1. How Populations Grow
Read the lesson title aloud to students.

2. Essential Question Learning Objectives
How can I explain the difference between exponential and logistic growth?
Learning Objectives
Describe how ecologists study populations.
Identify factors that affect population growth.
Describe exponential growth.
Describe logistic growth.
Click to reveal each learning objective in turn.
Read the objective aloud or ask a volunteer to do so.
Distribute the lesson worksheet and instruct students to use vocabulary terms from the presentation to build a concept map. Tell students to be sure their concept maps include all of the following vocabulary terms: population density, age structure, immigration, emigration, exponential growth, logistic growth, carrying capacity.

3. Describing Populations
Geographic range
Density and distribution
Growth rate
Age structure
Remind students that a population is a group of organisms of a single species that lives in a given area. Researchers study populations’ geographic range, density and distribution, growth rate, and age structure.

4. Geographic Range
Tell students that the area inhabited by a population is called its geographic range. A population’s range can vary enormously in size, depending on the species. A bacterial population in a rotting pumpkin, for example, has a range smaller than a cubic meter. The population of cod in the western Atlantic, on the other hand, covers a range that stretches from Greenland down to North Carolina.
Draw students’ attention to the photo of Salvinia. Tell students that in 1998, this floating fern was discovered in a small pond in Houston. Salvinia had been imported as an easy-to-grow aquarium plant. But some found their way into natural bodies of water and began to spread. Salvinia plants can double their dry weight in less than three days, rapidly forming floating mats that block sunlight and crowd out native species essential to local aquatic animals and waterfowl. Salvinia has been reported in Texas, all other Gulf Coast states, and Arizona.
Point out that Salvinia’s natural range includes southeastern Brazil and northern Argentina. But humans have carried Salvinia to tropical and subtropical areas in Africa, India, Australia, and other South Pacific islands. It is spreading across the southern United States largely because tiny pieces survive attached to boats and other recreational gear.

5. Density and Distribution
Tell students that population density refers to the number of individuals per unit area. Populations of different species often have very different densities, even in the same environment. For example, a population of ducks in a pond may have a low density, while fish in the same community may have a higher density.
Explain that distribution refers to how individuals in a population are spaced out across the range of the population—randomly, uniformly, or mostly concentrated in clumps.
Have volunteers come to the board to draw lines connecting the photos with their correct distribution patterns.
Click to reveal the lines showing the correct pairings.

6. Growth Rate Growth rate = 1 Population size is unchanged.
Population size is growing.
Growth rate < 0
Population size is decreasing.
Tell students that a population’s growth rate determines whether the size of the population stays the same, increases, or decreases over time. Salvinia populations in their native habitats stay more or less the same size over time. In other words, those Salvinia populations have a growth rate around zero. Salvinia populations in Texas and other southern states, by contrast, have very high growth rates, which means that those populations are increasing rapidly in size. Populations can also have negative growth rates, which means that they are decreasing in size. For example, populations of cod off the coast of New England have dropped so low due to overfishing that even using the latest hi-tech equipment, total catch has fallen dramatically.
Draw students’ attention to the three statements on the screen. Read each statement and ask students to identify for each whether the population size is growing, decreasing, or is unchanged.
Click to reveal the correct answers in turn.
Tell students that the photo shows a population of bacteria.
Ask: Imagine a few bacteria enter a host’s body and start to reproduce. Would you expect the growth rate to be zero, greater than zero, or less than zero?
Answer: If the bacteria are reproducing in a new host where there are plenty of resources, the growth rate is probably greater than zero.
Ask: Suppose after a few days the host is given an antibiotic. After several days, would you expect the growth rate to be zero, greater than zero, or less than zero?
Answer: After the antibiotic has been working for a few days, the population of bacteria has probably started to decrease, so the growth rate would be less than zero.
Bacterial population

