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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 demand
TECK Reply
the amount of a good that buyers are willing and able to purchase
what is population
Amadou Reply
The people living within a political or geographical boundary.
what happens to price and quantity when demand curves shift to the right
Asha Reply
price level goes up. quantity demand increases
example- inferior goods
demand law
Its states that higher the price the of the commodity, and lower the quantity demanded
I am confused but quantity demand will increase.
No. That's the law of supply
the price goes down and quantity demanded increases
what happens to price and quantity when supply curve shifts left?
Asha Reply
price level will increase
quantity demand will decrease
what is inflation
Pop Reply
inflation is a general and ongoing rise in the level of prices in an entire economy.
is the pasistance increase in the price of a country economy
how does inflation affects the economy of a country? what is deflation?
deflation can simply be define as the persistence decrease in price of a countrys economy
the revenge of malthus relates "revenge" with "commodity prices". collect data for 3 commodoties and check their price evolution
Jamshi Reply
what is elasticity
dubela Reply
Elasticity is an economics concept that measures responsiveness of one variable to changes in another variable.
Computer software represents
Mboledi Reply
पर्यावरण राज्यों में से किस राज्य में शिष्य शिक्षक अनुपात 30 से अधिक वाले विद्यालयों का प्रतिशत न्यूनतम होता है
plz Reply
Hey what are you trying to mean?
what is Asset
like a banana
demand is the process whereby consumers are willing and able to purchase a particular product at various price over a given period of time
Samuel Reply
The law of dinimish
Frank Reply
What is the law of dinimish
What is the law of dinimish
What is the law of dinimish
opportunity cost is to forgo something for another.
jackie Reply
what is financial market
Asheeru Reply
what is demand
Levinel Reply
Demand is an economic principle referring to a consumer's desire to purchase goods and services and willingness to pay a price for a specific good or service.
explain any three exceptions to the law of demand
Emma Reply
Which event leads to a diploid cell in a life cycle
Nicole Reply

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Source:  OpenStax, University of georgia biology. OpenStax CNX. Dec 09, 2013 Download for free at https://legacy.cnx.org/content/col11585/1.6
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