Host-Parasitoid Models
Parasitoids are parasitic insects whose larvae develop by feeding in, or on, the bodies of other host insects (called arthropods). We make the following general assumptions about the interaction of the host and parasitoid species:
  1. hosts that escape parasitism give rise to the next generation of hosts
  2. the fraction of hosts that are parasited is a function (to be specified) of the rate of encounter of the two species
  3. the next generation of parasitoids come from parasited hosts
Furthermore, we will limit our attention to species of hosts and parasitoids with non-overlapping generations, typically found in temperate zones. Consequently, we will use difference equations to model the interaction of host-parasitoid interactions. To set up these equations, we use the following variables and parameters:

Hn Density of host at generation n
Hn+1 Density of host at generation n+1
Pn Density of parasitoid at generation n
Pn+1 Density of parasitoid at generation n+1

k Reproductive rate of host
a Searching efficiency constant of parasitoid
c Average number of viable eggs deposited by parasitoid on a single host
f(Hn, Pn) Fraction of hosts not parasited

The densities of the host and parasitoid are now assumed to change according to the following pair of difference equations:


Hn+1 = k Hn f(Hn, Pn)

Pn+1 = c Hn [1 - f(Hn, Pn)]

We will specify several types interactions by using appropriate forms for function f.


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