7. Age Structure Only certain age groups can reproduce.
Only females produce offspring.
Explain that to fully understand a plant or animal population, researchers need to know more than just the number of individuals it contains. They also need to know the population’s age structure and the number of all individuals with male or female reproductive organs that a population contains.
Ask students to consider why knowing how many animals of each age group are in a population would be important. Ask them also to consider why it would be particularly important in animal populations to know how many females were in the population. Allow students to share several ideas before emphasizing that knowing numbers of individuals at different ages is important because most plants and animals cannot reproduce until they reach a certain age. Also, among most animals, only females can produce offspring.
Click to reveal the bullet points.
Ask: For a given animal species, which population would have a greater growth rate—one in which 90 percent of the individuals were juveniles, or one in which 90 percent of the individuals were of reproductive age?
Answer: the population in which the majority are of reproductive age

8. Population Growth 3. Immigration 1. Births
# of individuals that enter or leave the population
Tell students that factors that affect population size are birth rate, death rate, and the rate at which individuals enter (immigrate to) or leave (emigrate from) the population.
Use the diagram to explain how these factors cause a population to increase or decrease:
Explain that populations can grow if more individuals are born than die in any period of time. In other words, a population can grow when its birthrate is higher than its death rate. If the birthrate equals the death rate, the population may stay the same size. If the death rate is greater than the birthrate, the population is likely to shrink.
Point out that birth means different things in different species. Lions are born much like humans are born. Codfish, however, release eggs that hatch into new individuals.
Explain that a population may grow if individuals move into its range from elsewhere, a process called immigration. For example, an oak grove in a forest produces a bumper crop of acorns one year. The squirrel population in that grove may increase as squirrels immigrate in search of food. On the other hand, a population may decrease in size if individuals move out of the population’s range, a process called emigration. For example, a local food shortage or lack of other limiting resource can cause emigration. Young animals may emigrate from the area where they were born to find mates or establish new territories.
Have volunteers come to the board to label the diagram representing a fish population with “births,” “deaths,” “immigration,” and “emigration.”
Click to reveal the correct labels.
Ask: What two factors add individuals to the fish population?
Answer: births and immigration
Ask: What two factors remove individuals from the fish population?
Answer: deaths and emigration
Ask: If the fish population stays the same size for a one-year period, what can you assume about the number of individuals removed from the population due to death and emigration during that time?
Answer: That number is equal to the number of individuals added to the population by birth or immigration.
3. Emigration
2. Deaths

9. Exponential Growth J-shaped curve
Under ideal conditions with unlimited resources and protection from predators and disease, a population will grow exponentially.
J-shaped curve
Population is rapidly increasing at a constant rate.
Tell students that if you provide a population with all the food and space it needs, protect it from predators and disease, and remove its waste products, the population will grow. It can grow because members of the population will be able to produce offspring. Later, those offspring will produce their own offspring. Then, the offspring of those offspring will produce offspring. So, over time, the population will grow. In such a scenario, the size of each generation will be larger than the generation before it, a situation that is called exponential growth.
Click to reveal the statement about conditions for exponential growth.
Ask students to consider how bacteria and elephants differ in terms of their population structure and the time it takes to produce a next generation. Guide students to realize that bacteria reproduce much more rapidly than species like elephants. Point out that this difference has consequences for their patterns of population growth.
Lead a discussion in which students compare the graphs:
Ask: How does the shape of the line representing the growth of the bacterial population compare to the shape of the line representing the growth of the elephant population?
Answer: They are very similar.
Ask: How do the graphs differ?
Sample answers: The x-axis of the bacteria graph is marked in two-hour increments; the x-axis of the elephant graph is marked in 250-year increments. The y-axis of the graph representing the bacterial population is marked in increments of 100,000; the y-axis of the graph representing the elephant population is marked in increments of 5 million.
Ask: Why are different time increments used in the two graphs?
Answer: Elephants reproduce at a much slower rate than bacteria.
Describe for students a hypothetical experiment with a single bacterium that divides to produce two cells every 20 minutes: We supply it with ideal conditions—and watch. After 20 minutes, the bacterium divides to produce two bacteria. After another 20 minutes, those two bacteria divide to produce four cells. At the end of the first hour, those four bacteria divide to produce eight cells. After three 20-minute periods, we have 2 × 2 × 2, or 8 cells. Another way to say this is to use an exponent: 23 cells. In another hour (six 20-minute periods total), there will be 26, or 64 bacteria. In just one more hour, there will be 29, or 512. In one day, this bacterial population will grow to an astounding 4,720,000,000,000,000,000,000 individuals. If this growth continued without slowing down, in a few days this bacterial population would cover the planet.
Draw students’ attention to the graph for bacterial growth:
Explain that if you plot the size of this population on a graph over time, you get a J-shaped curve that rises slowly at first and then rises faster and faster.
Click to reveal the circle around the area where the population is rapidly increasing and the label.
Explain that if nothing interferes with this kind of growth, the population will become larger and larger, faster and faster, until it approaches an infinitely large size.
Point out that, unlike bacteria, a female elephant can produce a single offspring only every two to four years. Newborn elephants take about ten years to mature. But as can be seen in the elephant graph, if exponential growth continued, the result would be impossible. In the unlikely event that all descendants of a single elephant pair survived and reproduced, after 750 years there would be nearly 20 million elephants.
Click to reveal the circle showing the data point for 20 million elephants.

