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Faculty Publications in the Biological Sciences Papers in the Biological Sciences

2001

Optimal patch-leaving behavior: A case study using the parasitoid rubecula

Brigitte Tenhumberg University of Nebraska - Lincoln, [email protected]

Mike A. Keller University of Adelaide, [email protected]

Hugh P. Possingham University of Queensland, [email protected]

Andrew J. Tyre University of Nebraska-Lincoln, [email protected]

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Tenhumberg, Brigitte; Keller, Mike A.; Possingham, Hugh P.; and Tyre, Andrew J., "Optimal patch-leaving behavior: A case study using the parasitoid Cotesia rubecula" (2001). Faculty Publications in the Biological Sciences. 192. https://digitalcommons.unl.edu/bioscifacpub/192

This Article is brought to you for free and open access by the Papers in the Biological Sciences at DigitalCommons@University of Nebraska - Lincoln. It has been accepted for inclusion in Faculty Publications in the Biological Sciences by an authorized administrator of DigitalCommons@University of Nebraska - Lincoln. Published in Journal of Ecology 70 (2001), pp. 683–691; doi: 10.1046/j.1365-2656.2001.00530.x Copyright © 2001 British Ecological Society; published by Wiley-Blackwell. Used by permission.

Submitted November 23, 2000; revised March 23, 2001; published online December 20, 2001.

Optimal patch-leaving behavior: A case study using the parasitoid Cotesia rubecula

Brigitte Tenhumberg, Mike A. Keller, Hugh P. Possingham, and Andrew J. Tyre

Department of Applied and Molecular Ecology, University of Adelaide, Waite Campus, Private Bag 1, Glen Osmond, South Australia, 5064, Australia

Abstract 1. Parasitoids are predicted to spend longer in patches with more hosts, but previous work on Cotesia rubecula (Mar- shall) has not upheld this prediction. Tests of theoretical predictions may be affected by the definition of patch leaving behavior, which is often ambiguous. 2. In this study whole plants were considered as patches and assumed that wasps move within patches by means of walking or flying. Within-patch and between-patch flights were distinguished based on flight distance. The qual- ity of this classification was tested statistically by examination of log-survivor curves of flight times. 3. Wasps remained longer in patches with higher host densities, which is consistent with predictions of the marginal value theorem (Charnov 1976). Under the assumption that each flight indicates a patch departure, there is no rela- tionship between host density and leaving tendency. 4. Oviposition influences the patch leaving behavior of wasps in a count down fashion (Driessenet al. 1995), as pre- dicted by an optimal foraging model (Tenhumberg, Keller & Possingham 2001). 5. Wasps spend significantly longer in the first patch encountered following release, resulting in an increased rate of superparasitism. Keywords: Cox’s proportional hazards model, host density, oviposition

Introduction predators prey consumption results in a decreased en- counter rate with the remaining prey, while in parasit- The optimal exploitation of patchily distributed re- oids parasitism in a patch results in more time wasting sources has attracted considerable attention from be- inspecting and rejecting, or parasitizing already para- havioral ecologists and a large body of theory has sitized hosts (= avoiding or engaging in superparasit- been amassed (Stephens & Krebs 1986; Perry & Pi- ism). Some parasitoid species may not be able to detect anka 1997). The most basic prediction is that a con- the difference between parasitized and unparasitized sumer should leave a patch when the rate of return in hosts (host discrimination), thus increasing the risk of that patch drops below the average rate of return else- superparasitism. The benefit of superparasitism is gen- where in the environment (Charnov’s marginal value erally expected to be low (Visser, van Alphen & Nell theorem; Charnov 1976). Therefore, consumers are pre- 1992), although this varies among species and with dicted to stay longer on patches with higher prey den- time interval since previous parasitism (Field, Keller & sity. Patch use by Cotesia rubecula (Marshall) (Hyme- Calbert 1997). In addition, parasitoid foraging behavior noptera: ), a solitary larval parasitoid of the can be influenced by limited egg supply (Minkenberg, cabbage butterfly, (L.) (Lepidoptera: Pieri- Tatar & Rosenheim 1992). Hence, the patch leaving be- dae), was examined in this paper.One important as- havior of parasitoids is expected to be influenced by sumption of Charnov’s model is that fitness returns both host density and the total number of ovipositions from foraging in a patch decrease over time. However, (e.g. van Alphen & Vet 1986; Godfray 1994). Thus, the the underlying process for this decreasing patch prof- rate of return as a function of time for parasitoids is itability differs between predators and parasitoids. In likely to be much more complicated than for predators.

