Population Biology: Carrying capacity, demographics, and cycles

All monarch butterflies are one species. But did you know that monarch butterflies in North America exist in two separate populations? These two populations can interbreed but generally will not. So, what exactly is a “population,” and why is understanding the distinction crucial to species’ survival on Earth? Let’s find out!

You may have seen bright orange Monarch butterflies around your neighborhood at certain times of the year. As winter sets in, populations of monarchs from the US and Canada migrate south to Mexico to their overwintering spots. There, they shelter by the millions in forests of Oyamel trees, something they’ve been doing for so long that local people consider monarchs the souls of their ancestors. The monarchs arrive there in early November, coinciding with the Day of the Dead (Día de Muertos) in Mexico.

Although all monarch butterflies are one species (Danaus plexippus), they exist in two populations in North America. Biologists use the word population to refer to groups of the same species that live and interbreed in distinct geographic areas. The eastern monarch population spends summers in the central-eastern US and its winters in Mexico. The western monarch population spends both summer and winter along the US Pacific Coast. Because of the great distance between them, the two populations are unlikely to interbreed. As a result, they are considered separate populations. Being in the same species means they can interbreed; being in different populations means they do not.

Meanwhile, something has been happening to the eastern monarch population. Figure 1 shows the amount of forest (in hectares) occupied by eastern monarchs at their winter spot from 1993 to 2015. The downward trend in their population over time is apparent. In fact, the number of eastern monarchs has declined by more than 80.0% since monitoring began. Today, eastern monarchs are listed as an endangered species. Biologists attribute their decline to herbicide use, deforestation, and climate change (Echevarria 2022).

All populations change over time based on migrations and resources such as food and shelter. Abiotic factors, or nonliving physical and chemical parts of the environment, such as temperature and humidity, also affect populations. A population may be growing fast, leveling off, or declining, depending on the complex interplay of its characteristics and environmental influences. Population biology is the study of these population dynamics and causes of change.

Figure 1: Eastern monarch butterflies counted at their overwintering area in Mexico through 2015.

image © Public Domain
Comprehension Checkpoint
True or False: In the study of population biology, “population” refers to a group of the same species that live in distinct geographic regions and do not interbreed.

Roots of population biology

“It will be evident to everyone how important it is to carry on the fisheries in accordance with certain well-defined rules based on a thorough knowledge of the nature and mode of life of the fish, if the future of fisheries is not to be seriously endangered."

– American zoologist Spencer Fullerton Baird, 1878

The roots of population biology trace back to when people who regularly harvested from specific populations of animals, such as fish or deer, attempted to understand how and why the populations fluctuated over time.

What does the Salmon Child sculpture (Figure 2) suggest about the relationships between native American Wiyot people and salmon fisheries?

For millennia, the Pacific Northwest (American Indian) nations, including the Swyamish, Swinomish, Tulalip, Duwamish, and Lummi Nation, depended on salmon. These native tribes understood salmon populations as a food source and a vital part of their lives and ecosystems. Accordingly, they needed to carefully manage the fish populations through “an intimate knowledge of all the factors that affected fish life,” coupled with a “spiritual reverence for salmon.” (Hillaire 2016)

However, by the 19th century, European settlers began harvesting fish as commodities to be sold and shipped to faraway places. This led to a sharp decline in some fish populations, including Pacific salmon. In response, the US Congress authorized the creation of the US Commission of Fish and Fisheries in 1871 to oversee fish harvest, with Spencer F. Baird as the first Commissioner. So began the field of Fisheries Biology.

Nevertheless, tensions continued. Conflicts between the Pacific Northwest nations and white commercial fishermen over fish harvest rights resulted in the “Fish Wars” of the 1970s. The dispute highlighted the importance of understanding fish population dynamics. Fortunately, by this time, population biology had become prevalent. Scientists were in a position to help resolve the conflict and protect the fish population.

Population growth

Some of the earliest formal research on population biology focused on the growth rates of human populations. Only later was the discipline applied to other animals. English economist Thomas Robert Malthus raised the alarm in the late 18th century with his premise that human population growth would continue exponentially, outpacing growth in food supplies. The result? Starvation and catastrophe (Malthus 1798).

Decades later, Belgian mathematician Pierre François Verhulst countered Malthus. Verhulst argued that the human population would level off as it encountered food limitations and then maintain a stable size. Verhulst developed a mathematical function for what he called “logistic growth” (Verhulst 1838). This also introduced the idea that there is a maximum population size of humans that can be sustained by the food and other resources available on Earth. 

