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:

P_{t+1} = r N_{t} (1 - f_{i} ( P_{t} )) f_{2} ( Q_{t} )

Q_{t+1} = r N_{t} ( 1 - f_{i} ( P_{t} )) ( 1 - f_{2} ( Q_{t} ))

The model helps to describe the dynamics between the population levels of three different species populations -- Host ( N_{t} ), Parasitoid ( P_{t} ), and Hyperparasitoid ( Q_{t} ). r is the number of eggs laid by a host that survive through the larvae, pupae, and adult stages. e_{1} and e_{2} are the number of eggs laid by a parasitoid and hyperparasitoid, respectively, that survive though larvae, pupae, and adult stages. f_{1} is the fraction of hosts not parasitized. f_{2} is the fraction of parasitoids not hyperparasitized. a_{i} and k_{i} are parameters for the f_{i}'s. T is the last generation considered with the simulation. N_{1}, P_{1}, and Q_{1} are the initial conditions.

The sequence N_{t} is displayed in the graph in BLUE, the sequence P_{t} is given in BROWN, and the sequence Q_{t} is given in PURPLE.

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

r =

a_{1} =

k_{1} =

e_{1} =

a_{2} =

k_{2} =

e_{2} =

N_{1} =

P_{1} =

Q_{1} =

T =

References:

To be added.