Modeling population growth answers


  • Population Growth and Regulation
  • Electricity , Water Activity Overview: The key underlying demographic trends that strain energy and water resources are population growth and economic growth. Other key trends are the impacts of global climate change and policy choices, whereby policy makers push for more water-intensive energy and more energy-intensive water.

    As the population increases, more people demand more energy and water. However, because of economic growth, which happens in parallel, the demand for energy and water increases faster than the population. Problem Statement: Describe the nature of exponential growth in human populations. Project Deliverables: Students should use technology to research global historical estimates and population records. They should then create a mathematical model based on the data. Many population curves exist online, but students should not copy and paste them for the purpose of this assignment.

    After creating their models, students should compare them with the widely accepted population curves to see how well they have modeled historical population trends. Historical data will not allow for the creation of predictions of the future, but many of the population curves will contain future predictions based on possible trajectories for population growth.

    Resources: Exponential population growth can be represented using a simple J curve, but reality is more complex and limited, and could be represented using an S curve. The United States Census Bureau has collated many different resources into a comprehensive historical estimate of world population. The spreadsheet program automatically generated the scatterplot, which was then adapted to a logarithmic scale in order to better show the trend.

    Since , there is a slight downturn in the rate of population growth. The exponential trendline superimposed over the scatterplot resembles the sigmoidal curve above. Gleick, ed. All Rights Reserved. Except where otherwise noted, content on this site is licensed under a Creative Commons Attribution 4.

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    Chapter Population and Community Ecology Population Growth and Regulation By the end of this section, you will be able to: Explain the characteristics of and differences between exponential and logistic growth patterns Give 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 make use of a variety of methods to model population dynamics.

    An accurate model should be able to describe the changes occurring in a population and predict future changes. Population Growth The two simplest models of population growth use deterministic equations equations that do not account for random events to describe the rate of change in the size of a population over time. The first 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 by the English clergyman Thomas Malthus.

    Malthus published his book in stating that populations with abundant natural resources grow very rapidly; however, they limit further growth by depleting their resources. The early pattern of accelerating population size is called exponential growth. The best example of exponential growth in organisms is seen in bacteria.

    Bacteria are prokaryotes that reproduce largely by binary fission. This division takes about an hour for many bacterial species. If bacteria are placed in a large flask with an abundant supply of nutrients so the nutrients will not become quickly depleted , the number of bacteria will have doubled from to after just an hour.

    In another hour, each of the bacteria will divide, producing bacteria. After the third hour, there should be 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 to more than 16 billion bacteria. When the population size, N, is plotted over time, a J-shaped growth curve is produced [Figure 1] a.

    The bacteria-in-a-flask example is not truly representative of the real world where resources are usually limited. However, when a species is introduced into a new habitat that it finds suitable, it may show exponential growth for a while. In the case of the bacteria in the flask, some bacteria will die during the experiment and thus not reproduce; therefore, the growth rate is lowered from a maximal rate in which there is no mortality.

    The growth rate of a population is largely determined by subtracting the death rate, D, number organisms that die during an interval from the birth rate, B, number organisms that are born during an interval. The growth rate can be expressed in a simple equation that combines the birth and death rates into a single factor: r. Logistic Growth Extended exponential growth is possible only when infinite natural resources are available; this is not the case in the real world.

    The successful ones are more likely to survive and pass on the traits that made them successful to the next generation at a greater rate 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 world, with its limited resources, exponential growth cannot continue indefinitely.

    Exponential growth may occur in environments where there are few individuals and plentiful resources, but when the number of individuals gets large enough, resources will be depleted and the growth rate will slow down. Eventually, the growth rate will plateau or level off [Figure 1] b. This population size, which is determined by the maximum population size that a particular environment can sustain, is called the carrying capacity, or K.

    In real populations, a growing population often overshoots its carrying capacity, and the death rate increases beyond the birth 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 fashion rather than existing right at it. The formula used to calculate logistic growth adds the carrying capacity as a moderating force in the growth rate.

    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 three different sections to an S-shaped curve. Initially, growth is exponential because there are few individuals and ample resources available. Then, as resources begin to become limited, the growth rate decreases. Finally, the growth rate levels off at the carrying capacity of the environment, with little change in population number over time.

    Figure 1: When resources are unlimited, populations exhibit a exponential growth, shown in a J-shaped curve. When resources are limited, 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 environment 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 resources and, thus, an equal chance for survival.

