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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

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. 
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)
What is cell wall
Taiwo Reply
cell wall is the outemost rigid covering of the plants ,that provides protection to the plants.
what is ecology, ecosystem?
Nkeng Reply
what is digestive system
Lucky Reply
digestive system is the human syman system that icludes esopuges stomach o braking down of food in to useful substance to our body
definition of biology basics
Ritu Reply
the potential energy of a molecule can be inquired by their number of?
Jesus Reply
what is the full meaning of RNA
Ayo Reply
ribose nucleic acid
Ribonucleic acid
Ribo Nucleic Acid
discuss, describe at least three (3) methods that could be used to improve photosynthesis..
Marvel Reply
Improve the efficiency with which plants capture light Improve the efficiency by which plants turn light into energy The smart canopy concept develop crop planting schemes that increase the penetration of sunlight into lower-level leaves.
what is osmosis
Aon Reply
movement of water molecule from higher to lower concentration through a semipereable membrene.
what of in the case of solute
osmosis is the movement of molecules from higher concentration region to lower concentration region through semi-permeable membrane.
in case of solute means that water moves from the region with lower solutes to the region with higher solute. so it is vice versa to water.
what are the hydrophilic and hydrophobic region of the plasma membrane?
Samuel Reply
hydrophilic in other word it called water loving and hydrophobic region other word is region that does not contact with water in the plasma membrane.
the phospholipids
recognizing living things
Emmanuel Reply
Species A has 12 pairs of chromosomes and Species B has 11 pairs of chromosomes. Explain what occurs during mitosis and during meiosis in the hybrid that allows normal development and growth from zygote to adult, but causes the adults to be sterile.
Christina Reply
what is the origin of angiosperms?
unknown group of gymnosperms of triassic period.
ouky but what about the concept of monophyletic and polyphyletic? where angiosperms is between that two concept?
Why does water move through a membrane?
Christina Reply
Explanation: Water can diffuse through the lipid bilayer even though it's polar because it's a very small molecule. Water can also pass through the cell membrane by osmosis, because of the high osmotic pressure difference between the inside and the outside the cell
How many bones are in the human skeleton
Treasure Reply
it is about 270 bones at birth and decreases to 206 bones in adulthood.
procce of digestion of proteins a long human alimentarycanal
Carson Reply
This is accomplished by enzymes through hydrolysis.

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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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