BIOLOGY SEMESTER ONE
LAB 9
LAB 9: POPULATION GROWTH
Lab format: this lab is delivered though lab kit
Relationship to theory: In the textbook (Reece et al., 9th ed.), this lab is related to the following unit:
LEARNING OBJECTIVES
After completing this laboratory, you should be able to:
1.
2.
3.
4.
Describe how populations grow.
Describe how resources affect population growth
Discuss how human population is increasing
Use a spreadsheet program (e.g. Microsoft Excel) to manipulate data
INTRODUCTION
Population growth
Species have a high reproductive potential (capacity for population growth). For example insects and
fish typically lay several hundred eggs, while clams can release several thousand eggs. Normally, this
huge potential is kept in check by the carrying capacity of the environment (resources become too
scarce to support further growth).
The capacity for growth is a measure of the success of a population of a species. Because there are so
many interactions between individuals and the environment, measuring how well populations grow is
often complex. Population biologists frequently use mathematical growth models to help them study
real populations.
Population models might seem like all theory and math, but they help us understand real ecological
systems in simpler terms. They are used for testing theories, making predictions, and for making
decisions about managing or conserving species’ populations. Models help conservation biologists and
wildlife managers make decisions, like how large a nature reserve should be to sustain a population.
Although the factors that control a population's growth are fairly complex, ecologists have found that
some relatively simple equations do a reasonable job of modeling population growth. Many models for
population growth have been put forward, but one of the more commonly-used equations is the
exponential equation of population growth:
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Where:
dN / dt means “change in N per unit time
r is the per capita rate of increase
rmax is a special case of r (intrinsic rate of increase). Under optimum conditions, it refers to the
birth rate – the death rate.
As the population size (N) increases, the rate of population increase
(dN/dt) also gets larger.
While the exponential model can describe some populations in ideal environments, it is generally too
simple. The logistic model is one step in complexity above the exponential model. It is more realistic and
is the basis for most complex models in population ecology. Don't forget, though, that even this model
simplifies the true complexities found in population biology.
Where:
Nt+1
is the change in population size (N) for the next
generation.
r
is the innate capacity for increase (a reproduction
rate). It is equal to the birth rate minus the death rate (b-d).
Nt
is the population size of the current generation.
K
is the maximum size the population can attain (Sometimes called the carrying capacity).
ACTIVITY 1: POPULATION GROWTH IN A SIMPLE ECOSYSTEM
Equipment
1 package of dry yeast
65mL lukewarm water
400mL cool water
25mL sugar
1.25 L of flour
Bowl for mixing
Test tube
Ruler
Vegetable oil
Marking pen
Calculator
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Procedure
1. Add a package of dry yeast to lukewarm water and sprinkle about a tablespoon (25mL) of
sugar into the mixture to get yeast growth started
2. After 10 min or so, add the yeast mixture to flour
3. Add most of the remaining cool water and stir
4. Obtain a test tube, ruler, and a small portion of the dough
5. Put a drop or two of vegetable oil in your test tube and roll the tube to distribute the oil on
the interior wall.
6. Pack a centimeter of dough in the bottom of the tube
7. Record the starting time and dough height for the tube in the results section
8. Measure and record the height of the dough at 15-min intervals for 2 hours. The rising of
the dough is caused by accumulation of carbon dioxide generated by the yeasts. Since the
rate of carbon dioxide production is proportional to the yeast population size, the height of
the dough is an indirect measure of yeast growth
9. Graph the growth of your yeast in the results section. Which mathematical model does it
approximate? What are the potential limits of growth in this closed system? (8 marks)
ACTIVITY 2: LIMITATIONS OF THE ENVIRONMENT
Introduction
In optimal conditions (e.g., plenty of resources, low
competition, etc.), populations grow in a predictable
pattern. Early growth is relatively slow, after which
growth is rapid. This rapid, logarithmic phase of growth
represents the organism's biotic potential, which is its
maximal reproductive capacity if given unlimited
resources. The number of individuals at a given
generation during logarithmic growth can be determined
from the following formula:
Where:
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N = the number of individuals at a given generation
a = the number of individuals present initially
n = number of generations
This equation shows how fast populations can grow. For example, consider Escherichia coli, a common
bacterium that can divide every 20 minutes in ideal conditions. In only one day (1440 min), these
bacteria can produce 72 (1440 divided by 20) new generations. Therefore, if we start our experiment
with one bacterium, the number of bacteria present after one day would be:
N= (1)(272) bacteria
N= 40,000,000,000,000,000,000,000 bacteria = 4 x 1022 bacteria
This many bacteria would weigh about 3.2 million kilograms. Bacteria aren't the only organisms having
such an incredible biotic potential. For example, a single pair of Atlantic cod and their descendants
reproducing without hindrance would in six years completely fill the Atlantic Ocean. The 80 offspring
produced every six months by a pair of cockroaches produce 130,000 roaches in only 18 months enough to overrun any apartment or kitchen! .
Environmental resistance and carrying capacity
Organisms in the "real world" do not always reproduce at maximum rates, and populations do not grow
at ever-increasing rates. Maximum logarithmic growth cannot be sustained because environmental
resistance includes limiting factors such as disease, accumulation of waste products, and lack of food.
Ultimately the size and growth of a population is balanced by the environment: environmental
resistance prevents a population from continuing to reproduce at its biotic potential.
