Behav Ecol Sociobiol (2010) 64:627–637 DOI 10.1007/s00265-009-0880-9
ORIGINAL PAPER
Dynamic response to danger in a parasitoid wasp Bernard D. Roitberg & Karen Zimmermann & Thomas S. Hoffmeister
Received: 21 August 2009 / Revised: 23 October 2009 / Accepted: 28 October 2009 / Published online: 18 November 2009 # Springer-Verlag 2009
Abstract Despite the multitude of work on patch time allocation and the huge number of studies on patch choice in the face of danger, the patch leaving response of foragers perceiving cues of danger has received relatively little attention. We investigated the response of parasitoid insects to cues of danger both theoretically and experimentally. Using stochastic dynamic theory, we demonstrate that patch-leaving responses in response to the detection of danger should be seen as a dynamic decision that depends upon reproductive options on the current host patch and on alternative patches that might be found after leaving the current patch. Our theory predicts a sigmoidal response curve of parasitoids, where they should accept the danger and stay on the patch when patch quality is high and should increasingly avoid the risk and emigrate from the patch with
Communicated by J. Lindström B. D. Roitberg Evolutionary and Behavioral Ecology Research Group, Department of Biology, Simon Fraser University, Burnaby, BC V5A 1S6, Canada K. Zimmermann : T. S. Hoffmeister Institute of Ecology and Evolutionary Biology, FB 2, University of Bremen, 28359 Bremen, Germany B. D. Roitberg (*) Behavioral Ecology Research Group, Department of Biosciences, Simon Fraser University, Burnaby, BC, Canada e-mail:
[email protected]
decreasing patch quality and decreasing costs of traveling to an alternative host patch. Experiments with females of the drosophilid parasitoid Asobara tabida that were exposed to a puff of formic acid (a danger cue) at different times through their patch exploitation confirmed the theoretical predictions (i.e., a sigmoid response curve); however, the predicted curve was significantly steeper than observed. We discuss the impact of dynamic patch-exit decisions of individual foragers on population and community dynamics. Keywords Patch leaving . State-dependent model . Fear . Bayesian updating Over the past 25 years, two concepts have captured the attention of many behavioral ecologists: (1) patch time allocation and (2) risk of predation (Krebs and Davies 1993). Surprisingly, however, few studies have focused on the risk of predation on patch time allocation, and fewer still have developed explicit theory to deal with this problem, but see Nonacs (2001). An exception is the elegant work of Brown and colleagues on desert rodent systems (e.g., Kotler et al. 2004) where specific predictions regarding giving up densities of food items have been derived and tested. In contrast, two recent reviews on patch-exit decisions in insect parasitoids by van Alphen et al. (2003) and Wajnberg (2006) pay little attention to mortality risks. This lack of integration of the two aforementioned concepts is unfortunate because (1) parasitoids are excellent model systems for studying patch time allocation (Waage 1978), (2) these small, mostly defenseless creatures must forage under considerable
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predation risk (Rosenheim et al. 1995; Heimpel et al. 1997; Brodeur and Rosenheim 2000; Meyhofer and Klug 2002), and (3) foraging decisions by parasitoids lead directly to reproduction; thus, there is a tight relationship between such decisions and fitness (Roitberg et al. 2001). In this paper, we attempt to rectify this shortcoming by developing and testing foraging models for parasitoids on depleting patches where predators may lurk. Parasitoids are unique foragers in that they can transform their prey (host) items from good (healthy) to poor (parasitized) through their actions but do not remove such prey from patches as they exploit them. Thus, when these hosts are re-encountered, parasitoids must choose to accept (superparasitize) or reject them. Furthermore, in terms of patch depletion, as the density of healthy hosts decreases, the density of alreadyparasitized hosts increases in a directly inverse manner, meaning that not only do parasitoids spend more and more time searching for individual good hosts but they also spend more and more time encountering (in general) poor quality, already-parasitized hosts. A variety of mechanisms have been proposed for how parasitoids might deal with this issue, but again, risk of predation is generally not considered in such models (van Alphen et al. 2003; Wajnberg 2006). Risk of predation may be considered at two or more levels. First, there is the overall risk of early mortality that can shape parasitoid life history evolution (Rosenheim 1996; Sevenster et al. 1998; Ellers et al. 2000). Second, the actual risk at a specific patch may vary over time and space; thus, parasitoids must estimate local risk just as they must estimate local patch value. Over time, presence or absence of predator-related cues can provide information of inherent local danger (Houtman and Dill 1998). It is this latter issue that we consider, i.e., how do parasitoids adjust patch time allocation decisions as they acquire information regarding patch quality and danger in an uncertain world. This is a topic that has rarely been addressed by behavioral ecologists (e.g., Wajnberg 2006).
