Most models of host-parasitoid interactions consider parasitoid attack
rates or, more accurately, encounter rates to be limited by the abili
ty of the parasitoids to find suitable hosts. Some models extend this
limitation to include the length of time it takes a parasitoid to hand
le each host. Here we consider host-parasitoid dynamics in the context
of parasitoid encounter rates being limited by the number of eggs tha
t each parasitoid has to lay when the host is at high densities and by
the ability of individual parasitoids to find hosts when the host is
at low densities. Although the encounter rate function we obtain is ma
thematically equivalent to previously obtained encounter rate function
s that include handling time, the stability properties of the resultin
g host-parasitoid system have heretofore not been fully explored. Our
analysis indicates in the absence of host density self-regulating mech
anism that the well-known condition in which host-parasitoid interacti
ons cannot be stable unless the proportion of hosts escaping attack ha
s a sufficiently clumped distribution (i.e., k less than or equal to 1
in the negative binomial model, where k is the negative binomial para
meter) still applies and that the intrinsic growth rate of the parasit
oid population must exceed the intrinsic growth rate of the host popul
ation by a factor that both is greater than one and increases as the d
egree of dumping associated with the proportion of hosts that escape a
ttack increases (i.e., as k --> 0 in the negative binomial model).