Patch Time Allocation by the Parasitoid Diadegma semiclausum (Hymenoptera: Ichneumonidae). III. Effects of Kairomone Sources and Previous Parasitism

Journal of Insect Behavior, Vol. 17, No. 6, November 2004 ( C 2004) Patch Time Allocation by the Parasitoid Diadegma semiclausum (Hymenoptera: Ichneumonidae). III. Effects of Kairomone Sources and Previous Parasitism X. G. Wang 1,2 and M. A. Keller 1 Accepted April 1, 2004; revised June 24, 2004 We investigated the effects of kairomone sources and previous parasitism on the patch-leaving behavior of Diadegma semiclausum, a solitary endoparasitoid of larval Plutella xylostella. Individual female wasps were released onto an experimental plant, and were allowed to freely leave for an alternative host plant placed upwind of the experimental plant in a wind tunnel. In one experiment, the experimental plant was either intact, contained host damage alone, or contained both hosts and host damage. In another experiment, the plant was infested with either unparasitized hosts, hosts parasitized previously by the female herself, or parasitized by Cotesia plutellae, another larval endoparasitoid of P. xylostella. We analyzed the influence of kairomone sources, host types, and within-patch foraging experience on the patch-leaving tendency of D. semiclausum by means of the proportional hazards model. Presence of host damage, and unsuccessful host encounters as a result of host defenses decreased the parasitoids patch-leaving tendency, while successful oviposition, self-superparasitism, and rejection of parasitized hosts increased their patch-leaving tendency. 1 Plant and Pest Science, School of Agriculture and Wine, University of Adelaide, South Australia 5064, Australia. 2 To whom corresponding should be addressed at University of Hawaii, College of Tropical Agriculture and Human Resources, 7370 Kuamoo Road, Kapaa, Hawaii 96746. E-mail: xingeng@ hawaii.edu. 761 0892-7553/04/1100-0761/0 C 2004 Springer Science+Business Media, Inc.

762 Wang and Keller A conceptual model of the parasitoid s patch-leaving behavior is proposed on the basis of the results of current and previous studies. KEY WORDS: Diadegma semiclausum; foraging behavior; kairomone; parasitoids; patchleaving tendency; patch time allocation; proportional hazards model; superparasitism. INTRODUCTION Patch time allocation is of utmost importance in determining a parasitoid s foraging success, particularly for time-limited parasitoids (Godfray, 1994; van Alphen et al., 2003). Insights obtained from many theoretical and empirical studies suggest that patch-leaving decisions in parasitoids are fundamentally dynamic in response to their informational state about the foraging environment (Stephens and Krebs, 1986; Haccou et al., 1991; Hemerik et al., 1993; Driessen et al., 1995; Nelson and Roitberg, 1995; Vos et al., 1998; Driessen and Bernstein, 1999; Wajnberg et al., 2000; Tenhumberg et al., 2001; Pierre et al., 2003). Information about initial patch quality and within-patch foraging experience may be used as important variables in patch-leaving decisions (Waage, 1979; Haccou et al., 1991; Hemerik et al., 1993; Driessen et al., 1995). Many parasitoids responded to patch odors emitted from feeding activities of their hosts (Vet and Dick, 1992; Geervliet et al., 1998; Shaltiel and Ayal, 1998; Li and Liu, 2003; Ohara et al., 2003b). Patch residence time of parasitoids is often influenced by the presence of host-associated cues, such as kairomone sources (Nelson and Roitberg, 1995; Shaltiel and Ayal, 1998; Driessen and Bernstein, 1999; Li and Liu, 2002; Ohara et al., 2003b; Wang and Messing, 2003). As assumed in two behavioral mechanism models, a parasitoid may set up a basic tendency to stay in a given patch based on its initial assessment of the patch s kairomone concentration; with a decreasing responsiveness to the patch s odor it finally leaves the patch if no host encounter occurs (Waage, 1979; Driessen et al., 1995). However, an assessment based on kairomone concentration might not be a reliable measure of actual patch quality, as other wasps may have already exploited the same patch. It is unknown if a parasitoid can distinguish any differences in kairomone sources between healthy vs. parasitized hosts. Furthermore, quantitative responses of parasitoids to kairomone levels could be influenced by other factors such as interpatch distance (Wang and Keller, 2003). Therefore, within-patch foraging experience (such as direct encounters with hosts) should play additionally important roles, as they provide a parasitoid with updated information on the availability of hosts (Pierre et al., 2003).

