Calculator Inputs
Use the responsive input grid below. It shows three columns on large screens, two on medium screens, and one on mobile screens.
Example Data Table
| Variable | Example Value | Meaning |
|---|---|---|
| Colonization rate (c) | 0.45 | Empty patches are colonized fairly quickly. |
| Extinction rate (e) | 0.18 | Occupied patches face moderate local extinction risk. |
| Initial occupancy (p₀) | 0.35 | Thirty five percent of patches start occupied. |
| Total patches (N) | 120 | Landscape contains one hundred twenty habitat patches. |
| Time step and duration | 0.20 and 20 | Used for the Euler style occupancy simulation. |
| Detection probability and visits | 0.70 and 3 | Three visits produce strong detection coverage. |
| Equilibrium occupancy | 0.60 | Expected long run occupancy under these rates. |
| Net change at start | 0.039375 | Occupancy increases initially because c exceeds e. |
Formula Used
Meaning: occupancy changes through colonization of empty patches and extinction within occupied patches.
Meaning: this discrete update approximates the continuous Levins patch occupancy model over each chosen time step.
Meaning: equilibrium occupancy exists only when colonization exceeds extinction.
Meaning: repeated visits increase the chance of observing an occupied patch when detection is imperfect.
Meaning: this links true occupancy to the proportion likely detected during surveys.
How to Use This Calculator
- Enter colonization and extinction rates for your focal species.
- Provide the current occupancy as a fraction or percent.
- Set total patch count to convert proportions into occupied patches.
- Choose a time step and simulation duration for the trajectory.
- Enter detection probability and the number of survey visits.
- Press Calculate Occupancy to show the result block above the form.
- Review equilibrium occupancy, next-step change, detection performance, and the graph.
- Use the CSV and PDF buttons to export the results.
Frequently Asked Questions
1) What does patch occupancy mean?
Patch occupancy is the proportion of habitat patches currently occupied by a species. It summarizes landscape level presence without tracking every individual organism.
2) When does the model predict persistence?
Persistence is predicted when colonization exceeds extinction. In the Levins framework, that means c is greater than e, which produces a positive nonzero equilibrium occupancy.
3) Why include total patch count?
Total patch count converts occupancy proportions into expected occupied patches. That helps ecologists interpret the model using actual sites or habitat fragments.
4) What is equilibrium occupancy?
Equilibrium occupancy is the long run proportion of occupied patches predicted by the model. It is calculated as 1 minus e divided by c when colonization exceeds extinction.
5) Why add detection probability?
Real surveys often miss species even when patches are occupied. Detection probability helps estimate how much observed occupancy may fall below true occupancy.
6) What does the time step control?
The time step controls the size of each simulation update. Smaller steps usually create smoother trajectories and better approximate continuous dynamics.
7) Can this model represent all metapopulations?
No. It is a simplified model. Real systems may require patch quality, spatial distance, rescue effects, stochasticity, or species specific detection models.
8) How should I interpret a zero equilibrium result?
A zero equilibrium suggests colonization does not overcome extinction. Under current rates, long term regional occupancy is not expected to persist.