Art a Which of the Following Is an Example of a Population?

Chapter 19: Population and Community Ecology

Population Growth and Regulation

Learning Objectives

By the end of this section, you lot will be able to:

• Explain the characteristics of and differences between exponential and logistic growth patterns
• Requite examples of exponential and logistic growth in natural populations
• Give examples of how the carrying capacity of a habitat may change
• Compare and contrast density-dependent growth regulation and density-independent growth regulation giving examples

Population ecologists brand use of a multifariousness of methods to model population dynamics. An accurate model should be able to describe the changes occurring in a population and predict hereafter changes.

Population Growth

The two simplest models of population growth use deterministic equations (equations that do not business relationship for random events) to describe the rate of change in the size of a population over time. The get-go of these models, exponential growth, describes theoretical populations that increase in numbers without any limits to their growth. The second model, logistic growth, introduces limits to reproductive growth that become more intense as the population size increases. Neither model adequately describes natural populations, but they provide points of comparison.

Exponential Growth

Charles Darwin, in developing his theory of natural selection, was influenced past the English clergyman Thomas Malthus. Malthus published his book in 1798 stating that populations with arable natural resources grow very chop-chop; however, they limit further growth by depleting their resources. The early blueprint of accelerating population size is chosen exponential growth.

The best instance of exponential growth in organisms is seen in leaner. Leaner are prokaryotes that reproduce largely past binary fission. This partitioning takes almost an hr for many bacterial species. If thousand bacteria are placed in a big flask with an abundant supply of nutrients (so the nutrients will not become rapidly depleted), the number of bacteria will have doubled from 1000 to 2000 after only an hour. In another hr, each of the 2000 bacteria will carve up, producing 4000 bacteria. Later the third hour, in that location should be 8000 bacteria in the flask. The important concept of exponential growth is that the growth rate—the number of organisms added in each reproductive generation—is itself increasing; that is, the population size is increasing at a greater and greater rate. After 24 of these cycles, the population would have increased from g to more than xvi billion bacteria. When the population size, N, is plotted over time, a J-shaped growth bend is produced ([Effigy i]a).

The bacteria-in-a-flask case is not truly representative of the real world where resource are usually limited. However, when a species is introduced into a new habitat that it finds suitable, information technology may testify exponential growth for a while. In the case of the leaner in the flask, some bacteria volition dice during the experiment and thus non reproduce; therefore, the growth rate is lowered from a maximal charge per unit in which there is no mortality. The growth rate of a population is largely adamant past subtracting the expiry rate, D, (number organisms that die during an interval) from the nascence charge per unit, B, (number organisms that are born during an interval). The growth rate tin be expressed in a simple equation that combines the birth and death rates into a single factor: r. This is shown in the following formula:

[latex]\text{Population growth }=\text{ }rN[/latex]

The value of r can be positive, meaning the population is increasing in size (the rate of change is positive); or negative, pregnant the population is decreasing in size; or zero, in which case the population size is unchanging, a condition known as nix population growth.

Logistic Growth

Extended exponential growth is possible only when infinite natural resource are available; this is non the case in the real earth. Charles Darwin recognized this fact in his description of the "struggle for existence," which states that individuals will compete (with members of their own or other species) for limited resource. The successful ones are more likely to survive and pass on the traits that fabricated them successful to the next generation at a greater charge per unit (natural selection). To model the reality of limited resources, population ecologists developed the logistic growth model.

Carrying Capacity and the Logistic Model

In the real earth, with its limited resources, exponential growth cannot continue indefinitely. Exponential growth may occur in environments where in that location are few individuals and plentiful resource, simply when the number of individuals gets large plenty, resources will be depleted and the growth rate will slow down. Somewhen, the growth rate will plateau or level off ([Effigy 1]b). This population size, which is determined past the maximum population size that a detail environs can sustain, is called the conveying capacity, or K. In real populations, a growing population often overshoots its carrying chapters, and the death charge per unit increases beyond the nativity rate causing the population size to decline back to the carrying capacity or below it. Most populations usually fluctuate around the carrying capacity in an undulating manner rather than existing right at it.

