# SCI 225, Lab 1 Population growth Purpose To introduce you to the theoretical and actual implications of population growth. Completion and submittal instructions Download this lab as a Word document and enter your responses directly into the form. Submit your completed lab into the Lab 1 submission folder for grading and feedback.

SCI 225, Lab 1: Population growth

Purpose:  To introduce you to the theoretical and actual implications of population growth.
Completion and submittal instructions: Download this lab as a Word document and enter your responses directly into the form. Submit your completed lab into the Lab 1 submission folder for grading and feedback.
Part One: Environmental resistance and carrying capacity
It is fundamental to ecology to study populations, viz., plants, animals, humans. As populations can grow incredibly fast, abundant resources of nutrients and space usually produce unlimited growth for a time and a growth curve for populations with a geometric, or “J” shape. The traits that allow such growth include survival rates through (1) a population’s reproductive age, (2) the age of the first reproduction, (3) the number of offspring per generation, and (4) the number of times a species reproduces in its lifetime.
Of course, the simplest population model is one based on unlimited growth occurring in discrete pulses, or advances, by the geometric growth model. This growth is represented as:
N t = N 0  λt
where
N t          = the number or organisms at time t ;
N 0       = the number of individuals present initially;
λ          = average number of offspring left by an individual during one time interval;
t           = number of time intervals (i.e., generations)
This calculation shows how quickly populations can grow. Consider Escherichia coli, a common bacterium that divides into two every 20 minutes (or λ = 2) in ideal conditions. In one day (or after 1440 minutes), these bacteria go through t  = 72 (or, 1440/20) generations. Therefore, if we start with one bacterium (N 0), then after one day the number of bacteria would be:
N t        = (1 bacterium) × (272 bacteria after 1 day), or 4.7 × 1021 bacteria!
That many bacteria would weigh 2.3 million kilograms! This calculation shows that populations can grow extraordinarily with high λ-values, short generation times, but only with unlimited resources over short periods of time. Other organisms with high biotic potential, like bacteria, include codfish and cockroaches. Why aren’t we overrun with codfish and cockroaches? Before going to the next page, draft your answer to that question here.

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Organisms in the “real” world do not usually reproduce at their maximum rates. These rates are not sustainable due to environmental resistance to maximum growth, which increases due to, for example, disease, accumulation of waste products, and lack of food. Overall, size and growth of a population is a function of environment as well as reproductive traits. Which ONE of the four traits listed at the beginning of this lab would be most influenced by environmental resistance?

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To understand the effect of environmental resistance on growth rates, complete the table (below) for a growing but limited population of bacteria. For comparison, calculate the size of a theoretical population of E. coli with unlimited resources. Its population doubles every 20 minutes. After filling in the table, below plot the growth of both theoretical and actual populations.
Time                        Size of population (103 bacteria per mL)
Generation              Hours    Minutes                  Theoretical                        Actual
1                          0             0                             8                                  8
2                          0           20                            16                                 15
3                          0           40                            32                                 28
4                          1             0                       _________                          48
5                          1           20                       _________                         120
6                          1           40                       _________                         220
7                          2             0                       _________                         221

 100
 200
 300
 400
 500
 600

0                                                                           1                                                                          2
Time (hours)

How did growth of the actual population compare with that of the theoretical population during the early stages of the experiment? During the later stages? Two answers required.

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How long did it take the actual population to double during the early stages of the experiment? Middle stages? Later stages? Three short answers required.

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When was growth of the actual population at its most rapid? One short answer required.

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When was growth of actual population at its slowest? What factors inhibited growth?

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As population goes up, the environmental resistance increasingly slows the growth rate until it reaches zero and the population size remains constant. This is called logistic population growth, and the model for this is a sigmoid curve.
Sustainable growth is when the birth rate equals the death rate. This population size is known as the carrying capacity of the environment. Population size remains near the carrying capacity as long as limiting factors are constant.

Part Two: Examining population growth
Our global population is growing fast! For any population to survive, no matter its geographic reach, there must be adequate resources to sustain the world’s population; otherwise, the same four traits (outlined at the start of this lab) that allow growth will influence survival rates of that global population. And not all nations possess the same amount or quality of resources.
Consider these data on the next page.

Year                        Human Population
8000 B.C.                           5,000,000
4000 B.C.                         86,000,000
A.D. 1                            133,000,000
1500                             515,000,000
1750                             728,000,000
2000                           6,200,000,000
2040                          13,000,000,000 (projected)

Now plot these data (above) within the axes (below):
15 Billion

12 Billion
9 Billion

6 Billion

 2 Billion

3 Billion

 1 Billion

 6000 B.C.
 8000 B.C.
 2000 B.C.
 4000 B.C.
 A.D. 1

How does the shape of the graph (above) compare with those you made for bacteria?

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What do you conclude from your graph of human population growth?

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Another important of a population is its doubling time. In 1850, the doubling time for the human population was 135 years. Today, the doubling time is about 40 years. Consequently, during that same 40 years we must also double our resources if we simply want to maintain our current standard of living. If we want to improve our standard of living, we then must more than double our resources!
The doubling time for populations in developed countries is about 120 years but in developing countries it is about 30 years. What is the significance of this?

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As a point of interest, the birthrate among Americans has climbed to its highest since 1971. The birthrate hit 2.1 in 2006, which means that each female theoretically has 2.1 offspring. At this rate, each generation equally replaces itself. Among industrialized countries, this is a high birthrate. In contrast to the USA, the global population has increased hugely during the past three centuries.
Although the birthrate has remained constant (at about 30 per thousand), the death rate has fallen from about 30 per 1000 to its current level of about 13 per 1000. The difference between these two birthrates (17 per 1000) means the human population is growing at a rate of about 1.7% per year. Here’s what this means:
Each hour the world’s population grows by 11,000; by each year, it grows by 90,000,000. That annual increase equals the combined populations of Great Britain, Ireland, Iceland, Belgium, The Netherlands, Sweden, Norway, and Finland.
Can the current growth rate of humans continue? Why or why not?

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What will happen when Earth’s population exceeds its carrying capacity?

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How might the growth of the human population affect plant and animal populations?

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From an ecological standpoint, how does the growth human population affect ecosystems?

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For instructor use only:  This score sheet has been provided to make it easier to grade this lab. You may use this score sheet or not at your discretion.
Students: You may wish to review the following chart before submitting your lab so you better understand how points will be distributed.  Please do not write in the chart.

 Question Score Value 1 2 2 2 3 2 4 2 5 2 6 2 7 2 8 2.5 9 2.5 10 2.5 11 2.5 12 3 13 3 Total: 30