The theory Consider a world comprised of patches that harbor eight-host larvae; this density was chosen because the experiments that follow employed eight-larva patches. However, our conclusions do not depend upon that particular density. Each of those patches may also harbor predators such that, on average, the probability of a host-foraging parasitoid suffering mortality during a single time period, t, is µf(d).
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The parasitoid’s environment is characterized by the patch she forages in from both its level of danger, d, and the number of healthy hosts it harbors or quality, q, for which she searches in a random fashion. When a parasitoid enters a new patch, we assume that she is able to accurately determine host density, q, in that patch. We assume that such patches have not been previously exploited. However, over time, hosts will become parasitized, and we assume that (1) the parasitoid cannot determine whether a given host has already been parasitized until she has handled it and assessed it for a host-marking pheromone (Hoffmeister and Roitberg 2002) and (2) she will accurately track the relative densities of healthy and parasitized hosts. Thus, at the outset, the density of healthy larvae, q ¼ q^ ¼ 8. In addition, upon entering the patch, the estimate of the risk of predation µ is a function of the danger level at that patch, which we define as d. Upon entry, the parasitoid bases its estimate of danger on the global probability of predator presence, d^ (Table 1). As the parasitoid searches for hosts, at each time step, t, she must update her estimate of patch quality and danger and must decide whether to abandon this patch or stay. In fact, there are several decisions a host-foraging wasp must make. First, if the wasp chooses to abandon the patch,
Table 1 Explanation of symbols used in the stochastic dynamic programming model Symbol Meaning λ π d^ d
q^ q η wh wp mt tt to μo(d)
μf(d)
Probability of encountering a host, set at 0.065 Probability of detecting a predator Global probability of predator presence within the habitat=0.2 Estimated danger of predator presence, works with a linear operator, with +=perceiving predator cue=d-prior×0.1+dpred×0.9, with −=perceiving no predator cue=d-prior× 0.5+ d^ ×0.5 Initial patch quality=initial number of hosts in the patch=8 Current patch quality=number of healthy hosts in the patch Probability of an encountered host to be healthy Fitness return from oviposition into a healthy host=0.9 Fitness return from oviposition into a parasitized host=0.05 Per unit time mortality rate while traveling=0.05 Travel time between patches=50 time units Handling time when ovipositing=3 time units Per unit time mortality rate while ovipositing, function of d moðdÞ ¼ expðd bÞwith default β=2=mortality factor, making mortality rate higher while ovipositing than while searching Per unit time mortality rate while of a host-foraging parasitoid, function of d mf ðdÞ ¼ expðd Þ
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she will travel for some time tt before arriving at a new patch. The payoff from arriving at this new patch must be discounted by the probability of surviving a patch-search flight ð1 mt Þtt . The danger and host quality upon arrival at ^ the new patch equals the global average d^ and q, respectively. If a wasp chooses to remain at the current patch, she commences searching and at the same time scans the environment for cues of predator presence (assuming the cues involved in host search and predator scanning are independent). If this choice is made, several events can unfold with different probabilities. First, the parasitoid may simultaneously encounter a host with probability λ and detect the presence of a predator with probability π. If so, she will update her estimate of survival probability on the patch [1−µf(d+)] and must also decide whether to attack the host or not. If she attacks the host, she is especially vulnerable against predator attack, since escape is impossible if attacked while ovipositing, whereas the likelihood of attack is a function of d yielding, µo(d). Upon attack, the wasp detects the quality of the host and decides whether to accept that host for oviposition or whether to reject the host. If she encounters a healthy host with probability ηq, she will accept it for oviposition and receive a fitness increment wh =0.9 (essentially the