Population growth (zoology)

In nature, animals of a particular species rarely occur by themselves. Instead, they usually exist with other individuals of the same species. Biologists use the term “population” to refer to an aggregation of organisms of a given species that live in the same general location at the same time. In some cases, populations can be well-defined, such as herds of cattle or flocks of geese. In other cases, a population is not well defined, often because several species may be found in the same location. For example, a meadow may contain intermingled populations of several species, including daisies, timothy grass, earthworms, and grasshoppers.

Biologists study animal populations to determine how many individuals are in a given population at a given time, to understand how populations change across time, and to identify environmental factors that contribute to population fluctuations. The population of most species of plants, animals, and microbes changes over time. Some populations increase or decrease steadily, while others fluctuate regularly. The fertility, mortality, and migration of the animal impact these changes. While these are naturally occurring phenomena, many human activities interfere with animal populations and significantly influence these population factors. Thus, populations are generally dynamic rather than static when viewed over time.

Population Behaviors

Most populations change so much over time because there is a constant turnover of new animal generations. That is, new individuals are constantly being born, hatched, or germinated while others die. Moreover, animals may enter a population by immigration and leave by emigration. The number of births and new immigrants rarely exactly matches the number of deaths and emigrants. Because changes in population size are common in nature, biologists aim to understand these changes. One approach has been to model populations using a simplified graphical or mathematical summary of the actual changes that are occurring in the species of interest. The relationship between a model and the actual population that it represents is similar to that between a map and the area of land that it represents. Because modeling is such an important aspect of population biology, a biologist who studies population must often have a good background in mathematics.

Perhaps the simplest model of population behavior is the difference equation, which states that the number of individuals in a population at some specified time in the future is equal to the number at present, plus the number of births, minus the number of deaths, plus the number of new immigrants, minus the number of emigrants. Thus, by knowing how many individuals are on a site at a given time and knowing the usual number of births, deaths, immigrants, and emigrants, one can predict the number of individuals on the site at some future time.

The number of births, deaths, immigrants, and emigrants varies by location and across time. For example, on a site with abundant food and space and with favorable physical conditions for growth and development, births and immigration will be much greater than deaths and emigration. Thus, the population will increase. Conversely, if food or space is limited or if the physical conditions are more severe, losses to the population through death and emigration will equal or exceed gains through birth and immigration. Thus, the population will remain constant or decline.

Biologists often are concerned about what happens in extreme conditions because such conditions define the limits within which the population normally operates. When conditions are very bad, a population normally declines rapidly, often to the point of local extinction; when conditions are very good, a population will increase. That increase is attributable to the fact that each individual normally has the capacity to produce many offspring during their lifetime. Other individual organisms, particularly many invertebrates and plants, can produce hundreds of thousands of offspring in their lifetimes.

Influences on Birth and Death Rates

At least three different traits influence the reproductive output of a given species. The first is the number of offspring per reproductive period (elephants produce only one child at a time, whereas flies can lay thousands of eggs). The second is the age at first reproduction (most dogs can reproduce when less than three years old, whereas humans do not usually become fertile until they reach the age of thirteen or fourteen). The third is the number of times that an individual reproduces in its lifetime (salmon spawn, that is, lay eggs only once before they die, whereas chickens lay eggs repeatedly). Even under ideal conditions, death must also be considered when examining population growth. Most organisms have a maximum life span determined by their innate physiology and cannot be exceeded, even if they are supplied with abundant food and kept free from disease.

Population biologists frequently express birth and death in the form of rates. This can be done by counting the number of new births and deaths in a population during a predetermined period and then dividing by the number of individuals in the population. That will give the per capita (per individual) birth and death rates. For example, suppose that during a year, there were thirty births and fifteen deaths in a population of one thousand individuals. That per capita birth rate would be 0.030, and the per capita death rate would be 0.015.

Next, one can subtract the death rate from the birth rate to find the per capita rate of population growth. That rate should be greatest under ideal conditions—when the birth rate is greatest and the death rate is least. That per capita rate of population growth is called the “maximal intrinsic rate of increase” or the “biotic potential” by population biologists, and it is a very important attribute. It is often symbolized as rmax or referred to as “little r.” Normally, rmax is considered an inherent feature of a species. As one might expect, it varies greatly among different types of organisms. For example, rmax, expressed per year, is 0.02-1.5 for birds and large mammals, 4-50 for insects and small invertebrates, and as high as 20,000 for bacteria.

