- 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
What factors limit population sizes?
- In nature, population size and growth are limited by many factors. Some are density-dependent, while others are density-independent.
- Density-dependent limiting factors cause a population's per capita growth rate to change—typically, to drop—with increasing population density. One example is competition for limited food among members of a population.
- Density-independent factors affect per capita growth rate independent of population density. Examples include natural disasters like forest fires.
- Limiting factors of different kinds can interact in complex ways to produce various patterns of population growth. Some populations show cyclical oscillations, in which population size changes predictably in a cycle.
All populations on Earth have limits to their growth. Even populations of bunnies—that reproduce like bunnies!—don't grow infinitely large. And although humans are giving the idea of infinite growth a run for its money, we too will ultimately reach limits on population size imposed by the environment.
What exactly are these environmental limiting factors? Broadly speaking, we can split the factors that regulate population growth into two main groups: density-dependent and density-independent.
Density-dependent limiting factors
Let's start off with an example. Imagine a population of organisms—let's say, deer—with access to a fixed, constant amount of food. When the population is small, the limited amount of food will be plenty for everyone. But, when the population gets large enough, the limited amount of food may no longer be sufficient, leading to competition among the deer. Because of the competition, some deer may die of starvation or fail to have offspring, decreasing the per capita—per individual—growth rate and causing population size to plateau or shrink.
In this scenario, competition for food is a density-dependent limiting factor. In general, we define density-dependent limiting factors as factors that affect the per capita growth rate of a population differently depending on how dense the population already is. Most density-dependent factors make the per capita growth rate go down as the population increases. This is an example of negative feedback that limits population growth.
Density-dependent limiting factors can lead to a logistic pattern of growth, in which a population's size levels off at an environmentally determined maximum called the carrying capacity. Sometimes this is a smooth process; in other cases, though, the population may overshoot carrying capacity and be brought back down by density-dependent factors.
Graph plots population size versus time. Logistic growth results in a curve that gets increasingly steep then levels off when the carrying capacity is reached, resulting in an S-shape.
Density-dependent limiting factors tend to be biotic—living organism-related—as opposed to physical features of the environment. Some common examples of density-dependent limiting factors include:
- Competition within the population. When a population reaches a high density, there are more individuals trying to use the same quantity of resources. This can lead to competition for food, water, shelter, mates, light, and other resources needed for survival and reproduction.
- Predation. Higher-density populations may attract predators who wouldn’t bother with a sparser population. When these predators eat individuals from the population, they decrease its numbers but may increase their own. This can produce interesting, cyclical patterns, as we'll see below.
- Disease and parasites. Disease is more likely to break out and result in deaths when more individuals are living together in the same place. Parasites are also more likely to spread under these conditions.
- Waste accumulation. High population densities can lead to the accumulation of harmful waste products that kill individuals or impair reproduction, reducing the population’s growth.
Photograph of a lemming. It is a small, chubby rodent that resembles a guinea pig.
Density-dependent regulation can also take the form of behavioral or physiological changes in the organisms that make up the population. For example, rodents called lemmings respond to high population density by emigrating in groups in search of a new, less crowded place to live. This process has been misinterpreted as a mass suicide of sorts in popular culture because the lemmings sometimes die while trying to cross bodies of water.
Density-independent limiting factors
The second group of limiting factors consists of density-independent limiting factors that affect per capita growth rate independent of how dense the population is.
Image of a forest fire with elk standing in a river for safety.
As an example, let's consider a wildfire that breaks out in a forest where deer live. The fire will kill any unlucky deer that are present, regardless of population size. An individual deer's chance of dying doesn't depend at all on how many other deer are around. Density-independent limiting factors often take the form of natural disasters, severe weather, and pollution.
Unlike density-dependent limiting factors, density-independent limiting factors alone can’t keep a population at constant levels. That’s because their strength doesn’t depend on the size of the population, so they don’t make a "correction" when the population size gets too large. Instead, they may lead to erratic, abrupt shifts in population size. Small populations may be at risk of getting wiped out by sporadic, density-independent events.
In the real world, many density-dependent and density-independent limiting factors can—and usually do—interact to produce the patterns of change we see in a population. For example, a population may be kept near carrying capacity by density-dependent factors for a period then experience an abrupt drop in numbers due to a density-independent event, such as a storm or fire.
However, even in the absence of catastrophes, populations are not always stably at carrying capacity. In fact, populations can fluctuate, or vary, in density in many different patterns. Some undergo irregular spikes and crashes in numbers. For instance, algae may bloom when an influx of phosphorous leads to unsustainable growth of the population. Other populations have regular cycles of boom and bust. Let's take a closer look at these cycles.
