BIOE 103 Population Growth

Transcription

1 BIOE 103 Population Growth

2 Attu Island, Alaska 2

3 Battle for the Aleutian Islands June 7, 1942 Japanese invade Attu Island May 11, 1943 United States retakes island. Terrible fighting. 3

4 1944. Coast Guard establishes a LORAN station on nearby St. Matthew Island 19 men at station 29 reindeer released for emergency food 4

5 St. Matthew LORAN station abandoned in 1945 Note: This is not a photo of the Saint Matthew LORAN station 5

6 reindeer on island 6

7 In 1963, US Fish and Wildlife Service biologist notes: David Klein We counted 6,000 of them. They were really hammering the lichens. -David Klein 7

8 Three years later Saint Matthews Island is covered with skeletons. Only 42 survivors observed. All reindeer dead soon after. 8

9 Summary: Reindeer on Saint Matthew s Island Reindeer released on Island 1957 Fish & Wildlife Service counts 1350 reindeer Population increased to 6000 reindeer. Evidence of overgrazing Island covered in skeletons. 42 survivors Population extinct. 9

10 Reindeer on two other Aleutian Islands had similar histories 10

11 Today s questions - Why do some populations grow so fast? - And why do they sometimes crash 11

12 World population (in billions) Hopefully this will help humanity avoid a similar fate Year 12

13 This process is illustrated by a hypothetical example. Imagine a little boy gets two rabbits for his birthday 13

14 Six months later, two the rabbits make four more rabbits 6 months 14

15 and so on 6 months 1 year 15

16 Let us assume that rabbit population Time months 4 1 year years? 2 years? 2.5 years? doubles every half year Number of rabbits How many rabbits will there be? 15 years 16

17 <10 years later 1,000,000+ rabbits Why does this happen 17

18 Number of rabbits Why does this happen? 1,000, , , , ,000 instead of this? Year 18

19 The bigger the rabbit population gets, the faster it grows because the more rabbits there are, the more babies they have. 19

20 Case study: Rabbits in Australia 1859, 2 dozen rabbits were released into Australia by English colonists "The introduction of a few rabbits could do little harm and might provide a touch of home, in addition to a spot of hunting. - Thomas Austin, English settler to Australia, 1859, Member, Victoria Acclimatisation Society 20

21 21

22 Australia is sheep country 16 rabbits eat as much as 1 sheep 22

23 1870: 2 million rabbits were killed per year with no noticeable affect 23

24 In 1881, ranches were being abandoned due to rabbits 24

25 Fences were built to stop the spread of rabbits Fences did not stop invasion. 25

26 Rabbits contributed to extinction of many native species of Australia Pig-footed bandicoot Toolache wallaby Desert rat kangaroo 26

27 Rabbit infestation still a problem Myxoma virus released in % of rabbits died soon after. But survivors had genes that gave them resistance to disease, and their offspring were resistant. Rabbit population increased again. 27

28 What scientific, historical, or cultural principles does this illustrate? Give me general principle that does not specify what I should or should not do. 28

29 Could human populations grow like rabbits? On average, each family on the earth has 3 children. Consider a village of 100 adults. How many adults will there be in the village in one generation later? 29

30 Human population On average, each family on the earth has ~3 children. Consider a village with 100 adults how many children would you expect them to have? 100 adults = 50 couples 50 couples x 3 children per couple = 150 children 30

31 Population Size of village 10 generations later ~6000 adults Why is the village growing faster and faster? Generation This population is growing in similar fashion as the rabbits in Australia. 31

32 Human populations can grow faster and faster because more people have more babies 100 adults 150 children Population grows by adults 1500 children Population grows by

33 World population (in billions) Population of the earth suggests that something like this is occuring Year 33

34 Population We are going to define this as exponential growth Warning: Not everything that grows quickly is exponential growth Generation 34

35 Exponential growth Growth that increases by a constant percentage or proportion each unit of time e.g. 1% per year 2% per decade 100% per 2 months 2x as much every century 35

36 Contrast with linear growth Linear growth Increases by a constant number each unit of time E.g., Water filling a bathtub Savings in a mattress Distance traveled 4 gallons / minute $100 / month 60 miles / hour 36

37 An example of exponential growth: Scot s Pine after last ice age (see textbook) 37

38 Census Bozeman s population is growing approximately 2% per year 30,000 25,000 20,000 15,000 The line on the graph shows a population growing exactly 2% per year. 10,000 5, Year 38