probability that that an offspring will survive to become an adult), and the patch quality estimate decreases by 1. Finally, we assume that there is a time cost, to, associated with oviposition in a host. Thus, time advances to units and qðt þ to Þ ¼ qðtÞ 1. A parasitoid may encounter an already parasitized host instead of a healthy one as described above (1 −ηq). If she accepts a previously parasitized host (i.e., the host already harbors one or more eggs), she gets a small fitness increment, wp =0.05, due to larval competition that will ensue within that host. If she rejects that host, she receives no fitness increment and time advances one unit. The parasitoid can choose not to attack; when danger from oviposition is very high, it may pay to wait until danger has subsided. Under that circumstance, the host will escape, and the probability of host detection remains at the patch average λ. Second, the parasitoid may detect a host but no predator. If so, she updates (decreases) her estimate of danger, given some prior d(t). She then must decide whether to attack that host or not, and everything is as above except for the new lower danger estimate. Third, the parasitoid may not detect a host but might detect predator presence. If so, she updates (increases) her danger estimate and time moves one unit.
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Fourth, the parasitoid may detect neither host nor predator and updates (decreases) her danger estimate, and as such, time moves on one unit. For the Bayesian updating of the danger estimate, we assume that a parasitoid enters a patch with a global ^ Danger level d estimate of danger level defined as d. relates to a probability of getting killed from predator attack per unit time and depending upon activity (foraging vs. ovipositing). When cues of predators become available, the estimate is updated in a way that this most recent estimate is most important in a weighted linear operator equation (see Mangel 2006; Roitberg and Mangel 2010). Similarly, when no cue is perceived, the estimated danger value is decreased, yet at a lower rate than the increase. This response pattern is typical for an excitation response (Cooperband and Allan 2009). If predator presence is perceived, then posterior estimate=0.1×prior+0.9×danger level at predator presence; if no predator presence is perceived, then posterior ^ This estimate = 0.5 × prior + 0.5 × global danger level d. equation generates a rather steep predator–presence decay curve; however, we do not expect the qualitative nature of our predictions to change, though they might generate parasitoids that remain in patches longer than expected in the absence of predator cues if patches are estimated to be safe after just a few sequences of foraging under such circumstances. Taken together, the scenarios above can be constructed as a discrete time state variable model (Clark and Mangel 2000) where the two state variables are the quality of the patch, indexed by healthy host density, q, and the parasitoid’s danger information state (d) regarding its estimate of survival (1−µ). There are two stochastic elements in the model based on the likelihood of encountering a host, λ, and the likelihood of detecting a predator, π. Below is the state variable model. A list of the parameters and their values is shown in Table 1. Notice the five max terms: All five indicate that a decision should be made that maximizes expected future lifetime reproductive success. The first decision (line 1 vs. the sum of the remaining events) refers to the leave vs. stay option, the second (sum of lines 2–4 vs. line 5) refers to attack vs. desist attacking a host of unknown quality decision, while the third max (line 3 vs. 4) refers to ovipositing in vs. desist ovipositing in an alreadyparasitized host. Decisions 4 and 5 are duplicates of decisions 2 and 3 but are applicable to when no predator cues have been encountered as opposed to a current encounter with a predator cue; thus, the new value information state is d− and not d+ as above representing increase and decrease in the posterior value, respectively. Lines 10 and 11 refer to the possibility that a predator cue
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is or is not encountered when a host is not encountered; thus, there are no decisions to be made regarding the
attack on a host. However, once again, danger estimates are again updated.
