<< Chapter < Page Chapter >> Page >
Population growth  =   r N

The value of r can be positive, meaning the population is increasing in size (the rate of change is positive); or negative, meaning the population is decreasing in size; or zero, in which case the population size is unchanging, a condition known as zero population growth    .

Logistic growth

Extended exponential growth is possible only when infinite natural resources are available; this is not the case in the real world. Charles Darwin recognized this fact in his description of the “struggle for existence,” which states that individuals will compete (with members of their own or other species) for limited resources. The successful ones are more likely to survive and pass on the traits that made them successful to the next generation at a greater rate (natural selection). To model the reality of limited resources, population ecologists developed the logistic growth    model.

Carrying capacity and the logistic model

In the real world, with its limited resources, exponential growth cannot continue indefinitely. Exponential growth may occur in environments where there are few individuals and plentiful resources, but when the number of individuals gets large enough, resources will be depleted and the growth rate will slow down. Eventually, the growth rate will plateau or level off ( [link] b ). This population size, which is determined by the maximum population size that a particular environment can sustain, is called the carrying capacity    , or K . In real populations, a growing population often overshoots its carrying capacity, and the death rate increases beyond the birth rate causing the population size to decline back to the carrying capacity or below it. Most populations usually fluctuate around the carrying capacity in an undulating fashion rather than existing right at it.

The formula used to calculate logistic growth adds the carrying capacity as a moderating force in the growth rate. The expression “ K N ” is equal to the number of individuals that may be added to a population at a given time, and “ K N ” divided by “ K ” is the fraction of the carrying capacity available for further growth. Thus, the exponential growth model is restricted by this factor to generate the logistic growth equation:

Population growth  =   r N   [ K N K ]

Notice that when N is almost zero the quantity in brackets is almost equal to 1 (or K / K ) and growth is close to exponential. When the population size is equal to the carrying capacity, or N = K , the quantity in brackets is equal to zero and growth is equal to zero. A graph of this equation (logistic growth) yields the S-shaped curve ( [link] b ). It is a more realistic model of population growth than exponential growth. There are three different sections to an S-shaped curve. Initially, growth is exponential because there are few individuals and ample resources available. Then, as resources begin to become limited, the growth rate decreases. Finally, the growth rate levels off at the carrying capacity of the environment, with little change in population number over time.

Questions & Answers

Given that the elasticity of supply for a good is 2 and the percentage change in price is 45%.What is the percentage change in quantity supplied
Mbe Reply
state and explainfour function of a costumer service
Egba Reply
the circular flow model of the economy is a simplification showing how the economy works and the relationship between income,production and spending in the economy as a whole
Anna Reply
what is circular flow
Ntokozo Reply
what is economics?
Dorcas Reply
Economics is defined as the science that study human behaviour as a relationship between ends and scarce means which have alternative uses.
economics is a social science concerned with the production,distribution, and consumption of goods and services
in 2021 Amazon reduced the annual subscription fee for its prime membership service which provides free two_day shipping on many goods and other benefits, from $119 to $99. Zoppa consulting, an investment firm estimated that before the price reduction, prime had 62million subscribers globally. If so, what is the arc elasticity of demand for a prime membership.
Joan Reply
Differences between microeconomics and macroeconomics
tatiana Reply
Macroeconomics deal with the economy as a whole.that is an economy affect the firm ,government and the households eg.unemployment, whilst Microeconomics deal with the the decision making of households,firm and government separately.
what is Economics
Ebem Reply
the branch of knowledge concerned with the production, consumption, and transfer of wealth and has Influence by sociology!!!!
Economics is the study of how humans make decisions when they want to fulfil their requirements and desires for goods, services and resources.
Economics is the study how humans make decisions in the faces of scarcity.
economic is the study of how human make decision in the fact of scarcity.
Economics is a social science which study human behavior as a relationship between earn and scarce mean which have alternative uses
what is market structure
market structure in economics depicts how firms are differentiated and categorised based on types of goods they sell and how their operations are affected by external factors and elements.
what is economic theory
what is demand
Gooluck Reply
demand is the willingness to purchase something
demand is the potential ability or williness to purchases something at a particular price at a given period of time..
Demand refers to as quantities of a goods and services in which consumers are willing and able to purchase at a given period of time. Demand can also be defined as the desire backed by ability to purchase .
what is demand
John Reply
is the production of goods in scarcity
Demand refers to as quantities of a goods and services in which consumers are willing and able to purchase at a given period of time.
Demand refers to the quantity of goods and services that a consumer is willing and able to buy at a given price over a period of time
Do high interest rate in a country increase investment
what is demand of supply
music Reply
What is the meaning of supply of labour
Anthonia Reply
what is production?
Elizabeth Reply
Production is basically the creation of goods and services to satisfy human wants
importance of tertiary and example
Production is the process of producing goods and services to satisfy human needs and want.
under what condition will demand curve slope upward from left to right instead of normally sloping downward from left to right
Atama Reply
how i can calculate elasticity?
Tewekel Reply
Difference between extinct and extici spicies
Amanpreet Reply
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now

Source:  OpenStax, Environmental biology. OpenStax CNX. Aug 10, 2015 Download for free at https://legacy.cnx.org/content/col11863/1.1
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Environmental biology' conversation and receive update notifications?