39 Census Question: How many people will there be in Bozeman in 2050 if population grows 2% per year? 70,000 60,000 50,000 40,000 30,000 20,000 10, Year 39

40 Bozeman population growing 2% per year Population ,500 people Amount of increase 2% of 27,500 = 27, = 550 Population in 2001 = 27, = 28,050 40

41 Census If Bozeman s population increases 2% per year: 71,000 in ,000 60,000 50,000 40,000 30,000 20,000 Notice that population is starting to explode. 10, Year 41

42 Exponential Growth Example: Savings account earning 1% interest per year Year Balance 1 $ $ $ $ $1.00 of interest $1.01 of interest (1 of interest on interest) $1.02 of interest Growth rate increases when you earn interest on interest (compound interest) 42

43 Savings account doubles in value after 70 years Doubles In 70 years Year 43

44 Bank account earning 1% interest After 1000 years, there will be 2 million dollars in the account Year 44

45 Explosive property of exponential growth Definition of exponential growth Growth that increases by a constant percentage each unit of time Property Anything growing exponentially will eventually explode in size (even if growth rate is small). 45

46 Back to the bank account that earns 1% interest per year Year Doubles every 70 years 46

47 Amount of money in bank for interest rate of 0.5%, 1% and 2% 47

48 Tell me how doubling time is related to interest rate 48

49 Doubling time depend on growth rate % growth per year doubles every 35 years 1% growth per year Doubles every 70 years Year 49

50 Doubling property of exponential growth Definition of exponential growth Growth that increases by a constant percentage each unit of time Property Anything growing exponentially has a constant doubling time 50

51 Doubling time (DT) formula Doubling time = ln(2) / r (don t worry about this) 70 / r where r = percentage rate of increase You will need to use this formula on the exam. 51

52 Census Practice Problem #1 How long will it take for Bozeman to double in size? 30,000 25,000 20,000 Bozeman s population is growing approximately 2% per year. 15,000 10,000 5, Year 52

53 Solution: Doubling time = 70 / r = 35 years Doubling time = 70 / 2 = 35 years 53

54 Practice Problem #2 Year Population , ,000 When will population reach 60,000 if it grows exponentially? 54

55 Solution Year Population , ,000 Population grew by 3,000. Percentage increase = 3,000 / 30,000 = 10% Will double in 70 / 10 = 7 years. 55

56 Practice Question #3 Jane buys $10,000 in stocks at age 25. Dick buys $10,000 in stocks at age 35. The stocks increase in value 7% per year. Dick and Jane both retire at age 65. How much are their stocks worth at that time? 56

57 Doubling time = 70 / 7 = 10 years Age Jane s stocks Dick s stocks 25 $10, $20,000 $10, $40,000 $20, $80,000 $40, $160,000 $80,000 Dick s investment grew in value for 30 years & doubled 3x. Jane s investment grew in value for 40 years & doubled 4x. 57

58 Exponential growth A personal example Jessica Aspen Born December 5, 2003 birth ~6 pounds Weight at 2 months ~12 pounds 58

59 How much should she weigh at 4 months if she grew exponentially? Age Weight 0 6 lbs 2 months 12 lbs 4 months? 59

60 2 months / 12 pounds Weight Age (in months) 60

66 Obviously, little girls don t grow exponentially Jessie s 1 st birthday 21 pounds 66

67 Review of exponential growth Will occur if population grows by constant percentage (r) per year Will result in explosive growth Has a doubling time equal to 70 / r 67

68 Practice problem: Bacteria in bottle 1 bacteria placed in bottle at 11:00 68

69 One minute later: 2 cells 69

70 2 minutes later 3 minutes later 4 cells 8 cells 70

71 4 minutes later 5 minutes later 16 cells 32 cells 71

72 Bottle full at noon 72

73 When was bottle half full? 73

74 Doubling Times in Bottle 74

75 World population (in billions) This may have profound implications for Earth Year 75

76 2. Topic 2: Why exponential growth is rare in nature. 76

77 Number of wolves Wolf population in Yellowstone grew quickly after reintroduction wolves released in 1995 and 1996 Population grew to 174 by

78 Number of wolves and then something happened

79 Number of wolves Why did population stop growing?

80 Why did Yellowstone population stop growing? Disease (as population size grows, diseases spreads more easily) Wolves killing wolves (Park became crowded, and wolves fought over territory) Notice: wolves didn t have fewer offspring when the population became large. The population stopped growing because many wolves died. 80

