Main content

## AP®︎/College Biology

### Course: AP®︎/College Biology > Unit 8

Lesson 3: Population ecology- Exponential and logistic growth in populations
- Exponential & logistic growth
- Population regulation
- Population regulation
- Population growth rate based on birth and death rates
- Per capita population growth and exponential growth
- Logistic growth versus exponential growth
- Population ecology review
- Population ecology

© 2023 Khan AcademyTerms of usePrivacy PolicyCookie Notice

# Population ecology review

## Key terms

Term | Meaning | |
---|---|---|

Population | A group of individuals that belong in the same species and live in the same area; for example, the stray cats of New York City | |

Population ecology | The ecological study of how biotic (living) and abiotic (non-living) factors influence the density, dispersion, and size of a population | |

Population size ( | The number of individuals in the population; for example, | |

Density | The number of individuals per unit area or volume; for example, | |

Density-dependent factor | Referring to any characteristic that changes population size (is affected by population density; for example, competition | |

Density-independent factor | Referring to any characteristic that changes population size (not affected by population density; for example, natural disasters like an earthquake | |

Dispersion | The pattern of spacing among individuals within the boundaries of a population; for example, a clumped dispersion | |

Carrying capacity ( | The maximum population size (max | |

Exponential growth | Growth of a population in an ideal, unlimited resources environment; for example, bacteria left on a nutrient-enriched petri dish overnight | |

Logistic growth | Leveling off of exponential growth due to limiting resources; for example, the current human population |

## How many bunnies are on an island?

Imagine that you're a population ecologist sent out to a newly discovered island in the Pacific Ocean. Your speciality as a population ecologist is studying various bunny populations on the mainland. However, now your task is to go out and answer a bunch of new questions related to the population ecology of the bunnies on this new island. What are some things that you, as a population ecologist, are interested in figuring out?

First and foremost, you need to figure out just $N$ , is the total number of individuals in the population. For example, if there are $100$ bunnies on the island, the population size is $100$ , or $N=100$ .

*how many*bunnies there are in the population. In population ecology, the**population size**, symbolized asHowever, what if you wanted to know more than just how many bunnies there are on the island? Sometimes a more interesting value to an ecologist is not just the size of the population, but also, how the population size is

*distributed*or*dispersed*throughout a given area. In this case, some questions of interest would be:*How exactly is the population spread out within a given area?**Are there many bunnies tightly packed together in one area of the island? Or are they more evenly spread out all over the island?*

In order to answer these new questions, an ecologist would look at the

**density**of the population, or the number of individuals per the unit area or volume.For example, imagine that the only food source for the bunnies is found on one hilltop at the center of the island. You can now ask (and answer) questions such as:

*How are the bunnies distributed on the island?*With only one single food source, they would most likely all be densely packed at the center of the island.*What if there were many food sources spread throughout the island? How would this change the bunny population's distribution?*In this case, we would expect to see a more evenly dispersed bunny population throughout the island.

To make more sense of the different possible ways populations may be distributed within a given area, an ecologist can focus on the

**dispersion**of the population, or the pattern of spacing among individuals within the boundaries of a population. In ecology, individuals in a population may be distributed in a three general ways: uniform, random, or clumped dispersion.Often times, the dispersion of individuals in a population provides more information about how they interact with each other—and with their environment—than a simple density measurement.

## Population dynamics

In addition to knowing the density and dispersion of a population, another factor that is important to study in population ecology is how the population size ($N$ ) is changing over time. It's important to remember that ecology is a

*dynamic*study, meaning that it involves looking at the*changes*that happen to groups of organisms and how those changes affect their constant interactions with the biotic and abiotic factors of their environment. Ecologists use a variety of mathematical methods to model

*population dynamics*(how populations change in size and composition over time). Let's look at some examples of these dynamics and the how they could apply the island bunnies.### Exponential growth

Some models represent population growth $N$ ) is undergoing

*without*environmental constraints in which the population size (**exponential growth**. In other words, this model shows the growth of a population in an ideal environment with unlimited resources. This can be depicted as a*J-shaped curve*on a graph that models population growth.For example, if the bunnies on the island had unlimited resources (e.g. food, water, shelter, mates), their population size ($N$ ) would continue to grow exponentially. In this "perfect" world of unlimited resources, there are no environmental constraints to reduce their population size ($N$ ), and therefore, the island, given enough time, would be absolutely full of bunnies hopping around everywhere!

### Logistic growth

In reality, exponential growth is difficult to sustain over long periods of time for any population (including the bunnies) because resources are limited in nature. If this is the case, what would happen to the bunny population after it begins to face such limitations to growth? In order to answer this question, we can use a different growth model used by ecologists known as the

**logistic growth**model.In the logistic growth model, the population experiences a leveling off of exponential growth due to limiting resources. In turn, the shape of the graph, which was formerly a

*J-shaped curve*, now shifts to an*S-shaped curve*on a graph that models population growth.What exactly determines this "leveling off" of the population's growth? In population ecology, $K$ , represents the maximum population size that can be supported by the available resources in an environment. Once carrying capacity ($K$ ) has been reached, populations tend to fluctuate around ($K$ ), periodically going slightly over and under this population size based on the available resources in the environment.

