In another hour, each of the organisms will double, producing ; after the third hour, there should be bacteria in the flask; and so on. The important concept of exponential growth is that the population growth rate, the number of organisms added in each reproductive generation, is accelerating; that is, it is increasing at a greater and greater rate.
After 1 day and 24 of these cycles, the population would have increased from to more than 16 billion. When the population size, N, is plotted over time, a J-shaped growth curve is produced.
Exponential population growth : When resources are unlimited, populations exhibit exponential growth, resulting in a J-shaped curve. When resources are limited, populations exhibit logistic growth. In logistic growth, population expansion decreases as resources become scarce. It levels off when the carrying capacity of the environment is reached, resulting in an S-shaped curve. The bacteria example is not representative of the real world where resources are limited.
Furthermore, some bacteria will die during the experiment and, thus, not reproduce, lowering the growth rate. Therefore, when calculating the growth rate of a population, the death rate D; the number organisms that die during a particular time interval is subtracted from the birth rate B; the number organisms that are born during that interval.
This is shown in the following formula:. The birth rate is usually expressed on a per capita for each individual basis. Additionally, ecologists are interested in the population at a particular point in time: an infinitely small time interval. A further refinement of the formula recognizes that different species have inherent differences in their intrinsic rate of increase often thought of as the potential for reproduction , even under ideal conditions.
Obviously, a bacterium can reproduce more rapidly and have a higher intrinsic rate of growth than a human. The maximal growth rate for a species is its biotic potential, or r max , thus changing the equation to:. Logistic growth of a population size occurs when resources are limited, thereby setting a maximum number an environment can support.
Exponential growth is possible only when infinite natural resources are available; this is not the case in the real world. The successful ones will survive to pass on their own characteristics and traits which we know now are transferred by genes to the next generation at a greater rate: a process known as natural selection.
To model the reality of limited resources, population ecologists developed the logistic growth 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 becomes large enough, resources will be depleted, slowing the growth rate. Eventually, the growth rate will plateau or level off.
This population size, which represents the maximum population size that a particular environment can support, is called the carrying capacity, or K. The formula we use to calculate logistic growth adds the carrying capacity as a moderating force in the growth rate. Thus, the exponential growth model is restricted by this factor to generate the logistic growth equation:. Thus, population growth is greatly slowed in large populations by the carrying capacity K.
This model also allows for negative population growth or a population decline. A graph of this equation yields an S-shaped curve; 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, growth levels off at the carrying capacity of the environment, with little change in population size over time.
C The population will show an Allee effect. D The population will increase exponentially. E The carrying capacity of the environment will increase. Please read the paragraph below and review Figure Researchers in the Netherlands studied the effects of parental care given in European kestrels over five years.
The researchers transferred chicks among nests to produce reduced broods three or four chicks , normal broods five or six chicks , and enlarged broods seven or eight chicks. They then measured the percentage of male and female parent birds that survived the following winter.
Both males and females provide care for chicks. Figure A Female survivability is more negatively affected by larger brood size than is male survivability. C Both males and females had increases in daily hunting with the enlarged brood size. D There appears to be a negative correlation between brood enlargements and parental survival. E Chicks in reduced brood treatment received more food, weight gain, and reduced mortality. B has become so large that it will have difficulty surviving and reproducing.
C is viable and stable at its carrying capacity. D has exceeded its carrying capacity. E is in crash decline. B the maximum population size that a particular environment can support.
C fixed for most species over most of their range most of the time. D determined by density and dispersion data. E the term used to describe the stress a population undergoes due to limited resources. A increased birth rate B removal of predators C decreased death rate D competition for resources E favorable climatic conditions. A Stable environments with limited resources favor r-selected populations.
B K-selected populations are most often found in environments where density-independent factors are important regulators of population size. C Most populations have both r- and K-selected characteristics that vary under different environmental conditions. D The reproductive efforts of r-selected populations are directed at producing just a few offspring with good competitive abilities. E K-selected populations rarely approach carrying capacity.
B producing large numbers of gametes when employing internal fertilization versus fewer numbers of gametes when employing external fertilization. C the emigration of individuals when they are no longer reproductively capable or committing suicide. D increasing the number of individuals produced during each reproductive episode with a corresponding decrease in parental care. E high survival rates of offspring and the cost of parental care. B number of reproductive females in the population, age structure of the population, and life expectancy.
C age when reproduction begins, how often reproduction occurs, and how many offspring are produced per reproductive episode. D how often reproduction occurs, life expectancy of females in the population, and number of offspring per reproductive episode. E the number of reproductive females in the population, how often reproduction occurs, and death rate. A Pioneer species of plants produce many very small, highly airborne seeds, whereas large elephants that are very good parents produce many offspring.
