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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 1798 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 1000 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 1000 to 2000 after just an hour. In another hour, each of the 2000 bacteria will divide, producing 4000 bacteria. After the third hour, there 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 1000 to more than 16 billion bacteria. When the population size, N , is plotted over time, a J-shaped growth curve    is produced ( [link] 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 . This is shown in the following formula:

Questions & Answers

difference between DNA and RNA
Eyitayo Reply
what determines the aeration level in the soil
Shola Reply
what is homeostasis?
Sarita Reply
What is biology
Don Reply
Biology z the study of life
GOLDEN
what's biology
buran
biology is the study of living nd none living organism
Chinaza
Biology is the study of life
Quadri
yes Sir
Said
what's cell biology
Prince
biology is the study of life
Raheal
what is asexual reproduction,?
Awoi Reply
A type of reproduction which does not involve the fusion of gametes or a change in the number of chromosomes
Serena
Reproduction without sex... In which form a single organism or cell makes a copy of itself.
Serena
Please explain the concept of mitosis and meiosis
Serena
I guess you could use it for study buddies and brushing up on what you need to
Serena
what is mitosis
Klp
Asexual reproduction?
Serena
why pepsin and trypsin released in active form?
Yacqub
mitosis is the type cell division in which two daughter cells have same no. of chormosomes
syed
Hi
Don
chromosome number remains the same in mitosis
mc
Ello
Henry
Hii
Nikky
Yrr help me.
Nikky
Physical chemistry..... Koi h jo mujhe physical chem ki notes send kr ske
Nikky
what is asexual reproduction
Targbe
what makes golgi body in plants
Abdulkareem Reply
name the membrane of the plants
Abdulkareem
how can turners syndrome be corrected before birth
Balinda
which animal survive from being preyed just because of being humble, slow, and not aggressive
Balinda
During organs transplantation, the organs cannot be taken from just anybody since the graft would be rejected sooner or later due to
Liter Reply
Non-MHC compatibility on the organ and an attack from the patient's immune system.
Eric
what makes golgi body in plants
Abdulkareem
why trypsin and pepsin released in active form
Yacqub
what is integument system
Joy Reply
Cellular respiration
Lucy Reply
what are the characteristics of living things
Ruth Reply
Movement Respiration Nutrition/Feeding Irritability/Sensitivity Growth Excretion Reproduction Deat/Life span
Hashim
What makes children from the same father and mother sometimes don't look alike?
Hashim
identification of problems
Nana Reply
what happens in the process of raising the human arms
Nana
what is biology
Brandi Reply
first step in scientific method
Brandi
In an investigation the pancreatic duct of a mammal was blocked.It was found that the blood sugar regulation remained normal while food digestion was impaired.Explain
Mac Reply
To begin with, obstruction of pancreatic duct will alter the blood sugar level as the juices responsible for glucose regulation will be rendered inconsequential. This will in turn affect the rate of digestion and absorbtion of digested food substances by the Villus .
Muktar
characteristics of algae
OMIME Reply
Algae are eukaryotic organisms. Algae do not have roots and stems. Algae have chlorophyll and helps in carrying out photosynthesis.
Aditi
Cell wall is the rigid layer enclosed by membranes of plants and prokayortic cell, it maintains the shape of the cell and serve as a protective barrier.
chizoba Reply
ECOLOGY: is a branch of biology that studies the interactions among organisms and their biophysical environment, which includes both biotic and abiotic components. 
chizoba
via nutrient cycles and energy flows. For instance, the energy from the sun is captured by plants through photosynthesis. Photosynthesis is a biological process through which plants manufacture their own food with the aid of light from the sun and frc sources (e.g. cabon dioxide and water)
chizoba

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Source:  OpenStax, Concepts of biology. OpenStax CNX. Feb 29, 2016 Download for free at http://cnx.org/content/col11487/1.9
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