81 When resources are limited: Individuals often compete. Many may die This is true for many species: wolves competing for elk in Yellowstone or trees competing for sunlight 81

82 In nature, lack of food, water, or space prevents sustained exponential growth 82

83 Populations either stabilize at carrying capacity or destroy their resources and crash 83

84 Carrying capacity The maximum number of individuals an environment can sustain. 84

85 3. World s population is growing 1% per year This trend is impossible to continue 85

86 Census The population of Russia is declining This trend is also impossible to continue 86

87 Let s think about what it is required for populations to be stable (which ultimately is what we want) 87

88 Elephants work hard raising their offspring* How many offspring does each female need to raise for an elephant population to remain stable? *Gestation lasts 22 months. Nursing for 2 years. Sexual maturity at 12 years old. 88

89 Chinook salmon lay 5000 eggs each. And do no parenting. 89

90 How many offspring must each mother have survive to have a stable population? Elephants Salmon 90

91 Answer: Stable populations have 2 surviving offspring per adult Populations will grow exponentially if each family has more than two offspring 91

92 For a population to be stable, each adult must replace himself/herself Each female must have two offspring grow up. 92

93 The material that follows will not be covered Spring

94 4. Real populations have people of different ages This affects how populations grow

95 Niger Average woman has 8 children Population growth rate = 3% per year DT = 70 / 3 = ~23 years Life expectancy at birth: 41 years

96 Look at Niger s population growth (in separate File)

97 Exponentially growing populations have this shape of an age pyramid Old folks Children Adults Lots of children. Relatively few adults.

98 Imagine two big changes in Niger Health care reduces child mortality Education reduces birth rate to 2 children per family* *As we will discuss later, when women are educated they usually choose to have fewer children.

99 What will happen if all the children in Niger have two children when they grow up? (2 million) (Niger 2000)

100 If all the children have 2 children when they grow up: 2 million ADULTS 2 million CHILDREN (Niger 2000)

101 It is easy to think that the population will stop growing if everyone has 2 children. 2 million ADULTS 2 million CHILDREN (Niger 2000)

102 But look at Niger now Niger million young adults 2.0 million children (0.9 million) (2 million)

103 When children grow up, there will be more adults in Niger than now. Population will grow for awhile. Niger million children 0.9 million young adults (2.0 million) (2 million)

104 Population will eventually become stable with two children per family Age pyramid will look like this: Same number of children as adults. New Zealand (2025)

105 What can we learn from this age diagram?

106 Look at population growth in United States 106

107 Compare United States Year 2000 United States Year

108 What did we learn from these diagrams? 1. Growing populations have a lot of kids. 2. Populations can grow for awhile even when each family has 2 children. 3. Stable populations have large proportions of old people.

109 One of the biggest mistakes young workers make is to not invest in their retirement EARLY This is because investments grow exponentially which means they grow faster and faster 109

110 Study guide Read chapter 3, especially Population Ecology Be able to describe the history of reindeer on Saint Matthew Island, and the history of rabbits in Australia. Be able to extract a lesson from the history of reindeer on Saint Matthew Island or rabbits in Australia. Be able to define exponential growth, and describe its properties. Be able to recognize what kinds of growth are exponential. Be able to explain why populations grow exponentially. Be able to use formula DT = 70 / r. Be able to define carrying capacity and explain what causes it. Be able to look at an age pyramid and tell if a population is stable, growing, or shrinking. Be able to predict how changes in birth rate will affect populations. 110

111 Sample question Thirty wolves were introduced into Yellowstone National Park in Park biologists believed the population would grow by 36% per year, and that the carrying capacity of the park was approximately 250. If this is correct, approximately how many years would it take for the wolf population in the park to reach carrying capacity? 111

112 Sample question This graph shows the number of people (in billions) on Earth from the year 0 A.D. to the year Given this data, did the number of people on grow exponentially during this time period? 112

113 Sample questions The population of the United States was approximately 300 million when my first daughter was born in 2003 and has been growing at 1% per year. If this continues for the rest of my daughter s life, how many people will there be in the United States when she is an old woman? Explain your reasoning and deal with the uncertainty in this problem as best you can. In 1970, the average Chinese family had 5.8 children. Today that number is approximately 1.7, but the population of China is increasing by approximately 200,000 every week. How this can be? Use a diagram, equation, or graph or whatever else you need for your explanation. 113