Logistic Population Growth Equation, Definition & Graph - Video & Lesson Transcript 6

Logistic Population Growth: Equation, Definition & Graph. An error occurred trying to load this video. Try refreshing the page, or contact customer support. You must create an account to continue watching. Register to view this lesson. As a member, you'll also get unlimited access to over 75,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed. Already registered? Login here for access. You're on a roll. Keep up the good work! Just checking in. Are you still watching? 0:00 Logistic Population Growth 0:50 Graphing & Equation for Growth 2:15 Below Carrying Capacity 3:05 Near Carrying Capacity 3:35 Larger Than Carrying Capacity 4:05 Lesson Summary. Want to watch this again later? Log in or sign up to add this lesson to a Custom Course. Recommended Lessons and Courses for You. Lynn has a BS and MS in biology and has taught many college biology courses. 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. 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. 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.)