# Population

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## Exercise 1 Modeling Population Growth

In this exercise, you will use dice to model population growth. Each die will represent an individual; new individuals will be born, and individuals will also die. You will track the entire population until the population density (number of individuals) reaches 100.

### Procedure

1. Before you begin to model population growth, examine the rules listed below and shown in Figure 4.

### Rules:

• Each die represents 1 individual of the population.
• You will roll the dice to investigate births and deaths of the population.
• The number of dots on each die will represent a birth, a death, or neither birth nor death.
• Birth = 1, 4
• Death = 6
• Neither = 2, 3, 5

1. Select 4 dice and place them in the cup. These dice represent the 4 individuals comprising generation 1, the initial population.

Note: The color of the dice does not matter.

1. In Data Table 1, record the “Initial population size (N)” (for the first generation, the initial population size is 4).
2. Cover the cup with your hand and shake the dice. Gently pour the dice onto a table or work surface.

Important Note! Pouring the dice out too quickly or too high from the work surface may result in lost dice. Take care not to inadvertently lose individuals.

1. Determine the number of individuals that were born (any dice displaying numbers 1 and 4). Determine the number of individuals that died (any dice displaying number 6). See Figure 5.

1. Record the “Number of births (B)” and the “Number of deaths (D)” in Data Table 1.
2. Remove any dead individuals. For example, in Figure 5 above, the dead individual should be removed from the population and returned to the bag.
3. Add a die for each birth. For example, in Figure 5 above, 2 dice should be added to the population.
4. Calculate the final population size and record the value in Data Table 1. Use the following equation:

Final population size = N + B - D$\text{Final population size = N + B - D}\text{}$

1. Count the number of dice in your population to ensure that it equals the value recorded for “final population size” and return the dice to the cup.
2. To obtain data for generation 2, repeat steps 3-10.

Note: Because you will be starting with a very small population, extinction is a possibility, but the odds are against it. If your population does go extinct, start again.

1. Continue rolling the dice and recording data until your population size reaches a minimum of 100.
2. Once you have reached a population size of 100, calculate the change in population size for each generation. Record each value in Data Table 1. Use the following equation:

Change in population size = Final population size – Initial population size$\text{Change in population size = Final population size – Initial population size}\text{}$

1. Graph the initial population size for each generation. To do this, create a scatter plot with the generations on the independent axis (x-axis) and the initial population size on the dependent axis (y-axis). Consider whether the population growth you modeled showed a linear pattern, exponential pattern, or no pattern.
2. Upload an image of the graph into Graph 1.
3. Graph the change in population size for each generation. To do this, create a bar graph with the generations on the independent axis (x-axis) and the change in population size on the dependent axis (y-axis). Consider whether changes in population size were greatest when the population was smaller or larger.
4. Upload an image of the graph into Graph 2.

#### Exercise 1 - Questions

1. How many generations did it take to reach a population size of 100?

2. Consider the mode of reproduction modeled in your population. Would sexual reproduction or asexual reproduction likely be the cause of a birth? Are individuals of the species likely or unlikely to have separate male and female sexes?

3. Did the modeled population exhibit linear growth, exponential growth, or no pattern? Use Graph 1 to support your answer.

4. Were changes in population size greatest when the population was smaller or larger? Which generation exhibited the greatest change in size? Use Graph 2 to support your answer.

5. What resource constraints were placed on the modeled population?

6. Could the modeled population exhibit indefinite growth? If so, how? Is indefinite growth observed in nature? Explain why or why not

## Exercise 2 Investigating a Human Population

In this exercise, you will investigate demography of a human population. You will collect birth and death information from a cemetery and analyze trends in the population.

### Procedure

1. Research your local area to find a cemetery that you may visit for this exercise.

Note: If you are unable to access a cemetery, you may use the data provided in the “HOL Supplied Cemetery Data” Supplemental Document. If you choose to do this, skip to step 9.

1. Print a copy of Data Table 2, to bring with you to the cemetery. Travel to a cemetery during the day, ensure that conditions are safe and public access is permitted.
2. In Data Table 2, record the name, birth date and date of death for 80 deceased individuals. As you collect data, be sure to spread out within the full sampling area. Individuals of the same family or who died in shared years will often be grouped together, and the goal is to take a representative sample of all individuals in the population.
3. Record the cemetery name and location in Data Table 2.
4. Determine how old each person was when they died, and record your data in Data Table 2. Use the following equation:

Age at death = Birth year – Death year$\text{Age at death = Birth year – Death year}\text{}$

1. Investigate the first names of each individual and record the sex (M for male; F for female) in Data Table 2. If the name is gender-neutral, such as Jean, Lynn, or Pat, you may leave the area blank. Ensure that any data you recorded by hand is present in the document that you report to your instructor.