2n
o 3 ^ q; ^ t þ tt ; T ð1 mt Þtt F d; ; 9 8n 7 6 o to 7 6 > > > > 7 6 hq wh þ 1 moðdÞ F ðd þ ; q 1; t þ to ; T Þ þ > > > > 7 6 > 8 9 > to > > 7 6 > > þ = > þ : ; 7 6 > > ð ; q; t þ 1; T Þ 1 m F d > > f ðdÞ 7 6 > > > > 7 6 > > > > 7 6 þ ; : 1m 7 6 f ðdÞ F ðd ; q; t þ 1; T Þ 9 8n 7 6 o to 7 6 > > F ðd; q; t; T Þ ¼ max6 > > 7 h w þ 1 m F ð d ; q 1; t þ t ; T Þ þ o > > q h oðdÞ > > 7 6 > > 8 9 > > 7 6 t o > > = > 7 6 : ; > > 1 mf ðdÞ F ðd ; q; t þ 1; T Þ > > 7 6 > > > > 7 6 > > > > 6 ; 7 : 1m 7 6 f ðdÞ F ðd ; q; t þ 1; T Þ 7 6 7 6 þ 7 6 ðð1 lÞp Þ 1 mf ðdÞ F ðd ; q; t þ 1; T Þþ 5 4 ðð1 lÞð1 p ÞÞ 1 mf ðdÞ F ðd ; q; t þ 1; T Þ
The model was solved numerically via backwards induction (Clark and Mangel 2000) with each time unit equivalent to 7 s with the maximum time set at 1,225 s. For each combination of patch quality q and danger level d, we generated a decision matrix holding the optimal decision whether to stay or leave the patch. We chose a range of values that seemed realistic and general, though we readily admit that we do not possess hard data to back up all of these choices. For example, we chose, as the default travel time, the minimum time required such that no wasps would emigrate in the absence of a predator cue; this matches well with our observations on our experimental animals (see below). Note, however, that based upon an informal sensitivity analysis, altering the values does not affect the major conclusion that response to predator cues should depend upon the value of the current patch, the current danger at that patch, and the cost of seeking a new patch. Figure 1 shows how those three factors interact at time=1 when the solutions had long since converged for a given set of parameter values. Several insights emerge from inspection of this figure. First, with decreasing travel costs and increasing danger on the patch, wasps are predicted to only accept the risk on the patch and continue foraging at increasingly higher patch qualities. Consequently, they are predicted to leave patches for a wide range of travel costs and danger levels when patch quality is low. On the other hand, at low travel cost to alternative patches, even moderate levels of estimated danger should be sufficient to make the parasitoids leave patches that have been exploited to 50% of their original value, whereas at high
danger levels, we expect parasitoids to emigrate at high rates almost regardless of the patch quality. While Fig. 1 shows the range of responses of foraging wasps that could be expected, it is however not clear what
Fig. 1 Threshold surface for the likelihood to leave a patch of a given quality (number of healthy hosts still available on an eight-host patch) as a function of perceived danger level and the costs to reach alternate patches. Parasitoids facing combinations of conditions above the surface are predicted to leave the patch immediately, whereas they are predicted to remain on the patch and continue foraging for hosts facing conditions below the surface. Predictions are derived from our state-dependent backward induction model. See Table 1 for default values used
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patterns of patch allocation could be expected at the wasp population level. To gain more insights into the time allocation issue, we developed a simulation model for wasps that were assumed to “know” the theory and then compared those results with data collected from natural parasitoids under experimental conditions. The simulation proceeded as follows: We built a forward iteration as described by Clark and Mangel (2000). The simulation stochastically followed individual parasitoids as they foraged in eight-host patches and drew behavioral responses to the patch from the output from the state variable model as described above. The simulations, which were designed to match the laboratory experiments described below, proceeded as follows. One hundred parasitoids were individually released on eighthost larva patches and allowed to forage for prey hidden in the patch medium. Each time period, a random number was drawn to determine if a host was encountered. Encounter rate was set at 0.065 encounters per time unit to produce a functional response that mimicked those of the real wasps as well as the observed rate of patch exits that occurred prior to encounters with predator cues. Each time period, the parasitoid first drew the decision to stay or leave from the state variable model, and if it chose to stay, a random number was drawn to determine if an encounter with a host occurred. If so, a further weighted random number was drawn to determine if the host was healthy or already parasitized; weighting was determined by the ratio of healthy to parasitized hosts. Again, the decision to superparasitize or reject was taken from the state variable model. Finally, at a predetermined time of 1, 5, 10, 15 or 20 min from the start of a replicate, the computer wasp was exposed to a danger cue and observed for its response i.e., keep foraging or leave the patch. The replicate was terminated thereafter. In total, we ran 500 replicates, 100 for each of the five predator-exposure times. Figure 2 shows a sigmoidal response curve from our simulated parasitoids: If the danger cue is perceived after a short time of foraging (between 1 and 5 min) and thus at high residual patch quality, the large majority of wasps will stay in the patch and continue foraging. In contrast, the vast majority of wasps will leave the patch if the danger cue is perceived after 15 or 20 min of foraging time. After 10 min of foraging time, almost exactly 50% of the wasps are predicted to leave the patch in response to the perception of a danger cue.
