Many solitary parasitoids are able to discriminate between

Transcription

1 Behavioral Ecology Vol. 8 No. 2: State dependent superparasitism in a solitary parasitoid: egg load and survival Etienne Sirot, Henri Ploye, and Carlos Bernstein Biometrie, Genetique et Biologic des Populations, UMR CNRS 5558, Universite Lyon I, 43 Boulevard du 11 Novembre 1918, Villeurbanne cedex, France In solitary parasitoids, luperparasitism (the allocation of an egg to an already parasitized host) has a payoff, measured in offspring produced and costs, measured in eggs and time invested. Solitary parasitoids that are capable of host discrimination must adopt the strategy that ensures the best use of both their egg load and available lifetime. In this paper, we develop a statedependent model denning the optimal strategy of superparasitism for a solitary parasitoid species with overlapping generations. The fitness measure we use is based on the growth rate of the number of genotype copies. The model predicts that the tendency to superparasitize should increase as the egg load of the parasitoid increases, or as its life expectancy decreases. The model also predicts that under particular conditions wasps should show partial preferences for parasitized hosts. These predictions were tested with the parasitoid Vmturia cantsctns (Hymenoptera; Ichneumonidae). The tendency of the wasps to superparasitize in the presence of both healthy and parasitized hosts was correlated to egg load and access to food before the experiment A complementary experiment, where parasitized hosts were given sequentially to parasitoids, showed that V cantsctns exhibits partial preferences toward superparasitism. These experimental results and a previous work support the predictions of the model. Kty words: Hymtnoptero, Ichnnimonidae, optimal foraging, partial preference, solitary parasitoids, superparasitism, statedependence, Vtntvria cantsctns. [Behav Ecol 8: (1997)] Many solitary parasitoids are able to discriminate between healthy and parasitized hosts (Bakker et al., 1985; Salt, 1961; Volkl and Mackauer, 1990). However, under certain conditions, many of them superparasitize (Hubbard et al, 1987; Janssen, 1989). Theoretical studies showed that superparasitism may be an adaptive strategy, provided that a second or later laid egg still has a chance to result in an adult parasitoid (Hubbard et al., 1987; hvasa et al., 1984; Mangel 1989a, 1992; Roitberg et al, 1992; van Alphen and Visser, 1990; van der Hceven and Hemerik, 1990; Visser et al., 1992a; Weisser and Houston, 199S). The goal of the present work is to study the conditions in which a solitary parasitoid should resort to superparasitism, taking into account its egg load and survival probability. Separately, both are known to be of importance in opposition decisions in insects (Minkenberg et al, 1992; Roitberg et al., 1992). A solitary parasitoid encountering both healthy and parasitized hosts can be compared to a predator encountering two kinds of prey. Thus, its behavior can be studied using the classical diet model (MacArthur and Pianka, 1966). In this case, the currency used to define* the optimal strategy is the rate of offspring production (Janssen, 1989), inwcad of the rate of energy gain, as in the classical model (van Alphen and Visser, 1990). The rate of offspring production is an appropriate measure of fitness, since it is linked to the rate of increase of the representation of the genotype of the female, i.e., to the rate at which this genotype will spread in the population (Sibly, 1991). Models based in this approach lead to interesting and testable predictions, mainly concerning the influence of environmental conditions on the behavior of the parasitoid (see van Alphen and Visser, 1990). By including a representation of the physiological state of the parasitoids, modification of these "rate-maximizing models" (Charnov and Stephens, 1988; Speirs et al., 1991), and dynamic programming models (Mangel and dark, 1988) con- Received 5 September 1995; revued June ; accepted 1 July /97/J5.00 C 1997 International Society for Behavioral Ecology siderabty completed the theoretical knowledge of superparasitism. These models are rich in details and allow to draw predictions on how, throughout its life, the animal should modify its behavior in response to its internal state (e.g., Iwasa et al., 1984; Mangel, 1989a). These models generally use total lifetime progeny as currency. This quantity, ignores the rate at which animals reproduce. Hence, it is a good representation of the rate of spread of genotypes in the case of animals with discrete generations, where the rate of spread of a genotype is equivalent to the number of offspring per generation, but it is inadequate in the case