PhysSandbox
Classical MechanicsWaves & SoundElectricity & MagnetismOptics & LightGravity & OrbitsLabs
🌙Astronomy & The Sky🌡️Thermodynamics🌍Biophysics, Fluids & Geoscience📐Math Visualization🔧Engineering🧪Chemistry

More from Biophysics, Fluids & Geoscience

Other simulators in this category — or see all 42.

View category →
NewUniversity / research

Leslie Matrix Age-Structured Population

Fertility and survival matrix model: total population trajectory, dominant eigenvalue lambda, and stable age distribution.

Launch Simulator
NewUniversity / research

SIR Vaccination Threshold

Herd-immunity threshold simulator: R_eff = R0(1-v), SIR outbreak curves, peak infected, and final size vs vaccine coverage.

Launch Simulator
NewUniversity / research

Reaction-Diffusion Turing Patterns

Activator-inhibitor reaction-diffusion toy with spots, stripes, worms presets, diffusion ratio, and schematic dispersion relation.

Launch Simulator
NewUniversity / research

Hodgkin–Huxley Action Potential

Squid-axon HH ODEs: membrane voltage V(t) and gating (m, h, n); step stimulus and Na⁺/K⁺ conductance traces.

Launch Simulator
NewUniversity / research

Cardiac Action Potential

FitzHugh–Nagumo/Noble-style cardiac toy: fast upstroke, plateau-like repolarization, refractory recovery gate, and S1-S2 premature-stimulus capture vs block.

Launch Simulator
NewUniversity / research

Calcium Waves / IP3 Oscillator

Li-Rinzel-style IP3 receptor oscillator: cytosolic Ca, ER store, calcium-induced calcium release, SERCA refilling, flux traces, and a Ca–h phase portrait.

Launch Simulator
PhysSandbox

Interactive physics, chemistry, and engineering simulators for students, teachers, and curious minds.

Physics

  • Classical Mechanics
  • Waves & Sound
  • Electricity & Magnetism

Science

  • Optics & Light
  • Gravity & Orbits
  • Astronomy & The Sky

More

  • Thermodynamics
  • Biophysics, Fluids & Geoscience
  • Math Visualization
  • Engineering
  • Chemistry

© 2026 PhysSandbox. Free interactive science simulators.

PrivacyTermsContact
Home/Biophysics, Fluids & Geoscience/Logistic Harvest & Maximum Sustainable Yield

Logistic Harvest & Maximum Sustainable Yield

A logistic population grows as rN(1-N/K). Constant harvest subtracts H, producing the classic maximum sustainable yield at N=K/2 with H_MSY=rK/4. Below MSY there are two equilibria: a lower unstable collapse threshold and an upper stable stock. Above MSY no positive equilibrium remains.

Who it's for: Ecology, fisheries science, environmental management, and differential equations courses.

Key terms

  • Logistic growth
  • Harvest
  • Maximum sustainable yield
  • Collapse threshold
  • Equilibrium
  • Carrying capacity

When H exceeds MSY no positive equilibrium exists. Below MSY there are two equilibria: the lower one is a collapse threshold and the upper one is stable.

Live graphs

Population model

0.45 1/y
100
9/y
70

Measured values

Maximum sustainable yield11.25
Collapse threshold27.64
Stable stock72.36
Final N72.36

How it works

Logistic population growth with constant harvest, maximum sustainable yield, stable equilibrium, and collapse threshold.

Key equations

dN/dt = rN(1−N/K) − H
MSY occurs at N=K/2 with H_MSY=rK/4

Frequently asked questions

Why can a stock collapse even below MSY?
Below MSY the lower equilibrium is unstable. If the population starts below that threshold, harvest exceeds biological growth and the stock declines.
Is MSY a management recommendation?
It is a simple textbook benchmark. Real management adds uncertainty, age structure, economics, and precautionary buffers.