Lab experiments We used the larval parasitoid Asobara tabida as our model species for our experiments. Females of this parasitoid attack several drosophilid species on a variety of decaying
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Fig. 2 Escape response from patches of simulated wasps (circles and solid line; thin solid lines represent the 95% confidence interval to the curve) in response to a danger cue presented to them at different times of foraging in the patch (circles). For comparison of slope and inflection point, the response curve ±95% confidence interval of live wasps from our experiment (see Fig. 4 for details) is given here as well (dash dotted line)
plant substrates in nature (Janssen et al. 1988) by laying single eggs into the body cavity of their hosts (Carton et al. 1986). The A. tabida population was maintained on 2–3-day-old Drosophila subobscura larvae that were placed in a 125-ml plastic vial containing artificial diet, consisting of agar, sugar, apple sauce, brewer’s yeast, cornmeal, water, and Nipagin® as fungicide at 18±1°C, 70% relative humidity, and 16-h photophase. Two to four female and one to two male A. tabida wasps that were at least 5 days old were added to the vial. Newly emerged parasitoids were removed and placed into plastic vials with agar that were sealed off by a foam plug and contained a drop of honey as food. Patches for experiments were prepared in 4.3-cm Petri dishes containing a thin layer of agar. Forty micro liters of a viscous yeast suspension (3.75 g yeast in 3 ml fresh water) were spread out as circular patch of 2.5-cm diameter. Eight second instar D. subobscura larvae were introduced to the patch about 20 min before an experimental trial started. This ensured that the larvae had moved across the patch and had left behind kairomone, i.e., chemical substances that inform a foraging parasitoid about the presence of host larvae (Nordlund 1981). To provide a putative danger cue to the searching parasitoid, we used a setup that allowed us to deliver a puff of formic acid at a predetermined time to the experimental patch. Formic acid may either act as an irritating substance per se or might simulate the presence of ants, which are common predators of parasitoids in nature (Völkl 1992; Heimpel et al. 1997). Note, however, that
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some specialized secondary parasitoids are chemically defended against ants, but the majority of primary parasitoids are not (Hubner and Dettner 2000). Puffs of formic acid were delivered with a device consisting of two flexible Nalgene PVC tubes (34.5 and 59.5 cm), a rubber stopper with two holes, a syringe (20 ml), 500 μl of formic acid, a glass flask (height, 6.5 cm and diameter, 2.7 cm) and cotton wool (up to a height of 1.5 cm in the flask). Cotton wool was placed into the flask, and the formic acid was added. Each of the two tubes was inserted into the stopper sealing the flask. One tube was connected to the syringe that was used to push a defined volume of air through the flask containing formic acid, the other tube’s ending placed at 7 cm distance from the Petri dish. To deliver the danger cue to the parasitoid, 20 ml of air was pushed though the flask via the syringe, and thus a puff of air saturated with formic acid contacted the Petri dish with the foraging parasitoid. While our theory was laid out to be very general wherein cues of danger might repeatedly be sensed by a foraging animal in a variety of sequences, we restrict our experiment to the simple case where such cues are sensed only at a single predetermined time in any particular replicate. All experimental trials took place in a walk-in chamber at 18°C, 70% humidity, and 16 h photophase. One day prior to an experimental trial, the wasps were allowed to oviposit in hosts for 0.5 h to gain experience. Prior to each trial, the wasps were stored in gelatin capsules for at least 5 min and then introduced individually onto the patch containing eight healthy host larvae. We chose that host density because it is known