Logistic Population Growth: Equation, Definition & Graph
Populations tend to get larger until there is no longer enough food or space to support so many individuals. This type of growth is called logistic population growth, and you can learn more about it in this lesson.
What Is Logistic Population Growth?
A group of individuals of the same species living in the same area is called a population. The measurement of how the size of a population changes over time is called the population growth rate, and it depends upon the population size, birth rate and death rate. As long as there are enough resources available, there will be an increase in the number of individuals in a population over time, or a positive growth rate. However, most populations cannot continue to grow forever because they will eventually run out of water, food, sunlight, space or other resources. As these resources begin to run out, population growth will start to slow down. When the growth rate of a population decreases as the number of individuals increases, this is called logistic population growth.
Graphing Logistic Population Growth
Logistic Growth
If we look at a graph of a population undergoing logistic population growth, it will have a characteristic S-shaped curve. The population grows in size slowly when there are only a few individuals. Then the population grows faster when there are more individuals. Finally, having lots of individuals in the population causes growth to slow because resources are limited. In logistic growth, a population will continue to grow until it reaches carrying capacity, which is the maximum number of individuals the environment can support.
Equation for Logistic Population Growth
We can also look at logistic growth as a mathematical equation. Population growth rate is measured in number of individuals in a population (N) over time (t). The term for population growth rate is written as (dN/dt). The d just means change. K represents the carrying capacity, and r is the maximum per capita growth rate for a population. Per capita means per individual, and the per capita growth rate involves the number of births and deaths in a population. The logistic growth equation assumes that K and r do not change over time in a population.
Logistic Growth Equation
Let’s see what happens to the population growth rate as N changes from being smaller than K, close or equal to K and larger than K. We will use a simple example where r = 0.5 and K = 100.
Populations Size Smaller Than Carrying Capacity
If N is very small compared to K, then the population growth rate will be a small positive number. This means the population is slowly getting larger because there are a few more births than deaths. For example, if N = 2, the population growth rate is 0.98. (Remember the units are individuals per time. We didn’t specify time in this example because it depends upon the species, but it is often measured in years or generation times.)
Logistic Growth Equation When N=2
Looking for a Similar Assignment? Order now and Get 10% Discount! Use Coupon Code “Newclient”
The post Logistic Population Growth: Equation, Definition & Graph appeared first on Superb Professors.
For any questions, feedback, or comments, we have an ethical customer support team that is always waiting on the line for your inquiries.