683 684 Tenhumberg et al. in Journal of Animal Ecology 70 (2001)

The boundaries of theoretical patches are unambigu- Materials and methods ous. In reality, patch boundaries may be ambiguous be- cause they depend on the forager’s perception of the en- and plants vironment (Ayal 1987). What is considered to be a patch Parasitic wasps, C. rubecula , and their hosts the cab- by an observer may not necessarily agree with what is bage white butterfly, P. rapae, were collected from gar- considered to be a patch by a forager. A further compli- dens near Adelaide, South Australia. The rearing meth- cation arises when patches have a hierarchical structure ods for these insects were described elsewhere (Keller and foraging behavior changes between patch levels 1990). Cabbage plants with 8–10 fully expanded leaves (Kotliar & Wiens 1990; Keller & Tenhumberg, in press). were infested with 2–4-day-old larval P. rapae 1 day be- The patch hierarchy for C. rubecula could range from fore the experiment. Mated C. rubecula were marked fields of host plants, down to individual host plants, sin- with a dot of colored enamel paint (Testor Corp., Rock- gle leaves on host plants and, finally, down to individ- ford, Illinois) on the thorax to allow individual identi- ual hosts on leaves. For all these reasons, it is important fication in the field. The wasps were held overnight in and often difficult to correctly match the scale of the ob- 150-mm Petri dishes with honey, a cabbage leaf and servation unit to the scale of the theoretical model (Ad- eight host larvae. This ensured that the wasps were not dicott et al. 1987; Ayal 1987; Godfray 1987). Identifying hungry, and had experience with hosts and host-associ- appropriate patch boundaries is critical to rigorously ated kairomones. testing theoretical predictions. In agricultural contexts, we expect female C. rubecula to spend most of their life Experimental design and implementation within a single cabbage field and optimize their- off spring production among cabbage plants (M. Keller, The experiment was carried out in the Waite Cam- personal observation). To explore this hypothesis patch pus Arboretum in summer 1988, 1989 and 1990. On the leaving behavior was studied in an array of several cab- day of the experiment cabbage plants infested with 0, bage plants (= single patches) each bearing different 1, 2 and 5 host larvae, which had fed on the plant for numbers of host insects. 1 day, were arranged randomly in a Latin square de- After defining a particular area as a patch and choos- sign marked by gridlines on the ground (Figure 1). A ing an appropriate study unit, it can also be difficult to new arrangement was used for each experiment. Prior determine when a forager actually leaves each patch. to release, wasps were exposed in a 150-mm Petri dish Some parasitoids, such as C. rubecula, often take flight to a cabbage leaf with feeding damage of P. rapae for immediately after attacking a host caterpillar, but sub- two min. The tendency of wasps to fly away when han- sequently return to the same plant (Nealis 1986). Such dled was overcome by this exposure. Wasps were re- revisits also occurred without a host having been at- leased from a 15 × 50-mm vial supported 50 mm above tacked. The high frequency and variable duration of the ground by a wooden block (n = 3 wasps in 1988, these short flights raises the question of how to distin- n = 13 wasps in 1989, and n = 2 wasps in 1990). As soon guish between inter- and intra-patch flights. Landing on another plant is not a reasonable criterion for defin- ing the end of a patch visit, because in a limited experi- mental habitat wasps will sometimes return to the same plant by chance, even after having ‘left’. Intra- and in- ter-patch flights were distinguished quantitatively using a statistical method designed for behavioral data analy- sis: log survivor curves (Scherer & Ekman 1982; Haccou & Meelis 1994). In this paper, identifying the correct cut-off point for intra-patch flights was crucial for detecting the- influ ence of host density and oviposition on patch leaving behavior. As expected from the marginal value theo- rem (Charnov 1976), the leaving tendency of C. rubecula was negatively correlated with host density. Leaving tendency was increased by high oviposition rates, sug- gesting that C. rubecula uses a countdown rule (Driessen et al. 1995). In addition, wasps spent much longer on the first patch after release compared to subsequent patch Figure 1. Layout of field plot showing the positions of cabbages and visits. This study of the patch leaving behavior of C. ru- grid lines. Potted cabbage plants were placed into buried pots so that becula is unique because the wasps were observed under the soil level was flush with the ground. Wasps were released in the centre of the grid. Light sand was spread on the ground to facilitate field conditions. Our conclusions highlight the- impor observations. Shade cloth around the perimeter (dotted line) mini- tance of correctly identifying patch-leaving behavior. mized wind gusts. Optimal patch-leaving behavior: A case study using the parasitoid Cotesia rubecula 685 as a wasp flew from the release vial, her behavior was equal to x. Ln[S(x)] is a straight line with a slope of −λ for recorded by two observers on a cassette recorder. The an exponential distribution with parameter λ. If a set of ob- behavior, position within the experimental arena and servations consists of a mixture of different behavior cate- leaf number visited was transcribed with event record- gories, i.e. a mixture of within and between patch flights, ing