constant r and K).

What is a Maximum Sustainable Yield?

Maximum Sustainable Yield (MSY) is a concept used in environmental science and fisheries management that refers to the largest long-run average catch that can be taken from a stock under a given set of assumptions and environmental conditions. The goal of MSY is to balance harvest with the stock’s ability to replenish so the population remains sustainable over time.

How to Calculate Maximum Sustainable Yield?

The following steps outline how to calculate the Maximum Sustainable Yield (MSY).

  1. First, determine the carrying capacity of the environment (K) in units of the species (or biomass).
  2. Next, determine the intrinsic rate of increase (r) per unit time.
  3. Next, gather the formula from above: MSY = (r × K) ÷ 4.
  4. Finally, calculate the Maximum Sustainable Yield (MSY).
  5. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem:

Use the following variables as an example problem to test your knowledge.

Carrying capacity of the environment (K) = 100 units of the species

Intrinsic rate of increase (r) = 0.2 per time period