10. Logistic Growth S-shaped curve
When a population’s growth slows and then stops, following a period of exponential growth
S-shaped curve
Population growth may slow down when birthrate decreases, death rate increases, or both.
Growth rate equals zero at carrying capacity.
Most natural populations follow a logistic growth curve
Point out that the planet is not covered with either elephants or bacteria. So, exponential growth cannot explain population growth fully.
Draw students’ attention to the S-shaped curve in the graph. Tell them that this curve represents what is called logistic growth. Logistic growth occurs when a population’s growth slows and then stops, following a period of exponential growth. Many familiar plant and animal populations follow a logistic growth curve.
Click to reveal the definition of logistic growth.
Explain that something has to happen to keep a population from growing exponentially forever. Point out that population growth in real-world populations is logistic growth. This kind of growth shows three distinct phases.
Describe the three phases of population growth. After describing each phase, ask for a volunteer to go to the board and draw an arrow connecting the phase with the region on the graph that represents it.
Click to reveal the correct arrows.
Phase 1: Exponential growth: After a short time, the population begins to grow exponentially. During this phase, resources are unlimited, so individuals grow and reproduce rapidly. Few individuals die, and many offspring are produced, so both the population size and the rate of growth increase more and more rapidly.
Phase 2: Growth slows down: In real-world populations, exponential growth does not continue for long. At some point, the rate of population growth begins to slow down. This does not mean that the population size decreases. The population still grows, but the rate of growth slows down, so the population size increases more slowly.
Phase 3: Growth stops: At some point, the rate of population growth drops to zero. This means that the size of the population levels off. Under some conditions, the population will remain at or near this size indefinitely.
Ask: During which phase does the population grow most rapidly?
Answer: Phase I
Ask: During which phase does the population size stabilize?
Answer: Phase III
Remind students that a population grows when more organisms are born (or added to it) than die (or leave it). Thus, population growth may slow for several reasons. Growth may slow because the birthrate decreases. Growth may also slow if the death rate increases—or if births fall and deaths rise. Population growth may also slow if the rate of immigration decreases, the rate of emigration increases, or both.
Misconception Alert: Several common misconceptions about population growth are revealed when students are asked to graph population growth. Two common errors in students’ graphs are: (1) the omission of Phase II, in which growth slows—students show rapid growth followed by abrupt change to no growth; and (2) the placement of the initial point representing the starting population at the origin, or (0, 0), thus implying the impossible—a population growing from zero. Use the graph to help address these common misconceptions. Point out Phase II in the graph, and explain that this phase represents a population that is still growing, but more slowly than during Phase I. Also point out the initial point on the graph, and have students note that it is not at the origin. Remind them that all populations must start with at least one individual (in the case of asexually reproducing organisms) or one pair of organisms.