Patch Time Allocation in Parasitoids 763 Successful oviposition has been regarded as the most rewarding experience, which increases (Driessen et al., 1995) or decreases (Waage, 1979) a parasitoid s patch leaving tendency (see van Alphen et al., 2003 for a review). Other within-patch foraging experiences that have been shown to influence a parasitoid s patch-leaving tendency include encounter with parasitized hosts and rejection of parasitized hosts or superparasitism. A number of parasitoids demonstrated increased probabilities of leaving a patch upon detection of previously parasitized hosts (van Lenteren, 1991; van Alphen and Vet, 1986; Hemerik et al., 1993; Rosenheim and Mangel, 1994; Wajnberg et al., 1999; Pierre et al., 2003). We investigated the patch-leaving behaviors of Diadegma semiclausum (Héllen) (Hymenoptera: Ichneumonidae) in a series of three studies (Wang and Keller, 2003, in press). In the previous studies, it was found that the parasitoid s patch-leaving tendency decreased with increasing interpatch distance, unsuccessful host encounter, and increasing host density and clustered host distribution, but increased with successful oviposition and oviposition rate. Several other studies have observed the behavioral response of D. semiclausum to host plants, and shown that the parasitoid was more attracted to host-infested plants than uninfested plants (Li and Liu, 2002; Wang and Keller, 2002; Ohara et al., 2003b). It was also found that the parasitoid stayed longer on infested plants than intact plants. However, the presence or absence of host larvae on infested plants did not affect patch residence time of D. semiclausum (Li and Liu, 2002; Ohara et al., 2003a), although neither study considered the effect of within-patch foraging experience on the parasitoid s patch residence time. To obtain a through understanding of the parasitoids patch-leaving behavior, we need to investigate the parasitoid s patch-leaving behavior under different conditions, and analyze the parasitoid s patch-leaving tendency using the Cox proportional hazards model (Cox, 1972), that enables us to estimate the relative importance of various factors on the patch-leaving tendency (Haccou et al., 1991). The current study was to determine if presence of kairomone sources, previous parasitism by the female herself or female Cotesia plutellae Kurdjumov (Hymenoptera: Braconidae), as well as other within-patch foraging experience influence the patch-leaving tendency of D. semiclausum. Both D. semiclausum and C. plutellae are the most important larval parasitoids of the diamondback moth, Plutella xylostella L. (Lepidoptera: Plutelliade) (Wang and Keller, 2002). They were introduced into Australia in the 1950s and have become widespread (Waterhouse and Norris, 1987). However, D. semiclausum is the dominant parasitoid in the mild seasons (e.g., Wang et al., 2004).

764 Wang and Keller MATERIALS AND METHODS Insects, Host Plant, and Experimental Setup Laboratory populations of both P. xylostella and D. semiclausum were established from field collections in Adelaide, Australia. C. plutellae was imported from Taiwan and had been reared for about 10 generations prior to experiments. P. xylostella was maintained on potted cabbage plants Brassicae oleracea L. var. capitata, while both D. semiclausum and C. plutellae were reared on P. xylostella larvae under laboratory conditions (25 C, 14L:10D, 50 70% RH). All experiments used potted cabbage plants with five or six expanded leaves, second and third instar P. xylostella, and 2 3 d old mated D. semiclausum and C. plutellae female wasps. For detailed procedures regarding the insect cultures and wasp handling prior to experiments see Wang and Keller (2002). Two experiments were conducted using a similar set-up in a wind tunnel (160 65 65 cm) under controlled conditions (24 25 C, 50 70% RH, balanced illumination provided by two 36 W fluorescent lamps on each side and two 18 W lamps on each end of the test section). The wind speed was set at 30 35 cm/s. For each observation, an experimental plant was placed 60 cm downwind of an extra plant in the tunnel. A female wasp was released 30 cm downwind of the experimental plant on a stand about equal in height with the odor source from the experimental plant. Once the wasp arrived onto the experimental plant, its foraging behavior and location on each leaf were recorded continuously with an event recorder (The Observer 3.0 for Windows; Noldus, 1991) until the wasp left the experimental plant for the extra plant. Experiment I consisted of three treatments of the experimental plant: (1) clean, without host and host damage; (2) infested with three unparasitized P. xylostella larvae 24 h prior to the observation by placing each larva on one of three randomly selected leaves of the plant, but all three larvae were removed immediately prior to the release of the experimental wasp (i.e., the plant contained only host damage and hostassociated cues); and (3) infested with three unparasitized P. xylostella as treatment (2), but the larvae remained on the plant (i.e., the plant contained both hosts and their damage). Each treatment was replicated 19 24 times. Experiment II also consisted of three treatments of the experimental plant that was infested by (1) three unparasitized P. xylostella larvae; (2) three P. xylostella larvae that had been previously parasitized by the experimental wasp herself just before they were placed on the plant; and (3) three P. xylostella larvae that had been previously parasitized by a

