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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

what is biology
PEACE Reply
what is biology
Ysabella Reply
biology is a study of living things
PEACE
Biology is a diverse branch of science that deals with mostly living things
Emmanuel
yes
Swapnil
What happen when inhibit the transcription?
Swapnil
what is the effect of not doing sexual intercourse
SUZAN Reply
what is the mechanism of cellular respiration
Rita Reply
what is enzyme
garry Reply
They are organic catalysts that alter the rate of chemical reactions in the body.
Iyadi
what is a cell
Praize Reply
what is biology
Mordi Reply
biology is the study of living organisms and their interactions with one another and their environments
Ysabella
which of the following event does not occur during some stages of interface?
Bangha Reply
What is microfilaments
KHalid Reply
What is multicellular organisms
Ovie Reply
these are organisms with more than two cells
Bangha
the process when a male toad fertilizer a female eggs is called what?
Ahrebe Reply
Fertilization
Gyamfi
how did unicellular organisms form plants and animals or is it that different unicellular organisms formed plants and animald
YXNG Reply
yes
James
thanks
YXNG
name the components of faeces
Damali
undigested carbohydrate, fibre
Sandra
what are unicellular organisms..?
Sackson
they have only one cell
Sandra
faeces contains many undigested food materials, after the food has been digested then it will be absorbed in the blood stream for assimilation.,......... but the remains toxic materials are stored in the rectum these toxic materials are the faeces and it contains bile salts, the polysaccharides .
James
nice.
Sandra
thanks
James
unicellular organisms are the ones with only single cell.
James
thanks for your answers guys.
Sackson
Ok
Richard
what is class bryophyta
Emefa Reply
how many stages do we have in glycolysis?
Damali
10 stages
Elisha
the presence of a membrane enclosed nuclosed is a characteristics of what
Addai Reply
eukaryotic cell
captain
hetreothalism in fungi
Lekhram 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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