of anirnalt with overlapping generations. In this case, an animal that maximizes its total number of offspring will not always outcompete the others. In many situations, and independently on whether the population is growing, decreasing or stable, it can be outmatched by one that produces fewer offspring but faster (Giske et al, 1993). In this paper we present an optimality model for parasitoids with overlapping generations, which uses a currency that takes into account all these considerations. This quantity is based on the rate of increase of the number of genotype copies, but it includes a representation of the physiological state of each of these copies and follows the evolution of the state of the foraging parasitoid. We also present the results of behavioral observations of superparasitism in Ventuna cantsctns (Hymenoptera: Ichneumonidae), a thelytokous solitary endoparasitoid of phydtid meal moths. Finally, we compare these experimental results and those of a recently published work (Fletcher et al, 1994) with the predictions of the model. A MODEL FOR THE INFLUENCE OF STATE- DEPENDENCE AND ENVmONMENTAL TRAITS ON THE DECISION OF SUPERPARASrnSM A solitary and pro-ovigenic parasitoid with egg load * is searching for hosts in a patch. We consider the behavior of die parasitoid during a short time interval AT. AT'u short compared to the life span of the parasitoid but large enough for one host encounter. The survival rate of the parasitoid for that

2 Sirot et al State dependent superpamitism 227 time interval, s, depends on its age, level of energy reserves, and environmental conditions. We assume that, within AT, the activity of the parasitoid does not influence s. On the patch, the parasitoid finds both healthy and parasitized hosts. We assume that the parasitoid can discriminate between them and that it can accept or reject already parasitized hosts. Unparasitized hosts are always accepted. The handling time for an oviposition in both kinds of hosts is <*. The rejection time for an already parasitized host is ^ The number of expected offspring from an oviposition in a healthy host is u and from an oviposition in a parasitized host is u As a consequence of the low probability of success of superparasitism, we consider that v < u (Bakker et al, 1985; Salt, 1961; Sirot E, unpublished; Visser et al, 1992b). The encounter rates with healthy and parasitized hosts are constant and represented by the parameters A 4 and A^ We assume that the parasitoid has full knowledge of all the relevant variables and parameters. The proportion of parasitized hosts acceptedforparasitism, together with the encounter rates with healthy and parasitized hosts (A* Ap determines the number of eggs bud per unit of time, c This parameter represents the strategy of the animal. The parameter p represents the proportion of parasitized hosts accepted that results in strategy r For given values of A t and A^ r will vary from r. (no superparasitism, p 0) to r M (full acceptance of superparasitism, p *= /). Intermediate values of r correspond to the acceptance for oviposition of an intermediate proportion of parasitized hosts. If the parasitoid adopts strategy r, then it will lay r eggs and produce R(r) offspring per unit of time. The parasitoid finds A t healthy hosts and Ap parasitized hosts per unit of searching time. For this reason, the number of eggs laid and the number of offspring produced in the interval AT arc (HoUing, 1959): and r(/>)a7*> X t -AT -AT (1) (2) fa.e) Figure 1 The contribution J(s,t) to the fitness of a genotypefora parasitoid a* a function of its egg load i and for two possible mortality rates s. The goal of the model is to find the strategy that nutimnm AF, Le., the strategy that leads to the highest rate of increase of the number of genotype copies, weighted by the contribution of each individual to tile fitness of the genotype. Remember that f 0 " 1 and go" 1- We can also take, without loss of generality, AT equal to unity. This gives: AF - fts.nj s + R(r) - f[s,t) The maximum value of the fitness measure is achieved when (daf)/(dr) «0. We calculate this quantity: 3AF df(s,e-r). dr(r) dr dr dr dfls,e-j)d(t-r) dr(r) df[s,*-r) { dr(r) m ' 3(<-r) dr 3r ' 3(«~r) dr Hence the optimal strategy r* should verify: d/(s,e-r>) d{* r) dr(r*) - 0. (5) dr Expressing p as a function of r in Equation 1 and replacing p by its value in Equation 2 yields: r(v(l +X 4 f 4 +A.,0 \ k u(t k t,)) +\ i (u-v) A(T)UI = r At the beginning of the interval AT and ignoring previously produced offspring, the number of genotype copies of a given parasitoid it go" 1 (the parasitoid itself). At the end of the interval, the mean number of copies is: s go + R(r) AT, which is the sum of the probability that the parasitoid will