Population Growth Lab

Name: ______Date: ______Class: _____Seat: ______

Population Growth Lab

Introduction

This lab exercise explores rates of population growth using several different models of population structure. Within each model you will examine the effects of varying population parameters such as initial population size, birth rate, death rate and age at first reproduction on the rate of population growth.

Exercise 1: The Bacterial Model

In bacteria, a given individual has the potential to divide every 20 minutes with unlimited resources to give two new individuals. By definition, there is no overlapping of generations since each “new” individual is only “half” of the “parent” individual in the previous generation. Also, the “birth rate” is fixed at two “offspring” per individual.

Graph each of the curves below on one sheet of graph paper all on a single graph. On your graph, each millimeter of height graphed will represent one individual in the population. Be sure to label the graph according to the population structure model and each growth curve according to the population parameters used.

Growth Curve 1: Begin with one bacterium that gives rise to two which now comprise the second generation. Those two each divide to give rise to a total of four in the third generation and those four give rise to eight in the forth generation and so on. Calculate and plot the size of the population for 10 generations.

Non-overlapping generations/Bacteria/double
Generation / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10
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Growth curve 2: Change the initial population size to three bacteria and calculate and plot the population size for 10 generations.

Non-overlapping generations/bacteria/triple
Generation / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10
#

Growth Curve 3: Begin with three bacteria. Following reproduction at each generation, impose 10% morality (but round to the nearest whole individual). For example, the second generation would have 6-1 (0.6 rounded to 1) = 5 individuals which then reproduce to give rise to the third generation. After mortality, the third generation would have 10-1 = 9 individuals. Calculate the plot the population size for the rest of the 10 generations.

Non-overlapping generations/bacteria triple with 10% mortality
Generation / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10
#

Growth Curve 4: Begin with three bacteria and change the mortality rate to 20%.

Non-overlapping generations/bacteria triple with 20% mortality
Generation / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10
#

Answer the following questions on the back of the graph paper for these curves:

1. What was the effect of tripling the initial population size on the population sizes of the subsequent generations?

2. Did the addition of mortality to the population change the shape (J or S) of the growth curve?

3. What would the mortality factor need to be to prevent the population from growing?

Exercise 2: The Perennial Plant Model

Many organisms reproduce repeatedly in a lifetime and their populations will have parents and offspring alive and reproducing at the same time: that is, there will be overlapping generations. Consider a perennial plant. In any given season, a parent plant will produce seeds that may germinate and grow to reproductive size by the next season. In the following season, then, the parent plant and offspring will all reproduce.

Growth Curve 1: Begin with one plant that produces 2 seeds that successfully germinate and grow to reproductive size by the next generation. In generation 2, the population will consist of 3 individuals (the parent and 2 offspring) that then produce 2 seeds each. Calculate the population size for generations 3-10 and plot the growth curve (until the population size exceeds the space available on the paper.

Overlapping generations/Plants/each plant produces 2 seed
Generation / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10
#

Growth Curve 2: Begin with one plant as before, but change the birth rate to 3 seeds that successfully germinate and reproduce. Calculate and plot the population size for 10 generations.

Overlapping generations/Plants/each plant produces 3 seed
Generation / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10
#

Growth Curve 3: Begin with one plant and use a birth rate of 3 seeds, but this time impose a 10% mortality on each generation. In calculating mortality, round to the nearest whole individual.

Overlapping generations/Plants/each plant produces 3 seed 10% mortality
Generation / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10
#

Answer the following questions on the back of the graph paper for these curves:

1. How does population growth in this model with overlapping generations compare to population growth in the bacteria model?

2. What was the effect of increasing the birth rate by 50% on the population growth curve?

3. Did the addition of mortality to the population change the shape (J or S) of the growth curve?

Exercise 3: Human Model

Humans and other long lived organisms have populations with overlapping generations and age structure. Age structure implies that not all ages will have the same birth rates or death rates and, in fact, some age classes will not reproduce at all. In addition to the effects of birth rates and death rates, the age structure of the population has important influences on the rate of population growth.

Calculating population sizes in populations with age structure is more complex than in the previous examples and is done by using a life table. An example of a life table is given on the next page. The column on the left defines the age classes. In this example, age classes represent decades of human life and the last age class ends at age 80. The remaining columns record the numbers of individuals in each of the age classes in the subsequent generations. To fill in a life table, you must know the age specific birth rates and death rates in addition to the initial age distribution of the population.

To illustrate the method of filling in a life table, you will make some simplifying assumptions about the age specific birth and death rates. First assume that all individuals born into the population live to age 80 and then die. Alsoassume that individuals of reproductive age classes each produce one offspring per decade. Notice you are allowing each individual to produce offspring even though approximately half of the population is male. (You didn’t consider sex in the previous examples. In the construction of life tables it is common practice to consider only the female half o the population –numbers of females in each age class and the number of daughters produced—and assume that the population size would simply be doubled if the male half of the population were added. This practice assumes that the male and female subpopulations have the same age structure). Make the decades 21-30, 31-40 and 41-50 the reproductive decades.