software accurate to 1 s. Plants on which a larva was Ln[S(x)] will be concave upward. The set of all flight times parasitized during an observation were replaced with was tested for the presence of mixtures of exponential dis- fresh plants before the release of the next wasp. tributions with Darling’s test for mixtures (Haccou & Meelis 1994). After splitting the flight records into within Definition of patch departure patch and between patch flights based on the distance trav- An entire cabbage plant was defined as a “patch.” A eled, the flight record subsets were tested for exponential- patch-leaving event could be identified by several charac- ity against undetermined alternatives using Kolmogorov– teristics including onset of flight, flight destination (land- Smirnov tests. We further assessed the fit visually by ing on a different plant), flight duration or flight distance. examining the estimated survival curves for the points at Wasps leave a patch when they fly off a plant in search of which the expected straight line was outside the 95% con- another patch. However, wasps in this study frequently fidence limits of the survival curve. To demonstrate the ef- returned to the same plant. There are two possibilities for fect of patch definition on the interpretation of a wasp’s be- flights that lead back to the same plant. First, the wasps havior, the data were analyzed assuming either that a wasp could be actually “leaving,” and simply end up back leaves a patch as soon as she takes flight or that some short on the same plant either by chance or because there are distance flights represent within patch movements. no “better” plants around. In this case all flight events should be treated as patch departures and subsequent Covariates searches treated as new patch visits. The second possibil- Three covariates were included in the Cox’s propor- ity is that wasps could be flying simply as a more efficient tional hazards model: host density, oviposition, and means of reaching another part of the plant and not actu- whether a wasp was foraging on the first patch after re- ally leaving to move to another plant. In this case, return lease or a later patch. The last covariate was chosen to visits are part of the same patch visit. In the first case, all compensate for acclimatization behavior of wasps be- flights represent a single behavioral category, patch- de cause unpublished data by Mike Keller indicated atypi- parture, while in the second case flights off a plant repre- cal behavior of wasps directly after their release. sent a mixture of two behaviors, within patch movements The first two covariates were included because there and patch departures. is a range of theoretical and empirical evidence that Flights that returned the wasp to the same plant var- host density and oviposition influences the patch leav- ied in length from 1 to 222 s, while flights between two ing behavior of foraging parasitoids (Driessen & Bern- different plants varied from 1 to 254 s. Clearly, neither stein 1999). Depending on the parasitoid species each the destination nor the duration can be used to distin- oviposition either increases (countdown mechanism) or guish between “leaving” and “remaining” flights. C. decreases this leaving tendency (count-up mechanism; rubecula usually changed leaves on a plant by flying. Driessen & Bernstein 1999). Therefore, short distance flights could mainly be associ- In general, foragers are expected to stay longer on ated with searching all over a plant for hosts. To test this patches with higher resource density. According to hypothesis the data set was split into short distance and the marginal value theorem (Charnov 1976), a forager long distance flights, based on whether wasps flew over should leave a patch when the rate of return in a patch a grid cell line (see Figure 1). Note that a wasp could re- drops below the average rate of return elsewhere in turn to the same plant and be considered as “leaving” the environment. A parasitoid wasp reaches this leav- the patch. The shortest duration of those flights was 1 s ing threshold later in patches with higher host density. and returns to the same plant after crossing a grid cell In wild populations cabbage plants usually contain be- line accounted for 36% of flights. tween zero and two P. rapae hosts (Harcourt 1961; Ko- The two possible definitions of patch leaving (flying bayashi 1966; Jones 1977). Three common host densities off a plant and flying over a grid cell line) were exam- (0, 1 or 2 hosts per plant) and a very high density of 5 ined using ln–survivor curves. It is commonly assumed hosts per plant were chosen for this experiment. that a single “behavior” should have a constant proba- Most wasps left a patch either without ovipositing or bility of terminating, leading to an exponential distribu- after one oviposition. As a consequence, there was not tion of behavior durations (Haccou & Meelis 1994). This enough data for the Cox’s proportional hazard model assumption can be tested graphically by plotting the to test the effect of the number of previous ovipositions. logarithm of the “survivor” function Hence, the effect of the oviposition rate, the reciprocal of j the time before the previous oviposition, was included S(x) = / ( 1) n in the model instead. We used the whole data set to cal- where n is the total number of observations, and j is the culate the oviposition rate, instead of splitting the data number of observations with a duration greater than or according to the number of ovipositions. 686 Tenhumberg et al. in Journal of Animal Ecology 70 (2001)