The formula used to calculate logistic growth adds the conveying capacity as a moderating forcefulness in the growth charge per unit. The expression "K – N" is equal to the number of individuals that may be added to a population at a given fourth dimension, and "Thou – N" divided by "K" is the fraction of the carrying capacity available for further growth. Thus, the exponential growth model is restricted by this factor to generate the logistic growth equation:

[latex]\text{Population growth }=\text{ }rN\text{ }\left[\frac{K-North}{K}\correct][/latex]

Observe that when Northward is almost nada the quantity in brackets is well-nigh equal to 1 (or 1000/K) and growth is shut to exponential. When the population size is equal to the carrying capacity, or N = K, the quantity in brackets is equal to zero and growth is equal to zero. A graph of this equation (logistic growth) yields the S-shaped curve ([Figure 1]b). It is a more realistic model of population growth than exponential growth. There are 3 unlike sections to an Due south-shaped bend. Initially, growth is exponential because there are few individuals and ample resources available. Then, as resource begin to become limited, the growth rate decreases. Finally, the growth rate levels off at the carrying chapters of the environment, with little change in population number over time.

Figure 1: When resources are unlimited, populations showroom (a) exponential growth, shown in a J-shaped curve. When resources are express, populations exhibit (b) logistic growth. In logistic growth, population expansion decreases as resources become scarce, and it levels off when the carrying capacity of the surround is reached. The logistic growth curve is S-shaped.

Role of Intraspecific Competition

The logistic model assumes that every individual within a population will have equal access to resource and, thus, an equal adventure for survival. For plants, the amount of h2o, sunlight, nutrients, and space to grow are the important resources, whereas in animals, important resources include food, water, shelter, nesting infinite, and mates.

In the real world, phenotypic variation amongst individuals within a population means that some individuals will exist better adapted to their environment than others. The resulting competition for resource amongst population members of the same species is termed intraspecific contest. Intraspecific contest may not affect populations that are well below their carrying capacity, as resource are plentiful and all individuals tin obtain what they need. Nonetheless, as population size increases, this contest intensifies. In improver, the aggregating of waste material products can reduce carrying chapters in an surroundings.

Examples of Logistic Growth

Yeast, a microscopic fungus used to make bread and alcoholic beverages, exhibits the classical S-shaped curve when grown in a test tube ([Effigy 2]a). Its growth levels off as the population depletes the nutrients that are necessary for its growth. In the real world, however, at that place are variations to this idealized curve. Examples in wild populations include sheep and harbor seals ([Figure ii]b). In both examples, the population size exceeds the carrying capacity for short periods of time and then falls below the conveying capacity subsequently. This fluctuation in population size continues to occur every bit the population oscillates around its carrying chapters. Yet, even with this oscillation, the logistic model is confirmed.

Art Connection

Figure 2: (a) Yeast grown in ideal conditions in a test tube shows a classical Southward-shaped logistic growth bend, whereas (b) a natural population of seals shows existent-world fluctuation. The yeast is visualized using differential interference contrast lite micrography. (credit a: scale-bar data from Matt Russell)

If the major food source of seals declines due to pollution or overfishing, which of the following would probable occur?

1. The conveying capacity of seals would subtract, as would the seal population.
2. The carrying capacity of seals would decrease, but the seal population would remain the same.
3. The number of seal deaths would increase, but the number of births would besides increase, so the population size would remain the same.
4. The carrying capacity of seals would remain the same, only the population of seals would decrease.
   [reveal-answer q="640864″]Show Respond[/reveal-answer]
   [subconscious-answer a="640864″]A: The carrying chapters of seals would decrease, every bit would the seal population.[/hidden-answer]

Population Dynamics and Regulation

The logistic model of population growth, while valid in many natural populations and a useful model, is a simplification of real-world population dynamics. Implicit in the model is that the conveying capacity of the environment does not change, which is not the example. The carrying capacity varies annually. For instance, some summers are hot and dry whereas others are cold and wet; in many areas, the carrying capacity during the winter is much lower than it is during the summer. Also, natural events such as earthquakes, volcanoes, and fires can modify an environment and hence its carrying capacity. Additionally, populations do non usually be in isolation. They share the surroundings with other species, competing with them for the same resource (interspecific competition). These factors are too important to understanding how a specific population will grow.

Population growth is regulated in a variety of means. These are grouped into density-dependent factors, in which the density of the population affects growth rate and mortality, and density-contained factors, which crusade mortality in a population regardless of population density. Wild animals biologists, in particular, desire to understand both types because this helps them manage populations and prevent extinction or overpopulation.

Density-dependent Regulation

Near density-dependent factors are biological in nature and include predation, inter- and intraspecific competition, and parasites. Usually, the denser a population is, the greater its bloodshed rate. For example, during intra- and interspecific competition, the reproductive rates of the species will usually exist lower, reducing their populations' rate of growth. In addition, low prey density increases the mortality of its predator because it has more difficulty locating its nutrient source. Also, when the population is denser, diseases spread more than speedily amongst the members of the population, which affect the bloodshed rate.

