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 * 100

Doubling/Halving Time

doubling_time = abs(log(2) / growth_rate)

Variables

VariableDescriptionDefault
current_popCurrent Population500
birth_rateAnnual Birth Rate(per capita)0.12
death_rateAnnual Death Rate(per capita)0.1
yearsProjection Period(years)50
growth_rateDerived value= birth_rate - death_ratecalculated

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
  1. 01Net growth rate = 0.12 - 0.10 = 0.02 (2%/year)
  2. 02Projected = 500 x e^(0.02 x 50) = 500 x e^1.0 = 500 x 2.718 = 1,359
  3. 03Doubling time = ln(2) / 0.02 = 34.7 years