In the 1920s, American population biologist Raymond Pearl’s Law of Population Growth proposed that human and other animal populations grow according to the same laws. Moreover, Pearl proposed that populations grow logistically, like body growth, before leveling off to some maximum. At the time, most people, including scientists, thought of humans as fundamentally different from all other animals, so it was bold to claim that the same principles governed humans and animals.

Consider Figure 3. What do you notice about the documented trout population’s growth rate after it was introduced to a new lake?

Figure 3: Plot of size of a trout population (subfamily Salmoninae) over time.

You can see that growth is fast at first but gradually slows and eventually levels out. This trend is an example of the type of logistic growth that Pearl observed in fruit flies and in a human population in Algeria (Pearl 1925). In logistic growth, as a population becomes denser, its growth rate slows. So, we say that population growth is “density-dependent.” The density of organisms eventually reaches a maximum, termed the “carrying capacity” (or K). As the field of population biology took a distinctly mathematical approach, scientists recognized that as populations approach carrying capacity, they tend to waver around their maximum population size.

But what causes a population of animals to level off and hover around a maximum size once it approaches carrying capacity?

Comprehension Checkpoint
According to logistic growth, what happens to a population as it becomes denser?

Carrying capacity

“The carrying capacity is the limit of growth or development …,, beginning with the population, and shaped by processes and interdependent relationships between finite resources and the consumers of those resources”

- Mexican marine biologist Pablo Del Monte-Luna, 2004

Today’s scientists are still grappling with all the factors that determine when and why animal populations level off and hover around a maximum size reflecting their environments’ carrying capacity. The finite resources that limit population growth could include food, water, space, other physical resources, and suitable conditions of variables such as temperature and humidity.

For example, Indian marine biologist Prabhulla Chandran Lakshmi Devi and colleagues studied crab populations of various species in the Cochin Backwaters of Kerala, India, in relation to the resources in their environments. They found that good water quality was not the limiting resource for the crabs. Instead, crab populations were densest in areas with a muddy bottom, high salt concentration, lots of organic carbon (from decayed plants and animals), and mangrove patches (Devi et al. 2021).

But a population reaching carrying capacity is not just about the physical resources in its environment, it is also about interactions with other organisms, such as competition and predation (see our Animal Ecology module ).

American veterinary technician Elizabeth Ashley and colleagues studied causes of mortality in a population of harbor seals (Phoca vitulina) in the San Juan Islands (Ashley 2020). Using data from seal counts made by flyovers at low tide (when seals are the most visible laying on rocks), they plotted population size across study years from 1978 to 2020. Before 1978, fur hunting had decimated the harbor seal population. But, by 1978, the population was in the process of recovery. Ashley and her colleagues observed that it first grew rapidly, then leveled off at about 5,000 individuals, and remained stable after that. Why?

Figure 4: Size of harbor seal population in the San Juan Islands from 1978-2020 counts.

image © CC-BY: Ashley et al. 2020

Analysis of beached dead seals showed that the population remained stable because growth was balanced by deaths from starvation, predation, infections, and human interactions. This showed that as a population gets bigger relative to its available space, the individuals will likely suffer higher mortality. This is why growth slows as populations get denser.

Ashley’s work demonstrates that to understand growth rates, you must first understand demographics (the characteristics of a population, including age, sex, size, and reproductive rates).

Comprehension Checkpoint
Which would you expect as a population approaches carrying capacity?


Demography is the study of the characteristics of a population, typically using mathematics. Scientists use demographic parameters, such as population size, the ratio of males to females, or birth rates, among others, to track population changes over time.

For example, quillback rockfish (Sebastes maliger) are prized in the traditional, indigenous diets of British Columbia. Indigenous populations of Heiltsuk, Kitasoo/Xai'xais, Nuxalk, and Wuikinuxv living on the coast have historically regulated their fishing to sustainable levels. But as commercial rockfish harvesting began in the late 1970s, sustainable fishing became more difficult to achieve. In Figure 5, quillback rockfish body sizes are plotted over time, using fork lengths for measurement. “Fork length” is the distance from the tip of a rockfish’s snout to the center of the fork in its tail.

What do you notice about the size of quillback rockfishes over time?

