Publish Your Research Online
Get Recognition - International Audience
Request for an Author Account | Login | Submit Article
|HOME||FAQ||TOP AUTHORS||FORUMS||PUBLISH ARTICLE|
Models For Population GrowthBY: Sandhya Anand | Category: Others | Submitted: 2011-03-25 18:30:38
Article Summary: "Population models form an essential tool to study the dynamics and characteristics of a population. They aim to represent the changes to the population structure over time in mathematical equations. All models, mathematical or otherwise are abstract representations of reality. According to Levins, modeling is a balancing act bet.."
Population models form an essential tool to study the dynamics and characteristics of a population. They aim to represent the changes to the population structure over time in mathematical equations. All models, mathematical or otherwise are abstract representations of reality. According to Levins, modeling is a balancing act between three major parameters, generality, realism and precision.
Population models tend to characterize the general properties of the population and are idealized representations which ignore the existence of random variation among the members of the population.
These models are based on two patterns of growth of population namely exponential and geometric population growth patterns.
a. Exponential population growth assumes that populations grow in an exponential pattern. Individuals are added on a continuous scale to such populations. Bacteria and some kinds of insects fall into this group.
This is based on the Malthusian Principle which specifies the change in population density as
dN / dt = rN
The growth of population after t generations is given by the equation
N (t) = N (0) e rt
Where N (t) is the population density after t generations
N (0) is the initial population density
e is the base of natural logarithmic scale.
And r refers to the intrinsic rate of natural increase.
If r = 0 the population is stable. If r>0, then the population is found to be growing and if r<0, then the population will shrink and tend towards zero; i.e. they are facing extinction.
However, the second scenario where r>0 favoring unlimited growth of population is not true in nature. In natural ecosystems, the population growth is limited by other factors of the environment which clearly limits the population growth. In order to accommodate for these variations, a new model was proposed.
b. Geometric population growth models propose a geometric pattern of growth.
They describe the changes in populations across generations as a geometric increase in discrete intervals.
The population density after t+1 generation is defined by
N (t+1) = N (t) λ
Where 'λ' - geometric growth rate
This represents the proportional growth of population
If λ is 0.5 the population density gets reduced by 50 %. If λ is 1.5, the population density will increase by 50%. At λ=1, the population is considered to be stable.
The equation can also be represented as
N (t) = N (0)λ t
Where N (0) represents the initial population density.
When the equation is compared with that of exponential growth, we get the relation between geometric and exponential growth rates of population
As λ = er
Or ln λ = r
Geometric population growth rate is a derivative of this fundamental model and hence the two cannot be considered as separate.
There are four ways in which a population size can be altered, birth (B), death (D), immigration (I) and emigration (E). The change in population size is represented as
Δ N = B + I - D - E
Population size after t+1 generation is described as
N t+1 = Nt +Bt +It- Dt -Et
Closed populations does not have immigration or emigration, hence the equation is limited to rates of birth and death in such populations.
Here, It = 0 and Et = 0, and
N t+1 = Nt +Bt - Dt
When the birth and death rates are expressed as per capita rates the accuracy increases.
N t+1 = Nt +bt Nt - dt Nt
N t+1 = Nt + (bt- dt) Nt
Per capita rates are assumed to be constant over generations and this equation thus gives the geometric rate of growth. The difference b-d can be represented as a constant R, since b and d are assumed to be constants,
N t+1 = (1 +( bt- dt)) Nt
Hence, N t+1 = (1 +R) Nt
And N t+1 = λ Nt λ = 1+R
The difference between R, r and lambda is in the biological realm. It determines the type of reproduction in the population (either pulse or continuous), and survival rates (instantaneous or finite)
c. Logistic model
This model was developed by Verhulst in 1838 after the exponential growth models failed to accurately represent the characteristics of the original population, especially at lower values of r.
The model was further developed by Pearl, earning the title Verhulst-Pearl model.
The differential equation is given by
dN/dt = kN (1-N/K)
where K- carrying capacity of the population and N is the population size.
When N is smaller than K, this reaches the exponential growth rates.
About Author / Additional Info:
Comments on this article: (0 comments so far)
• Green Nanotechnology: Its Definition, Introduction and Goals
• What is Parthenogenesis? Applications of Parthenogenetic Stem Cells
• Colorful Bacteria
• Biogas Formation and an Urge For Its Intensive Utilization
Latest Articles in "Others" category:
• Biotechnology, Its Techniques and Human Health
• Techniques of Biotechnology
• Nanomedicine and Disease Treatment
• Biotechnology and Livestock
• Bioinformatics: Combination of Biotechnology and Information Technology
• Gene Patenting and Its Uses
• Polymerase Chain Reaction: A Technique of Biotechnology
• Pharmacogenomics: Benefits and Barriers
• Human Genome Project: Ethical and Legal Issues
• Plant and Animal Tissue Culture: Procedure, Benefits and Limitations
• Therapeutics and Biotechnology
• Biotechnology: A Revolutionary Field and Biotech Challenges
• Recombinant DNA Technology
• Environment and Biotechnology
• Biosensors: Role in Biotechnology
• Human Insulin and Recombinant DNA Technology
• Biotechnology and Its Applications
• Genetic Engineering and its Methods
• Types of Gene Mutations - Diseases Caused By Gene Mutation
Important Disclaimer: All articles on this website are for general information only and is not a professional or experts advice. We do not own any responsibility for correctness or authenticity of the information presented in this article, or any loss or injury resulting from it. We do not endorse these articles, we are neither affiliated with the authors of these articles nor responsible for their content. Please see our disclaimer section for complete terms.
Copyright © 2010 biotecharticles.com - Do not copy articles from this website.
ARTICLE CATEGORIES :
| Disclaimer/Privacy/TOS | Submission Guidelines | Contact Us