<< Chapter < Page Chapter >> Page >
d N d T  =  b N     d N  =  ( b   -   d ) N

Notice that the “ d ” associated with the first term refers to the derivative (as the term is used in calculus) and is different from the death rate, also called “ d .” The difference between birth and death rates is further simplified by substituting the term “ r ” (intrinsic rate of increase) for the relationship between birth and death rates:

d N d T  =  r N

The value “ r” can be positive, meaning the population is increasing in size; or negative, meaning the population is decreasing in size; or zero, where the population’s size is unchanging, a condition known as zero population growth    . A further refinement of the formula recognizes that different species have inherent differences in their intrinsic rate of increase (often thought of as the potential for reproduction), even under ideal conditions. Obviously, a bacterium can reproduce more rapidly and have a higher intrinsic rate of growth than a human. The maximal growth rate for a species is its biotic potential, or r max , thus changing the equation to:

d N d T = r max N
Both graphs (a) and (b) plot population size versus time. In graph (a), exponential growth results in a curve that gets increasingly steep, resulting in a J-shape. In graph (b), logistic growth results in a curve that gets increasingly steep, then levels off when the carrying capacity is reached, resulting in an S-shape
When resources are unlimited, populations exhibit exponential growth, resulting in a J-shaped curve. When resources are limited, populations exhibit logistic growth. In logistic growth, population expansion decreases as resources become scarce, and it levels off when the carrying capacity of the environment is reached, resulting in an S-shaped curve.

Logistic growth

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 will survive to pass on their own characteristics and traits (which we know now are transferred by genes) 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, slowing the growth rate. Eventually, the growth rate will plateau or level off ( [link] ). This population size, which represents the maximum population size that a particular environment can support, is called the carrying capacity, or K .

The formula we use to calculate logistic growth adds the carrying capacity as a moderating force in the growth rate. The expression “ K N ” is indicative of how many individuals may be added to a population at a given stage, 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:

d N d T = r max d N d T = r max N ( K   -   N ) K

Questions & Answers

there is no more other chapter
Sandeep Reply
Give tow examples for nutritional deficiency Diseases-
Singampalli Reply
How does a plant cell look like
Sang Reply
in a sleepers form
David
what do you mean ? I could not understand
Gul
a stage in mitosis wherein in spindle fibers begin to shorten to pu the sister chromatids away from each other towards the opposite ends of the cell
Earl Reply
a stage in interphase where chromosome s are duplicated
Earl
What is biodiversity
Sp Reply
Hmm
Hele
Name two secretions of Golgi apparatus
Daniel Reply
What contribute to evolution of eukaryotes
Chiquita Reply
hi
Nubia
hello
surya
how transpiration occur in aquatic plants
Sajid Reply
what is the study of allelemorph
Faith Reply
what is protein
Majid Reply
any of a class of nitrogenous organic compounds which have large molecules composed of one or more long chains of amino acids and are an essential part of all living organisms, especially as structural components of body tissues such as muscle, hair, etc., and as enzymes and antibodies.
Anirban
what is DNA replication?
Anirban Reply
separation of the DNA to produce new daughter cell. mostly in the form of meiosis
Faith
what is xenia
Mani Reply
can i get a broader difference between inductive reasoning and deductive reasoning
Daniel Reply
what are the types of tissues and there functions
Daniel
what is signal cascade?
nur Reply
it is the process by which plants produce their fo
Getabalew Reply
what are the substrates of this process
Fiko

Get the best Biology course in your pocket!





Source:  OpenStax, Biology. OpenStax CNX. Feb 29, 2016 Download for free at http://cnx.org/content/col11448/1.10
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

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

Ask