Figure 5: Plot of the fork lengths of captured Quillback Rockfish over time.

image © Public Domain

From these data, staff from the Central Coast Indigenous Resource Alliance—an organization dedicated to healthy ecosystems for First Nations—noted a decline in the sizes of quillback rockfishes. Larger female quillback rockfish have more offspring. As a result, the body size decline indicates a population that may be suffering from increasingly poor reproduction, resulting in shrinking. A female quillback rockfish may take more than ten years to reach maturity, so a population that has lost its large females will take a long time to recover even if fishing practices are changed (McGreer and Frid 2017).

Fishing regulations often limit fishers to keeping only larger fishes through size cutoffs, which may cull the big females essential to population stability. Indeed, females are so important that fisheries experts have invented the term BOFFFFs (“big, old, fat, fecund, female fish”). American marine ecologist Mark Hixon and colleagues emphasize that these BOFFFFs have been undervalued in fishery management and recommend that old individuals be protected to support fish population growth (Hixon et al. 2014).

Indeed, the distribution of ages in a population, or “age structure,” reveals a lot about the population’s growth rate.

Age structure

Age structure is often represented by a population pyramid that shows the proportion of individuals in each age category (see Figure 6). The use of population pyramids has its roots in the study of human populations. For example, compare the population pyramids for humans in Western Africa and Western Europe in 2019 shown in Figure 6. People are grouped into age categories shown on the y-axis.

What differences do you notice? What similarities?

Figure 6: 2019 population pyramids of Western Africa (left) and Western Europe (right) with age classes on the y-axis.

image © CC-BY 3.0: Population Pyramid

The distinct shapes of the pyramids show the different demographic characteristics of these populations of humans. In Western Africa, the population is young. The largest age category is just individuals up to four years old, with the proportion of people declining in older age categories, tapering to a tiny proportion of people in their 80s. The wider the pyramid, the faster the population is growing. So Western Africa’s pyramid-shaped structure indicates a population that is growing.

In Europe, however, the distribution of people across age categories is much more even, with most of the population in middle age (from 30 to 60 years old). This tower-shaped structure indicates a stable population, neither growing nor shrinking. The population pyramid is useful because it can tell us how a population is changing over time, even when the data is taken from a single point in time.

Additionally, in both populations, the percentage of males (blue) is roughly equal to the percentage of females (pink). Moreover, the oldest categories are heavily enriched for women, indicating that women have a longer life expectancy in both regions.

The same sorts of comparisons can also help biologists analyze the demographic characteristics of other animals to predict future population growth.

Comprehension Checkpoint
The distribution of ages throughout a population is also called _______.

Population cycles

"All animal populations fluctuate in numbers. These fluctuations may be small or large, regular or irregular."

– Charles J. Krebs, 1964

In the 1920s, Austrian-raised physical chemist Alfred J. Lotka wondered whether the same laws governed biological systems as physical systems that could be predicted with mathematical models. Using a hypothetical interaction of a plant and a plant eater, Lotka modeled his interaction and found that it could lead to regular variations in the two populations (Lotka 1925).

Italian mathematician Vito Volterra followed by analyzing predator-prey population dynamics mathematically, creating equations that would become known as the Lotka-Volterra equations (Volterra 1926). The equations predict that interactions between predators and prey regulate each of their populations in tandem. As prey become more abundant, so do predators, who then eat prey populations, reducing their abundance and predator populations. The result is a cyclical pattern of population growth and decline in both species.

Snowshoe hares (Lepus americanus) are the main food for Canadian lynxes (Lynx canadensis) in the northern forests they inhabit, which include the northernmost reaches of Canada such as the Yukon. When hares are abundant, lynxes eat little else. When hares are scarce, lynxes may prey on other small mammals, such as mice and squirrels, but are challenged to get enough nutrition.

Look at Figure 7. What do you notice about changes in snowshoe hare population sizes and lynx population sizes over time?

Figure 7: Population changes for snowshoe hares (black bars) and their lynx predators (red line) over time in the Yukon.

image © Myers 2018

The graphic shows that hare and lynx populations cycled over decades in similar ways. The hare populations peaked roughly every ten years, followed by a peak in lynx populations a year or two afterward. The linked cycles suggest the interdependence of the two species, as modeled in the Lotka-Volterra equations (see our Using Graphs and Visual Data in Science module).

But cycles in population size can have other causes as well. Australian zoologist Herbert Andrewartha was puzzled over regular outbreaks of thrips (Thysanoptera spp.) and grasshoppers (suborder Caelifera) that caused crop failures. His careful study revealed that weather aspects, including rainfall and temperature, explained changes in the insect populations (see our Linear Equations in Science module). Because weather is unaffected by insect population density, we call this a “density-independent factor” (Andrewartha and Birch 1954). We now know that the growth of an animal population is the result of a complex interplay of density-dependent and density-independent factors.

