Lotka-Volterra Calculator
Simulate predator-prey population dynamics using the classic Lotka-Volterra equations. Model ecosystem interactions, population cycles, and ecological stability.
Lotka-Volterra Equations
dx/dt = αx - βxy (Prey dynamics)
α = reproduction, β = predation rate
dy/dt = δxy - γy (Predator dynamics)
δ = efficiency, γ = death rate
Example Systems
Model Parameters
Prey Parameters
Prey growth rate without predators
Starting number of prey
Predator Parameters
Predator death rate without prey
Starting number of predators
Interaction Parameters
Rate of successful hunts
Prey converted to new predators
Simulation Settings
Smaller = more accurate
System Analysis
Stable Prey Pop.
20.0
Stable Predator Pop.
5.0
Period
N/A
Simulation Length
22.9
Population Statistics
Prey Population
Maximum
100.0
Minimum
1.0
Range
99.0
Predator Population
Maximum
17.7
Minimum
10.0
Range
7.7
Population Dynamics
Population Time Series Chart
Blue: Prey, Red: Predator
Data Points: 230
Final Populations: Prey: 1.0, Predator: 11.5
Management Recommendations
One or both populations went extinct
Consider reducing predation rate (β)
Increase prey reproduction rate (α)
Adjust initial population sizes
This system is not sustainable
Mathematical Background
Model Assumptions
- • Unlimited prey resources: Prey has unlimited food
- • Specialist predator: Predator only eats the prey species
- • Proportional encounters: Interaction rate depends on both populations
- • No external factors: No disease, climate change, or migration
- • Continuous reproduction: Populations can reproduce at any time
Parameter Interpretation
- • α (alpha): Prey birth rate without predation
- • β (beta): Predation efficiency per encounter
- • γ (gamma): Predator death rate without prey
- • δ (delta): Conversion of prey to new predators
- • Fixed points: Stable prey = γ/δ, Stable predator = α/β
Real-World Applications
Wildlife Management
Lynx-snowshoe hare cycles in Canada, wolf-deer dynamics in Yellowstone
Marine Ecology
Fish-shark interactions, plankton-fish dynamics in ocean ecosystems
Microbiology
Bacteria-bacteriophage systems, host-parasite interactions