Question

In which way does the lotka‒volterra predator‒prey model of population growth differ from the logistic model?

Answer 1

Model of population

Step-by-step explanation:

Logistic model

• Logistic model is a growth model which is also called S shaped or sigmoidal growth model
• This type of model mainly depends upon the carrying capacity of a given area and they invest their most energy in maintenance rather than reproduction
• Logistic model is represented by :

• 
  `dN/dT=rN(K-N/K)`
• where, r= reproductive rate; K= carrying capacity; N= initial population

Lotka Volterra model

• It is the model which describes the prey predator relationship
• Here it is expressed in the form of mathematical equations which helps in prediction of relationship between two species
• For species 1, equation is represented as:

• 
  `dN1/dT1=r1N1(K1-N1-\alpha N2/K1)\\`
• here,
  `\alpha` is the inhibitory effect of species 2 on species 1; r1 is the intrinsic growth rate; N1 is initial population of species 1; K1 is the carrying capacity of species 1; N2 is the initial population of species 2
• For species 2, equation is represented as:
• 
  `dN2/dT2=r2N2(K2-N2-\beta N1/K2)`
• here,
  `\beta` is the inhibitory effect of species 1 on species 2; r2 is the intrinsic growth rate of species 2; N2 is the initial population of species 2; K2 is the carrying capacity of species 2; N1 is the initial population of species 1
• There are certain conditions which helps us to determine the relationship between two species:
• If K2> K1/
  `\alpha` or K1> K2/
  `\beta` then there will be unstable coexistence between species 1 and species 2
• If K2< K1/
  `\alpha` or K1< K2/
  `\beta` then there will be stable coexistence between species 1 and species 2