still be alive and die number of offspring produced. The change in die number of copies is * go + R(T) AT gg. However, not all genotype copies are phenotypically equivalent. The foraging parasitoid is older and carries fewer eggs than its offspring. On the other hand, the eggs just laid need time to develop into adult parasitoids. Hence, copies of the same genotype make different contributions to diefitness of the genotype. Let the relative contribution to fitness of an egg just laid be f 0 m 1 and fls,t) the relative contribution of die current foraging parasitoid at the beginning of 471 At die end of this interval, die contribution of the foraging parasitoid is f[s,+rat). Taking into account that the different copies of die same genotype make different contributions to itsfitness,the change in number of genotype copies during AT becomes: aj (3) AF " f{i,*+at) s go + J o R(r) AT -fis.t)go. (4) In Equation 5, [df(s,*-r)]/[d(* rj] represents the partial derivative of the function / for the variable t r at the point (s,e r). If the condition of Equation 5 cannot be fulfilled, then the matimnm value of Af is reached when ris such that the quantity \s{df[s,e-r)]/[d(t-r)] - [dr(r)]/(3r)\ takes the lowest possible value. To find the optimal strategy, we must compare the values of s[df[s,t-r)]/[d(t-r)] and [dr(r)]/(dr) for all the values of r between r. and r^. When s is constant, fit,t) is an increasing function of *, because an insect can always be expected to perform better when it has more eggs to lay. Consider two individuals with large and relatively dose egg loads («, and e^, their contribution to fitness {fls.t,) and/fr,**)) will be closer still. This is so because the probability of laying all their eggs before death and realize the potential difference, is low. In opposition, if t, and t 2 are low, the parasitoids are less likely to be limited in time and the difference in fitness will be larger. For these reasons, f[s,e) is a convex function of t. If the survival rate is high, the parasitoids become less time-limited and more egglimited, so the leveling-off o(f(s,t) because of time limitation is decreased. Figure 1 represents the function f(s,t). t[df(s,e T)]/[d(e r)] is obtained by taking the derivative of the function /at the point (s,t r). So, to find the optimal strategy for egg load t, we have to move backward on the egg load axis, from «to * r When we increase r (more eggs are laid per unit of time), we move further backward. The f(s,t) curve gets steeper, because/is convex. Hence, s[df(s,t r)]/ [d(t r)] is an increasing function of r. Figure 2 shows an ex-

3 228 Behavioral Ecology VoL 8 No. 2 higbegglbaaj Figure 2 The function s[dfls,t r)]/[d(t r)1 as a function of the egg laying rate rforafixedmortality rate s and two possible egg loads t. ample of s[dffs,e r)]/[d(e r)]. The precise shape is arbitrary; but this is immaterial for the predictions of the modcl From Equation 3: dr(r) r (v(l + k t t t + X.Q - \ t u(t t - Q) dr 1 + t,(x, + X 4 ) So [dr(r)]/(dr) is independent of r. Predictions of die model Figure S shows, superimposed, [dr(r)]/(dr) and different curves for s[df(s,e r)]/[d(e r)] depending on egg load e and survival rate s. According to the previous section, the optimal strategy for a parasitoid having t eggs and survival probability * is defined by the relative position of the (s[df[s,e r)]/ [d(e r)]) curve with respect to the {[dr(r)]/(dr)) line. If the former is above the latter, the parasitoid should adopt strategy r m (never superparasitize). If it is below, it should adopt strategy T U (always superparasitize). These conditions correspond to AF being maximum respectively at the point r m and r^. If the curves intersect, then die parasitoid should accept only a proportion of parasitized hosts, the egg-laying rate being indicated by the intersection point r* (the point where (BAF)/ <*r) - O). Prediction 1: When survival is high, parasitoids should never superparasitize, irrespective oftgg load. The parasitoid should wait "for the best opportunity to lay all its eggs. In that condition, the best strategy is to maximize the total number of offspring, at the expense of the instantaneous reproduction rate. Prediction 2: When survival is low, parasitoids should always superparasitize, irrespective of egg load. When the risk of dying is high, time limitation prevails. The parasitoids should never reject any host to have the best reproduction rate during their short life. Prediction 3: In intermediate survival conditions, tht tendency to superparasitize should increase with the egg load of the parasitoid. Intermediate conditions correspond to a balance between egg and time limitation. Parasitoids with a large egg complement should always superparasitize, those with