<< 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

what is digestive system
Lucky Reply
digestive system is the human syman system that icludes esopuges stomach o braking down of food in to useful substance to our body
samrawit
definition of biology basics
Ritu Reply
the potential energy of a molecule can be inquired by their number of?
Jesus Reply
what is the full meaning of RNA
Ayo Reply
ribose nucleic acid
Nikita
Ribonucleic acid
Jesus
discuss, describe at least three (3) methods that could be used to improve photosynthesis..
Marvel Reply
Improve the efficiency with which plants capture light Improve the efficiency by which plants turn light into energy The smart canopy concept develop crop planting schemes that increase the penetration of sunlight into lower-level leaves.
Jesus
what is osmosis
Aon Reply
movement of water molecule from higher to lower concentration through a semipereable membrene.
Dr
what of in the case of solute
Aon
osmosis is the movement of molecules from higher concentration region to lower concentration region through semi-permeable membrane.
Broad
in case of solute means that water moves from the region with lower solutes to the region with higher solute. so it is vice versa to water.
Broad
what are the hydrophilic and hydrophobic region of the plasma membrane?
Samuel Reply
hydrophilic in other word it called water loving and hydrophobic region other word is region that does not contact with water in the plasma membrane.
Broad
the phospholipids
Jesus
recognizing living things
Emmanuel Reply
Species A has 12 pairs of chromosomes and Species B has 11 pairs of chromosomes. Explain what occurs during mitosis and during meiosis in the hybrid that allows normal development and growth from zygote to adult, but causes the adults to be sterile.
Christina Reply
what is the origin of angiosperms?
Broad
unknown group of gymnosperms of triassic period.
Aditi
ouky but what about the concept of monophyletic and polyphyletic? where angiosperms is between that two concept?
Broad
Why does water move through a membrane?
Christina Reply
Explanation: Water can diffuse through the lipid bilayer even though it's polar because it's a very small molecule. Water can also pass through the cell membrane by osmosis, because of the high osmotic pressure difference between the inside and the outside the cell
Babar
How many bones are in the human skeleton
Treasure Reply
203
Oyeleke
206
Babar
procce of digestion of proteins a long human alimentarycanal
Carson Reply
This is accomplished by enzymes through hydrolysis.
Jesus
what are the properties of lipids?
Isiah Reply
They are: Fatty acids, fats, oils, waxes, phospholipid, glycolipids, steroids and some vitamins
Rachel
lipids are made  up of a glycerol molecule with three fatty acid molecules attached to it. 
Jesus
explain why a fresh water fish excrete ammonia
Leonard Reply
plz answer my question
Leonard
sorry i meant it has a nucleous unlike plant cells lol
Lailah
Ammonia is the end product of protein catabolism and is stored in the body of the fish in high concentrations relative to basal excretion rates. Ammonia, if allowed to accumulate, is toxic and is converted to less toxic compounds or excreted
Rachel
cartilagenous fish's are ureolitic they excrete the waste in the form of urea as there undigested food mostly forms urea in their digestive system n much of the urea iz stored in the of the cartilagenous fish's. hence they are not a edible, but boney fish's excrete ammonia as they form less amount o
Babar
i really find some stuffs hard u guys are guru's
Orji
What are eukaryotic cells?
Nwosueke Reply
cell with no nucleous so not a plant cell
Lailah
eukaryotic cells are membrane bound organelles that have a membrane bound nucleus
ojeen

Get the best Concepts of biology course in your pocket!





Source:  OpenStax, Concepts of biology. OpenStax CNX. Feb 29, 2016 Download for free at http://cnx.org/content/col11487/1.9
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

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

Ask