Exponential Growth

By knowing the intrinsic rate of increase and the number of organisms in a population, one can predict much about the behavior of a population under ideal conditions. The rate at which the population grows is merely the intrinsic rate of increase (rmax) multiplied by the number of individuals in the population. For example, suppose that there are ten individuals in a population with an annual rmax of 2. That population would increase by an annual rate of twenty (which would be a healthy increase). Next, suppose that one returned to that population at some later time when the population was fifty individuals. At that point, the annual rate of population increase would be one hundred new individuals (which would be an even healthier increase). If the rate of increase were measured when the population reached five hundred, the annual rate of increase would be one thousand individuals.

Under such circumstances, the population would keep on growing at an ever-increasing rate. That type of growth is called “exponential growth” by population biologists, and it typifies the behavior of many populations in ideal conditions. If the number of individuals in a population undergoing exponential growth is plotted as a function of time, the curve would resemble the letter J. That is, it would be somewhat flat initially, but it would curve upward, and at some point, it would be almost vertical. Exponential population growth has been observed to a limited extent in many kinds of organisms, both in the laboratory and under field conditions, including protozoans, small insects, and birds. However, population growth is slowed by limiting factors. Resources like water, territory, and oxygen are called abiotic factors, while resources like food are called biotic factors. Additionally, decomposers are critical to all ecosystems, and their availability impacts the carrying capacity of a species.

Logistic Growth

Biologists have created a second model to account for the behavior of populations under finite resources and have called it logistic growth. If the number of individuals in a population undergoing logistic growth is plotted as a function of time, the curve resembles a flattened S shape. In other words, the curve is initially flat but then curves upward at a progressively faster rate, much like exponential growth. At some point (called the inflection point), however, the curve begins to turn to the right and flatten out. Ultimately, the curve becomes horizontal, indicating a constant population over time.

An important aspect of pure logistic growth is that the population approaches, but does not exceed a certain level. That level is called the carrying capacity and is represented by the symbol K in most mathematical treatments of logistic growth. The carrying capacity is the maximum number of individuals that the environment can support based on the space, food, and other resources available. When the number of individuals is much fewer than the carrying capacity, the population grows rapidly, much as in exponential growth. As the number increases, however, the rate of population growth becomes much less than the exponential rate. When the number approaches the carrying capacity, new population growth virtually ceases. If the population were to increase above the carrying capacity, there would be a net loss of organisms from the population.

Logistic growth studies in nature can be time-consuming, but logistic growth has been found in a number of experimental studies, particularly on small organisms, including protozoans, fruit flies, yeast, and beetles. Other animals evaluated with the logistical growth model include alligators, wildebeest, sheep, and harbor seals.

An important aspect of logistic growth is that, as the population increases, the birth rate decreases and the mortality rate increases. Such effects may be attributable to reduced space within which the organism can operate, to less food and other resources, to physiological and behavioral stress caused by crowding, and to increased incidence of disease. Those factors are commonly designated as being density-dependent. They are considered much different from the density-independent factors that typically arise from environmental catastrophes such as flooding, drought, fire, or extreme temperatures. For many years, biologists argued about the relative importance of density-dependent versus density-independent factors in controlling population size. It is recognized that some species are controlled by density-independent factors, whereas others are controlled by density-dependent factors.

Classically, when a species undergoes logistic growth, the population is ultimately supposed to stabilize at the carrying capacity. Most studies that track populations over the course of time, however, find that numbers actually fluctuate. How can such variability be reconciled with the logistic model? On the one hand, the fluctuations may be caused by density-independent factors, and the logistic equation, therefore, does not apply. On the other hand, the population may be under density-dependent control, and the logistic model can still hold despite the fluctuations. One explanation for the fluctuations could be that the carrying capacity itself changes over time. For example, a sudden increase in the amount of food available would increase the carrying capacity and allow the population to grow. A second explanation relates to the presence of time lags; that is, a population might not respond immediately to a given resource level. For example, two animals in a rapidly expanding population might mate when the number of individuals is less than the carrying capacity. The progeny, however, might be born several weeks or months later into a situation in which the population has exceeded the carrying capacity. Thus, there would have to be a decline, leading to the fluctuation.

Approaches to Studying Population Growth

Two main approaches can be used to investigate logistic and exponential population growth among organisms. One approach involves following natural populations in the field; the other involves setting up experimental populations. Each approach has its benefits and drawbacks, and ideally, both should be employed. To study population growth in the field, it is important to study a species from the time that it first arrives on a site until its population stabilizes. Thus, any species already present are automatically eliminated from consideration unless they are brought to local extinction, and a new population is then allowed to recolonize. Population growth studies can be profitably done on sites that are very disturbed and are beginning to fill up with organisms. Examples would be an abandoned farm field or strip mine, a newly created volcanic island, or a new body of water. Moreover, studies could also be done on a species that is purposely introduced to a new site.

