Christopher X J. Jensen
Associate Professor, Pratt Institute

Eco 101: Carrying Capacity

Posted 25 Jan 2016 / 0
Fundamentally, carrying capacity is a measure of the maximum density of a particular population

How many organisms of a particular species can an area support? What determines this maximum population density? The answer to these questions is captured by the ecological concept of carrying capacity.

The carrying capacity tells us how many organisms of a particular species can live in a location based on the abundance of resources in that location. A variety of different resources have the potential to set limits on the population size that can be sustained by a given environment.

Ways that carrying capacity can be expressed

Carrying capacity is most commonly expressed as a population density. For many organisms (for example, large terrestial species) that density will be expressed as the number of individuals per area. But for other organisms (for example, microscopic aquatic species) that density will be expressed as the number of individuals per volume of water or air. For linear habitats such as rivers and streams, carrying capacity might be measured as the number of individuals per distance (length).

Sometimes carrying capacity is expressed in terms of biomass — the total mass of living tissue — rather than number of individuals. Although the “total organismal biomass” concept may seem a bit more abstract than the “number of individual organisms” concept, there are many situations in which it is more valuable to know the density of biomass that can be sustained. Because individuals can vary significantly in size, biomass may provide a more accurate estimate of the carrying capacity than number of individuals. In the end, limiting resources are used to grow the population by creating new biomass, so carrying capacity expressed in terms of biomass can be more directly estimated based on a knowledge of the quantity (in other words, mass) of available resources.

Occasionally, carrying capacity is expressed as an abundance rather than a density. For example, we might talk about the “carrying capacity of the earth” and express that as the number of humans that the earth can sustain. Whenever we talk about a population’s carrying capacity as a quantity rather than a density, we must define the boundaries of that population. The entire earth obviously has clear boundaries, as do ponds and lakes, particular biomes on a particular continent, and freshwater river systems.

Factors that can influence the carrying capacity

Any resource that a particular species requires to survive and reproduce has the potential to influence the carrying capacity. For animals, food is an obvious limiting resource, so food availability may be the primary driver of carrying capacity. Plants compete for limited sunlight, so the total available insolation may determine their carrying capacity. In areas of low water abundance, maximum sustainable population size of both plants and animals may be determined by water availability.

Space can also influence the carrying capacity, particularly for species that require territory to survive. In grasslands and forests, plants compete for not just the nutrients in soil but also for the space that soil affords for growth. The marine intertidal zone is famous for its intense competition for available real estate. Sometimes defended territories just represent an area containing sufficient resources, so space and resources are often intertwined.

Mussel beds in the marine intertidal zone demonstrate how space can set a maximum density of individuals.

Estimating carrying capacity can be difficult

If carrying capacity is a function of limited resources, estimating carrying capacity should be relatively simple. All we need to know is the total availability of resources and the resource requirement per individual (or biomass):

${carrying\:capacity\:(individuals\:per\:area)} = \dfrac{resource\:availability\:per\:area}{resource\:abundance\:required\:per\:individual}$

Unfortunately, in most circumstances this kind of estimate is not so easy to make.

The first problem arises in knowing exactly what the resource requirements are for each individual in a population of interest. For some organisms these requirements have been measured, but not every species’ basic resource requirements are known with any precision. Resource requirements may also vary at different times of year or in different locations. If you don’t know what the resource requirements are for individuals in a population, you can’t estimate that population’s carrying capacity.

A second problem arises in deciding which resource to measure the availability of. Organisms require a variety of resources, any of which can limit population growth when scarce. The obvious strategy is to measure the resource that is most scarce relative to the requirement it meets (this is to follow Liebig’s law of the minimum). For example, if plants in an area are primarily limited by nitrogen availability, then one might use available nitrogen to estimate carrying capacity. This strategy works so long as the relative supply of other required resources remains constant. But if there is a sudden drought and water availability decreases dramatically, the carrying capacity of these plants might shift from being limited by nitrogen to being limited by water.

