AP Environmental Science
DoDEA Virtual High School
Population Logistic Growth: Virtual Lab
Name of Student:
Date:
Like the individual organism, the population is a real and functional unit in biology.
Defined as groups of organisms that are genetically and spatially distinct from other such
groups, the population is the fundamental unit of evolution. Populations are dynamic,
they grow, decline, colonize new populations, and go extinct. Understanding how and
why populations change over time is critical to such wide-ranging practical issues as pest
control, endangered species protection, and even human population growth. In this lab,
you will explore the effects of birth rate and survivability on population sizes, carrying
capacity and growth rate.
Please open the site below to complete your lab.
http://www.virtualbiologylab.org/Models/Model_LogisticGrowth.html
Begin this lab by taking a moment to view your parameters. This model illustrates
resource-limited population growth. Populations have a per-capita growth rate and
carrying capacity. Two populations are compared on three graphs: N vs time, dN/dt vs N,
and dN/Ndt vs N. Individuals in the populations are viewed in windows, illustrating that
even at carrying capacity, there are still births and deaths in the population.
The number of individuals in a population (N) will grow if individuals reproduce at a rate
sufficient to replace themselves plus some more. As the population grows over time,
more and more individuals reproduce at this rate and the overall population grows faster
and faster. This is the basis of the exponential growth model.
Based on this model, the potential for populations to grow can be extreme (actually infinite).
Imagine the bacterium E. coli, which has the ability to asexually reproduce by dividing once
every twenty minutes. One bacterium is microscopic and invisible to the naked eye, but if
one bacterium and its descendants reproduce every 20 minutes, the population will double in
size three times an hour. At this rate the mass of the bacteria population will outweigh the
Earth within two days! Obviously this doesn’t happen, or we all would have drowned in E.
coli by now. So what limits the growth of bacteria? A student once suggested that a popular
brand of spray disinfectant would do the trick. More generally though, population growth is
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limited because individuals reproduce less, and/or die more as resources (food, water, space,
etc.) are depleted, and/or they their environment with their waste products. One of the
assumptions of the exponential growth model is that resources are infinite, thus the
biologically unrealistic predictions.
The logistic population growth model is a simple modification of the exponential model
which produces much more realistic predictions. This model factors in negative feedback, in
which the realized per capita growth rate decreases as the population size increases. It also
introduces a theoretical carrying capacity, which is the maximum sustainable population
size. In this model the population growth rate for a given size is described by the equation
dN/dt = rN(1- N/K) , which adds:
(1- N/K), the negative feedback term containing
K, the carrying capacity
This equation is sometimes called the Verhulst-Pearl equation.
By inspection, one can see that when N is low, the negative feedback term approaches 1 and
the population grows more-or-less exponentially. However, when N approaches K, the
negative feedback term approaches 0 causing the overall growth rate to approach 0. It is
important to note that dN/dt is the change in the population size over time, that is to say that
when dN/dt = 0, the population size will remain stable.
Begin by sliding the tab on the top of the graph to make the simulation run more slowly.
(slide it to the left) about half way. Notice that your population in each sample is N=5. Click
the Go button and allow the graphs to proceed through approximately 500-600 ticks (the ticks
are counted in the upper left-hand corner). Hit the Go button again to pause the simulation at
about 500 ticks.
1. The Population Size graph on the left has a very distinct shape. Describe this shape.
2. This shape is representative of which type of population growth? (logistic or exponential)
3. Near the 500 tick mark, the population size begins to level out. Push the go button once
more for about another 500 ticks (total approximately 1000 ticks). What is the term for this
leveling out when the limit of an environment’s ability to support a population has been
reached?
4. Using your mouse, hover over the exact point when the red line has reached its maximum
level. What is the population size at this point?
What is the time this level is
reached?
5. In the second graph (Population Growth Rate), determine when the growth rate was
highest for the Red line. Give the population size (N) and the dN/d10 values by hovering
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over the spot on the graph with your mouse.
6. Using the population size you determined on #5, go back to the first graph (Population
Size) and locate when the population growth rate was at its fastest. Describe where you
find this point on the graph.
Adjusting the r and K factors can have affects on population growth.
7. Describe some of the characteristics common to organisms that are referred to as rstrategists or r-selected species. (use your text)
8. Describe some of the characteristics common to organisms that are referred to as k
strategists or k-selected species.
9. Reset your simulation by clicking the Setup button. For the red species, increase the r
value to 5.0. Click the Go button and let it tick for only 30 ticks (click Go again to pause
it). What do you notice about the population and growth rate of the red species as
compared to the blue (which is the same as the red was in the last simulation)?
10. Click Go again to allow the simulation to continue until you reach approximately 200
ticks. At what time did the red species reach its carrying capacity?
11. Reset your simulation again by clicking the Setup button. Move your r-value back
down to 1.0 for the red species and now move the K-value to 1000. Click go and watch
your simulation until approximately 600 ticks have passed. Is the TIME to reach
carrying capacity greatly different between the red and blue species in this simulation?
12. What is the difference between the red and blue populations when the K-value is
increased for the red species?
13. Repeat step 11and set your k-value to 50. Click Go and run the simulation until
approximately 500 ticks. In this simulation, what is the difference between the red and
blue populations when the k-value is decreased dramatically?
14. Reset your simulation and set your K-value back to 500. Now, adjust the r-value for
the red species to .2. Click Go and let the simulation run for1000 ticks. Click Go to
pause. Notice the blue population has already reached carrying capacity. Record the
time when it reached this point.
15. Now, click Go again to resume the simulation until you reach about 2500 ticks. At
what time did the red species reach its carrying capacity?
16. Which factor, birth-rate (r), or survivability (K) had the greatest impact on how fast a
population reached its carrying capacity?
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AP Environmental Science
DoDEA Virtual High School
17. Advances in medicine have come a long way in assisting humans with maintaining
healthier, longer lives as well as assisting with the healthy delivery of babies. When
thinking about human over population issues, which aspect do you think has had the
greatest impact on our exponential growth rate at this time? Is it our ability to keep
people alive (both young and old) through the use of medicines? Or is it our choices in
family size? (birth rate) Explain your answer based on the results of this experiment.
You do not need to address any ethical or cultural issues at this time – simply note which
may be the greatest contributor to human population numbers.
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