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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
  • Describe how natural selection and environmental adaptation led to the evolution of particular life history patterns

Although life histories describe the way many characteristics of a population (such as their age structure) change over time in a general way, population ecologists make use of a variety of methods to model population dynamics mathematically. These more precise models can then be used to accurately describe changes occurring in a population and better predict future changes. Certain models that have been accepted for decades are now being modified or even abandoned due to their lack of predictive ability, and scholars strive to create effective new models.

Exponential growth

Charles Darwin, in his theory of natural selection, was greatly influenced by the English clergyman Thomas Malthus. Malthus published a book in 1798 stating that populations with unlimited natural resources grow very rapidly, and then population growth decreases as resources become depleted. This accelerating pattern of increasing population size is called exponential growth    .

The best example of exponential growth is seen in bacteria. Bacteria are prokaryotes that reproduce by prokaryotic fission. This division takes about an hour for many bacterial species. If 1000 bacteria are placed in a large flask with an unlimited supply of nutrients (so the nutrients will not become depleted), after an hour, there is one round of division and each organism divides, resulting in 2000 organisms—an increase of 1000. In another hour, each of the 2000 organisms will double, producing 4000, an increase of 2000 organisms. After the third hour, there should be 8000 bacteria in the flask, an increase of 4000 organisms. 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 1000 to more than 16 billion. When the population size, N , is plotted over time, a J-shaped growth curve    is produced ( [link] ).

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 )    (number organisms that die during a particular time interval) is subtracted from the birth rate ( B )    (number organisms that are born during that interval). This is shown in the following formula:

Δ N  (change in number) Δ T  (change in time)  =  B  (birth rate) -  D  (death rate)

The birth rate is usually expressed on a per capita (for each individual) basis. Thus, B (birth rate) = bN (the per capita birth rate “ b ” multiplied by the number of individuals “ N ”) and D (death rate) = dN (the per capita death rate “d” multiplied by the number of individuals “ N ”). Additionally, ecologists are interested in the population at a particular point in time, an infinitely small time interval. For this reason, the terminology of differential calculus is used to obtain the “instantaneous” growth rate, replacing the change in number and time with an instant-specific measurement of number and time.

Questions & Answers

there are 3 trimester in human pregnancy
ROHIN Reply
I don't know answer of this question can u help me
ROHIN
yes
Bisa
what is a cell
Fatima Reply
what is genetic
Janet Reply
I join
Janet
what are the branchas of biology
Prisca Reply
zoology, ecology
Millicent
biochemistry,cytology,herpetology...etc
R0se
genetics, microbiology,botany and embryology
Muhammad
what is a cell
Kulunbawi Reply
cell is smallest unit of life. cells are often cell the building blocks of life...
Muhammad
the first twenty element
Orapinega Reply
what are the characteristics of living things?
R0se
growth,respiration,nutrition,sensitivity, movement,irritability, excretion,death.
Obinna
What is the difference between adaptation and competition in animals
Adeyemi Reply
What is biology
Adeyemi
it is a natural science stadey about living things
Zamiil
Biology is the bronch of science which deals with the study of life is called biology
Aziz
what is the x in 300 stands for?
Ogbudu Reply
the properties of life
Clarinda Reply
response to the environment, reproduction, homeostasis, growth,energy processing etc.....
Pushpam
hello.
Daniela
hi
MacPeter
Good
Thomas
what is reproduction
Tims
Reproduction is a fundamental feature of all known life,each individual organism exist as a result of re production.....or else Multiplying...
R0se
a complete virus particle known as
Darlington Reply
These are formed from identical protein subunitscalled capsomeres.
Pushpam
fabace family plant name
Pushpam Reply
in eukaryotes ...protein channel name which transport protein ...
Pushpam Reply
in bacteria ...chromosomal dna duplicate structure called
Pushpam
what is a prokaryotic cell and a eukaryotic cell
Matilda Reply
There are two types of cells. Eukaryotic and Prokaryotic cells. Prokaryotic cells don't have a nucleus or membrane enclosed organelles (little organs within that cell). They do however carry genetic material but it's not maintained in the nucleus. Prokaryotic cells are also one celled.
juanita
Prokaryotic cells are one celled (single celled).
juanita
Prokaryotic cells are Bacteria and Archea
juanita
Prokaryotic cells are smaller than Eukaryotic cells.
juanita
Eukaryotic cells are more complex. They are much bigger than Prokaryotic cells.
juanita
Eukaryotic cells have a nucleus and membrane bound organelles.
juanita
Eukaryotic cells are animals cells which also includes us.
juanita
Eukaryotic cells are also multicellular.
juanita
nice explaination
Amna
eukaryotic cells are individual cells .. but eukaryotes are multicellular organisms which consist of many different types of eukaryotic cells
Will
also eukaryotic cells have mitochondria. prokaryotic cells do not
Will
Good
John
in prokaryotes only ribosomes are present... in eukaryotes mitochondria ...glogi bodies ..epidermis .....prokaryotes one envelop but eukaryotes compartment envelop....envelop mean membrane bound organelles......
Pushpam
prokaryotic cell are cells dat have no true nuclei i.e no cell membrane while eukaryotic cell are cell dat have true nuclei i.e have cell membrane
Divine
grt
Thomas
we have 46 pair of somatic cell and 23 pair of chromosomes in our body, pls can someone explain it to me. pls
Matilda Reply
we have 22 pairs of somatic chromosomes and one pair of sex chromosome
Amna
thanks
Matilda
we have 23 pairs of chromosomes,22 pairs of somatic and one pair of sex chromosomes
Amna
23 chromosomes from dad & 23 chromosomes from mom 23 +23=46 total chromosomes
juanita
X & Y chromosomes are called sex cells, the very presence of a Y chromosome means the person is Male.
juanita
XX Female XY Male
juanita
If a Karyotype has more than 46 Chromosomes then nondisjunction occured. For example, having an extra chromosome 21 will cause Down Syndrome.
juanita
in mammal state the different vertebrae and their location in the body
Igbinigie Reply

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Source:  OpenStax, Biology. OpenStax CNX. Feb 29, 2016 Download for free at http://cnx.org/content/col11448/1.10
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