In population ecology, the Finite Rate of Increase (λ – lambda) represents the factor by which a population changes during a specific time interval. It is a fundamental metric used to understand whether a biological population is growing, stable, or declining.
λ = (Nt+n / Nt)1/n
Where:
Nt: The starting population size.
Nt+n: The population size after 'n' periods.
n: The number of time steps (years, months, etc.).
How to Interpret the Results
λ > 1: The population is increasing. (e.g., λ = 1.05 means 5% growth).
λ = 1: The population is stable (stationary).
λ < 1: The population is declining. (e.g., λ = 0.95 means 5% decline).
Finite Rate (λ) vs. Intrinsic Rate (r)
While λ describes the discrete change per time step, the Intrinsic Rate of Increase (r) describes the instantaneous rate of change. They are mathematically linked by the formula: r = ln(λ). Use λ for discrete census data and r for continuous mathematical modeling.
Real-World Example
Imagine a herd of deer that starts with 200 individuals. One year later, the herd has 230 individuals. To find the finite rate of increase:
Initial Population (Nt) = 200
Final Population (Nt+1) = 230
λ = 230 / 200 = 1.15
This means the population is increasing at a rate of 15% per year (λ = 1.15).
function calculateFRI() {
var initialPop = parseFloat(document.getElementById('initialPop').value);
var finalPop = parseFloat(document.getElementById('finalPop').value);
var n = parseFloat(document.getElementById('timeSteps').value);
var resultDiv = document.getElementById('friResult');
if (isNaN(initialPop) || isNaN(finalPop) || isNaN(n) || initialPop <= 0 || n 1) {
interpretation = "The population is currently growing.";
} else if (lambda === 1) {
interpretation = "The population is stable.";
} else {
interpretation = "The population is declining.";
}
document.getElementById('interpretation').innerHTML = interpretation;
resultDiv.style.display = "block";
}