B Female rabbits that suffer high predation rates may produce several litters per breeding season, and coconuts produce few fruits, but most survive when they encounter proper growing conditions. C Species that have to broadcast to distant habitats tend to produce seeds with heavy protective seed coats, and animals that are caring parents produce fewer offspring with lower infant mortality.
D Free-living insects lay thousands of eggs and provide no parental care, whereas flowers take good care of their seeds until they are ready to germinate. E Some mammals will not reproduce when environmental resources are low so they can survive until conditions get better, and plants that produce many small seeds are likely found in stable environments.
B dispersion. C Allee effect. D iteroparous reproduction. E semelparous reproduction. A offspring with good chances of survival B many offspring per reproductive episode C small offspring D a high intrinsic rate of increase E early parental reproduction. A the age at which reproduction begins, frequency of reproduction, and the number of offspring for each reproductive episode B the ratio of females to males, the length of the breeding season, and the number of offspring for each reproductive episode C the number of offspring produced over a lifetime by a breeding pair and the survivability of the offspring D timing breeding sessions with optimal environmental conditions and the number of offspring produced during each breeding session E the amount of parental care given after birth, the number of reproductive episodes per year, and the number of years females are capable of producing viable offspring.
As moose populations increase, for example, wolf populations also increase. Thus, if we are considering the logistic equation for the wolf population, SEE IMAGE which of the factors accounts for the effect on the moose population? A a recently abandoned agricultural field in Ohio B the sand dune communities of south Lake Michigan C the flora and fauna of a coral reef in the Caribbean D South Florida after a hurricane E a newly emergent volcanic island.
A the removal of toxic waste by decomposers B intraspecific competition for nutrients C earthquakes D floods E fires. A Density-dependent factors lead to fewer births and increased mortality. B Density-independent factors lead to fewer births and increased mortality. C Hormonal changes promote higher death rates in crowded populations. D Individuals voluntarily stop mating so that overcrowding does not occur. E The incoming energy decreases in populations experiencing a high rate of increase.
Sometimes intrinsic factors cause the population to increase in mortality and lower reproduction rates to occur in reaction to the stress of overpopulation. Which of the following is an example of intrinsic population control?
A Owl populations frequent the area more often because of increased hunting success. B Females undergo hormonal changes that delay sexual maturation and many individuals suffer depressed immune systems and die due to the stress of overpopulation.
C Clumped dispersion of the population leads to increased spread of disease and parasites, resulting in a population crash. E Because the individuals are vulnerable they are more likely to die off if a drought or flood were to occur. A Songbirds expend a tremendous amount of energy defending territories so that they spend less time feeding their young and fledgling mortality increases.
B Only the fittest males defend territories and they attract the fittest females so the best genes are conveyed to the next generation. C Songbird males defend territories commensurate with the size from which they can derive adequate resources for themselves, their mate, and their chicks.
D Many individuals are killed in the agonistic behaviors that go along with territorial defense. E Adult songbirds make improvements to the territories they inhabit so that they can produce successfully fledged chicks. A social pressure for birth control B earthquakes C plagues D famines E pollution.
C in converting human foods' meat biomass to plant biomass. D in making predictions about the global carrying capacity of humans.
E in determining which nations produce the least amount of carbon dioxide from the burning of fossil fuels. A education of global famine B improved worldwide health care C voluntary reduction of family size D improved sanitary conditions in the world's hospitals E reduction of casualties of war. Home » Modules » Population Dynamics. Background A major component of modern ecological research focuses on understanding what influences the abundance of organisms within a population, and why this abundance changes over time.
What causes fluctuations in abundance? The equation is: where the parameter r represents the intrinsic growth rate , K is the carrying capacity , and N 0 is the initial population size. Lesson Plan The following activity has been designed to teach basic principles of ecological population dynamics to high school and college level students. Student Objectives Explain what a population is in ecology.
Describe what r, K, and N 0 are in a population. Analyze how r, K, and N 0 can change population sizes over time both individually and together. Devise a way to stabilize a hypothetical fish population by varying r, K, and N 0 and propose a set of management strategies using these concepts. Justify this proposal in a group presentation. Activity Procedure Part 1: Changing r We will first focus on understanding r the intrinsic growth rate of a population and how it affects population dynamics or the size of populations over time.
For full page, click here. Use the interactive app above to complete the activity. First, become acquainted with the graph. What are the x and y axes? Use the slidebar to slowly increase the value of r, noting when the dynamics in the plot changes.
Describe the pattern of how the dynamics change as r increases. Note any changes in scaling of the y axis. Use the slidebar to change the value of K the carrying capacity.
Explain why this observed pattern is happening in terms of growth rate and carrying capacity. Describe what happens to the population size over time.
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