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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

Is the "growth and maintenance phase" in a cell's life cycle when cell division is about to occur
Somto Reply
what is the common name of Basidiomycetes
Ogechukwu Reply
الاجزاء النباتية لابد من تعقيمها قبل زراعتها في القوارير
whats this?
do you speak arabic?!
what are bio elements
Shahzad Reply
which are present In Body And such elements Have Great role in our Body there are 16 bio elements that maintains human Body but on The basis of amount There are 6 bio elements present in Concen. of 99% and More Valuable And Highly Concen. element is Oxygent with 65 %
how je pollution brought about
Lamina Reply
how je pollution brouhgt about
non is pollution brouhgt about
describe the anatomy of cell division
Ivanovic Reply
Complex traits such as height result from 
Ruben Reply
what is the difference between chloroplasts and mitochondria
Nkalubo Reply
chloroplast in plants and bacterial cell ; mitochondria in animal cells
Diagram of a living cell
Eliza Reply
what is cell
A cell is the smallest basic unit of life.
what's biology
Ogochukwu Reply
this is da study of living and non-living thing in an eco-system
it is the study of living and non living organism in the ecology
I agree with you dat biology is d study of living nd nonliving features
why do plants store carbohydrates in form of starch and not glucose?
Nutty Reply
Describe the structure of starch?
wat is diffusion
water is life!.. Discuss?
Nutty Reply
why do plants store carbohydrates in form if starch not glucose!
study of living thing
Dennis Reply
what is beyond a liveing cell
what is biology
Gabriel Reply
d study of living nd non living thing
what is vasectomy
Evelyn Reply
The surgical removal of d spermduct

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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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