Cox’s proportional hazards model (Cox & Oakes 1984; Kalbfleisch & Prentice 1990; Hac- The patch departure behavior of the wasps was mod- cou & Meelis 1994). The significance of the model was eled with methods from survival analysis, by assuming tested with likelihood ratio tests and the proportional- 2 there is some baseline rate at which wasps switch from ity assumption using the asymptotic χ test statistic T(G) searching within patches for hosts to searching between (Grambsch & Therneau 1994). In this test, significant patches for new patches, and that this patch departure non-proportionality is indicated by statistically signifi- rate is influenced by variables such as the host density cant P-values. The survival analysis was performed in within patches or the number of previous ovipositions s-plus, version 4.5 (MathSoft, Inc., Bagshot Surrey, UK). (Haccou et al. 1991; Haccou & Hemerik 1985). The patch departure rate is assumed to be a function Results of time, and certain events, called ‘renewal points’, re- set the patch departure rate to its initial value. In the sim- Patch leaving event plest case the amount of time spent searching in a patch is In 25–46% of cases C. rubecula returned to a plant the time between two renewal points (Haccou et al. 1991; without landing somewhere else (Figure 2). The fre- Hemerik, Driessen & Haccou 1993). The basic renewal quency of one or more return visits tended to be points for the analysis were landing in and departing higher on plants with 2 or more hosts compared to 0 from a patch. Oviposition events were defined as renewal or 1 host per plant. This is consistent with wasps be- points, because if oviposition is important, the transition ing more likely to land on plants with higher host den- rate will be different following an oviposition. sities. Moreover, wasps that returned at least once were One important feature of the analysis of behavioral also more likely to return multiple times on plants with durations is censoring, which occurs if the start or fin- more hosts. ish of a behavioral event was not observed (Haccou & The two different patch-leaving criteria were tested Meelis 1994). Including these records in the analysis is first. A patch-leaving event was characterized by either important because they contain the information that the (1) taking flight or (2) by flying longer distances (cross- behavior lasted at least for the observation time. If cen- ing at least one grid cell line). The ln-survivor curve of sored records were excluded, then the analysis would all flight times was concave, consistent with a mixture of be biased in favor of shorter behavioral records. Three “within-patch” flights and “patch-leaving” flights (Dar- −6 censoring events were found in the data: (1) experiment ling’s Kn = 37437, P < 10 , Figure 3a). However, under- ended before wasp left the plant; (2) a wasp inadver- taking long flights was also not a perfect discriminator tently slipped off the plant; and (3) oviposition. Oviposi- of patch-leaving events. The hypotheses that durations tion was a censoring event because the wasp might have of flights within one grid cell (Figure 3b; Komolgorov– left at a different time if no oviposition had occurred. Smirnov D = 0.0868, P = 0.0003) and flights that included The effect of covariates on patch departure rates was at least one grid cell change (Figure 3c; Komolgorov– examined using Cox’s proportional hazards model. The Smirnov D = 0.134, P = 0.003) were distributed exponen- cumulative patch departure rate, or ‘leaving hazard’ tially have to be rejected. However, the fit of the data in survival analysis terminology, was estimated as − to the exponential distribution within each component Ln[S(x)] (Haccou & Meelis 1994). The survivor function [S(x), equation 1] is estimated by patch leaving or ‘fail- ure’ events. We used the Kaplan–Meier estimator to cal- culate S(x) (Cox & Oakes 1984), because it accounts for censoring. The steeper the slope of −Ln[S(x)], the higher the patch leaving rate. In Cox’s proportional hazards model, the observed hazard rate is the product of a baseline hazard and a fac- tor that gives the joint effect of a set of covariates z1, … , zp. The effect of a covariate is assumed to be proportional across the full range of the baseline hazard (the ‘propor- tionality assumption’). The general form of the model is:

