1. Watch this Video
2. Study this Summary
Four Factors That Change Population Size
Population size is affected by only four factors:
- Births: Increase population size.
- Deaths: Decrease population size.
- Immigration: Organisms moving into an area increase population size.
- Emigration: Organisms leaving an area decrease population size.
Exponential Growth and Its Limits

Exponential growth occurs when a population increases rapidly over regular time intervals.
- Growth is proportional to the existing population.
- Population size doubles at a consistent rate.
- The line produced by plotting exponential growth is often referred to as a “J” curve
Mathematically, exponential growth follows the equation:
ΔN/ΔT = rN
- N: Population size
- T: Time
- r: Rate of increase
Examples of Exponential Growth:
- Invasive species entering a new environment.
- Early phase of bacterial infection.
- Spread of a virus in a new population.
Biotic potential (rmax): Exponential growth is link to (but not identical to) biotic potential: the maximum growth rate a population can achieve under ideal conditions.
Carrying Capacity, Limiting Factors and Environmental Resistance

Environments are finite, and can only support so many individuals. The maximum number of individuals an environment can support is its carrying capacity, symbolized by the letter (K).
As a population approaches its carrying capacity, limiting factors slow its growth. There are two categories of limiting factors:
- Density-dependent limiting factors: Increase in intensity as population density rises. These factors include
- Competition for resources
- Parasitism
- Predation
- Stress from overcrowding
- Density-independent limiting factors: Affect populations regardless of size.
- Natural disasters (hurricanes, floods, earthquakes)
- Human-caused environmental changes (oil spills, toxic chemical releases)
Logistic Growth Model
The logistic growth model (shown above) incorporates limiting factors and carrying capacity:
ΔN/ΔT = rN (K – N) / K
- Growth slows as population (N) approaches carrying capacity (K).
- At low population sizes, growth appears exponential.
- As population nears K, growth slows and eventually stops.
- The line produced by plotting logistic growth is often referred to as an “S” curve
What happens as population size (N) approaches carrying capacity (K)
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- Oscillations: Populations cycle above and below K as resources fluctuate.
- Catastrophic Overshoot: A population exceeds K, leading to resource collapse and population crash.
Predator-Prey Population Cycles
Predator and prey populations often oscillate over time. This was captured in data from 1840s to 1930s showing population oscillation involving lynxes (a predatory cat) and hares (the prey) in Canada.
- When hare populations rose, predator populations increased.
- As predators consumed more prey, prey populations declined.
- When prey declined, predator populations also dropped due to food scarcity.
Other factors were also at work in this oscillation, especially fluctuations in food availability for prey species.
3. Master these Flashcards
[qdeck style=”width: 600px !important; min-height: 450px !important;” bold_text=”false” qrecord_id=”sciencemusicvideosMeister1961-Population Growth Flashcards, APBioVideoPath”]
[h] Population Ecology
[i]
[q json=”true” yy=”4″ unit=”8.Ecology” dataset_id=”AP_Bio_Flashcards_2022|11b6669b3e510″ question_number=”393″ topic=”8.3-4.Population_Ecology”] Ultimately, only four variables affect the size of any population. What are they?
[a] Population size is a function of births, deaths, immigration, and emigration.
[q json=”true” yy=”4″ unit=”8.Ecology” dataset_id=”AP_Bio_Flashcards_2022|11a5aa85c7910″ question_number=”394″ topic=”8.3-4.Population_Ecology”] What is exponential growth?
[a] Exponential growth is the growth of a population in which the number of individuals added is proportional to the amount already present. As a result, the bigger the population, the bigger the increase.
[q json=”true” dataset_id=”AP_Bio_Flashcards_2022|8bc500335071b” question_number=”395″ unit=”8.Ecology” topic=”8.3-4.Population_Ecology”] Explain the formula for exponential growth.
[a] The formula for exponential growth is: change in N/t = rN, where
- N = population size
- t = time
- r= rate of increase
[q json=”true” dataset_id=”AP_Bio_Flashcards_2022|8badb7bc6871b” question_number=”396″ unit=”8.Ecology” topic=”8.3-4.Population_Ecology”] In a graph, what does exponential growth look like?
[a] When exponential growth is plotted (with time as the X-axis and population size as the Y-axis) the result is a J-shaped curve: a slow takeoff followed by an increasingly steep rise in population.
[q json=”true” yy=”4″ unit=”8.Ecology” dataset_id=”AP_Bio_Flashcards_2022|1195837349d10″ question_number=”397″ topic=”8.3-4.Population_Ecology”] In biological systems, when does exponential growth occur?
[a] In any biological system, exponential growth can only happen for a limited period, during which a population has the resources (food, space, etc) that let it grow without constraints. This might happen when an invasive species arrives in a new environment, free from the predators that might have held it in check in its previous environment. It can also happen during the early phases of a bacterial infection, or during a disease outbreak (when a pathogen can spread exponentially).
[q json=”true” yy=”4″ unit=”8.Ecology” dataset_id=”AP_Bio_Flashcards_2022|11886ab067510″ question_number=”398″ topic=”8.3-4.Population_Ecology”] What is biotic potential? How is it represented?