    For plants, the amount of water, sunlight, nutrients, and space to grow are the important resources, whereas in animals, important resources include food, water, shelter, nesting space, and mates. In the real world, phenotypic variation among individuals within a population means that some individuals will be better adapted to their environment than others.

    The resulting competition for resources among population members of the same species is termed intraspecific competition. Intraspecific competition may not affect populations that are well below their carrying capacity, as resources are plentiful and all individuals can obtain what they need. However, as population size increases, this competition intensifies. In addition, the accumulation of waste products can reduce carrying capacity in an environment. 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 [Figure 2] a.

    Its growth levels off as the population depletes the nutrients that are necessary for its growth. In the real world, however, there are variations to this idealized curve.

    Examples in wild populations include sheep and harbor seals [Figure 2] b. In both examples, the population size exceeds the carrying capacity for short periods of time and then falls below the carrying capacity afterwards. This fluctuation in population size continues to occur as the population oscillates around its carrying capacity. Still, 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 S-shaped logistic growth curve, whereas b a natural population of seals shows real-world fluctuation.

    The yeast is visualized using differential interference contrast light micrography. The carrying capacity of seals would decrease, as would the seal population. The carrying capacity of seals would decrease, but the seal population would remain the same. The number of seal deaths would increase, but the number of births would also increase, so the population size would remain the same.

    The carrying capacity of seals would remain the same, but the population of seals would decrease. Implicit in the model is that the carrying capacity of the environment does not change, which is not the case. The carrying capacity varies annually. For example, 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 alter an environment and hence its carrying capacity. Additionally, populations do not usually exist in isolation. They share the environment with other species, competing with them for the same resources interspecific competition.

    These factors are also important to understanding how a specific population will grow. Population growth is regulated in a variety of ways. These are grouped into density-dependent factors, in which the density of the population affects growth rate and mortality, and density-independent factors, which cause mortality in a population regardless of population density.

    Wildlife biologists, in particular, want to understand both types because this helps them manage populations and prevent extinction or overpopulation. Density-dependent Regulation Most 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 mortality rate. In addition, low prey density increases the mortality of its predator because it has more difficulty locating its food source.

    Also, when the population is denser, diseases spread more rapidly among the members of the population, which affect the mortality rate. Density dependent regulation was studied in a natural experiment with wild donkey populations on two sites in Australia.

    The high-density plot was twice as dense as the low-density plot. From to the high-density plot saw no change in donkey density, while the low-density plot saw an increase in donkey density. The difference in the growth rates of the two populations was caused by mortality, not by a difference in birth rates.

    The researchers found that numbers of offspring birthed by each mother was unaffected by density. Figure 3: This graph shows the age-specific mortality rates for wild donkeys from high- and low-density populations.

    The juvenile mortality is much higher in the high-density population because of maternal malnutrition caused by 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 individual deer will be killed in a forest fire regardless of how many deer happen to be in that area. Its chances of survival are the same whether the population density is high or low.

    The same holds true for cold winter weather. In real-life situations, population regulation is very complicated and density-dependent and independent factors can interact.

    A dense population that suffers mortality from a density-independent cause will be able to recover differently than a sparse population. For example, a population of deer affected by a harsh winter will recover faster if there are more deer remaining to reproduce. Figure 4: The three images include: a mural of a mammoth herd from the American Museum of Natural History, b the only stuffed mammoth in the world is in the Museum of Zoology located in St.

    Petersburg, Russia, and c a one-month-old baby mammoth, named Lyuba, discovered in Siberia in A mammoth population survived on Wrangel Island, in the East Siberian Sea, and was isolated from human contact until as recently as BC.

    We know a lot about these animals from carcasses found frozen in the ice of Siberia and other northern regions. It is commonly thought that climate change and human hunting led to their extinction. A study concluded that no single factor was exclusively responsible for the extinction of these magnificent creatures. The maintenance of stable populations was and is very complex, with many interacting factors determining the outcome.

    However, because of economic growth, which happens in parallel, the demand for energy and water increases faster than the population. Problem Statement: Describe the nature of exponential growth in human populations. Project Deliverables: Students should use technology to research global historical estimates and population records.

    Population Growth and Regulation

    They should then create a mathematical model based on the data. Many population curves exist online, but students should not copy and paste them for the purpose of this assignment.

    After creating their models, students should compare them with the widely accepted population curves to see how well they have modeled historical population trends. Historical data will not allow for the creation of predictions of the future, but many of the population curves will contain future predictions based on possible trajectories for population growth. Resources: Exponential population growth can be represented using a simple J curve, but reality is more complex and limited, and could be represented using an S curve.