Density dependent regulation was studied in a natural experiment with wild ass populations on two sites in Commonwealth of australia. ¹ On one site the population was reduced by a population control programme; the population on the other site received no interference. The high-density plot was twice every bit dense as the low-density plot. From 1986 to 1987 the loftier-density plot saw no alter in donkey density, while the low-density plot saw an increase in donkey density. The difference in the growth rates of the 2 populations was caused by mortality, not by a difference in birth rates. The researchers found that numbers of offspring birthed past each mother was unaffected by density. Growth rates in the 2 populations were different more often than not because of juvenile mortality caused by the mother'due south malnutrition due to scarce high-quality food in the dense population. [Effigy three] shows the departure in historic period-specific mortalities in the 2 populations.

Figure 3: This graph shows the historic period-specific bloodshed rates for wild donkeys from high- and depression-density populations. The juvenile mortality is much higher in the high-density population because of maternal malnutrition caused past a shortage of high-quality food.

Density-independent Regulation and Interaction with Density-dependent Factors

Many factors that are typically physical in nature cause mortality of a population regardless of its density. These factors include weather, natural disasters, and pollution. An private deer will be killed in a wood fire regardless of how many deer happen to exist in that expanse. Its chances of survival are the same whether the population density is high or low. The same holds true for common cold wintertime weather.

In real-life situations, population regulation is very complicated and density-dependent and independent factors can collaborate. A dense population that suffers bloodshed from a density-contained cause will be able to recover differently than a sparse population. For example, a population of deer affected past a harsh winter will recover faster if there are more than deer remaining to reproduce.

Evolution in Action

Why Did the Woolly Mammoth Go Extinct?

Figure 4: The iii images include: (a) 1916 mural of a mammoth herd from the American Museum of Natural History, (b) the only stuffed mammoth in the earth is in the Museum of Zoology located in St. Petersburg, Russia, and (c) a one-month-old infant mammoth, named Lyuba, discovered in Siberia in 2007. (credit a: modification of piece of work by Charles R. Knight; credit b: modification of work past "Tanapon"/Flickr; credit c: modification of work by Matt Howry)

Woolly mammoths began to go extinct near 10,000 years ago, soon after paleontologists believe humans able to hunt them began to colonize N America and northern Eurasia ([Figure four]). A mammoth population survived on Wrangel Island, in the East Siberian Ocean, and was isolated from human contact until as recently as 1700 BC. We know a lot about these animals from carcasses establish frozen in the water ice of Siberia and other northern regions.

It is commonly thought that climate change and human hunting led to their extinction. A 2008 study estimated that climate change reduced the mammoth's range from 3,000,000 square miles 42,000 years ago to 310,000 square miles 6,000 years ago. ⁱⁱ Through archaeological evidence of kill sites, it is likewise well documented that humans hunted these animals. A 2012 written report concluded that no single factor was exclusively responsible for the extinction of these magnificent creatures. ³ In addition to climate change and reduction of habitat, scientists demonstrated another important factor in the mammoth'south extinction was the migration of human hunters across the Bering Strait to Due north America during the last ice age 20,000 years ago.

The maintenance of stable populations was and is very complex, with many interacting factors determining the outcome. It is important to recall that humans are also part of nature. Once nosotros contributed to a species' decline using archaic hunting technology but.

Demographic-Based Population Models

Population ecologists take hypothesized that suites of characteristics may evolve in species that pb to particular adaptations to their environments. These adaptations impact the kind of population growth their species feel. Life history characteristics such every bit nascency rates, age at first reproduction, the numbers of offspring, and even death rates evolve just like beefcake or behavior, leading to adaptations that affect population growth. Population ecologists have described a continuum of life-history "strategies" with K-selected species on ane end and r-selected species on the other. 1000-selected species are adapted to stable, predictable environments. Populations of K-selected species tend to be close to their carrying capacity. These species tend to have larger, but fewer, offspring and contribute big amounts of resources to each offspring. Elephants would be an instance of a K-selected species. r-selected species are adapted to unstable and unpredictable environments. They have large numbers of small offspring. Animals that are r-selected exercise not provide a lot of resources or parental care to offspring, and the offspring are relatively cocky-sufficient at nascency. Examples of r-selected species are marine invertebrates such every bit jellyfish and plants such as the dandelion. The two extreme strategies are at two ends of a continuum on which real species life histories will exist. In addition, life history strategies practice not need to evolve as suites, but tin can evolve independently of each other, and then each species may have some characteristics that tendency toward ane extreme or the other.

