Calculator Inputs
Plotly Preview Graph
This preview uses the example values below. Submit your own values to refresh the graph and result table.
Example Data Table
| Scenario | Total Patches | Occupied | Mean Local Pop. | K | Colonization | Extinction | Habitat Quality | Connectivity % | Detection | Growth | Steps |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Forest amphibian | 40 | 18 | 55 | 90 | 0.24 | 0.12 | 1.10 | 18 | 0.85 | 0.08 | 10 |
| Island bird | 25 | 12 | 34 | 60 | 0.19 | 0.15 | 0.95 | 12 | 0.78 | 0.05 | 8 |
| Wetland insect | 60 | 28 | 22 | 40 | 0.31 | 0.09 | 1.18 | 24 | 0.82 | 0.11 | 12 |
Formula Used
This calculator combines observed patch occupancy, imperfect detection correction, Levins-style metapopulation dynamics, and logistic local growth to estimate both present and projected total size.
Detection-corrected occupancy: p_corr = min(1, p_obs / d)
Effective colonization: c_eff = c × q × (1 + k / 100)
Effective extinction: e_eff = e / q
Equilibrium occupancy: p_eq = max(0, min(1, 1 − e_eff / c_eff))
Effective occupancy: p_eff = (p_corr + p_eq) / 2
Current metapopulation size: M₀ = P × p_eff × N̄
Patch update: p_t+1 = p_t + c_eff p_t (1 − p_t) − e_eff p_t
Local growth update: N_t+1 = N_t + rN_t(1 − N_t / K)
Projected size: M_t = P × p_t × N_t
Here, P is total patches, O is observed occupied patches, d is detection probability, c is colonization rate, e is extinction rate, q is habitat quality, k is connectivity percentage, N̄ is mean local population, r is growth rate, and K is local carrying capacity.
How to Use This Calculator
- Enter the total number of habitat patches in the landscape.
- Add the number of patches currently observed as occupied.
- Provide the average number of individuals per occupied patch.
- Set local carrying capacity to limit within-patch growth.
- Enter colonization and extinction rates for one time step.
- Adjust habitat quality and connectivity to reflect landscape structure.
- Use detection probability to correct for missed occupied patches.
- Add local growth rate and choose the number of projection steps.
- Press the calculate button to show results above the form.
- Use the CSV and PDF buttons to save the result summary.
Frequently Asked Questions
1) What does metapopulation size mean?
Metapopulation size is the estimated total number of individuals distributed across multiple habitat patches, not just the number in one patch.
2) Why is detection probability included?
Field surveys may miss occupied patches. Detection probability adjusts observed occupancy upward when imperfect observation would otherwise underestimate regional abundance.
3) What is equilibrium occupancy?
Equilibrium occupancy is the long-run fraction of patches expected to remain occupied when colonization and extinction pressures balance over time.
4) How do colonization and extinction affect results?
Higher colonization supports recolonization of empty patches, while higher extinction removes occupied patches. Their balance strongly shapes persistence and projected abundance.
5) Why are habitat quality and connectivity separate inputs?
Habitat quality influences survival and stability within patches. Connectivity affects dispersal among patches. Together they alter colonization success and extinction pressure.
6) What does carrying capacity change in the model?
Carrying capacity limits how large each occupied local population can grow. It keeps projected abundance biologically realistic under positive growth rates.
7) Can I use a negative local growth rate?
Yes. A negative value models local decline inside occupied patches, which is useful for stressed habitats, resource shortages, or deteriorating conditions.
8) Is this calculator a substitute for field ecology studies?
No. It is a planning and teaching tool. Field data, species-specific dynamics, demographic structure, and spatially explicit models may still be necessary.