11. Carrying Capacity
The maximum number of individuals of a particular species that a particular environment can support
Population stabilizes at carrying capacity.
Ask: What happens when the birthrate and the death rate are the same, and when immigration equals emigration?
Answer: Population growth stops.
Point out that the population may still rise and fall somewhat, but the ups and downs average out around a certain population size.
Draw students’ attention to the broken horizontal line through the region of the graph where population growth levels off.
Click to reveal a black box highlighting this portion of the graph.
Tell students the point at which that line intersects the y-axis represents what ecologists call the carrying capacity. Carrying capacity is the maximum number of individuals of a particular species that a particular environment can support. Once a population reaches the carrying capacity of its environment, a variety of both biotic and abiotic external factors can affect the population in ways that stabilize it at that size.
Click to reveal the definition of carrying capacity and the label specifying that population stabilizes at carrying capacity.

12. Overview: How Populations Grow
1. “Ten individual per square hectare” is a description
of population
2, When resources are limited, a population will grow .
3. When growth rate is , the population is growing.
density
logistically
greater than zero
Have volunteers fill in the blanks with the terms that correctly complete the statements.
Click to reveal the correct answers.

13. Limits to Growth
Read the lesson title aloud to students.

14. Limiting Factors
Limiting factors determine the carrying capacity of an environment for a species.
Point out that scientists classify limiting factors into two groups: density-dependent factors and density-independent factors.
Click to reveal circles and labels showing how the factors are grouped.
Tell students that they will learn more about these groups of factors in the slides that follow.
Ask: How might each of these factors increase the death rate in a population?
Answer: Competition: Organisms may not have enough resources to survive; Predation: Organisms die when they are eaten; Parasitism and disease: Organisms are killed; Natural disaster and unusual weather: Organisms are killed or resources are diminished.
Distribute the lesson worksheet and instruct students to create a Venn diagram comparing the two categories of limiting factors, density dependent and density independent, which they will learn about in the slides that follow.
Density dependent
Density independent

15. Density-Dependent Factors
Limiting factors that depend on a population size.
Density-dependent limiting factors operate strongly when population density reaches a certain level.
Tell students that density-dependent limiting factors operate strongly when population density—the number of organisms per unit area—reaches a certain level.
Explain that these factors do not strongly affect small, scattered populations as much. Density-dependent limiting factors include competition, predation, herbivory, parasitism, disease, and stress from overcrowding. Note that some of these involve abiotic external factors and others involve biotic external factors.

16. Competition More individuals use up resources sooner.
Individuals may compete for food, water, space, sunlight, shelter, mates, territories.
Tell students that when populations become crowded, individuals compete for food, water, space, sunlight, and other resources that are limited. Some individuals obtain enough to survive and reproduce. Others may obtain enough to live but not enough to raise offspring. Still others may starve or die from lack of shelter. Thus, competition for changing resource bases that are limited can lower birthrates, increase death rates, or both.
Lead a short discussion guiding students to make their own conclusions about how competition can affect population growth. Remind students that four general factors affect population growth.
Ask: What four factors affect population growth?
Answer: birthrate, immigration, death rate, emigration
Then, guide students to tie these factors to competition.
Ask: How can competition affect the birthrate of a population?
Answer: If competition results in individuals not obtaining enough resources to reproduce, the birthrate of the population may decrease.
Ask: How can competition affect the death rate of a population?
Answer: If individuals cannot obtain enough resources to survive, the death rate may increase.
Ask: How can competition affect the rates of immigration and emigration?
Answer: If there is not much competition for the resources in an ecosystem, individuals from other ecosystems may move in, increasing immigration rate. If competition for resources is severe, the rate of emigration may increase as individuals seek other ecosystems in which to live.
Click to reveal the bullet points onscreen.
Close the discussion by reiterating the following:
Competition is a density-dependent limiting factor, because the more individuals in an area, the sooner they use up resources. Often, space and food are related. Many grazing animals compete for territories in which to breed and raise offspring. Individuals that can’t establish and defend a territory cannot breed. Competition can also occur among members of different species that attempt to use similar or overlapping resources that are limited. This type of competition is a major force behind evolutionary change.