Some populations undergo cyclical oscillations in size. Cyclical oscillations are repeating rises and drops in the size of the population over time. If we graphed population size over time for a population with cyclical oscillations, it would look roughly like the wave below—though probably not quite as tidy!
Graph with population on the y axis and time on the x axis. Population numbers oscillate over time, producing a wave shape.
Where do these oscillations come from? In many cases, oscillations are produced by interactions between populations of at least two different species. For instance, predation, parasite infection, and fluctuation in food availability have all been shown to drive oscillations. These density-dependent factors don't always create oscillations, however. Instead, they only do so under the right conditions, when populations interact in specific ways.
Case study: lemmings
As an example, let's look at a population of lemmings found in Greenland. For years, this population had cyclical oscillations in size, with a period—the length of a full cycle—of about four years. Ecologists found that the cycle could be explained by interactions between the lemming and four predators: the owl, fox, skua—a bird—and stoat. The owl, fox, and skua are opportunistic predators that can use various food sources and tend to eat lemmings only when they are abundant. The stoat, in contrast, eats pretty much only lemmings.
Photograph of a stoat
So, why does the cycle happen? Let's start by following the lemmings at a low point in their cycle. Because the population density is low, the owls, skuas, and foxes will not pay too much attention to the lemmings, allowing the population to increase rapidly. As the lemming population grows, the stoat population also grows, but with a lag. This reflects that stoats reproduce only once a year—unlike lemmings, which reproduce more or less constantly—and can only leave numerous offspring after they've had a period in which their food source, lemmings, is abundant.
As the lemming density increases, owls, foxes, and skuas are attracted and start preying on the lemmings more frequently than when they were scarce. This acts as a density-dependent limit to lemming growth, and it keeps lemmings from getting ahead of the stoats in numbers. The stoat population thus overshoots and becomes large enough that it kills off many of the lemmings, leaving few to reproduce and causing a lemming population crash. This crash is followed by a stoat crash with a one-year delay, as the stoats wind up with a greatly reduced food supply. And then the cycle begins again.
This general pattern of interaction is represented in the graph below. You can see that prey population numbers—such as those of lemmings—drop first and are then followed by predator numbers—such as those of the stoat.
Graph with population on the y axis and time on the x axis. Prey and predator numbers oscillate over time, both producing a wave-shaped curve. The prey population drops first and is followed with a lag by the predator population. The prey population then recovers first, followed by the recovery of the predator population.
Are other factors besides predator-prey interactions driving this pattern? It's possible, but ecologists were able to reproduce the oscillating pattern in a computer model based only on predation and reproduction data from the field, supporting the idea that predation is a driving factor.
Sad fact: some lemming populations are no longer oscillating. They peaked—per their usual cycle—in 1998 but never recovered from the crash that followed. Ecologists think this may be due to unusually warm winters and changes in snowfall in the Arctic, which may have reduced the snowpack that usually provides protection to the lemmings as they raise their young. As a result, species that are predators of lemmings may die out in regions where the lemming populations have crashed.
Case study: lynx and hares
One other famous example of this type of predator-prey interaction involves the Canada lynx—the predator—and snowshoe hare—the prey—whose populations have been shown to co-vary in cycles, with a drop in hare numbers predicting a drop in lynx numbers. This is the example you’re most likely to see in your textbook. At first, scientists thought that lynx predation was the key factor that made the hare population drop. We now know that other factors are likely involved, such as availability of food for the hares. Either way, this is another example in which density-dependent factors produce cyclical changes in a population.
Top panel: The graph plots number of animals in thousands versus time in years. The number of hares fluctuates between 10,000 at the low points and 75,000 to 150,000 at the high points. There are typically fewer lynxes than hares, but the trend in number of lynxes follows the number of hares.
Bottom panel: photographs of lynx and hare
Want to join the conversation?
- What factors can be representative of a population near carrying capacity?(8 votes)
- is Population stays under carrying capacity logistic or exponential.(1 vote)
- logistical population growth has a carrying capacity, exponential doesn't.(5 votes)
- With population regulation, what category would human related disasters fall in? Density dependent or density independent?(1 vote)
- Independent. Even though people are living beings, people's mistakes can cause disasters:
Oil spills are people's mistakes, but the oil which affects the other populations is not a living organism. A wildfire caused by an out-of-control campfire is still a wildfire.(1 vote)