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 broken into three parts. First, they locate plants which may harbor their hosts, then they assess the quality of these plants to decide whether to search them further for hosts and, finally, if they decide to accept a plant for further search, they exploit the plant by searching for hosts and attacking them when they are found. We study the way that parasitoids assess plant quality by developing a mathematical model based on behavioral observations of foraging parasitoids that attack aphids which infest crucifers. Assessment of plants is based on the concentration of cues produced by hosts that inhabit them. Parasitoids are more likely to exploit plants on which more host cues are detected, and the willingness of a parasitoid to exploit a given plant depends on the quality of other plants that have been visited recently. Plants whose quality exceeds a certain threshold will be accepted for exploitation. The threshold for plant acceptance will change with the experience of the parasitoid, increasing when plants heavily infested with hosts are encountered, decreasing when uninfested plants are encountered. We analyze several rules that might describe how the acceptance threshold 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 hosts on plants and find how the proportion of hosts attacked depends on host density.