In either case, one needs to survey the population periodically to assess the number of individuals that it contains. The size of the population can be determined directly or by employing sampling techniques such as mark-recapture methodologies. The number of individuals can then be plotted on a graph (on the y-axis) as a function of time (on the x-axis).

To study population growth in experimental conditions, one sets up an artificial habitat according to the needs of the species in question. For example, investigators have examined population growth in protozoans (unicellular animals) by growing populations in test tubes filled with food dissolved in known volumes of water. Others have grown fruit flies in stoppered flasks. Still, others have grown beetles in containers filled with oatmeal or other crushed grain. In those cases, it was typically necessary to replenish the food to keep the population going. Whenever the population was placed into an artificial habitat with a nonrenewable food source, it would generally consume all the food and then die out.

More detailed experiments can be performed to test whether density-dependent mortality is occurring. Such experiments would involve setting up a series of containers with different densities of organisms and then following the mortality of those organisms. In theory, mortality rates should be highest in containers that have the greatest densities of organisms and lowest in containers with the sparsest populations. One could also examine the birth rate in those containers, with the expectation that birth rates should be highest in the sparsest containers and lowest in those that have the most organisms. The investigation should be long enough to allow the population to reach equilibrium at the carrying capacity. For short-lived organisms such as protozoans or insects, that could take days, weeks, or months. For longer-lived organisms such as fish or small mammals, one to several years may be required. For long-lived animals, a truly adequate study may take decades.

Another consideration in studying exponential and logistic population growth is that immigration and emigration should be kept to a minimum. Thus, organisms that are highly active, such as birds, large mammals, and most flying insects, would be extremely difficult to study. Finally, one can set up numerous populations and expose each to a slightly different set of conditions. That would enable the researcher to ascertain which environmental factors are most important in determining the carrying capacity. For example, populations of aquatic invertebrates could be monitored under a range of temperature, salinity, pH, and nutrient conditions.

Implications of Logistic Growth

Since exponential growth is unrealistic in practical terms for almost all populations, its scientific usefulness is limited. However, the concepts derived from logistic growth have important implications for biologists and nonbiologists alike. One important aspect of logistic growth is that the maximum population growth rate occurs when the population is about half the environment’s carrying capacity. When populations are sparse, there are simply too few individuals to produce many progeny. When populations are dense or near the carrying capacity, there is not enough room or other resources for rapid population growth. Based on that relationship, those who must harvest organisms can do so at a rate that allows the population to reestablish itself quickly. Those who can apply this concept in everyday work include wildlife managers, ranchers, and fishermen. Indeed, quotas for hunting and fishing are often set in a way that allows the population to be thinned sufficiently without depleting it too severely.

There are two problems that biologists must confront when using the logistic model to manage populations. First, it is often difficult to establish the carrying capacity for a given species on a particular site. One reason is that the populations of many species are profoundly affected by density-independent factors, as well as by other species, in highly complex and variable ways. Further, some species have a maximum rate of population growth at levels well above or well below the level (one-half of the carrying capacity) that is normally assumed. This may be caused by environmental resistance, natural population oscillations in a given ecosystem, or density-independent factors, like a change in the chemical makeup of the water in a lake or a temperature fluctuation that causes a decrease in the maximum population stability of a species. Thus, the logistic model typically gives only a very rough approximation of the ideal size of a population. However, the logistic model is useful because it emphasizes that all species have natural limits to the sizes of their populations.

In the twenty-first century, measuring population decreases over time is critical to wildlife conservation, advising policymakers, preventing extinctions, and preserving Earth’s delicate biomes. Some research indicates that between 1970 and 2020, the world’s population of vertebrates declined nearly 70 percent. Freshwater animal populations declined by more than 80 percent. Accurately measuring these populations and tracking effective methods of increasing populations among vulnerable species is essential.

Principal Terms

Carrying Capacity: The number of individuals of a given species that a site can support

Emigration: The process whereby individuals leave a site and move elsewhere, leading to a decrease in the size of the population

Exponential Growth: A pattern of population growth in which the rate of increase becomes progressively larger over time

Immigration: The process by which new individuals arrive at a site from elsewhere, leading to an increase in the size of the population

Intrinsic Rate of Increase: The growth rate of a population under ideal conditions, expressed on a per-individual basis

Logistic Growth: A pattern of population growth that involves a rapid increase in numbers when the density is low but slows as the density approaches the carrying capacity

Population: A group of individuals of the same species that live in the same location at the same time

Bibliography

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