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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

must all prokaryotic cells posses a cell wall?
chris Reply
what is biology?
Cathy Reply
biology is basically the study of life
Robert
that's true
Tonia
it's the study of living things
Tonia
What is a celiac disease
Falase Reply
distinguish between properties and characteristics
Elee Reply
what are organelles
Elee
organelles are substances that makes up a cell
chris
what is biology
Prevail Reply
biology is science that studies life
Elee
it's the study of living and non living things
now that we have an estimate for the diameter of the cell.what estimate can we make about the volume of the cell?
faxhood Reply
why too much insulin result in low blood sugar
Leri Reply
For example, too much exercise can cost you to lose to much weight. Too much insulin will pull to much sugar out of your systemic system into your cells.
Eric
difference between DNA and RNA
Eyitayo Reply
DNA is deoxyribonuclaic acid. Deoxy refers to a lack of oxygen. The Ribose moity is missing an OH group. I think it is missing from the second C of the ring. RNA is ribonucleic acid. DNA has our genetic code in on it. RNA is translated from DNA and carries the blue print for protein synthesis.
Eric
The OH group on RNA prevents it from being reactive. But it is very unstable though. Would you want such a power tool floating around in your body, no. And you have three types of RNA: mRNA, tRNA and rRNA. Please let me know it this helped?😄
Eric
o
Browse
Eric answered this question perfectly
what determines the aeration level in the soil
Shola Reply
what is homeostasis?
Sarita Reply
It means balance in a biological system.
Eric
What is biology
Don Reply
Biology z the study of life
GOLDEN
what's biology
buran
biology is the study of living nd none living organism
Chinaza
Biology is the study of life
Quadri
yes Sir
Said
what's cell biology
Prince
biology is the study of life
Raheal
Biology is a science subject that deals with the study of living things and how they interact with there environment
chris
what is asexual reproduction,?
Awoi Reply
A type of reproduction which does not involve the fusion of gametes or a change in the number of chromosomes
Serena
Reproduction without sex... In which form a single organism or cell makes a copy of itself.
Serena
Please explain the concept of mitosis and meiosis
Serena
I guess you could use it for study buddies and brushing up on what you need to
Serena
what is mitosis
Klp
Asexual reproduction?
Serena
why pepsin and trypsin released in active form?
Yacqub
mitosis is the type cell division in which two daughter cells have same no. of chormosomes
syed
Hi
Don
chromosome number remains the same in mitosis
mc
Ello
Henry
Hii
Nikky
Yrr help me.
Nikky
Physical chemistry..... Koi h jo mujhe physical chem ki notes send kr ske
Nikky
what is asexual reproduction
Targbe
what makes golgi body in plants
Abdulkareem Reply
name the membrane of the plants
Abdulkareem
how can turners syndrome be corrected before birth
Balinda
which animal survive from being preyed just because of being humble, slow, and not aggressive
Balinda
Plants have golgi body's also. Plants are eukaryotic cells. And membrane bound organelles are a characteristic of eukaryotic cells. Moreover golgi body's are creatted from the ER. Also do not forget plants have plastids and animal cells do not.
Eric
During organs transplantation, the organs cannot be taken from just anybody since the graft would be rejected sooner or later due to
Liter Reply
Non-MHC compatibility on the organ and an attack from the patient's immune system.
Eric
what makes golgi body in plants
Abdulkareem
why trypsin and pepsin released in active form
Yacqub
Let us remember MHC'S on our cells. This is how our cells determine self from n o n s e l f. Transplanted tissue has to have a certain amount markers. These have to match to the recipiant's markers. Even with this, immunosuppresant medacine is prescribed to the recipient.
Eric
Even with these measures the body may still reject the transport. This can occur even after the recipient excepting the transport for some time.
Eric
what is integument system
Joy Reply
This system is our skin. This includes the skin lining our alimentary system which includes the tissue from our mouth to our anus. Our skin is our largest organ system. It is mostly made up of epithelial tissue.
Eric

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Source:  OpenStax, Concepts of biology. OpenStax CNX. Feb 29, 2016 Download for free at http://cnx.org/content/col11487/1.9
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