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Life Table 1: Begin with 1 individual in the population in age class 21-30 in generation 1. As illustrated by the arrow, this individual moves into the 31-40 age class in generation 2. In addition, this individual produces 1 offspring that is entered into the 0-10 age class at the top of the generation 2 column. In generation 3, the original individual has moved into the 41-50 age class, her original offspring is in the 11-20 age class. The original individual is still reproductive and will produce 1 offspring that enters the 0-10 age class in generation 4. For each generation, then you must consider the survivors of the previous generation and their offspring.

Age Class / G1 / G2 / G3 / G4 / G5 / G6 / G7 / G8 / G9 / G10
0-10 / 1
11-20 / 1
21-30 / 1 / 1
31-40 / 1 / 1
41-50 / 1 / 1
51-60 / 1 / 1
61-70 / 1 / 1
71-80 / 1 / 1
Total Population Size / 1
# offspring produced this generation = # individuals in reproductive age classes x 1 offspring each. Enter in 0-10 age class of next column /
1 /

Life Table 2: To save time, Life table 2 has been filled in for you. Notice that it begins with 1 individual in the population in the age class 11-20. This is a pre-reproductive age class, so this individual did not reproduce until the next generation. Study the table carefully. You will need to understand it in order to answer the questions at the end of the exercise.

Age Class / G1 / G2 / G3 / G4 / G5 / G6 / G7 / G8 / G9 / G10
0-10 / 0 / 1 / 1 / 1 / 1 / 2 / 3 / 3 / 4
11-20 / 1 / 1 / 1 / 1 / 1 / 2 / 3 / 3
21-30 / 1 / 1 / 1 / 1 / 1 / 2 / 3
31-40 / 1 / 1 / 1 / 1 / 1 / 2
41-50 / 1 / 1 / 1 / 1 / 1
51-60 / 1 / 1 / 1 / 1
61-70 / 1 / 1 / 1
71-80 / 1 / 1
Total Population Size / 1 / 1 / 2 / 3 / 4 / 5 / 6 / 9 / 12 / 16
# offspring produced this generation = # individuals in reproductive age classes x 1 offspring each. Enter in 0-10 age class of next column / 0 / 1 / 1 / 1 / 1 / 2 / 3 / 3 / 4 / 6

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Life Table 3: As in life table 2, begin with 1 individual in the 11-20 age class, but this time, make this a reproductive age class. Fill out the life table for 10 generations.

Age Class / G1 / G2 / G3 / G4 / G5 / G6 / G7 / G8 / G9 / G10
0-10
11-20
21-30
31-40
41-50
51-60
61-70
71-80
Total Population Size
# offspring produced this generation = # individuals in reproductive age classes x 1 offspring each. Enter in 0-10 age class of next column

Life Table 4: Begin with 10 individuals in each age class. Use a birth rate of 2 offspring per decade for the three reproductive age classes 21-30, 31-40, 41-50. Fill out the life table for 10 generations.

Age Class / G1 / G2 / G3 / G4 / G5 / G6 / G7 / G8 / G9 / G10
0-10 / 10 / 60
11-20 / 10
21-30 / 10
31-40 / 10
41-50 / 10
51-60 / 10
61-70 / 10
71-80 / 10
Total Population Size / 80
# offspring produced this generation = # individuals in reproductive age classes x 2 offspring each. Enter in 0-10 age class of next column / 60

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Life Table 5: To save time, Life Table 5 has been filled in for you. Study it carefully; you will need an understanding of it to answer questions later in lab. Notice the initial population size and how this table is different than table 4.

Age Class / G1 / G2 / G3 / G4 / G5 / G6 / G7 / G8 / G9 / G10
0-10 / 10 / 90 / 90 / 90 / 330 / 570 / 810 / 1530 / 2970 / 5130
11-20 / 10 / 10 / 90 / 90 / 90 / 330 / 570 / 810 / 1530 / 2970
21-30 / 10 / 10 / 10 / 90 / 90 / 90 / 330 / 570 / 810 / 1530
31-40 / 10 / 10 / 10 / 10 / 90 / 90 / 90 / 330 / 570 / 810
41-50 / 10 / 10 / 10 / 10 / 10 / 90 / 90 / 90 / 330 / 570
51-60 / 10 / 10 / 10 / 10 / 10 / 10 / 90 / 90 / 90 / 330
61-70 / 10 / 10 / 10 / 10 / 10 / 10 / 10 / 90 / 90 / 90
71-80 / 10 / 10 / 10 / 10 / 10 / 10 / 10 / 10 / 90 / 90
Total Population Size / 80 / 160 / 240 / 320 / 640 / 1200 / 2000 / 3520 / 6480 / 11,520
# offspring produced this generation = # individuals in reproductive age classes x 3 offspring each. Enter in 0-10 age class of next column / 90 / 90 / 90 / 330 / 570 / 810 / 1530 / 2970 / 5130 / 8730

Life Table 6: Use the same initial population and birth rate as in Table 5, but his time impose a mortality rate of 10% per age class per generation. Round to the nearest whole individual. The numbers of individuals at each age class at each generation from the original population are already filled in for you. Be sure you understand how to get these numbers.

