# Population Growth

## Growth Limiting Factors

Population growth is limited by environmental factors, which contribute to the carrying capacity of a population. There are two broad types of these limiting factors: density-dependent and density-independent.

**Density-dependent factors** will inhibit the growth rate, by increasing the death rate or decreasing the birth rate, based on the population density. An example of this is with limited resources: as the population density increases, food may become more scarce, increasing competition and limiting the population. Factors such as territory, water, food, light, etc. are examples of density-dependent factors. As infectious diseases experience increased transmission with higher population density, they too are a density-dependent factor.

**Density-independent factors** will change the birth and death rates, but they will not change with the population density. An example of this could be a drought, which would limit the population regardless of its size. Such factors are typically abiotic and include things such as natural disasters, pollutants, and climate.

# Calculating Population Growth

It is sometimes important to calculate the change in size of a population. There is a fairly simple equation to do so, which is seen to the right where:

N = population size

t = time

B = births

D = deaths

That may not always be the entire story, however, as individuals can leave the population without being born or dying. So this equation can be extended to the lower one, where:

I = immigrations

E = emigrations

At its essence, this equation can be simplified to:

change in population = those coming into the population - those leaving the population

If the answer you get is positive, the population has grown. If it is negative, the population is shrinking.

Let's look at a quick example.

A population of 86 penguins had 17 births and 8 deaths this past summer. Two penguins were taken from the flock to be added to a zoo and no new penguins migrated in. How has this population changed over the past year?

### Click here for the solution

(population change)/(1 year) = (births + immigrations) - (deaths + emigrations)

(population change)/(1 year) = (17+0) - (8+2)

(population change)/(1 year) = (17) - (10)

population change in one year = 7 penguins

Reproduction without constraints can result in the exponential growth of a population.

N = population size

t = time

rmax = maximum per capita growth rate of the population (the biotic potential)

When populations are limited due to growth limiting factors and carrying capacity, it is common to see logarithmic growth models, especially in K-selected species.

N = population size

t = time

rmax = maximum per capita growth rate of the population (the biotic potential)

K = carrying capacity