"We already know many of the mechanisms involved in population dynamics, hence new questions of how they act together seem to be a most promising direction for a better understanding of outbreaks as well as population cycles."

– Norwegian ecologist Harry P. Andreassen, 2021

Scientists today are still studying and modeling these complex dynamics (see our Modeling in Scientific Research module). Tanzanian mathematician Alanus Mapunda and colleagues built on the Lotka-Volterra equations, modeling populations of predators and prey in the Serengeti region of Africa (Mapunda 2019). Their models were relevant to ongoing conservation concerns, namely the effects of human harvest and drought on Serengeti wildlife. Their findings demonstrated that:

  • Human harvest of prey populations indirectly reduced predator populations;
  • Drought directly reduced both predator and prey populations; and
  • The combined impact was even more pronounced.


Mapunda and his colleagues considered conservation strategies, including creating hunting-restricted wildlife reserves and constructing dams to mitigate drought. Their resulting models showed improved persistence of both predators and prey, especially if both conservation strategies were employed.

Thus, modern use of mathematical modeling of population dynamics plays a key role in conservation. And understanding why populations change, in some cases headed towards extinction, has become a crucial part of population biology research. With few resources being dedicated to conservation, we need the best possible science telling us how to support threatened populations.

Comprehension Checkpoint
Variation in population size can be entirely explained by density-dependent factors like food.

Population tipping points

Populations do not always change cyclically. Depending on birth rates and death rates, they may grow dramatically or decline and collapse. The phrase “tipping point” was originally used to analyze how human populations changed over landscapes. Now the phrase is used in biology to refer to thresholds that, if exceeded, may not allow an animal population to recover. A challenge in conservation research is to read the indicators of imminent tipping points so that a population can be brought back from the brink before it is too late.

Chinese physicist Lei Dai worked with laboratory populations of yeast to look for signs of an impending population collapse (Dai et al. 2012). He found that yeast populations begin dramatically slowing their growth as they approach tipping points. Applying the findings to populations of honeybees in Pennsylvania, Dai concluded that they are showing early warning signs of collapse. According to Dai, as populations approach collapse, their population size fluctuations get more dramatic.

Returning to fisheries, German biologist Christian Möllmann and colleagues recently monitored western Baltic cod (Gadus morhuapopulations (Möllmann et al. 2021).

Looking at the plot of cod catch over time (Figure 8), what do you notice?

Figure 8: Tons of western Baltic cod captured from 1990 to 2020.

image © CC BY 4.0: Möllmann et al. 2021

Möllmann’s team concluded that a tipping point occurred during the 2000s (i.e., a point of no return for the Western Baltic Cod population). They blame the population collapse on two key factors:

  • Unsustainable levels of fishing; and
  • Global climate change warming ocean environments outside of the Western Baltic Cod’s tolerance level (see our Factors that Control Earth's Temperature module).

Whether it is yeast, honeybees, or fishes, organisms are subject to what scientists call the “Allee effect,” when a population gets so small that it cannot recover effectively, even when the major causes of mortality are removed. There are various reasons that a much-reduced population might not recover. For western Baltic cod, critically small populations have lower mating success, lower egg fertilization rates, insufficient vigilance for predators, and low genetic variation. These factors contribute to the tipping point and can lead to irreversible population decline. For honeybees in Pennsylvania, the Allee effect may include other parameters, such as having too few adult bees to perform all the roles in the hive for gathering food and taking care of eggs and larvae (Paiste 2014).

As conditions continue changing globally and death rates rise, birth rates decline, or a combination of both, we can expect to see more populations approaching tipping points. Scientists and policymakers are scrambling to sustain populations in the face of climate change. Fisheries biologists at the National Oceanic and Atmospheric Administration (NOAA) race to manage populations of Pacific cod, pollock, and other important food species (Holsman et al. 2020). Argentinian mammalogist Enrique Alberto Crespo works to understand how to achieve a sustainable balance between human uses of the ocean and the needs of top predators such as sea lions and fur seals (Crespo 2022).

Regardless of the species, all animal populations are subject to the same rules of growth and decline. As conditions on Earth continue changing, understanding these rules becomes increasingly important.

Devin Reese, PhD. “Population Biology” Visionlearning Vol. BIO-6 (2), 2023.


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