0.081093
per period
50
%
8.4472
%
1.084472
0.081093
per period
50
%
8.4472
%
1.084472
The Population Growth Rate Calculator computes the intrinsic rate of natural increase (r) from observed population sizes at two time points. It also provides the total percent change, the per-period growth rate, and the finite growth rate (lambda). These metrics are fundamental for comparing growth across species, populations, and time periods.
Enter the initial population, the population at a later time, and the time elapsed between measurements. This tool is used in ecology for population viability analysis, wildlife management, and conservation planning.
The intrinsic growth rate is calculated from the exponential growth model:
r = ln(Nt / N0) / t
Where ln is the natural logarithm. Related measures include:
Total percent change = ((Nt - N0) / N0) x 100
Per-period growth rate (%) = (e^r - 1) x 100
Finite growth rate: lambda = e^r
Lambda greater than 1 indicates growth, lambda equal to 1 indicates stability, and lambda less than 1 indicates decline. The value r is the continuous-time equivalent, used in differential equation models.
Inputs
Results
A population growing from 500 to 750 over 5 periods has r = 0.081, meaning about 8.4% growth per period, and lambda = 1.084.
Inputs
Results
A population declining from 1000 to 600 over 10 periods has a negative r = -0.051 and lambda = 0.95, indicating a 5% decline per period.
The intrinsic growth rate r is the continuous-time growth rate used in differential equation models (dN/dt = rN). Lambda is the discrete-time finite growth rate (Nt+1 = lambda x Nt). They are related by lambda = e^r. Both convey the same information: r > 0 means lambda > 1 (growth), r = 0 means lambda = 1 (stable), r < 0 means lambda < 1 (decline).
In conservation, r (or lambda) is used to assess population viability. A population with lambda consistently below 1 (negative r) is declining and may face extinction without intervention. Population viability analysis (PVA) uses growth rates to project future population sizes and estimate extinction probabilities over time horizons of decades to centuries.
This calculator computes the average growth rate over the entire observation period. If growth varies seasonally or between years, the calculated r represents the geometric mean rate. For more detailed analysis of variable growth, stochastic population models or time-series methods that account for environmental and demographic variation should be used.
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