Note: This concludes the outdoor portion of this exercise; the rest of Exercise 2 may be performed from home.

1. Report your data to the instructor. Photograph the sheet(s) of data you recorded. Upload the image into Photo 1.
2. Record a summary of the population. Address each of the following questions, and record data in Data Table 3.
• What were the first and last birth years?
• What were the first and last death years?
• How many individuals died before 1950? How many died after 1950?
• How many individuals are male and female?
3. In the next steps, you will calculate the probability of dying within a given cohort. As shown in Data Table 4, cohorts are age classes. For example, cohort 1 includes individuals that died between the ages of 1 and 9; cohort 2 includes individuals who died between the ages of 10 and 19. Examine Data Table 4 and study the following descriptions for each column heading:
• Cohort (X) - The age intervals of deceased individuals.
• Number of Deaths (D) - The number of individuals that died in each cohort.
• Frequency of Population in Cohort (d) - The portion of the population that died in each cohort.
• Frequency of Survivorship Entering the Cohort (l) - The portion of the population that enters the cohort.
• Probability of Death within a Cohort (Q) - The probability that any given individual will die within a cohort.
4. Count the number of people who died in each cohort (age interval). Record your data under “Number of deaths (D)” in Data Table 4.
5. Calculate the “Frequency of population in cohort (d).” Record each value as a number with two decimal places. Use the following equation:

d = D / Total Population Size$\text{d = D / Total Population Size}\text{}\text{}$

Note: “Frequency of survivorship of cohort (l)” is based on entry into the cohort. Thus, the first cohort listed will always have a value of 1.00 because 100% of the population was born, entering into the cohort. A value of 1.00 has been entered for cohort # 1 in Data Table 4. With each subsequent cohort, values of “l” will decrease.

1. Calculate the “Frequency of survivorship of cohort (l)” for cohort # 2. Record each value as a number with 2 decimal places. Use the following equation:

Icohort2 = Icohort1 – dcohort1${\text{I}}_{\text{cohort2}}{\text{= I}}_{\text{cohort1}}{\text{– d}}_{\text{cohort1}}$

1. Calculate the “Frequency of survivorship of cohort (l)” for each of the remaining cohorts. For example, “Frequency of survivorship of cohort (l)” for cohort 3 will be calculated as:

Icohort3 = Icohort2 – dcohort2I${\text{cohort3}}_{}{\text{= I}}_{\text{cohort2}}{\text{– d}}_{\text{cohort2}}$

Note: The final recorded “l” in Data Table 4 should be equivalent or very close to the final recorded “d.”

1. Calculate the “Probability of death (Q).” Record each value as a number with 2 decimal places.Use the following equation:

Q = d/I$\text{Q = d/I}\text{}\text{}$

Note: The probability of death is a frequency and may be interpreted as a percentage. For example, if Q = 0.30 for cohort # 1, then there is a 30% probability that a given individual will die between the ages of 1 to 9.

Note: To find Q, use data within a single cohort: Qcohort1 = dcohort1 / lcohort1

1. Create a bar graph of the probability of death within each cohort. Plot the cohort age interval (1-9, 10-19, etc.) on the independent axis (x-axis), and plot the probability of death on the dependent axis (y-axis).
2. Upload an image of the graph into Graph 3.

#### Exercise 2 - Questions

2. Overall, does human mortality tend to be greatest at young ages or older ages?

3. How many individuals were male, and how many were female? How many individuals were you unable to assign a gender to?

4. Using the raw data in Data Table 2, calculate the average age at death for males and for females. What inferences can you make about male versus female age at death?

5. If the government made significant cuts in social services, such as prenatal and infant care, how might your data be affected?

Generation 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Initial Population Size (N) Number of births (B) Number of Deaths (D) Final Population Size (N+B-D) Change in Population Size (Final-Initial) Observation First Birth year last birth year first death year last death year number of indivduals who died before 1950 number of people who died after 1950 number of males number females Data # 1 2 3 4 5 6 7 8 Cohort (X) Number of Deaths (D) Frequency of population in cohort (d) 1-9 10-19 20-29 30-39 40-49 50-59 60-69 70+ Total 80 1 frequency of survivorship entering the cohort (I) Probability of death within a cohort (Q) 1

ProfessorMarko
School: UT Austin

Attached.

Exercise 1
Graph 1

Population Growth
90

Initial Population Size

80
70
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20
10
0
0

2

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Generation

Graph 2

Change in Population Size
30

Change in Population Size

25
20
15
10
5
0
1
-5

2

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Generations

10

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16

EXERCISE 1 - QUESTIONS
1. How many generations did it take to reach a population size of 100?
It took 16 generations fo...

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Review

Anonymous
Awesome! Exactly what I wanted.

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