Food is a common limiting resource, but measuring food availability can lead to unreliable estimates of carrying capacity. This is because all food does not contain the same nutrients in the same proportions. The more the nutrient profile of a given food type matches the needs of a species, the better the availability of that food type approximates the carrying capacity for a population of that species.

Even if we can reliably estimate both the resource requirements and resource availability for a given population, estimating carrying capacity with the equation above assumes that only individuals in this particular population compete for these resources. For many resources, members of one species compete not only with each other but also with members of other species. This means that the carrying capacity of Species A will depend on the population size of Species B if both consume the same limiting resource. For this reason, in some ecological communities it may make more sense to talk about the carrying capacity of several species in total rather than each particular species.

How carrying capacity and population growth rate do — and don’t — interact

A fundamental property of carrying capacity is that it influences the effective population growth rate. Imagine a population seeded by dropping a few individuals into a resource-rich environment. At first — because resources are abundant — this population grows at its maximum population growth rate, a function of:

1. that species’ reproductive output;
2. the rate of survival of offspring; and
3. the developmental time required to transition from offspring to adult.

As the population expands exponentially, its growth accelerates, depleting resources more rapidly. As population density increases, so does competition for resources. Competition for resources can cause the reproductive output of individuals to decrease, the survival rate of offspring to decrease, and/or the developmental time of offspring to increase.

Any of these changes in response to competition can cause the population to grow more slowly. This pattern of growth is often labeled density dependent because the effective growth rate of the population depends on the density of that population. Eventually, at some population density, competition for scarce resources becomes so intense that the population ceases to grow. This population density at which the population growth rate is zero is the carrying capacity.

Some populations can temporarily “overshoot” their carrying capacity. If the actual population density exceeds the density at carrying capacity, we expect the population to shrink (in other words, the population growth rate becomes negative) because the resource requirements of the population exceed the resource availability.

If a population’s density relative to its carrying capacity can influence its population growth rate, does that mean that changes in population growth rate can change the carrying capacity?

Although there is some controversy about the relationship between population growth rate and carrying capacity, it should be noted that many changes to population growth rate have no impact on the carrying capacity. For example, the presence of a predator or a parasite can depress the growth rate of a population, but predators and parasites don’t affect carrying capacity unless they reduce the availability of resources. This means that populations that are being victimized by predators or parasites either grow more slowly towards their carrying capacity or stop growing before they reach carrying capacity.

Equilibrium is not necessarily carrying capacity

If the goal of estimating the carrying capacity is to determine the stable population size that can be supported by the resources in a given habitat, doesn’t that mean that a population at equilibrium is a population at carrying capacity?

Not necessarily.

As discussed above, there are other factors that can cause a population’s growth rate to stabilize before it reaches the density at carrying capacity. A predator may be keeping the population at a stable density below carrying capacity by consuming many offspring. Parasites can have similar effects by lowering rates of survival and reproduction. It is important to note that parasites and predators reduce the stable population density by lowering effective growth rates before competition for resources stabilizes growth. This means that in populations regulated by predators and/or parasites, there will likely be excess (unutilized) resources in the environment.

If predators kill prey at a high enough rate, they may create an equilibrium below the prey’s carrying capacity

It should be noted that there is not total agreement on the definition of carrying capacity, and sometimes you will encounter carrying capacity defined as any stable population equilibrium. The problem with the “any equilibrium” definition of carrying capacity is that it muddles a number of different potential causes of a stable population. If a population is stable in density, we would like to be able to differentiate the cause, as a population at carrying capacity has very different ecological effects than a population held at an equilibrium density below carrying capacity.

This post was written for students in my Ecology and Ecology for Architects courses. As such, a lot of nuance is excluded from this post. If you are interested in a more in-depth discussion of carrying capacity from both a theoretical and historical perspective, I recommend Hixon 2008.

This post is part of my Eco 101 series

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