**carrying capacity**, symbolized as## Population growth regulation

As you saw in the logistic growth model, the bunny population's growth, along with all other populations' growth, will always end up having to face some kind of resistance to growth, particularly when the population reaches carrying capacity ($K$ ). As a population ecologist, it's also worth trying to figure out what exactly are the factors that

*regulate*, or influence, the size and growth of the bunny population?The bunny population's growth is influenced by two main factors–

**density-dependent factors**, in which the density of the bunny population at a given time affects its growth rate, and**density-independent factors**, which influence growth rate of the bunny population*regardless*of its population density.In the table below, examples of density-dependent factors are shown. With these factors, an $N$ ).

*increase*in population density causes each of these factors to exert an even*stronger*influence on the population size (### Density-dependent factors

Factor | Explanation | Island bunnies |
---|---|---|

Competition | In crowded populations, increasing population density intensifies competition for resources and may cause a decrease in population size ( | Lots of bunnies = lots of competition for limited resources |

Predation | As a prey population gets more and more dense, predators may have easier access to feed on that species | Lots of bunnies = lots of easy targets for predatory cats on island |

Disease | In dense populations, diseases can spread more rapidly and may cause a decrease in population size ( | Lots of bunnies = lots of hosts for diseases |

### Density-independent factors

Density-independent factors are quite different. Many abiotic (non-living) factors influence the death rate of a population

*regardless*of its density, including weather, natural disasters, and pollution. An individual bunny may be killed in a catastrophic earthquake on an island regardless of how many bunnies happen to be in that area. Its chances of survival are the same whether the population density is high or low, thus exemplifying a density-independent factor.As you can see, population ecology is about a lot more than just counting bunnies on an island. Instead, with a deep understanding of all the different factors that affect the bunny population, you, as the population ecologist, can now describe the dynamic

*changes*occurring in the population and, importantly, even predict*future*changes based on what is already known about the bunnies' past and present population dynamics. Off to the next island!## Common misconceptions

- Students might mistakenly think that once a population reaches its carrying capacity (
), it no longer changes in population size. This is definitely$K$ *not*true in population ecology!**Populations do not permanently remain at carrying capacity (**Remember that ecology is a dynamic study that ).$K$ *always*involves ever-changing factors influencing populations and their growth. Most stable population sizes fluctuate around , as opposed to remaining exactly at that value.$K$ ${}^{4}$ - Students might mistakenly think population growth models can
*only*be either exponential or logistic...this is*not*the case!**Population growth rates aren't exclusively exponential or logistic in their growth pattern.**Population growth models are on a spectrum that can*range*from exponential to logistic. Growth patterns often fluctuate anywhere between purely exponential and purely logistic growth. - Students might mistakenly think that population sizes are always increasing. However,
**population sizes aren't always growing.**Sometimes, a population might be experiencing serious enough issues that*decrease*the population size ( ). A decrease in population size is caused by a$N$ *negative*growth rate, which can be due to a variety of factors like disease, famine, or natural disasters that lead to widespread deaths over a given time period.

## Want to join the conversation?

- How isn't population growing when people are having babies and, what is a negative growth rate(10 votes)
- Human populations are growing as long as the death rate doesn't surpass the birth rate. In case it does, we're speaking of a
**negative growth rate**.

Hope this helps!(6 votes)

- If people have babies shouldn't the population increase .?(5 votes)
- it is increasing and the only way it would stop is if the death rate surpassed the birth rate(3 votes)

- Crecimiento de una población en un entorno ideal de recursos ilimitados; por ejemplo, las bacterias que quedan en una placa de Petri enriquecida con nutrientes durante la noche(5 votes)
- How might a population capacity change in an environment; what's an example?(3 votes)
- If a population is at capacity due to predators, and then some of those predators die due to a virus. The population then doesn’t have as many predators holding it back and the population is able to increase.(4 votes)

- what is a negative growth rate(3 votes)
- A negative growth rate is when the number of birth is smaller than the number of death, i.e. the number of individuals decrease in a population.(1 vote)

- Did ever find a solution to what happened in Australia?(2 votes)
- I heard about a time when Napoleon was hunting and was swarmed by so many bunnies he had to retreat. Haha!(3 votes)

- At what time did the bunny population grow?(2 votes)
- What do we say if the population of the predators increases? Is it a density-independent factor?(2 votes)
- What are the main factors that affect the growth of a population?(1 vote)
- Isn't pollution technically a density-dependent factor? Pollution requires the increase density of a given species which in turn generates more pollution. What classifies pollution? In the case of a natural disaster when the ash from a volcanic eruption or the gases from within the crust of the earth are released because of an earthquake should we consider this abiotic process pollution?

We as humans seem to be propelled to mitigate the fallout of such events as natural disaster as if we were an intrinsic property of these natural phenomenon. Is natural disaster and thus abiotic pollution actually a logical phenomenon and fundamental and not a disaster or pollution? Should we only classify pollution as a harmful substance introduced into an ecosystem by biological factors and especially in the event of failure to control such pollution?

I have heard so many arguments that try to justify humanities contributions to pollution by comparing it to pollution that comes from natural abiotic phenomenon, and I was thinking if we change what classifies pollution maybe we could focus better on what is actually pollution. Then certainly pollution would only be biotic and thus a density-dependent factor.(1 vote)