Host-Parasitoid-Hyperparasitoid Model
by Mike Martin

This page generates plots and data for a discrete SIR Model with a constant total population and births and deaths proportional to population sizes. The model equations are:

Nt+1 = r Nt f1 ( Pt )

Pt+1 = r Nt (1 - fi ( Pt )) f2 ( Qt )

Qt+1 = r Nt ( 1 - fi ( Pt )) ( 1 - f2 ( Qt ))


where

The model helps to describe the dynamics between the population levels of three different species populations -- Host ( Nt ), Parasitoid ( Pt ), and Hyperparasitoid ( Qt ).   r is the number of eggs laid by a host that survive through the larvae, pupae, and adult stages.   e1 and e2 are the number of eggs laid by a parasitoid and hyperparasitoid, respectively, that survive though larvae, pupae, and adult stages.   f1 is the fraction of hosts not parasitized.   f2 is the fraction of parasitoids not hyperparasitized.   ai and ki are parameters for the fi's.   T is the last generation considered with the simulation.   N1, P1, and Q1 are the initial conditions.  

The sequence Nt is displayed in the graph in BLUE, the sequence Pt is given in BROWN, and the sequence Qt is given in PURPLE.

Enter in the values of the non-negative parameters (described above), then press the "Evaluate" button.

r =  


a1 =  

k1 =  

e1 =  


a2 =  

k2 =  

e2 =  


N1 =  

P1 =  

Q1 =  


T =  




References:

To be added.