Patch Time Allocation in Parasitoids 765 female C. plutellae just before they were placed on the plant. All larvae were placed on the experiment plant 24 h prior to the observation by placing each of them on one of three randomly selected leaves of the plant. To obtain hosts previously parasitized by C. plutellae or D. semiclausum,asingle female wasp was caged into a Petri dish containing a piece of cabbage leaf and three second or third instar P. xylostella larvae until each larva was observed to be stung by the wasp. Each treatment was replicated 20 25 times. In both experiments, the extra plants were always infested by three unparasitized P. xylostella larvae 24 h prior to the experiments. Each experimental or extra plant was examined again immediately prior to each observation to ensure the presence of the required number of hosts. One or two female wasps were observed in a random order for each treatment of either experiment on each observational date between 900 and 1600 h. All hosts were dissected to determine parasitism, superparasitism, or multiparasitism immediately following the observations. Data Analysis Mean numbers of attacks, stings and ovipositions, and mean oviposition rate per hour were compared among treatments within each experiment using Kruskal Wallis tests (JMP 4.0, SAS Institute, Cary, NC). Patch residence time, defined as the time between arriving on the experimental plant for the first time and leaving the experimental plant for the last time, was compared among treatments of each experiment using Bonferroni procedures for multiple comparisons (Log-rank test, survival analysis, JMP 4.0, SAS) (Haccou and Meelis, 1994). In five cases, the parasitoid flew directly to the extra plant when the experimental plant was empty in Experiment I. In the survival analysis the five cases were treated as censored observations (Haccou and Meelis, 1994). The effects of kairomone resources, previous parasitism and withinpatch foraging experience on the patch-leaving tendency of D. semiclausum were analyzed using Cox s proportional hazards model. In order to understand if decision-making by the parasitoid varied with changed environmental conditions, data for the two experiments were independently analyzed. A detailed description of the proportional hazards model (Cox, 1972) can be found in the literature dealing with survival analysis (e.g., Collett, 1994; Allison, 1997) and its application in analyzing the patch-leaving tendency of parasitoids (Haccou et al., 1991). Presence or absence of host damage, presence of both hosts and host damage were considered as primary covariates in Experiment I

766 Wang and Keller Table I. Explanatory Covariates Selected for Analyzing the Patch-Leaving Tendency of D. semiclausum by Means of the Proportional Hazards Model Covariates Experiment I Is the plant presented with hosts and damage? Does the plant only contain host damage? Was the previous encounter unsuccessful? Did the previous encounter involve an oviposition? Cumulative number of ovipositions Rate of last oviposition Experiment II Did the female experience oviposition prior to release? Was the previous encounter unsuccessful? Did the previous encounter involve an oviposition? Did the previous encounter involve superparasitism? Did the previous encounter involve multiparasitism? Was a parasitized host rejected at the last encounter? Cumulative number of ovipositions Rate of last oviposition (Table I). In addition, three covariates regarding within-patch foraging experience including unsuccessful host encounter, oviposition, and rate of poviposition were also considered as they were found to significantly influence the parasitoid s patch-leaving tendency in previous studies (Wang and Keller, 2003, in press). These three covariates were also selected for the data analyses of Experiment II. In Experiment II three additional covariates that were found to be important in other studies including encounters with parasitized host, superparasitism, and rejection of parasitized hosts (van Lenteren, 1991; Hemerik et al., 1993; Nelson and Roitberg, 1995; Wajnberg et al., 1999) were also tested (Table I). Although self-superparasitism and rejection of parasitized hosts were found not to be significant variables in a previous study (Wang and Keller, in press), it is possible that those factors could turn out to be important as the foraging environment has changed and the wasps would experience it differently. Prepatch oviposition experience may influence a parasitoid s expectation about future patch quality. Because in the second treatment of Experiment II each female wasp had three ovipositions in unparasitized hosts 24 h prior to the test, an additional variable regarding prepatch oviposition experience was also considered. We employed a standard likelihood ratio test through iterative regression methods as used for other studies (Collett, 1994; Wajnberg et al., 1999; Wang and Keller, 2003), to identify the significant covariates influencing the patch-leaving tendency of D. semiclausum. All analyses were performed

