Simulation Inputs
The page stays single-column overall, while the calculator fields use a responsive 3-column, 2-column, and 1-column layout.
Example Data Table
This sample uses the logistic model for a medium-sized species population under mild harvesting pressure and low environmental noise.
| Parameter | Example value | Interpretation |
|---|---|---|
| Model | Logistic | Growth slows near the carrying limit. |
| Initial population | 120 | Starting abundance at time zero. |
| Time steps | 24 | Twenty-four simulation intervals. |
| Intrinsic growth rate | 0.22 | Strong but realistic biological growth potential. |
| Carrying capacity | 800 | Environmental limit for sustained abundance. |
| Birth rate / Death rate | 0.10 / 0.04 | Net demographic contribution is positive. |
| Immigration / Emigration | 2 / 1 | Net inflow adds one individual per step. |
| Shock | Step 12 at 0.88 | Represents a sudden habitat disturbance. |
Formula Used
Effective growth rate: r_eff = r + birth_rate - death_rate
Exponential model: N(t+1) = N(t) + [r_eff × N(t) - harvest × N(t)] × dt + (immigration - emigration) × dt
Logistic model: N(t+1) = N(t) + [r_eff × N(t) × (1 - N(t)/K) - harvest × N(t)] × dt + net migration × dt
Ricker model: N(t+1) = N(t) × exp[r_eff × (1 - N(t)/K) × dt] - harvest term + net migration
Predator-prey prey equation: Prey(t+1) = Prey(t) + [r_eff × Prey × (1 - Prey/K) - a × Prey × Predator - harvest × Prey] × dt + net migration × dt
Predator equation: Predator(t+1) = Predator(t) + [b × a × Prey × Predator - m × Predator] × dt
Environmental stochasticity: the growth term is multiplied by 1 ± stochasticity. Shock multiplier: population values are scaled at the selected shock step.
How to Use This Calculator
- Select the biological model that best matches your scenario.
- Enter starting abundance, time horizon, and step interval.
- Set growth, births, deaths, migration, and harvesting values.
- Provide carrying capacity for crowding-based models.
- For predator-prey mode, enter predator-specific parameters.
- Add stochasticity or a timed shock to test disturbances.
- Press Run Simulation to display results above the form.
- Review summary metrics, charted trajectories, and the full results table.
- Use the export buttons to save simulation outputs as CSV or PDF.
Frequently Asked Questions
1. Which model should I choose first?
Use exponential for unchecked growth, logistic for resource-limited growth, Ricker for discrete density dependence, and predator-prey when consumer interactions strongly shape the system.
2. What does carrying capacity represent?
Carrying capacity is the approximate abundance that local resources can support over time. As population size approaches that value, net growth slows.
3. Why include separate birth and death rates?
Separate demographic rates let you test management, disease, fertility shifts, or survival changes without changing the baseline intrinsic growth setting.
4. What does stochasticity change?
Stochasticity introduces random variation into growth, helping you explore environmental uncertainty, volatile habitats, and unstable population paths.
5. How should I interpret a shock multiplier?
A value below one simulates a crash, disturbance, or die-off. A value above one simulates a sudden boost, restocking event, or improved habitat.
6. Why can predator-prey cycles oscillate?
Predators increase when prey is abundant, then prey declines under predation. Reduced prey later lowers predator numbers, allowing prey recovery and renewed cycling.
7. Can I use this for conservation planning?
Yes, it is useful for scenario testing and educational planning. Real conservation decisions still need field estimates, uncertainty bounds, and validated species-specific data.
8. What does “approaching steady state” mean?
It means the last two simulated values changed very little. The modeled system may be nearing equilibrium under the chosen assumptions.