p

h(t, z) = λ0(t) exp ∑ (βizi) (2) i = 1 Figure 2. Box and whisker plots of the number of return visits to a plant before landing on a different plant (18 wasps). The median num- where h(t,z) denotes the observed hazard rate, λ0(t) ber of returns was 0 in all cases. The box plots indicate the mean (dot- the baseline hazard, t is the time since the last renewal ted line), 75th percentile (top of box), 90th percentile (whisker) and point, and β , …β are the relative contributions of the the 95th percentile (dot). The percentage values below the box refer 1 p to how often wasps returned to land on the same plant one or more covariates. The form of λ (t) is left unspecified. λ (t) 0 0 times after taking flight. The sample sizes indicate the number of ini- and β , …β are estimated by likelihood maximization tial visits to plants at each host density. 1 p Optimal patch-leaving behavior: A case study using the parasitoid Cotesia rubecula 687

Figure 3. Log-survivor plots for flight durations by C. rubecula. Be- havioral durations that are exponentially distributed will be a straight line. Concave up survivor functions indicate a mixture of exponential distributions. The bold solid line is the observed survivor function, the thin solid lines are 95% confidence limits and the dotted line is the ex- pected survivor function under an exponential distribution. The fre- quency histograms show the number of flights of each duration: (a) all flights; (b) flights within one grid cell.; (c) flights including at least one grid cell change. was drastically improved by breaking the distribution Table 1. Distribution of ovipositions on plants with differ- into two components. For within grid cell flights, devi- ent host densities. Entries in bold highlight cases where wasps ations from an exponential distribution occur primarily laid more eggs than there were hosts available, and superpar- in very long lasting flights (< 2% of 589 flights) and this asitism certainly occurred. excess of long flights could represent true patch depar- Host density Number of ovipositions tures misclassified as within-patch flights by our crite- 0 1 2 3 4 9 rion. For between grid cell flights the deviations are pri- marily in very brief flights (< 16% of 178 flights) and this 1 26 6 1 0 0 0 excess could be true within-patch flights misclassified as 2 54 8 3 0 0 0 5 98 16 10 4 1 2 patch-leaving events. The overall percentage of misclas- sification of patch leaving or staying was small (< 5% of 767 flights), so a wasp was considered to have left a patch as soon as she crossed a grid cell line. available, 30% of all ovipositions resulted in superpar- asitism (The percentage of hosts that contained 1, 2, 3, Oviposition behavior or 4 eggs per host was 70, 19, 6 and 5%, respectively). C. rubecula often left plants without finding hosts, This suggests that some hosts were more attractive, eas- and also superparasitized hosts during the experiment. ier to detect or more accessible than others. Wasps left a plant without encountering a host 78% of the time. Female wasps sometimes laid more than one Leaving tendency egg at higher host densities, however, there was no sig- The effect of (1) host density, (2) oviposition rate, nificant effect of host density on the relative frequency and (3) whether or not the wasp was searching on the of 0, 1, or 2 or more ovipositions (test of independence, first patch on leaving tendency of C. rubecula were es- G = 6.55, P = 0.47, d.f. = 7; Table 1). Even though most timated with a Cox’s proportional hazards model. wasps did not lay more eggs than there were hosts The proportionality assumption was fulfilled for all co 688 Tenhumberg et al. in Journal of Animal Ecology 70 (2001)

Table 2. Summary of the model selection procedure for the Cox’s proportional hazards model Initial model Deviance ΔD d.f. Covariate tested P Baseline hazard only 611.6 12.4 3 Density, oviposition rate, and first patch < 0.0001 6.9 1 Density 0.0002 3.5 1 Oviposition rate 0.008 1.6 1 First patch 0.08 Baseline + Density 604.7 3.6 1 Oviposition rate 0.009 2.2 1 First patch 0.037 Baseline + Density 601.1 2 1 First Patch 0.042 + Oviposition rate