Age Class / G1 / G2 / G3 / G4 / G5 / G6 / G7 / G8 / G9 / G10
0-10 / 10 / 90
11-20 / 10 / 9
21-30 / 10 / 9 / 8
31-40 / 10 / 9 / 8 / 7
41-50 / 10 / 9 / 8 / 7 / 6
51-60 / 10 / 9 / 8 / 7 / 6 / 5
61-70 / 10 / 9 / 8 / 7 / 6 / 5 / 5
71-80 / 10 / 9 / 8 / 7 / 6 / 5 / 5 / 5
Total Population Size / 80
# offspring produced this generation = # individuals in reproductive age classes x 3 offspring each. Enter in 0-10 age class of next column / 90

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Life Table 7: Life table 7 has the data filled in for you. Notice it begins with the same initial population and birth rate (3 offspring per decade). All age classes except the next to last (61-70) use a 10% mortality rate. For the 61-70 age class, a 5% mortality rate was used. This model shows the advances of geriatric medicine.

Age Class / G1 / G2 / G3 / G4 / G5 / G6 / G7 / G8 / G9 / G10
0-10DR = 10% / 10 / 90 / 81 / 72 / 261 / 414 / 531 / 954 / 1725 / 2712
11-20DR = 10% / 10 / 9 / 81 / 73 / 65 / 235 / 373 / 478 / 859 / 1553
21-30DR = 10% / 10 / 9 / 8 / 73 / 66 / 59 / 212 / 336 / 430 / 773
31-40DR = 10% / 10 / 9 / 8 / 7 / 66 / 59 / 53 / 191 / 302 / 387
41-50DR = 10% / 10 / 9 / 8 / 7 / 6 / 59 / 53 / 48 / 172 / 272
51-60DR = 10% / 10 / 9 / 8 / 7 / 6 / 5 / 53 / 48 / 43 / 155
61-70DR = 10% / 10 / 9 / 8 / 7 / 6 / 5 / 5 / 48 / 43 / 39
71-80 / 10 / 10 / 9 / 8 / 7 / 6 / 5 / 5 / 43 / 41
Total Population Size / 80 / 154 / 211 / 254 / 483 / 842 / 1285 / 2108 / 3617 / 5932
# offspring produced this generation = # individuals in reproductive age classes x 1 offspring each. Enter in 0-10 age class of next column / 90 / 81 / 72 / 261 / 414 / 531 / 954 / 1725 / 2712 / 4296

Life Table 8: Life Table 8 also has the data filled in. It too begins with the same initial population and birth rate. All age classes except the first (0-10) use a 10% mortality rate. For the first age class, a 5% mortality rate was used. This model simulates a reduction in infant mortality.

Age Class / G1 / G2 / G3 / G4 / G5 / G6 / G7 / G8 / G9 / G10
0-10DR = 5% / 10 / 90 / 81 / 75 / 276 / 441 / 570 / 1053 / 1923 / 3054
11-20DR = 10% / 10 / 10 / 85 / 77 / 71 / 262 / 419 / 542 / 1000 / 1827
21-30DR = 10% / 10 / 9 / 9 / 77 / 70 / 64 / 236 / 377 / 488 / 900
31-40DR = 10% / 10 / 9 / 8 / 8 / 70 / 63 / 58 / 212 / 339 / 439
41-50DR = 10% / 10 / 9 / 8 / 7 / 7 / 63 / 57 / 52 / 191 / 305
51-60DR = 10% / 10 / 9 / 8 / 7 / 6 / 6 / 57 / 51 / 47 / 172
61-70 / 10 / 9 / 8 / 7 / 6 / 5 / 5 / 51 / 46 / 42
71-80 / 10 / 9 / 8 / 7 / 6 / 5 / 5 / 5 / 46 / 41
Total Population Size / 80 / 154 / 215 / 265 / 512 / 909 / 1407 / 2343 / 4080 / 6780
# offspring produced this generation = # individuals in reproductive age classes x 1 offspring each. Enter in 0-10 age class of next column / 90 / 81 / 75 / 276 / 441 / 570 / 1053 / 1923 / 3054 / 4932

Answer the following questions using the data in the life tables:

1. What effect did changing the initial age distribution of the population have on population growth? (Life Tables 1,2 3)

2. What effect did changing the age at first reproduction have on population growth? (Life Table 2)

3. What effect did increasing the birth rate by 50% have on population growth? (Life Table 4)

4. What effect did changing age specific mortality have on population growth? (Life Tables 5, 6, 7, and 8)

AP Biology MinzenmayerPage 1