The Effects of Temperature and Host Refuge on Insect Host-Parasite Models 1

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Abstract
The addition of host refuge to the Nicholson-Bailey or Hassell-Varley models was found to have a major effect on the stability of the models. If a refuge exists for a constant proportion of the host population, then stability is not affected, but if a constant number of hosts are in a refuge, then apparent limit cycles or damped oscillations are obtained. Experimental investigation suggests that the degree of host refuge in complicated laboratory “mazes” is temperature dependent at low but not at high temperatures. Cage studies in cotton fields indicate that the functional response of the parasite, Trichogramma pretiosum Riley, to the host, eggs of Trichoplusia ni Hübner, is a nearly linear function up to about 18.4 hosts/m 2 . In addition, there exists a nearly linear relationship between the functional and numerical responses of the parasite as determined from cage experiments. Both of these assumptions are contained in the Nicholson-Bailey and Hassell-Varley models. These cage experiments indicate that the assumptions are probably not seriously violated in the system which was studied.

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