Table 3. Final coefficients for each of the three covariates predators and parasitoids in controlling pest popula- β SE (β) z P tions. In this study, the influence of oviposition and host density on the patch leaving behavior of C. rubecula was Host density −0.1995 0.0509 −3.92 < 0.0001 examined. There is a large body of evidence amassed Oviposition (rate/min) 0.0678 0.0182 3.74 0.0002 that both factors strongly influence the foraging behav- 1st Patch −0.5983 0.3180 −1.88 0.06 ior of parasitoids in the laboratory. This study is unique because our experiments were set up in the field. In ad- dition, our study highlights the importance of correctly variates (host density: χ2 = 0.05688, P = 0.8115; ovipo- defining patch-leaving behavior and identifies acclima- sition: χ2 = 0.05141, P = 0.8206; 1st patch: χ2 = 0.86404, tization behavior in C. rubecula for the first time. P = 0.3526). The results are summarized in Tables 2 and Field observations of behavior are important in eluci- 3. A decreasing leaving tendency is indicated by a nega- dating interactions between parasitoids and their hosts. tive β-value resulting in longer patch times. Even though there are difficulties associated with track- ing small, freely flying insects, observations in the field 1. Host density had a negative effect on leaving ten- can reveal how changes in weather, the seasonal charac- dency of C. rubecula (negative β-value). For ex- teristics of plants, and the availability of hosts affect the ample, the leaving tendency was 20% smaller foraging behavior and success of parasitic wasps (Casas [exp(−0.1995) = 0.8] on plants with one host com- et al. 1993). Also, behavior observed in laboratory arenas pared to plants with no host. For wasps that left a may not reflect what happens in the field. For example, plant without laying an egg, this resulted in longer the braconid wasp Diaeretiella rapae (McIntosh) responds average patch residence times on plants with higher to odors associated with brassicaceous host plants in a host densities (33, 48, 95 and 115 s on plants with 0, 1, Y-tube olfactometer (Read, Feeney & Root 1970). How- 2 and 5 hosts, respectively). ever, this was not observed in field experiments, pos- 2. The effect of oviposition rate was opposite to that of sibly because the laboratory arena did not take into host density (positive β-value). So, if wasps had two account the distance over which attraction occurs (Shee- ovipositions per minute the leaving tendency in- han & Shelton 1989). creased by 7% compared to one oviposition per min- ute [exp (0.0678) = 1·07]. Optimal patch leaving 3. Whether or not a wasp was in the first patch (first patch covariate) did not significantly reduce the de- Optimal foraging theory assumes that an animal’s viance on its own, but was a marginal contributor behavior is shaped by natural selection and, as a con- when the other two covariates were included. The sequence, may have evolved to follow certain leaving tendency of wasps during the first patch visit rules of thumb that result in behavior close to the op- was 45% smaller [exp(−0.5983)] than the leaving ten- timal behavior. This paper focuses on the role of host dency on patches visited later. density, and oviposition or oviposition rate on the patch-leaving behavior of C. rubecula. Our results sug- Under the assumption that all flights, either within or gest that the initial leaving tendency of C. rubecula de- between grid cells, are patch-leaving events, there was creases with increasing host density. Wasps may es- no significant influence of host density on leaving ten- timate the host density by means of the kairomone dency (Likelihood Ratio statistic 0.73, d.f. = 1, P = 0.39). concentration, which has been demonstrated for other parasitoid species (Waage 1978, 1979; Galis & van Al- phen 1981; Dicke et al. 1985; Geervliet et al. 1998; Thom- Discussion sen 1999). The effect of host density on the leaving tendency broadly follows from the marginal value the- Studying patch leaving behavior of parasitoids is im- orem and general rate-maximizing theory (Charnov portant because it improves our understanding of the 1976). The higher the host density, the higher is the po- underlying mechanisms of behavior, and the impact of tential offspring production in the current patch rela- Optimal patch-leaving behavior: A case study using the parasitoid Cotesia rubecula 689 tive to the environmental average, consequently wasps The results presented in this paper contradict recently should exploit patches with higher host densities more published experiments on the patch leaving behavior of thoroughly. C. rubecula at the scale of a single leaf (Vos, Hemerik & Waage (1979) proposed a model connecting the influ- Vet Louise 1998). The authors report a lower tendency to ence of host density and oviposition. He suggested that leave infested leaves compared to uninfested leaves, but a parasitoid leaves a patch when her “responsiveness” to there was no difference in the tendency to leave leaves the patch drops below a critical value. The leaving ten- of different host densities. Host encounters increased the dency calculated in this paper would be the inverse of the patch residence time suggesting an incremental mecha- responsiveness. The initial responsiveness