What this calculator does
Lotka–Volterra predator–prey rates works out instantaneous population growth rates for a classic predator–prey pair. Enter your own figures above and the answer updates as you type: nothing is fixed in the code, so the result reflects exactly the numbers you supply.
The formula this calculator evaluates is printed under the tool and explained below, so you can check the working by hand or reuse it in a spreadsheet.
The formula
FormuladPrey/dt = αPrey − βPrey·Predator; dPredator/dt = δPrey·Predator − γPredator
The inputs explained
| Field | What to enter |
|---|---|
| Prey population | A number. Starts at 1000. |
| Predator population | A number. Starts at 50. |
| Prey growth rate α (/year) | A number, measured in /year. Starts at 0.5. |
| Predation rate β | A number. Starts at 0.02. |
| Predator growth efficiency δ | A number. Starts at 0.01. |
| Predator death rate γ (/year) | A number, measured in /year. Starts at 0.3. |
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How the answer changes with prey population
Every other input is held at the calculator’s starting values while prey population varies. Select any row to load that scenario into the calculator.
How the answer changes with prey population
| Prey population | Prey growth rate dPrey/dt | Predator growth rate dPredator/dt | Prey trend |
|---|---|---|---|
| 500 | -250.0 /year | 235.0 /year | declining |
| 750 | -375.0 /year | 360.0 /year | declining |
| 1,000 | -500.0 /year | 485.0 /year | declining |
| 1,500 | -750.0 /year | 735.0 /year | declining |
| 2,000 | -1,000.0 /year | 985.0 /year | declining |
| 3,000 | -1,500.0 /year | 1,485.0 /year | declining |