[a] Biotic potential is the maximum rate at which a population can expand. It’s represented by rmax.
[q json=”true” dataset_id=”AP_Bio_Flashcards_2022|1c0f35b12e05″ question_number=”399″ unit=”8.Ecology” topic=”8.3-4.Population_Ecology”] What is carrying capacity?
[a] Carrying capacity (K) is the maximum number of individuals that a particular environment can support.
[q json=”true” yy=”4″ unit=”8.Ecology” dataset_id=”AP_Bio_Flashcards_2022|1178fde1a0d10″ question_number=”400″ topic=”8.3-4.Population_Ecology”] What is the logistic growth model?
[a] The logistic model of population growth shows how a population’s growth rate decreases as it reaches its carrying capacity (E).
[q json=”true” dataset_id=”AP_Bio_Flashcards_2022|8b3769203731b” question_number=”401″ unit=”8.Ecology” topic=”8.3-4.Population_Ecology”] Describe the equation for logistic growth.
[a] The logistic growth model can be represented by the equation N/t = rN (K-N)/K, where
- N = population size
- t = time
- r= rate of increase
- K = carrying capacity
As a population reaches its carrying capacity, there will be increased environmental resistance, as density-dependent limiting factors slow and then stop a population’s growth.
[q json=”true” dataset_id=”AP_Bio_Flashcards_2022|8b0992761e71b” question_number=”402″ unit=”8.Ecology” topic=”8.3-4.Population_Ecology”] When plotted on a graph, what does logistic growth look like?
[a] When logistic growth is plotted (with the X-axis representing time and the Y-axis representing population size), the result is an “S-shaped” or “sigmoid” curve. The curve initially looks like an exponential growth curve (a J-curve) with a slow takeoff followed by a rapid rise (A and B). But as N approaches carrying capacity, the amount of increase slows (C) and then drops to zero (D) as the population stabilizes at its carrying capacity (E).
[q json=”true” yy=”4″ unit=”8.Ecology” dataset_id=”AP_Bio_Flashcards_2022|1139665cdd910″ question_number=”403″ topic=”8.3-4.Population_Ecology”] In relationship to population growth, what are limiting factors?
[a] Limiting factors prevent a population from increasing at its biotic potential, and cause a population’s size to stabilize at or below the environment’s carrying capacity.
[q json=”true” dataset_id=”AP_Bio_Flashcards_2022|1a2d4013d205″ question_number=”404″ unit=”8.Ecology” topic=”8.3-4.Population_Ecology”] Define and describe density-dependent limiting factors.
[a] Density-dependent limiting factors intensify as the density of individuals within a population increases. These factors can be extrinsic (coming from outside the growing population) or intrinsic (from within the population).
Extrinsic factors include predation pressure, parasitism, and competition for increasingly scarce resources. Intrinsic factors can include the stress that’s induced by increased crowding and competition, lowering the birth rate. Territoriality can similarly decrease a population’s ability to expand beyond a certain density.
[q json=”true” dataset_id=”AP_Bio_Flashcards_2022|198a44d37a05″ question_number=”405″ unit=”8.Ecology” topic=”8.3-4.Population_Ecology”] Define and describe density-independent limiting factors.
[a] Density-independent limiting factors are those that are unrelated to a population’s size (symbolized by N). For example, hurricanes, floods, or earthquakes can all cause significant death in a population, lowering population size, regardless of that population’s density.
[q json=”true” yy=”4″ unit=”8.Ecology” dataset_id=”AP_Bio_Flashcards_2022|1125c13889d10″ question_number=”406″ topic=”8.3-4.Population_Ecology”] When a population grows and reaches its carrying capacity, the result might be stable oscillation around carrying capacity. Explain.
[a] In this scenario, the population overshoots the carrying capacity (E), lowering the available resources. This causes the population to decline (F). As the resource base recovers, the population resumes its growth until it again overshoots the carrying capacity (G), repeating the cycle.
[q json=”true” dataset_id=”AP_Bio_Flashcards_2022|22226ae15b55a5″ question_number=”407″ unit=”8.Ecology” topic=”8.3-4.Population_Ecology”] Sometimes, a population overshoots carrying capacity, which is followed by a catastrophic population decline. Explain.
[a] An overshoot (2) is where the population exceeds the environment’s carrying capacity. If this causes a significant depletion in environmental resources from which the environment can’t recover, then the population that caused the depletion, if it can survive at all, will do so at significantly reduced numbers.
[x]
[restart]
[/qdeck]
4. Tackle this Quiz
[qwiz qrecord_id=”sciencemusicvideosMeister1961-Population Growth Quiz, APBioVideoPath”]
[h] Population Growth
[i]
[q] The growth curve below can be described by a single letter: _____.
