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.
- 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
Frequently Asked Questions
What is the minimum viable population?
The minimum viable population (MVP) is the smallest number of individuals needed for a 95% chance of survival over a set period. For most vertebrates, estimates range from 500 to 5,000.
Does this model account for inbreeding?
No. This simple exponential model ignores genetic factors. Small populations face inbreeding depression, which reduces fitness and can accelerate decline.
What is an extinction vortex?
An extinction vortex occurs when declining populations suffer compounding problems: reduced genetic diversity, inability to find mates, and loss of social structure, each accelerating the decline.
Ready to run the numbers?
Open Species Population Viability Calculator