Enter the survivorship (lx) and fecundity (mx) for each age class. For demographic stability, fecundity should reflect female offspring per female.
Age Class (x)
Survivorship (lx)
Fecundity (mx)
1
2
3
Net Reproductive Rate (R₀):
0.00
What is the Net Reproductive Rate (R₀)?
The Net Reproductive Rate (NRR), denoted as R₀, is a fundamental concept in population ecology and demography. it represents the average number of female offspring that a female is expected to produce in her lifetime, taking into account the probability of her surviving to various ages.
In simple terms, R₀ tells us whether a population is growing, shrinking, or staying the same size. If every female replaces herself with exactly one daughter on average, the population remains stable.
The Mathematical Formula
To calculate the net reproductive rate, you sum the product of age-specific survivorship and age-specific fecundity across all age classes:
R₀ = Σ (lx * mx)
x: The age class or interval.
lx: Survivorship — the proportion of individuals surviving from birth to the beginning of age class x.
mx: Fecundity — the average number of female offspring produced by a female during the age interval x.
How to Interpret the Results
Once you have calculated the R₀ value, you can determine the trajectory of the population:
R₀ > 1: The population is increasing. Each female is producing more than one daughter on average.
R₀ = 1: The population is stable. This is often referred to as replacement-level fertility.
R₀ < 1: The population is decreasing. Females are not producing enough offspring to replace themselves.
Step-by-Step Calculation Example
Imagine a species with three age classes:
Age 1: Survivorship (lx) is 1.0 (all start here). Fecundity (mx) is 0 (too young to reproduce). Product: 1.0 * 0 = 0.
Age 2: Survivorship (lx) is 0.6. Fecundity (mx) is 1.5. Product: 0.6 * 1.5 = 0.9.
Age 3: Survivorship (lx) is 0.2. Fecundity (mx) is 2.0. Product: 0.2 * 2.0 = 0.4.
Total R₀: 0 + 0.9 + 0.4 = 1.3. Since 1.3 is greater than 1, this population is growing by 30% per generation.
Why Only Female Offspring?
Demographers usually focus on females because the number of females in a population is the primary limiting factor for reproductive output. While males are necessary for reproduction in most species, the "carrying capacity" for new births is dictated by the number of fertile females.
function addNrrRow() {
var table = document.getElementById("nrrBody");
var rowCount = table.rows.length;
var row = table.insertRow(rowCount);
var cell1 = row.insertCell(0);
var cell2 = row.insertCell(1);
var cell3 = row.insertCell(2);
cell1.innerHTML = rowCount + 1;
cell2.innerHTML = ";
cell3.innerHTML = ";
}
function calculateNRR() {
var lxs = document.getElementsByClassName("lx-input");
var mxs = document.getElementsByClassName("mx-input");
var totalR0 = 0;
var validData = false;
for (var i = 0; i 1.0001) {
interpDisplay.innerHTML = "Interpretation: The population is growing (R₀ > 1).";
interpDisplay.style.color = "#2e7d32";
} else if (totalR0 < 0.9999) {
interpDisplay.innerHTML = "Interpretation: The population is declining (R₀ < 1).";
interpDisplay.style.color = "#c62828";
} else {
interpDisplay.innerHTML = "Interpretation: The population is stable (R₀ ≈ 1).";
interpDisplay.style.color = "#1565c0";
}
resultBox.scrollIntoView({ behavior: 'smooth', block: 'nearest' });
}