Download Population Changes – Exponential and Logistic Growth

Population Changes – Exponential and Logistic Growth
Study Guide Topics:
 Explain population growth curves in terms of numbers and rates.
o S and J population curves describe a generalized response of populations to a particular set of conditions.
o Limiting factors will slow population growth as it approaches the carrying capacity of the system.
 Interpret graphical representations or models of factors that affect an organism’s niche.
Background:
The number of individuals in a population can change based on many variables. Density independent factors affect all
individuals in a population the same and may include physical factors such as climate, weather, or salinity or catastrophic
events such as floods, fires, or drought. Density dependent factors are more effective with a high-density population and
include food supply, disease, parasitism, competition and predation.
Populations show two types of growth, exponential and logistic. With exponential growth, a population increases by a fixed
percent and its resulting graph is the classic “J shaped” growth curve. Exponential growth occurs in nature with a small
population and ideal conditions; however, it cannot be sustained indefinitely. This is typical of microbes, invertebrates, fish,
and small mammals.
With logistic growth, due to of environmental resistance, population growth decreases as density reaches carrying capacity.
Carrying capacity (K) is the maximum number of individuals a habitat can support over a given period of time due to
environmental resistance. The graph of individuals vs. time yields an “S-shaped” growth curve. The maximum rate at which
a population can increase is its biotic potential. The biotic potential of a species is influenced by the age at which reproduction
begins, the time the species remains reproductive, and the number of offspring produced during each period of reproduction.
1. In an ecosystem many factors can limit the growth of population. These factors can be biotic or abiotic. In ecology
these are called limiting factors. Using the information above and your own knowledge, brainstorm as many factors as
you can.
2. In cooler climates, aphids (plant lice) go through a huge population increase during the summer months. In the fall,
their numbers decline sharply. Identify one density dependent and one density independent factor that regulates this seasonal
fluctuation.
3. Complete the following table for the two types of growth curves:
Growth curve
Exponential
Logistic
Shows unlimited,
unchecked growth
Growth limited by extrinsic
or intrinsic factors
Shape of curve
(S or J)
Shows carrying capacity
for a population.
Typical of short term
or long term growth
4. Directions: For each of the following scenarios answer whether it would be best represented by a logistic or exponential
growth curve. Justify your reasoning for each example.
a.
a strep bacterium invades your throat and reproduces for 4 hours
b. the flea population on a rat is monitored for 5 weeks with flea powder added
c.
loggerhead turtle populations are tracked for 5 years in the Atlantic
d. a lucky yeast cell falls into your glass of grape juice and reproduces for 10 hours
e.
bull frog population in a local pond is monitored for 3 seasons
Create a graph for each of the simulations below and answer the analysis questions.
Graph 1 : Yeast Growth in a 10 Hour Time Period
# Bacterial Cells
2
200
600
1000
1050
1045
4
6
8
10
Time (Hours)
0
2
5. Is the graph logistic or exponential? Explain.
6.
Will the graph continue to grow at the same rate? Explain.
7.
What do you predict will happen to this population after 20 hours? Justify your response.
8.
What type of feedback loop is represented by this situation?
#
10
15
30
90
Rabbits
Time
0
50
100
150
(Years)
Graph 2: Rabbit Growth in a 250 Year Time Period
9. Is the graph logistic or exponential? Explain.
250
700
800
900
1000
200
225
250
240
250
10. What is the carrying capacity of the graph? Explain.
11. What do you predict will happen to this population over the course of the next 100 years? Will it remain at the carrying capacity?
12. What type of feedback loop is represented by this situation?