Population Biology 3. Logistic Growth

We are trying to develop a mathematical model that helps us to understand patterns of population growth. So far our first attempt, the exponential growth model, did not help us to understand population growth (for reasons that I hope that you understand by now).

The "Real" world

In our attempt to think about population growth in the real world, we attempted to examine how per capita birth rates and per capita death rates should vary as population size varies. The model that describes this pattern of growth is known as the logistic growth model. It is important to realize that although this model is much more realistic, and therefore useful to us, than the exponential growth model, the logistic growth model still only examines what I call "the theoretical real world". That is, this model applies to our ideas about how populations should generally behave and do not thus relate directly to studying the population sizes of white tailed deer in central Texas or parrot fish on a coral reef in Fiji.

Logistic Growth

We have discussed why, in the real world, r should decrease as population sizes increase. If this is the case then there is a population size at which the per capita birth rate equals the per capita death rate. We call this population size the carrying capacity.

1) When populations are smaller than the carrying capacity we expect them to increase in size until they reach the carrying capacity.

2) When populations are larger than carrying capacity we espect them to decrease in size untile they reach the carrying capacity.

3) When the population size equals the carrying capacity we expect no change in the size of the population.

The logistic growth equation is a mathematical equation developed by biologists to describe patterns of population growth consistent with the ideas above. Before focusing on the biological isights that we can gain from the logistic growth model (the real purpose of everything we have been doing) it is important to really understand patterns of logistic growth. Hopefully, this powerpoint presentation will help you understand these patterns better.

Powerpoint Presentation

Click here for a powerpoint presentation entitled "Fun With Graphs- Logistic Growth"

http://www.slideshare.net/secret/gyB3cjnSplLw41

NOTE: THERE IS AN ERROR ON SLIDE 16 OF THIS PRESENTATION!!!

The title of the graph on slide 16 should read "Logistic Growth: dN/dt vs t (Not N), N initially << k"

The x-axis of the graph is TIME (please ignore the values of K on the x-axis because K does not belong on the time axis). The shape of the graph is correct. Make sure you change the x-axis to Time rather than Population Size.

Expected Learning Outcomes

By the end of this course a fully engaged students should be able to

- define the carrying capacity

- draw, and interpret the following graphs associated with logistic growth
a) how population size changes over time in logistic growth when the initial population size is much smaller than the carrying capacity
b) how population growth rate changes over time in logistic growth when the initial population size is much smaller than the carrying capacity
c) how the per capita growth rate varies over time in logistic growth

- discuss the causes for the shape of the s-curve (this answer will need to include a discussion of both math and biology)

- discuss the factors that regulate population size, be able to distinguish between density dependent and density independent factors that regulate population growth and give examples