Biology: Ecology: Population Growth and Carrying Capacity
Modeling how populations change over time
Biology: Ecology: Population Growth and Carrying Capacity
Modeling how populations change over time
Biology - Grade 9-12
- 1
Define population growth and explain why it is important in ecology.
Population growth is the change in the number of individuals in a population over time. It is important in ecology because it helps scientists predict resource use, competition, disease spread, species survival, and ecosystem stability. - 2
A rabbit population has 120 individuals at the start of spring. During spring, 45 rabbits are born, 18 die, 6 move into the area, and 3 leave the area. What is the population size at the end of spring?
Add births and immigration, then subtract deaths and emigration.
The population size is 150 rabbits. The calculation is 120 + 45 - 18 + 6 - 3 = 150. - 3
In one year, a population of 500 fish increases to 575 fish. Calculate the percent growth for that year.
Use percent growth = change in population divided by original population times 100.
The population increased by 75 fish, so the percent growth is 75 divided by 500 times 100, which equals 15%. - 4
Compare exponential growth and logistic growth. Include the typical shape of each graph and what happens to the population over time.
Exponential growth forms a J-shaped curve because the population increases faster and faster when resources are unlimited. Logistic growth forms an S-shaped curve because growth slows as resources become limited and the population approaches carrying capacity. - 5
A lake can support about 2,000 adult trout over many years. What term describes this maximum long-term population size, and what does it mean?
Think about the number of organisms an environment can support sustainably.
The term is carrying capacity. It means the largest population size the lake can support over time without using resources faster than they are replaced. - 6
The table shows a deer population over time: Year 1: 80, Year 2: 150, Year 3: 275, Year 4: 430, Year 5: 560, Year 6: 615, Year 7: 635, Year 8: 630. Estimate the carrying capacity and explain your reasoning.
Look for the population size where the values stop increasing much and begin to level off.
The carrying capacity is about 630 deer. The population grows quickly at first but then levels off around 630 to 635 deer, which suggests that the environment can support about that many deer. - 7
Classify each limiting factor as density-dependent or density-independent: competition for food, drought, disease spread, wildfire.
Competition for food and disease spread are density-dependent because their effects usually increase as population density increases. Drought and wildfire are density-independent because they can affect populations regardless of population density. - 8
A population of bacteria grows according to the logistic model growth rate = rN(1 - N/K). If r = 0.4, N = 200, and K = 1,000, what is the growth rate?
Substitute the values into rN(1 - N/K), then simplify the fraction inside the parentheses first.
The growth rate is 64 bacteria per time unit. The calculation is 0.4 times 200 times (1 - 200/1000), which equals 80 times 0.8, or 64. - 9
Using the logistic growth model, explain why a population grows more slowly when N is close to K.
In the expression (1 - N/K), think about what happens when N almost equals K.
A population grows more slowly when N is close to K because resources such as food, space, and water become limited. In the logistic model, the factor (1 - N/K) becomes very small, which reduces the growth rate. - 10
An island has abundant nesting sites and food after a storm removes many competitors. A bird population introduced to the island increases from 10 birds to 20, then 40, then 80 over equal time intervals. What type of growth is shown, and why?
Look for a repeated multiplication pattern in the population size.
The population shows exponential growth because it doubles during each equal time interval. This pattern suggests that resources are abundant and limiting factors are not yet strongly slowing growth. - 11
Describe what can happen when a population overshoots its carrying capacity.
When a population overshoots carrying capacity, it may use resources faster than they can recover. This can lead to increased competition, starvation, disease, lower birth rates, higher death rates, and a population crash. - 12
A graph of a yeast population shows a rapid increase for several hours, then a plateau, then a decline. Explain one likely reason for each part of the pattern.
The rapid increase likely occurs because yeast have plenty of sugar and space. The plateau likely occurs because resources become limited and the population reaches carrying capacity. The decline likely occurs because waste builds up or food runs out, causing more yeast to die. - 13
How can human activities increase or decrease the carrying capacity of an environment for a species? Give one example of each.
Carrying capacity changes when the availability of food, water, shelter, space, or safe habitat changes.
Human activities can increase carrying capacity by adding resources, such as planting native vegetation that provides food and shelter for birds. Human activities can decrease carrying capacity by destroying habitat, polluting water, or removing food sources, such as clearing wetlands used by amphibians. - 14
Scientists capture and mark 40 turtles in a pond. Later, they capture 50 turtles and find that 10 are marked. Use mark-recapture to estimate the pond's turtle population.
Use the proportion marked in the second sample to estimate the whole population.
The estimated turtle population is 200 turtles. Using the formula total population = marked first sample times total second sample divided by marked recaptured, the estimate is 40 times 50 divided by 10, which equals 200. - 15
A wildlife manager sees that a grassland's bison population has been above carrying capacity for two years. The grass is overgrazed, birth rates are falling, and young bison survival is low. Recommend one management action and explain how it could help.
One management action is to relocate some bison to another suitable habitat. This could reduce population density, lower competition for grass, allow the grassland to recover, and help the remaining bison have better survival and reproduction.