    The United States Census Bureau has collated many different resources into a comprehensive historical estimate of world population. The spreadsheet program automatically generated the scatterplot, which was then adapted to a logarithmic scale in order to better show the trend. Sincethere is a slight downturn in the rate of population growth.

    Malthus published his book in stating that populations with abundant natural resources grow very rapidly; however, they limit further growth by depleting their resources. The early pattern of accelerating population size is called exponential growth.

    The best example of exponential growth in organisms is seen in bacteria. Bacteria are prokaryotes that reproduce largely by binary fission. This division takes about an hour for many bacterial species. If bacteria are placed in a large flask with an abundant supply of nutrients so the nutrients will not become quickly depletedthe number of bacteria will have doubled from to after just an hour.

    In another hour, each of the bacteria will divide, producing bacteria. After the third hour, there should be 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 to more than 16 billion bacteria. When the population size, N, is plotted over time, a J-shaped growth curve is produced [Figure 1] a. The bacteria-in-a-flask example is not truly representative of the real world where resources are usually limited.

    However, when a species is introduced into a new habitat that it finds suitable, it may show exponential growth for a while. In the case of the bacteria in the flask, some bacteria will die during the experiment and thus not reproduce; therefore, the growth rate is lowered from a maximal rate in which there is no mortality. The growth rate of a population is largely determined by subtracting the death rate, D, number organisms that die during an interval from the birth rate, B, number organisms that are born during an interval.

    The growth rate can be expressed in a simple equation that combines the birth and death rates into a single factor: r.

    Logistic Growth Extended exponential growth is possible only when infinite natural resources are available; this is not the case in the real world. The successful ones are more likely to survive and pass on the traits that made them successful to the next generation at a greater rate 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 world, with its limited resources, exponential growth cannot continue indefinitely. Exponential growth may occur in environments where there are few individuals and plentiful resources, but when the number of individuals gets large enough, resources will be depleted and the growth rate will slow down. Eventually, the growth rate will plateau or level off [Figure 1] b.

    This population size, which is determined by the maximum population size that a particular environment can sustain, is called the carrying capacity, or K. In real populations, a growing population often overshoots its carrying capacity, and the death rate increases beyond the birth 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 fashion rather than existing right at it.

    The formula used to calculate logistic growth adds the carrying capacity as a moderating force in the growth rate. 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 three different sections to an S-shaped curve. Initially, growth is exponential because there are few individuals and ample resources available.

    Then, as resources begin to become limited, the growth rate decreases. Finally, the growth rate levels off at the carrying capacity of the environment, with little change in population number over time. Figure 1: When resources are unlimited, populations exhibit a exponential growth, shown in a J-shaped curve. When resources are limited, 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 environment 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 resources and, thus, an equal chance for survival.

    For plants, the amount of water, sunlight, nutrients, and space to grow are the important resources, whereas in animals, important resources include food, water, shelter, nesting space, and mates. In the real world, phenotypic variation among individuals within a population means that some individuals will be better adapted to their environment than others.

    The resulting competition for resources among population members of the same species is termed intraspecific competition. Intraspecific competition may not affect populations that are well below their carrying capacity, as resources are plentiful and all individuals can obtain what they need.

    However, as population size increases, this competition intensifies. In addition, the accumulation of waste products can reduce carrying capacity in an environment. 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 [Figure 2] a.

    Its growth levels off as the population depletes the nutrients that are necessary for its growth. In the real world, however, there are variations to this idealized curve.

    Examples in wild populations include sheep and harbor seals [Figure 2] b. In both examples, the population size exceeds the carrying capacity for short periods of time and then falls below the carrying capacity afterwards.

    This fluctuation in population size continues to occur as the population oscillates around its carrying capacity. Still, 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 S-shaped logistic growth curve, whereas b a natural population of seals shows real-world fluctuation. The yeast is visualized using differential interference contrast light micrography.

    The carrying capacity of seals would decrease, as would the seal population. The carrying capacity of seals would decrease, but the seal population naresh it c notes pdf remain the same.

    The number of seal deaths would increase, but the number of births would also increase, so the population size would remain the same. The carrying capacity of seals would remain the same, but the population of seals would decrease. Implicit in the model is that the carrying capacity of the environment does not change, which is not the case. The carrying capacity varies annually.

    For example, 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.


    Modeling population growth answers