Patch Time Allocation in Parasitoids 767 by the PHREG procedure of SAS software, Version 6.0 (Allison, 1997). The proportionality assumption of this model was verified by data stratification of the covariate under test, and then plotting estimated cumulative hazard rates at different levels of the covariate, and the goodnessof-fit of the model was checked by examining a residual plot (Allison, 1997). RESULTS Patch Time Allocation In Experiment I, mean ± SE residence time of D. semiclausum on the intact plants without host or host damage (103 ± 29 s, n = 20) was significantly lower than the residence time on plants containing host damage only (1015 ± 153 s, n = 24), or plants containing both hosts and their damage (977 ± 161 s, n = 19) (P < 0.05). Female wasps left quickly after landing on an intact plant. The presence or absence of host larvae on the infested plant did not effect patch residence time of the parasitoid (P > 0.05). In Experiment II, mean ± SE residence time of D. semiclausum on the plant containing hosts previously parasitized by C. plutellae (1656 ± 291, n = 20) was significantly higher than the residence times on the plants containing unparasitized hosts (978 ± 151, n = 25) or hosts parasitized previously by the female herself (841 ± 100, n = 21) (P < 0.05). However, there was no significant difference between the latter two residence times (P > 0.05). Mean numbers of attacks, stings, and ovipositions were higher on the plants containing hosts previously parasitized by C. plutellae than on the plants infested either with unparasitized hosts or hosts previously parasitized by the female herself (Table II). However, oviposition rate by D. semiclausum was not significantly different among treatments Table II. Mean ± SE Numbers of Attacks, Stings, Ovipositions, and Oviposition Rate Per Hour by D. semiclausum on Host Patches Infested with Types of Host Larvae of P. xylostella No. of No. of No. of Oviposition Host type N attacks stings ovipositions rate/h Unparasitized 25 2.5 ± 0.32a 1.4 ± 0.22a 1.3 ± 0.19a 8.1 ± 1.75a Self-parasitized 21 2.5 ± 0.35a 1.4 ± 0.16a 1.2 ± 0.15a 10.5 ± 3.03a Parasitized by C. plutellae 20 3.4 ± 0.39b 2.0 ± 0.27b 1.8 ± 0.24b 6.3 ± 1.18a Note. Values followed by the same letter within the same column were not significantly different (Kruskal Wallis test, P > 0.05).

768 Wang and Keller Table III. Experiment I: Estimated Regression Coefficients (β), Standard Errors (SE), and Hazard Ratios [exp(β)] for the Final Fitted Model that Included all the Significant Covariates Affecting the Patch-Leaving Tendency of D. semiclausum Covariates β SE χ 2 P exp(β) Presence of host damage 2.339 0.358 42.7 0.0001 0.096 Unsuccessful host encounter 1.074 0.402 7.1 0.0079 0.342 Cumulative number of ovipositions 0.488 0.164 8.9 0.0029 1.629 Note. χ 2 correspond to the likelihood ratio tests (α = 0.05). All of them were estimated with all other significant terms present in the model. (Table II). On the plant containing hosts previously parasitized by the female herself, 81.8 ± 6.1 % (mean ± SE, n = 21) of the stings resulted in self-superparasitism by the parasitoid, while on the plants infested with hosts previously parasitized by C. plutellae, 96.6 ± 2.7 % (mean ± SE, n = 20) of the stings by D. semiclausum resulted in multiparasitism. Patch-Leaving Tendency In Experiment I, the patch-leaving tendency of D. semiclausum increased with successful oviposition but decreased with unsuccessful host encounters and presence of host damage (Table III). The effect of presence of hosts or host damage on the parasitoid s patch-leaving tendency was also clearly shown when plotting the cumulative hazards rate (Negative log-survivor) against the rank of searching periods (Fig. 1). On the patches containing host damage only, the first derivative of the cumulative hazards curve at t = 0 was different from zero (Fig. 1). This suggests that the parasitoid has a basic tendency to remain on a patch with host damage. In Experiment II, the effects of oviposition and unsuccessful host encounter on the parasitoid s patch-leaving tendency were consistent with Experiment I (Table IV). In addition, rejection of parasitized hosts, self-superparasitism, and increasing oviposition rate increased the parasitoid s path-leaving tendency (Table IV). The leaving tendency was significantly decreased on the patch containing hosts previously parasitized by C. plutellae (Fig. 1). Both the final models were fitted well (Fig. 2). All the curves in Fig. 1 had a more or less concave shape, implying that the parasitoid s leaving tendency was an increasing function of the time already spent in the patch.