is determined nism. It is possible that there are genetic differences in by the concentration of kairomones in the patch, i.e. the patch leaving rules between wasps from Australian and parasitoid’s estimate of the host density (patch quality). If European populations. Differences between strains in nothing else happens the wasp leaves after a fixed giving- patch leaving responses following oviposition have been up time. If a host is encountered the responsiveness can reported for the parasitoid Venturia canscens (Graven- either increase (incremental mechanism; Waage 1979) or horst) (Waage 1979; Driessen et al. 1995). decrease (count down mechanism; Driessen et al. 1995). If the estimate of patch quality is poor, the incremental Important considerations for the design of foraging mechanism will ensure that a patch with lots of hosts is experiments not abandoned too early or that females do not waste too In our study we identified two factors influencing the much time on low quality patches. Alternatively, if a for- interpretation of the results: (1) definition of patch leav- ager’s estimate of patch quality is very good, e.g. because ing, and (2) acclimatization behavior. We discuss each of hosts are uniformly distributed among patches (Iwasa, these factors in turn. Higashi & Yamamura 1981; Driessen et al. 1995), a dec- Correctly identifying the cut-off point for a patch visit remental mechanism is more advantageous. In the litera- was crucial for detecting the effect of host density on the ture, there is evidence for both mechanism (see review in patch-leaving behavior predicted by optimal foraging Driessen & Bernstein 1999). theory. This highlights the importance of correctly defin- C. rubecula females frequently left patches after lay- ing patch-leaving behavior. According to Waage (1978, ing a single egg, and a high oviposition rate increased 1979) crossing a patch boundary elicits a change in be- the leaving tendency. Both results are consistent with havior. In the simplest case transition to leaving a patch a countdown mechanism, and qualitatively match the is identified by taking flight. Recognizing a change in be- predictions made by Tenhumberg et al. (2001). Both the havior is more difficult for animals, such as C. rubecula host distribution and a high risk of self-superparasitism that fly both within and between patches. We used log- can promote a countdown mechanism. In the field, cab- survivor curves to test whether our distinction between bage plants rarely contain more than two hosts (Har- within and between patch flights based on flight distance court 1961; Kobayashi 1966; Jones 1977). On plants with was correct. Although our distinction was not perfect, the two hosts, females have a 50% chance that the second percentage of misclassifications was low. A wasp’s patch host encountered already contains an egg. As C. rubec- leaving behavior was consistent with optimal foraging ula seem not to discriminate between healthy and para- theory only when departing flights were distinguished sitized hosts, females run a high risk of superparasitism from flights within the same patch. if they do not leave after the first oviposition. P. rapae We found that C. rubecula needs time to settle in a larvae tend to avoid each other by moving to a differ- new environment. This acclimatization behavior is ex- ent leaf or to a distant area of the same leaf. So, for two pressed in an extended patch time resulting in twice ovipositions to occur very close together in time (high as many ovipositions in the first patch when compared oviposition rate), the wasp most likely encountered the to subsequent patches. This results in correspondingly same host twice. higher superparasitism rates. The acclimatization be- Tenhumberg et al. (2001) constructed a stochastic dy- havior did not interfere with the detection of the effects namic programming model of the patch leaving behav- of oviposition rate and host density. However, for other ior of C. rubecula. The influence of the number of eggs questions, such as addressing the efficiency of parasit- laid in the current patch, and the distribution of hosts oids as biocontrol agents, it might be better to exclude among plants was included in the model. This model any acclimatization behavior from the experiment. For predicted both a positive response to host density and applied research questions it is important to know the a countdown response to oviposition as a consequence exploitation rate or what percentage of hosts escape par- of the basic biology of the system. The assumption that asitism. Both parameters will be influenced by acclima- females are unable to discriminate between parasitized tization behavior. An unusually long patch residence and healthy hosts is crucial for these predictions. Rosen- time will reduce the percentage of hosts escaping par- heim & Mangel (1994) demonstrated the sufficiency of asitism, as well as the foraging efficiency of parasitoids the cost of self-superparasitism to promote early depar- as they waste more time superparasitizing, or inspect- ture from incompletely exploited patches. ing and rejecting already parasitized hosts. 690 Tenhumberg et al. in Journal of Animal Ecology 70 (2001)

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