Local Extinction Rate Calculator

Calculator

Input method

Choose the dataset you actually have.

Time period

Must be greater than zero.

Time units

Rates are standardized to per year.

Initial occupied sites (N₀)

Used when method is sites.

Remaining occupied sites (N₁)

N₁ cannot exceed N₀.

Extinction events (k)

Used when method is events.

Taxa/populations tracked (n)

n must be positive.

Initial proportion (p₀)

Used when method is proportions.

Final proportion (p₁)

p₁ cannot exceed p₀.

Compute 95% confidence interval (sites/events only)

Example data table

Scenario	Method	Inputs	Key outputs
Habitat patches	Sites	N₀=120, N₁=95, t=5 years	p=0.2083, linear=0.0417/yr, exp=0.0468/yr
Monitored populations	Events	k=7, n=50, t=24 months	p=0.1400, linear=0.0700/yr, exp=0.0753/yr
Occupancy model output	Proportions	p₀=0.80, p₁=0.62, t=365 days	p=0.2250, linear=0.2250/yr, exp=0.2546/yr

Example outputs are illustrative and may differ slightly due to rounding.

Formula used

Extinction probability over the interval: p = (N₀ − N₁) / N₀ (or p = k / n).
Annualized linear rate: p_year = p / t_years.
Annualized exponential rate (hazard-style): r = −ln(S) / t_years, where S = N₁ / N₀.
Exponential half-life: t½ = ln(2) / r (if r > 0).
Optional 95% CI for p uses a Wilson binomial interval (sites/events only).

Interpretation tip: The exponential rate is often more stable when losses compound over time, while linear annualization is easier to explain in simple reporting.

How to use this calculator

Select the input method that matches your data source.
Enter the time period and choose units; outputs are per year.
Provide the required counts or proportions for the selected method.
Enable the confidence interval if you used sites or event counts.
Press Calculate; results will appear above the form.
Use CSV or PDF buttons to export the latest result.

FAQs

1) What does “local extinction” mean here?

It means disappearance from the monitored area or sites, not global species extinction. A population may persist elsewhere even if it vanishes locally.

2) Which method should I choose?

Use sites when you have occupied patches at two times. Use events when you tracked many taxa and counted extinctions. Use proportions for model-based occupancy outputs.

3) Why provide both linear and exponential rates?

Linear rates are intuitive and reportable. Exponential rates treat losses as compounding and can compare intervals more consistently when survival fractions drive change.

4) What if all sites are lost by the end?

The remaining fraction becomes zero, so the exponential rate tends toward infinity. In practice, report complete loss and interpret the time window as an upper bound.

5) Can I use months or days?

Yes. The calculator converts your input duration to years and reports annualized rates, helping you compare studies that use different time scales.

6) How is the 95% confidence interval computed?

For sites and event counts, the interval is a Wilson binomial confidence interval for the extinction probability over the interval. It is not computed for proportions.

7) Does detection probability affect results?

Yes. If surveys miss present populations, apparent extinctions can be inflated. Consider repeated surveys, occupancy models, or standardized protocols when detection is imperfect.

8) How should I report results in a paper?

Report the interval extinction probability, the duration, and the annualized rate type used. Include the sample size (sites or taxa) and uncertainty when available.