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goldfiish [28.3K]
3 years ago
12

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

Biology
1 answer:
Vika [28.1K]3 years ago
6 0
<h2>Model of population</h2>

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

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