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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 oxidation?
Rose Reply
 the state or result of being oxidized
Emmanuel
hahahaha thanks, but my teachers requires a thorough meaning about that
Rose
Is the process of oxidizing ,the addition of oxygen to a compound with a loss of electrons, always accompanied by reduction
Korletey
loss of electron....
Anwar
thank you. 😊
Rose
thank you. 😊
Rose
thank you. 😊
Rose
what is genetic
Chibawa Reply
name the enzymes that i found in the saliva
Valuables Reply
draw a bacterium cell and label
Kadijah Reply
What are the osmoregulatory functions of the kidney?
bisi Reply
filter
Meenu
What is ecology
Hebert Reply
what is cell
Etama Reply
cell is the basic unit of life
Asiatou
cell is the basic structural and functional unit of an living organism
Darshan
a cell is the smallest and most basic unit of a living thing
John
cell is the basic unit of life. we are made up of 60,000 billions of cells.Each cell carry out a specific function in the body.
Pallavi
A cell is the smallest basic functioning unit of life.
Ali
where is the pectoral gridle located?
Tiania Reply
What is hypotonic
Bright Reply
what is hypotonic
Dangaya
Hypotonic means weak solution
Ali
the difference between the two cells
Obeng Reply
explain the courses and the correction of lon term sightedness and short term sightedness
Isaac Reply
long sightedness is said to be like someone that can see far object clearly why short sightedness is someone that only can see near obect
SHEDRACK
why drinking excess alcohol causes thirst and dehydration
uwikuzo Reply
Can we chat about nutrition please?
Elia
yes
Uzair
sure
Uzair
Uhm why is it so important to follow the nutritional process?
Elia
BC it contribute to the source of life
SHEDRACK
what is reproduction
smart Reply
it is d act of bringing young ones to life
Oyebanji
to ensure survival of a species🚴‍♀️
Michelle
what is a genotype
Collins
what is hazardous
smart
a cell is the smallest unit of a living thing. so we all have cell
smart
It is the formation of a zygote resulting from the fusion of the sperm cell with the ovum.Thus,this results in the production of new species which are genetically dissimilar from their parent cells.
Pallavi
yes we all have cell round our body without the existances of cell them they will be no life in us as human
SHEDRACK
what is size of cell
Mohd Reply
what is size of Hart
Mohd
nanometers=um sign thingie
Michelle
microns=nanometers
Michelle
monomers and polymers of nucleic acids?
Jyrl Reply
dna and rna involvement
Michelle

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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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