[textentry single_char=”true”]
[c]IE o=
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[c]IEVudGVyIHdvcmQ=[Qq]
[c]ICo=[Qq]
[f]IE5vLiBKdXN0IHJ1biB0aGUgbGV0dGVycyBvZiB0aGUgYWxwaGFiZXQgdGhyb3VnaCB5b3VyIGhlYWQuIFdoaWNoIGxldHRlciBsb29rcyBtb3N0IHNpbWlsYXIgdG8gdGhlIGJsdWUgbGluZSBpbiB0aGUgZ3JhcGggYWJvdmU/[Qq]
[q] What letter is used to describe the growth curve below?
[textentry single_char=”true”]
[c]IF M=[Qq]
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[c]IEVudGVyIHdvcmQ=[Qq]
[c]ICo=[Qq]
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[q]The kind of population growth shown below is [hangman] growth. It only occurs when there are no [hangman] factors at work.
[c]ZXhwb25lbnRpYWw=[Qq]
[c]bGltaXRpbmc=[Qq]
[q]The kind of population growth shown below is called [hangman] growth. In this growth model, a population’s growth slows as it reaches the environments’ [hangman] [hangman].
[c]bG9naXN0aWM=[Qq]
[c]Y2Fycnlpbmc=[Qq]
[c]Y2FwYWNpdHk=[Qq]
[q]As a population grows within a confined geographical area, there come to be more individuals/unit of area or volume. The limiting factors that come into play in this situation are called [hangman] [hangman] limiting factors.
[c]ZGVuc2l0eQ==[Qq]
[c]ZGVwZW5kZW50[Qq]
[q]Environmental factors such as fires, floods, landslides, and volcanic eruptions would all be classified as [hangman] [hangman] limiting factors
[c]ZGVuc2l0eQ==[Qq]
[c]aW5kZXBlbmRlbnQ=[Qq]
[q]Limiting factors such as competition, parasitism, predation, and waste accumulation are all classified as [hangman] factors because they come from outside of the population itself.
[c]ZXh0cmluc2lj[Qq]
[q]Sometimes, a population’s growth can be impeded by stress that’s induced by overcrowding, which lowers the population’s birth rate. These types of limiting factors are called [hangman] factors.
[c]aW50cmluc2lj[Qq]
[q]In the diagram below, “D” represents the [hangman] [hangman].
[c]Y2Fycnlpbmc=[Qq]
[c]Y2FwYWNpdHk=[Qq]
[q]In the diagram below, “E” and “F” show the population [hangman] around its carrying capacity.
[c]b3NjaWxsYXRpbmc=[Qq]
[q] In the diagram below, which number or letter represents carrying capacity?
[textentry single_char=”true”]
[c]ID E=[Qq]
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[c]IEVudGVyIHdvcmQ=[Qq]
[c]ICo=[Qq]
[f]IE5vLiBDYXJyeWluZyBjYXBhY2l0eSBpcyB0aGUgbWF4aW11bSBwb3B1bGF0aW9uIHRoYXQgYW4gYXJlYSBjYW4gc3VwcG9ydC4gSW4gdGhpcyBncmFwaCwgdGFrZSBhIGxvb2sgYXQgd2hlcmUgdGhlIHJlc291cmNlIGJhc2UgKHN0YXJ0cykgdG8gZHJvcCBzdGVlcGx5IGRvd253YXJkLiBUaGF0JiM4MjE3O3MgYSBnb29kIGluZGljYXRpb24gdGhhdCB5b3UmIzgyMTc7dmUgZXhjZWVkZWQgdGhlIGNhcnJ5aW5nIGNhcGFjaXR5Lg==[Qq]
[q]The graph below shows the results of a computer model of the interaction between a population of predators and a population of prey. Which number represents the predator?
[textentry single_char=”true”]
[c]ID I=[Qq]
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[c]IEVudGVyIHdvcmQ=[Qq]
[c]ICo=[Qq]
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[q] In the diagram below, which letter represents the carrying capacity?
[textentry single_char=”true”]
[c]IE U=[Qq]
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[f]IE5vLCB0aGF0JiM4MjE3O3Mgbm90IGNvcnJlY3Qu[Qq]
[c]ICo=[Qq]
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[q] In the diagram below, which letter represents the point at which the population has reached the environment’s carrying capacity?
[textentry single_char=”true”]
[c]IE Q=[Qq]
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[c]IEVudGVyIHdvcmQ=[Qq]
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[c]ICo=[Qq]
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[q] Limiting factors such as competition, parasitism, predation, and waste accumulation are all classified as [hangman] factors because they come from outside of the population itself.
[c]IGV4dHJpbnNpYw==[Qq]
[f]IENvcnJlY3Qh[Qq]
[q] In the diagram below, which number or letter refers to the “overshoot.”
[textentry single_char=”true”]
[c]ID I=[Qq]
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[c]IEVudGVyIHdvcmQ=[Qq]
[f]IE5vLg==[Qq]
[c]ICo=[Qq]
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[q]Limiting factors such as disease from parasites, increased predation, and food scarcity is all density [hangman]. As this population continues to grow within the same area, these factors will become more [hangman].
[c]ZGVwZW5kZW50[Qq]
[c]aW50ZW5zZQ==[Qq]
[x][restart]
[/qwiz]
What’s next?
Please proceed to this next tutorial: Community Ecology: Species Interactions