How to Calculate Population Growth Rate Biology

How to Calculate Population Growth Rate in Biology

Understanding population dynamics is a cornerstone of ecology and conservation biology. The population growth rate helps scientists determine whether a species is thriving, declining, or remaining stable within an ecosystem. This calculator uses the fundamental components of population change—natality, mortality, immigration, and emigration—to compute the growth rate.

The Core Components

To accurately calculate the growth of a biological population, four specific variables must be tracked over a specific time period ($t$):

• Natality (B): The number of births produced by the population.
• Mortality (D): The number of deaths within the population.
• Immigration (I): The number of individuals moving into the population from elsewhere.
• Emigration (E): The number of individuals moving out of the population.

The Population Growth Formula

The simplest way to calculate the change in population size ($\Delta N$) is by balancing the inputs against the outputs:

$\Delta N = (B + I) – (D + E)$

To find the per capita growth rate ($r$), which allows for comparison between populations of different sizes, we divide the net change by the initial population size ($N_0$):

$r = \frac{(B + I) – (D + E)}{N_0}$

This result is often expressed as a percentage by multiplying by 100.

Interpreting the Results

• Positive Growth ($r > 0$): The population is increasing. Inputs (Births + Immigration) exceed outputs (Deaths + Emigration).
• Negative Growth ($r < 0$): The population is declining. Outputs exceed inputs.
• Zero Growth ($r = 0$): The population is stable, a state often referred to as Zero Population Growth (ZPG).

Exponential vs. Logistic Growth

The calculation above assumes a snapshot in time. In biology, populations tend to follow two main patterns:

1. Exponential Growth (J-Curve): Occurs under ideal conditions with unlimited resources. The population grows slowly at first and then accelerates rapidly. This is calculated as $dN/dt = rN$.

2. Logistic Growth (S-Curve): In reality, resources are limited. As the population approaches the environment's Carrying Capacity (K), growth slows down. This is calculated as $dN/dt = rN((K-N)/K)$.

Example Calculation

Let's say we are studying a population of deer:

• Initial Population ($N_0$): 1,000
• Births ($B$): 150
• Deaths ($D$): 50
• Immigration ($I$): 20
• Emigration ($E$): 10

Net Change: $(150 + 20) – (50 + 10) = 170 – 60 = 110$ deer.

Growth Rate ($r$): $110 / 1,000 = 0.11$.

Percentage: $11\%$. The population grew by 11% over the time period.