A SIMPLE MARKOV MODEL FOR THE ASSESSMENT OF HOST PATCH QUALITY BY FORAGING PARASITOIDS

Insect parasitoids search for their hosts using a method that may be b roken into three parts. First, they locate plants which may harbor the ir hosts, then they assess the quality of these plants to decide wheth er to search them further for hosts and, finally, if they decide to ac cept a plant for further search, they exploit the plant by searching f or hosts and attacking them when they are found. We study the way that parasitoids assess plant quality by developing a mathematical model b ased on behavioral observations of foraging parasitoids that attack ap hids which infest crucifers. Assessment of plants is based on the conc entration of cues produced by hosts that inhabit them. Parasitoids an more likely to exploit plants on which more host cues are detected, an d the willingness of a parasitoid to exploit a given plant depends on the quality of other plants that have been visited recently. Plants wh ose quality exceeds a certain threshold will be accepted for exploitat ion. The threshold for giant acceptance will change with the experienc e of the parasitoid, increasing when plants heavily infested with host s are encountered, decreasing when uninfested plants are encountered. We analyze several rules that might describe how the acceptance thresh old changes with parasitoid experience, and for each rule we show how the number of parasitoids willing to accept plants with various levels of infestation depends on the number of plants with various levels of infestation. We then consider different rules for exploitation of hos ts on plants and find how the proportion of hosts attacked depends on host density.