The growth of most populations levels off after a logarithmic phase because of limiting factors. This
stability occurs when the birth rate equals the death rate, and is referred to as the carrying capacity of
the ecosystem. In most populations, population size remains near the carrying capacity as long as
limiting factors are constant.
In the laboratory, you can measure the growth of real populations such as bacteria that reproduce
quickly. As bacteria reproduce in a clear nutrient broth, the broth becomes turbid. You can't accurately
count individual bacteria, but you can measure the increase in turbidity of a growing culture. More
turbidity means more bacteria. Turbidity values roughly estimate population size.
To understand the effects of environmental resistance, complete Table 1. This table provides actual
data for a growing but limited population of bacteria. For comparison you must calculate the size of a
theoretical population of E. coli if given unlimited resources. Every 20 minutes the population could
potentially double. After doing your calculations plot the growth of the theoretical and actual
populations in and XY scatter-plot in Excel. Be sure to include all appropriate titles, labels, and units.
(3 marks)
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TABLE 1: THEORETICAL AND ACTUAL GROWTH OF E. COLI BACTERIA
Generation
Time
Size of Population (103 bacteria per ml)
Minutes
Theoretical
Actual
8
8
16
15
1
2
20
3
40
28
4
60
48
5
80
120
6
100
220
7
120
221
ACTIVITY 3: DROSOPHILA POPULATION GROWTH
Population growth of Drosophila melanogaster (common fruit flies) can also be followed in the
laboratory even though they do not reproduce as quickly as bacteria. Drosophila has been chosen
because it's easy to count, reproduces every 7 to 10 days, and because each female produces many
offspring.
Equipment
2 glass jars of varying size- 1 approximately 250ml and the second around 750ml
2 rubber bands
2 squares of cheese cloth or fabric large enough to cover jar openings
A piece of ripe banana (peeled) or grapes (cut in half)
Procedure: measure population growth of fruit-flies
1. Bait the jars with the ripe fruit and leave in an open, in a warm place until flies appear. It may
take a few days. Put 1 small slice of banana, or one split grape, in the small jar, and put three
times this quantity in the large jar.
2. Cover the jars with fabric, securing them with the rubber bands, so no flies can enter or escape,
and record the initial number of flies.
3. Leave the jars in a secure place out of direct light. Do not open the jars at any time (the
Drosophila will get air through the fabric and nutrients from the fruit).
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4. Count the flies in the jar every day for 10 days. If there are too many flies in the vial to count,
put the vial in a refrigerator for several minutes--this will make the flies sluggish and easier to
count.
5. Using Microsoft Excel (or similar spreadsheet program), plot your data. (4 marks)
Hypothesis: Predict what you think the growth of the fly population in the small jar will be in
comparison the large jar population growth. (1 mark)
ACTIVITY 4: GROWTH OF HUMAN POPULATIONS
Our population is growing extremely quickly. Consider these data:
Year
8000 BC
4000 BC
1 AD
1650
1750
1800
1850
1900
1950
1960
1970
1980
1990
2000
Human Population (millions)
5
86
133
545
728
906
1130
1610
2400
2998
3659
4551
5300
6500 + (projected)
Data listed in the table above have tremendous implications. For example, if our population would have
stabilized after World War II, today we could provide all of our energy needs (and have a higher
standard of living) without having to burn any coal or import any oil.
Another important way of looking at a population is to examine its doubling time. In 1850, the doubling
time for our population was 135 years. Today, the doubling time is about 40 years. This means that
during the next 40 years we must double our resources if we are to maintain our current standard of
living. Improving our standard of living will require that we more than double our resources.
Each year there are about 90 million more people on Earth. That annual increase in our population
equals the combined population of Great Britain, Ireland, Iceland, Belgium, The Netherlands, Sweden,
Norway, and Finland.
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BIOLOGY SEMESTER ONE
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In the six seconds it takes to read this sentence, 18 more people will be added to our population. Each of
these people eats food, generates wastes, and, in their own small way, affects our earth.
At our present rate of growth (which is less than our biotic potential), in 2000 years our population will
weigh as much as the entire earth. And 4000 years later, it would weigh as much as the visible universe
and be expanding at the speed of light.
Procedure
1. Graph the data given in the human population data table, extending the data to predict the
population up to the year 2050. (4 marks)
QUESTIONS
Complete all of the bolded questions in the lab description above. Then answer the following:
1. What do you conclude from your data about population growth in yeast, E. coli, and Drosophila?
Discuss in the context of carrying capacity, limitations to growth, generation time, and doubling
time, using the graphs you have created to compare the population growth patterns. (10 marks)
2. How many more flies were in the larger jar at the population's peak than in the smaller jar? (1
mark)
3. How does the availability of resources affect population growth and size of Drosophila, and
yeast? Do your conclusions support or refute your hypothesis? (3 marks)
4. The doubling time in developed countries is about 120 years, while that in developing countries
is about 30 years. What is the significance of this? (2 marks)
5. What does the pattern of human population growth predict for the years 2020, 2030, and 2050?
Do you think these predictions are accurate? Why or why not? (5 marks)
6. Discuss what could happen when our population exceeds the Earth's carrying capacity. (3 marks)
BIBLIOGRAPHY
Johnson, R. a. (1992). Biology, Third Edition. St. Louis: Mosby-Year Book Inc.
Kardos, T. (2003). Easy Science Demos and Labs: Life Science. Portland: J. Weston Walch.
Vodopich, D. a. (1992). Biology Laboratory Manual, third Edition. St Loius: Mosby Year Book.
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