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 #

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?

AP Biology Minzenmayer Page 1 Name: ______Date: ______Class: _____Seat: ______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.

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 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?

AP Biology Minzenmayer Page 2 Name: ______Date: ______Class: _____Seat: ______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. Also assume 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.

******************************************************************************************************************* 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

AP Biology Minzenmayer Page 3 Name: ______Date: ______Class: _____Seat: ______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 0 1 1 1 1 2 3 3 4 6 in reproductive age classes x 1 offspring each. Enter in 0-10 age class of next column

******************************************************************************************************************* 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

AP Biology Minzenmayer Page 4 Name: ______Date: ______Class: _____Seat: ______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 60 in reproductive age classes x 2 offspring each. Enter in 0-10 age class of next column

******************************************************************************************************************* 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 = # 90 90 90 330 570 810 1530 2970 5130 8730 individuals in reproductive age classes x 3 offspring each. Enter in 0-10 age class of next column

AP Biology Minzenmayer Page 5 Name: ______Date: ______Class: _____Seat: ______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 90 in reproductive age classes x 3 offspring each. Enter in 0-10 age class of next column

******************************************************************************************************************* 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 0-10 DR = 10% 10 90 81 72 261 414 531 954 1725 2712 11-20 DR = 10% 10 9 81 73 65 235 373 478 859 1553 21-30 DR = 10% 10 9 8 73 66 59 212 336 430 773 31-40 DR = 10% 10 9 8 7 66 59 53 191 302 387 41-50 DR = 10% 10 9 8 7 6 59 53 48 172 272 51-60 DR = 10% 10 9 8 7 6 5 53 48 43 155 61-70 DR = 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 = # 90 81 72 261 414 531 954 1725 2712 4296 individuals in reproductive age classes x 1 offspring each. Enter in 0-10 age class of next column

AP Biology Minzenmayer Page 6 Name: ______Date: ______Class: _____Seat: ______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 0-10 DR = 5% 10 90 81 75 276 441 570 1053 1923 3054 11-20 DR = 10% 10 10 85 77 71 262 419 542 1000 1827 21-30 DR = 10% 10 9 9 77 70 64 236 377 488 900 31-40 DR = 10% 10 9 8 8 70 63 58 212 339 439 41-50 DR = 10% 10 9 8 7 7 63 57 52 191 305 51-60 DR = 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 = # 90 81 75 276 441 570 1053 1923 3054 4932 individuals in reproductive age classes x 1 offspring each. Enter in 0-10 age class of next column

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 Minzenmayer Page 7