Patch Time Allocation in Parasitoids 769 Fig. 1. Negative Log-Survival curves (cumulative hazards rates) for patch leaving by D. semiclausum as affected by presence of kairomone sources (Experiment I) and previous parasitism (Experiment II), i.e. graphical test on proportional assumption of the Cox s proportional hazards model (Cox, 1972). DISCUSSION The current study shows that presence of host damage decreased the patch-leaving tendency of D. semiclausum. Similar effects of kairomone sources on the patch-leaving tendency have also been demonstrated in other parasitoids (Haccou et al., 1991; Hemerik et al., 1993; van Roermund, 1994; van Steenis et al., 1996; Vos et al., 1998; Driessen and Bernstein, 1999). It suggests that female D. semiclausum may use kairomone resources to initially assess patch quality as assumed by the two behavioral

770 Wang and Keller Table IV. Experiment II: Estimated Regression Coefficients (β), Standard Errors (SE), and Hazard Ratios [exp(β)] for the Final Fitted Model that Included all the Significant Covariates Affecting the Patch-Leaving Tendency of D. semiclausum Covariates β SE χ 2 P exp(β) Unsuccessful host encounter 0.545 0.310 3.1 0.0791 0.580 Self-superparasitism 1.080 0.319 11.5 0.0007 2.943 Rejection of a parasitized host 1.791 0.492 13.3 0.0003 5.995 Cumulative number of ovipositions 0.390 0.134 8.4 0.0038 1.472 Oviposition rate 9.498 3.914 5.9 0.0152 13327 Note. χ 2 correspond to the likelihood ratio tests (α = 0.05). All of them were estimated with all other significant terms present in the model. mechanism models (Waage, 1979; Driessen et al., 1995). It is known that D. semiclausum was more attracted to infested plants than intact plants (Wang and Keller, 2002; Li and Liu, 2003; Ohara et al., 2003b), although the parasitoid s response to kairomone levels could be influenced by interpatch distance (Wang and Keller, 2003), and prepatch experience with host plants (Li and Liu, 2003). Furthermore, as shown in this study, a patch may have been previously exploited. Thus, additional information is needed in order to better track host availability. Unsuccessful host encounter decreased the patch-leaving tendency of D. semiclausum, while successful oviposition and increasing rate of oviposition increased the parasitoid s patch-leaving tendency. The effects of these within-patch foraging experiences on the parasitoid s patch-leaving tendency are consistent under various conditions as shown in previous studies (Wang and Keller, 2003, in press). Wang and Keller (2003, in press) discussed the adaptive significance of increasing patch-leaving tendency as a result of unsuccessful host encounter in relation to host defense. Many first encounters with new hosts were unsuccessful because the hosts often dropped from the plants. In this study about 40% of first attacks by the parasitoid did not lead to a successful sting (the ratios of stings to attacks were 62.1 ± 3.3, 63.9 ± 7.4, and 61.9 ± 7.3 for the three treatments of host type: unparasitized, self-parasitized, and parasitized by C. plutellae, respectively, see Table III). As a reaction, the parasitoid has to wait for a suspended host to come back and attack it again (i.e., using sit and wait strategy) (Wang and Keller, 2002). Thus, host handling by D. semiclausum involves a high cost in terms of time in order to overcome host defense. The interaction between host defense and the parasitoid s counter-defense could have profound effects on how natural selection operates on the parasitoid s searching strategy (Wang, 2001). The timesaving benefit would favor D. semiclausum to unnecessarily give up a discovered host when foraging in a relatively low host resource environment, and increasing tendency

Patch Time Allocation in Parasitoids 771 Fig. 2. Plot of the deviance residuals of the final fitted model with three covariates (Experiment I) and five covariates (Experiment II), against the order of searching periods. after an unsuccessful host encounter could be an adaptive strategy (Wang and Keller, 2003, in press). There are two problems for parasitoids using a countdown mechanism: (1) they would be trapped in patches with high kairomone concentration but low host availability due to previous parasitism; and (2) as host density and distribution of a parasitoid often vary in the field, they would be unable to distinguish among different host distributions. The increasing tendency to leave as a function of oviposition or increasing oviposition rate by D. semiclausum would help the parasitoid to better track the degree of patch depletion. The opposite effects of successful oviposition vs. unsuccessful encounter on the parasitoid s patch-leaving tendency may have balanced out the effect of host presence on the patch residence time, and this could explain why presence or absence of host larvae on the infested plant did

