Biological model, Public Economics

Biological Model

The most commonly used model of biological population is based on logistic growth model in which population is assumed to grow as a 'logistic curve' over time. In this model,  the population grows rapidly  in the early  stages as the abundance  of  food is more and  then the growth  rate slows down  and  then approaches asymptotically a level which is equal to its carrying capacity.

220_Biological Model.png

Diagram: Logistic Growth Curve

Observe that when plotted on graph the logistics curve is 'S' shaped and is given By

503_Biological Model 2.png

Where Nt is the number of organisms at a point of time t,

K is the carrying capacity, and

'r'  is maximum intrinsic per capita growth rate of population.

As the curve shows, the population initially increases at an  increasing rate and reaches a point at which the growth is maximum and after that, the growth is at a decreasing rate and then finally the growth stops when the population reaches the limit known as 'carrying capacity'. This indicates a limit of the stock, which is supported by a given habitat. By taking logarithm on both sides and differentiating, we obtain the growth rate.

By taking the logarithm of the logistic curve we obtain,

Equation 1

1110_Biological Model 3.png

By differentiating the above we obtain

Equation 2

1021_Biological Model 4.png

 

Here Nt is instantaneous rate of change of stock. When N approaches K, i.e., the carrying capacity, the effective per capita increase Nt/Nt declines linearly towards zero.

Nt= F (N) - h (t) where F (N) is natural growth rate.

The problem is to determine what pattern of harvest rates over time would cause the stocks to change in such a way as to maximize the value of yield it provides.

 

 

 

 

 

Posted Date: 12/19/2012 12:29:45 AM | Location : United States







Related Discussions:- Biological model, Assignment Help, Ask Question on Biological model, Get Answer, Expert's Help, Biological model Discussions

Write discussion on Biological model
Your posts are moderated
Related Questions
Normal 0 false false false EN-IN X-NONE X-NONE MicrosoftInternetExplorer4

Question: You are the Head of the Public Relations Department of an airline company. Your Chief Executive has asked you to make a presentation on crisis management to senior s

Normal 0 false false false EN-IN X-NONE X-NONE MicrosoftInternetExplorer4

Explain the nature &importance of micro economic?

Q. Show the Traditional decision analysis? Traditional decision analysis rests on the key assumptions about the type of information available to the decision maker. Powerful B

Industries in the country of Technologia invest in latest equipment that annually enhance productivity of private workers by three percent. Government employees do not profit from

Normal 0 false false false EN-IN X-NONE X-NONE MicrosoftInternetExplorer4


Introduce uncertainties in attainments of policy outcomes, winning of elections, optimistic and pessimistic expectations of agents and relate it to various adjustments and converge

stages and various coordination mechanisms involved in policy processes..