Section Summary

Populations with unlimited resources grow exponentially—with an accelerating growth rate. When resources become limiting, populations follow a logistic growth curve in which population size will level off at the conveying chapters.

Populations are regulated by a variety of density-dependent and density-independent factors. Life-history characteristics, such as historic period at outset reproduction or numbers of offspring, are characteristics that evolve in populations just every bit anatomy or behavior can evolve over time. The model of r– and K-pick suggests that characters, and possibly suites of characters, may evolve adaptations to population stability near the carrying capacity (K-selection) or rapid population growth and collapse (r-selection). Species will exhibit adaptations somewhere on a continuum between these 2 extremes.

Multiple Choice

Species with limited resource usually exhibit a(n) ________ growth curve.

1. logistic
2. logical
3. experimental
4. exponential

[reveal-answer q="432132″]Show Answer[/reveal-answer]
[hidden-answer a="432132″]one[/subconscious-reply]

The maximum growth rate characteristic of a species is called its ________.

1. limit
2. conveying capacity
3. biotic potential
4. exponential growth blueprint

[reveal-reply q="827518″]Show Answer[/reveal-respond]
[subconscious-respond a="827518″]3[/hidden-answer]

The population size of a species capable of being supported by the environment is called its ________.

1. limit
2. carrying capacity
3. biotic potential
4. logistic growth blueprint

[reveal-answer q="671162″]Prove Reply[/reveal-reply]
[hidden-respond a="671162″]2[/hidden-answer]

Species that have many offspring at one fourth dimension are usually:

1. r-selected
2. K-selected
3. both r- and K-selected
4. not selected

[reveal-respond q="300275″]Evidence Answer[/reveal-answer]
[hidden-answer a="300275″]one[/hidden-answer]

A forest burn is an instance of ________ regulation.

1. density-dependent
2. density-contained
3. r-selected
4. G-selected

[reveal-answer q="966755″]Testify Reply[/reveal-answer]
[subconscious-answer a="966755″]2[/hidden-answer]

Complimentary Response

Describe the growth at various parts of the Due south-shaped bend of logistic growth.

In the first part of the curve, when few individuals of the species are present and resource are plentiful, growth is exponential, similar to a J-shaped curve. Afterward, growth slows due to the species using upwardly resources. Finally, the population levels off at the carrying capacity of the surround, and it is relatively stable over time.

Give an example of how density-dependent and density-independent factors might interact.

If a natural disaster such equally a fire happened in the wintertime, when populations are low, it would have a greater effect on the overall population and its recovery than if the same disaster occurred during the summer, when population levels are high.

Footnotes

1. i David Choquenot, "Density-Dependent Growth, Trunk Condition, and Census in Feral Donkeys: Testing the Nutrient Hypothesis," Ecology 72, no. 3 (June 1991):805–813.
2. 2 David Nogués-Bravo et al., "Climatic change, Humans, and the Extinction of the Woolly Mammoth." PLoS Biol vi (April 2008): e79, doi:10.1371/journal.pbio.0060079.
3. 3 G.M. MacDonald et al., "Pattern of Extinction of the Woolly Mammoth in Beringia." Nature Communications three, no. 893 (June 2012), doi:10.1038/ncomms1881.

Glossary

nascence rate

the number of births within a population at a specific point in fourth dimension

carrying chapters

the maximum number of individuals of a population that can be supported by the limited resources of a habitat

death rate

the number of deaths within a population at a specific signal in time

density-dependent regulation

the regulation of population in which nativity and decease rates are dependent on population size

density-independent regulation

the regulation of population in which the death charge per unit is contained of the population size

exponential growth

an accelerating growth pattern seen in populations where resources are not limiting

intraspecific competition

the contest among members of the same species

J-shaped growth bend

the shape of an exponential growth curve

M-selected species

a species suited to stable environments that produce a few, relatively large offspring and provide parental care

logistic growth

the leveling off of exponential growth due to limiting resources

r-selected species

a species suited to changing environments that produce many offspring and provide trivial or no parental care

Due south-shaped growth curve

the shape of a logistic growth curve

zero population growth

the steady population size where nascency rates and death rates are equal

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Source: https://opentextbc.ca/conceptsofbiologyopenstax/chapter/population-growth-and-regulation/

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