17. Predator–Prey Relationships
Tell students that the effects of predators on prey and the effects of herbivores on plants are important density-dependent population controls. One classic study focuses on the relationship between wolves, moose, and plants on Isle Royale, an island in Lake Superior.
The graph shows that populations of wolves and moose fluctuate over time.
Make sure students understand that two separate sets of data are plotted on the graph. Point out the left and right vertical axes, which are numbered in different increments. Explain that the left vertical axis and the blue line represent the wolf population; the right vertical axis and the red line represent the moose population.
Ask: What general trends are shown in this graph?
Answer: An increase in the wolf population is usually accompanied by a decrease in the moose population. A decrease in the wolf population is usually accompanied by an increase in the moose population.
Use the graph to emphasize this cyclical nature of the predator-prey relationship:
Explain that sometimes, the moose population on Isle Royale grows large enough that moose become easy prey for wolves. When wolves have plenty to eat, their population grows. As the wolf population grows, wolves begin to kill more moose than are born. This causes the moose death rate to rise higher than its birthrate, so the moose population falls. As the moose population drops, wolves begin to starve. Starvation raises the wolves’ death rate and lowers their birthrate, so the wolf population also falls. When only a few predators are left, the moose death rate drops, and the cycle may repeat.
Click to reveal the black circle around the point representing the “CPV outbreak” on the graph.
Explain that the population at this time was affected by an outbreak of canine parvovirus (CPV).
Ask: Based on the graph, what effect did the canine virus outbreak have on the moose population?
Sample answer: The large decrease in wolf population is probably due to the virus. With a smaller wolf population, the moose death rate dropped, leading to a much higher population after several years.
Click to reveal the circle around the point showing wolf population growth around the year 2000.
Ask: What might explain this spike in the wolf population?
Sample answer: The large spike in moose population a few years before increased the amount of prey available, possibly increasing birth rate and decreasing death rate in the wolf population.
Tie the concept of predator–prey relationships to humans: Explain that in some situations, human activity limits populations. For example, humans are major predators of codfish in New England. Fishing fleets, by catching more and more fish every year, have raised cod death rates so high that birthrates cannot keep up. As a result, the cod population has been dropping. The cod population can recover if we scale back fishing to lower the death rate sufficiently. Biologists are studying birthrates and the age structure of the cod population to determine how many fish can be taken without threatening the survival of the population.

18. Herbivore Effects
Populations of herbivores and plants cycle up and down like populations of predators and prey.
Tell students that herbivory can also contribute to changes in population size. From a plant’s perspective, herbivores are predators. So it isn’t surprising that populations of herbivores and plants cycle up and down, just like populations of predators and prey. On parts of Isle Royale, large, dense moose populations can eat so much balsam fir that the population of these favorite food plants drops. When this happens, moose may suffer from lack of food.
Click to reveal the statement about herbivore and plant populations.
Guide students to make inferences about the connections between herbivory and wolf populations on Isle Royale.
Ask: If moose populations become very large, what will happen to wolf populations? What will happen to plant populations?
Answer: Moose populations will, after several years, increase. Populations of plants that the moose feed on will decrease.
Ask: If the plant populations decrease due to large moose populations, what will ultimately happen to the wolf population? Answer: Too many moose means too few plants. Moose populations will die off through increased predations and through starvation. With a smaller moose population, the wolf population will eventually decrease.