that A. tabida usually searches such patches well beyond the approximately 20 min maximum period we employed in this experiment (e.g., >2,000 s on patches with six or eight hosts; van Alphen and Galis 1983; Thiel and Hoffmeister 2009). Each female parasitoid was allowed to forage freely until at a predetermined time we delivered the danger cue by a puff of formic acid onto the patch as described above. Note that we only delivered the cue if a female was actively foraging on the patch at that time instant. Otherwise, we either waited until the female started searching for hosts again or stopped the experimental trial. This criterion allowed us to disentangle patch-qualitydependent patch-leaving behavior from parasitoid responses to our experimental cue. At the point of cue delivery, we noted whether the parasitoid would either immediately leave the patch or would continue foraging. Each wasp was repeatedly tested in five separate trials, each time employing a different time at which the danger cue was delivered, namely, after 1, 5, 10, 15, and 20 min into searching the patch, respectively. The order of the treatment times was randomized for each wasp, and only three treatments per day per wasp were carried out with at least half an hour in between experimental trials. If an oviposition occurred at the specified time or if the parasitoid was outside the patch,
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deliverance of the danger cue was postponed until the wasp commenced searching again. The response to the treatment as well as the exact time of presentation of the cue was recorded for analysis. Between the experiments, the wasps were stored solitarily in a walk-in chamber. All together, 545 replicates were generated; however, in some instances, the wasps stopped searching in one of their trials before the planned time of cue delivery. This happened in four, six, six, five, and six cases in experimental trials with cue delivery times of approximately 1, 5, 10, 15, and 20 min, respectively (i.e., 5% of experimental trials), again suggesting that patch leaving due to patch depletion per se is not a concern in our experiments. All wasps for which we received such censored data were eliminated from the statistical analysis that was consequently based on 490 experimental trials. An important component of our theory is patch depletion. To obtain such information as a function of foraging time, for a subset of wasps, the timing of each oviposition was noted using The Observer ® software until the experimental presentation of the danger cue.
Data analysis To analyze the patch depletion by A. tabida wasps, a ax Holling type 2 (y ¼ 1þbx ) functional response curve was fitted to the data as nonlinear regression in Sigma-Plot for the cumulative ovipositions individual wasps achieved on a foraging patch. Based on these estimates, we calculated the marginal returns in time intervals of i = 50 s, i.e., axi axi1 y ¼ 1þbx 1þbx . i i1 The binary data obtained for the leaving response of parasitoids were analyzed by means of a generalized linear model (GLM) for binomially distributed data and logit link function that was combined with a general estimating equation (GEE) to correct for the fact that we repeatedly measured responses from the same individuals. Since it is most likely that the response of a parasitoid is influenced by its response to the last presentation with the cue, we used a first-order autoregressive correlation matrix. Moreover, we checked whether the sequence in which we presented the different treatment times to a female parasitoid influenced her response to the danger cue. Data points in which the parasitoid left the patch before we presented her with the danger cue were eliminated from the observation.
Experimental results Within the maximal experimental time, i.e., 1290s, A. tabida wasps detected and parasitized an average of about six of the eight D. subobscura larvae present in the
Behav Ecol Sociobiol (2010) 64:627–637 ax experimental patch (Fig. 3, dashed line, y ¼ 1þbx with a= 0.025±0.0036, P
