Respuesta :
Model of population
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 :
- [tex]dN/dT=rN(K-N/K)[/tex]
- 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:
- [tex]dN1/dT1=r1N1(K1-N1-\alpha N2/K1)\\[/tex]
- here, [tex]\alpha[/tex] 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:
- [tex]dN2/dT2=r2N2(K2-N2-\beta N1/K2)[/tex]
- here, [tex]\beta[/tex] 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/[tex]\alpha[/tex] or K1> K2/[tex]\beta[/tex] then there will be unstable coexistence between species 1 and species 2
- If K2< K1/[tex]\alpha[/tex] or K1< K2/[tex]\beta[/tex] then there will be stable coexistence between species 1 and species 2