19. Parasitism and Disease
Parasites and diseases can spread quickly through dense host populations.
Stress from overcrowding can lead to lower birth rates, higher death rates, and higher emigration rates.
Tell students that parasites and disease-causing organisms feed at the expense of their hosts, weakening the hosts and causing stress or death. The ticks on the hedgehog in the photo, for example, feed on their host’s blood and carry diseases. Parasitism and disease are density-dependent effects because the denser the host population, the more easily parasites can spread from one host to another.
Click to reveal the first bullet point stating why disease is density dependent.
Remind students of the a dramatic drop in the wolf population around 1980 due to an outbreak of CPV. Explain that at that time, a virus accidentally introduced to the island killed all but 13 wolves—and all but three females. This drop in the wolf population enabled moose populations to skyrocket to 2,400. Those densely packed moose then became infested with winter ticks that caused hair loss and weakness.
Tell students that overcrowding can also lead to increased stress within a population. Explain that some species fight among themselves if overcrowded. Too much fighting can cause stress, which weakens the body’s ability to resist disease. In some species, overcrowding stress can cause females to neglect, kill, or even eat their own offspring. Thus, overcrowding can lower birthrates, raise death rates, or both. Stress can also increase rates of emigration.
Click to reveal the summary statement about effects of stress.

20. Density-Independent Factors
Density-independent limiting factors affect all populations regardless of population size and density.
Tell students that density-independent limiting factors affect all populations regardless of population size and density.
Environmental change, including unusual weather such as hurricanes, droughts, or floods, and natural disasters such as wildfires, can act as density-independent limiting factors. In response to such factors, a population may “crash.” After the crash, the population may build up again quickly, or it may stay low for some time.

21. Density-Independent Factors
Limiting factor that DOES NOT depend on the density of the population.
Examples: hurricanes, droughts, floods, wildfires
May sometimes tie in with density-dependent factors
Explain that events such as storms can nearly extinguish local populations of some species. For example, thrips, aphids, and other leaf-eating insects can be washed out by a heavy rainstorm. Waves whipped up by hurricanes can devastate shallow coral reefs. Extremes of cold or hot weather also can take their toll, no matter how sparse or dense a population is. More prolonged environmental changes, such as severe drought, can devastate populations. These kinds of environmental changes can thus affect ecosystem stability.
Tell students that the photo shows dead fish rotting on a receding shoreline due to drought conditions at Canyon Lake, Texas.
Ask: Why is drought a density-independent factor?
Answer: It can affect populations no matter how large or small they are.
Ask students to make inferences about the impact of the drought on a variety of populations in this ecosystem. For example, a population of water plants might become overcrowded as a result of a decrease in the water level of the river. Or, plants along the riverbank might dry out and die, limiting nesting places for some birds. Have volunteers discuss their inferences with the class.
Point out that sometimes, the effects of so-called density-independent factors can vary with population density. On Isle Royale, for example, the moose population grew exponentially for a time after the wolf population crashed. Then, a bitterly cold winter with very heavy snowfall covered the plants on which moose feed, making it difficult for all those moose to move around to find food. Because emigration wasn’t possible for this island population, many moose died from starvation. The effect of bad weather on this large, dense population were greater than it would have been on a small population. In a smaller population, there would have been less competition, so individual moose would have had more food available. This situation shows that it is sometimes difficult to say that a limiting factor acts only in a density-independent way.
Click to reveal the bullet point about the effects of density on density-independent factors.
Ask: Reconsider the drought scenario. Is it possible for drought to act as a density-dependent factor?
Sample answer: A large population might be affected by a drought more than a much smaller population due to competition for any water available.
Canyon Lake, TX

22. Overview: Limits to Growth
Flood waters cover a field of wildflowers.
Density dependent
Non-native snakes released into a wetland prey on native rodents.
Density independent
Flu virus spreads quickly in schools.
Have volunteers come to the board to draw lines matching examples with the correct category of limiting factors.
Click to reveal correct pairings.
Wildfires spread through a grassland.

23. Student Worksheet Answers
Exact layout of the concept map and specific intervening text will vary from student to student, but student concept maps should include the following terms with relevant links between them: population density, age structure, immigration, emigration, exponential growth, logistic growth, carrying capacity.