772 Wang and Keller not increase patch residence time of D. semiclausum, as observed in the current study and two previous studies (Li and Liu, 2002; Ohara et al., 2003a). Self-superparasitism and rejection of parasitized hosts further increased the patch-leaving tendency of D. semiclausum. In this study, both self-superparasitism and multiparasitism were common in D. semiclausum (Table III). D. semiclausum was able to discriminate among different types of hosts: unparasitized, parasitized by a conspecific female, and parasitized by the female herself (Wang, 2001). In the previous studies, when individual D. semiclausum females were released onto host plants contained unparasitized hosts, self-superparasitism also occurred but not very commonly (Wang and Keller, 2002, 2003). In the current study the female wasps we used were naïve and searched on patches containing hosts previously parasitized. Under such conditions, the female wasps may expect to compete with other parasitoids for limited host supplies. However, self-superparasitism should not be adaptive since the competition within a host would be between full sibs, of which only one would survive. Therefore, the parasitoid should increase its leaving tendency after each selfsuperparasitism. Similarly, each rejection of a parasitized host would provide a parasitoid with some information regarding the decreasing value of the patch the parasitoid is currently exploiting (van Alphen and Vet, 1986; van Lenteren, 1991), and that should also lead to a significant increase in the patch-leaving tendency (Wajnberg et al., 1999). The previous and current studies (Wang and Keller, 2003, in press) have elucidated the patch-leaving behavior of D. semiclausum under different conditions, and give detailed insights into the decision-making processes of D. semiclausum in patch leaving behaviors. Based on these results, a conceptual model of the patch-leaving behaviors of D. semiclausum can be suggested: (1) Upon arriving at an empty patch without kairomone sources, the parasitoid leaves it quickly. (2) The parasitoid has the ability to estimate initial patch quality in relation to kairomone concentration. Upon arriving at a patch containing kairomone sources, it set-ups a basic leaving tendency which is an increasing function of elapsed patch residence time. (3) The basic leaving tendency decreases with increasing interpatch distance, host density, or clustered host distribution. (4) Subsequent foraging experience within the patch provides the parasitoid with a more realistic assessment of and updated information on the availability of host and the degree of patch depletion. The parasitoid leaving tendency decreases with unsuccessful host

Patch Time Allocation in Parasitoids 773 Table V. A Summary of Covariates that Increased or Decreased the Patch-Leaving Tendency of D. semiclausum Increasing patch-leaving tendency Oviposition Self-superparasitism Rejection of a parasitized host Increasing rate of oviposition Decreasing patch-leaving tendency Presence of host-associated cues Unsuccessful encounter with host Increasing interpatch distance Increasing host density Increasing aggregation of host distribution encounters as a result of host defense, but increases with successful oviposition. (5) The patch-leaving tendency further increases when ovipositions occur in rapid succession or when the parasitoid is involved in rejection of a parasitized host or self-superparasitism. Therefore, the parasitoid s patch-leaving decisions are fundamentally dynamic in response to its informational state (Table V). The patch-leaving tendency has been investigated in a number of parasitoids by means of the proportional hazards model (see van Alphen et al., 2003 for a review). It should be emphasized that this statistical method can only provide a test of the relative importance of factors influencing a parasitoid s patch-leaving tendency under particular conditions. While the importance of some covariates and their effects may be consistent under different conditions, some factors could cease to be important when the environment has changed, as shown in this series of studies with D. semiclausum (Wang and Keller, 2003, in press). It is possible that more factors would be added to the list (Table V) when the parasitoid s foraging environment has changed. In general, the patch-leaving rules in D. semiclausum agree with the predictions of the marginal value theorem (Charnov, 1976) with respect to the effects of host density and interpatch distance on the parasitoid s patch time allocation, but for different reasons (Wang and Keller, 2003, in press). They also agree with the predictions of a countdown mechanism model (Driessen et al., 1995) regarding the effects of oviposition and oviposition rate on the parasitoid s patch-leaving tendency, and an incremental mechanism model (Waage, 1979) with respect to the effect of kairomone concentration on the basic leaving-tendency. Due to the complexity of patch-leaving behavior in parasitoids, statistical modeling should be a better approach to derive behavioral rules in parasitoids than the usual apriorioptimality modeling (Haccou et al., 1991; Hemerik et al., 1993). Comparison of the results from statistical modeling with the predictions of optimality

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