From the first lesson on Population Ecology we learned that the population growth rate (dN/dt) can be calculated as the product of the per capita growth rate (r) and the population size (N).
dN/dt = rN
This is the fundamental equation describing population growth and this equation is always true.
If we want to use this equation to analyze how population sizes change over time, then it makes sense to start by examining the simplest formulation of this equation which occurs when the per capita growth rate is constant. The equation dN/dt = rN when r is constant is known as the exponential growth equation and this equation describes a patter on growth known as exponential growth.
The graph plotting how population size changes over time is shown in the Exponential Growth article. This graph shows an exponential growth curve (sometimes known as the "j-curve"). If you have questions about why the graph has this shape let me know and I will try to explain it more thoroughly.
It is important that you are able to look at this graph and determine all of the information held in the graph. The exponential growth curve allows us to discuss how two parameters change over time- 1) the population size (shown by the x-axis) and 2) the population growth rate (shown by the slope of the line). I find that it is easier to discuss only one parameter at a time so let's start with the population size.
1) Over time, the population size increases (we know this because the line has a positive slope).
Now let's think about the population growth rate.
2) Over time, the population growth rate increases (we know this becasue the line gets steeper over time.
3) Over time, the rate at which the population growth rate increases over time, increases over time (we know this because the slope increases faster and faster over time).
Thus, if populations are growing exponentially then they keep increasing in size at an ever faster rate forever and ever.
Now try this-
Can you draw the following graphs?
1) plot how the population growth rate varies over time.
(hint- we have alredy described what this pattern will look like using words- just turn these words into pictures).
2) plot how the population growth rate depends on population size.
(hint- this graph is a little trickier, but we do have an equation that relates the two variables)
3) plot how the per capita growth rate varies over time.
(hint- think about what the basic assumption we made aboiut exponential growth)
4) plot how the per capita growth rate
(see the hint from number 3)
Exponential Growth is Unrealistic
Because population sizes keep increasing at ever faster rates for ever, exponential growth does not seem to be an accurate description of population growth in most animals, plants, and microbes. If this is an unrealistic model then why did I teach it to you? I started with exponential growth becasue it is the simplest model of population growth and scientists always like to describe the world using the simplest models that they can.
Obviously, in this case we have started with a model that is too simple to realistically describe the world. What is wrong with the exponential growth model? The fundamental assumption we made about exponential growth is that the per capita growth rate is constant. This must not be a realistic assumtpion.
It is important that you understand, and are able to explain, both the mathematical reasons and biological reasons that exponential growth is an unreasonable model of population growth. I tried to explain biologically why exponential growth is unrealistic in the "Exponential Growth" article and the attached Powerpoint presentation so take a look at those.
Suggested Readings
Here are some articles you should look at from the Encyclopedia of the Earth. I wrote these so they are brilliant!!!
Population Ecology
http://www.eoearth.org/article/Population_ecology
Exponential Growth
http://www.eoearth.org/article/Exponential_growth
Logistic Growth
http://www.eoearth.org/article/Logistic_growth
Carrying Capacity
http://www.eoearth.org/article/Carrying_capacity
Intraspecific Competition
http://www.eoearth.org/article/Intraspecific_competition
Powerpoint Presentation
Click here for the Powerpoint presentation "Why is Exponential Growth Unrealistic?"
http://www.slideshare.net/secret/IDPugQtl2wvONv
Expected Learning Outcomes
By the end of this course a fully engaged student should be able to
- draw and interpret the following graphs associate with exponential growth
a) how population size change over time in
exponential growth
b) how population growth rate varies over time in exponential growth
c) how per capita growth rate changes over time in exponential growth
e) how per capita growth rate depends on population size in exponential growth
- explain why exponential growth is an unrealistic pattern of growth for most species
- define and explain the carrying capacity
