Species Population Viability Calculator Formula
Understand the math behind the species population viability calculator. Each variable explained with a worked example.
Formulas Used
Projected Population
projected_pop = round(current_pop * pow(2.71828, growth_rate * years))Net Growth Rate
net_growth_rate = growth_rate * 100Doubling/Halving Time
doubling_time = abs(log(2) / growth_rate)Variables
| Variable | Description | Default |
|---|---|---|
current_pop | Current Population | 500 |
birth_rate | Annual Birth Rate(per capita) | 0.12 |
death_rate | Annual Death Rate(per capita) | 0.1 |
years | Projection Period(years) | 50 |
growth_rate | Derived value= birth_rate - death_rate | calculated |
How It Works
Population Viability Analysis
Population viability analysis (PVA) projects whether a species can sustain itself over time. The simplest model uses exponential growth.
Formula
N(t) = N0 x e^(r x t)
Where N0 is the current population, r is the net growth rate (birth rate minus death rate), and t is time in years. A positive r indicates growth; negative r indicates decline. The minimum viable population for most mammals is estimated at 500-5,000 individuals.
Worked Example
500 individuals with a 12% birth rate and 10% death rate, projected 50 years.
current_pop = 500birth_rate = 0.12death_rate = 0.1years = 50
- 01Net growth rate = 0.12 - 0.10 = 0.02 (2%/year)
- 02Projected = 500 x e^(0.02 x 50) = 500 x e^1.0 = 500 x 2.718 = 1,359
- 03Doubling time = ln(2) / 0.02 = 34.7 years
Ready to run the numbers?
Open Species Population Viability Calculator