few eggs left should avoid parasitized hosts, whereas insects with an intermediate egg load should accept only a proportion of already parasitized hosts. A TEST OF THE MODEL Materials»»wl methods Ftrst experiment The parasitoids. The parasitoids came from a strain of the solitary parasitic wasp V. canesctns (Gravenhorst), collected in Valbonne, South of France, in These animals were reared in a controlled environment (25 C, 75% RH) with the host Ephestia kuehmetta (Zeller) (Lepidoptera: Pyralidae), in a cage containing semolina (host food). Fifty newly emerged parasitoids were collected and isolated in glass tubes. Twentyfive parasitoids had a permanent access to food (50% diluted honey), 25 were deprived from food. All parasitoids were kept three days in these conditions before the experiment The expected life span after this three-day treatment is 16 (SE 1.01) days for the fed animals, assuming that they are fed for their whole fife, versus 2 (SE 0.08) for the unfed ones, assuming that they are neither fed after the experiment (Sirot, 1995). Experimental design. The first experiment was designed to test the influence of egg load on superparasitism in fed and unfed parasitoids. Host patches were made of Plexiglas discs of 14 cm diameter carved with 1 cm diameter and 3 mm deep circular cells. All the cells were filled with semolina and every alternate cell contained a single 21-day-old Ephestia kuehniella larva (third instar). All discs were covered with a tight gauze to prevent the larvae from leaving the cells. The discs were prepared three days before the experiment to obtain a good contamination of the semolina with the kairomone produced by the larvae (Driessen et al, 1995). Each disc contained 39 host larvae distributed in nine rows. On the day of the experiment, four rows of cells out of nine were covered with a strip of filter paper. This lets the host larvae underneath breath but protects them from the parasitoids' attacks. Each disc was placed in a plastic box containing 30 parasitoids, which immediately attacked the exposed larvae. The parasitoids and the strips of paper were removed after three hours. By that time, 21 larvae were parasitized (some might have being superparasitized), while 18 had been sheltered from the arracks. V. concerns recognizes already parasitized hosts through a chemical marker injected by the parasitoid at oviposidon (Hubbard et al, 1987). As it takes about 30 minutes before this marker becomes effective (Rogers, 1972), the discs were used for the experiment half an hour after the strip* were removed. A fed or unfed parasitoid was released on the disc and its behavior was recorded using a microcomputer. We recorded the moment the parasitoid started to probe with its ovipositor in a cell, as well as the duration of this action. After the attack of a larva, a particular movement of the abdomen ("cocking," Rogers, 1972) indicates the occurrence of an oviposition. The location of each cell indicated the nature of every attacked host (i.e., healthy or parasitized). Every parasitoid was allowed to wander through the (27 X 27 X 10 cm) experimental cage on or off the disc When it had spent six minutes outside the disc we ended the observations. This limit was fixed arbitrarily before the experiment was performed. At that time, the parasitoid was captured, killed and dissected. The total number of mature eggs in its oviducts were counted under a binocular microscope. During die experiment probing in cells containing healthy hosts did not always result in an oviposition, because probing in a cell was not always followed by the effective insertion of the ovipositor inside the host. The success of an attack depends on die balance between the ability of the larvae to escape and the skill of the foraging parasitoid. Let p, and p 0 represent the numbers of ovipositions and t, and tp are the times spent probing, in cells containing respectively parasit-

4 Sirot et al * Sate dependent nipeipirjiitum 229 % Determination of the optimal strategy (described by the egglaying rate r*). by the relithr position of the s[sj(i,*-r)]/ td(r-r)] curve and the [BR(r)]/ (BT) line, for different egg loads i and mortality rate* s. ized and healthy hosts. If we assume that healthy hosts are alway* accepted, then (pj/(tj, which represents the encounter rate of the parasitoid with healthy hosts, measures of its skill On the other hand, the ratio (/>,)/(';) depends both on the skill of the parasitoid and its willingness to accept parasitized hosts. This is why we have chosen SP» (/>,//,) /(po/1^ as a measure of the tendency of the parasitoid to superparasitize. Because of the very small probability of a parasitoid encountering and recognizing a self-parasitized host (the mean number of oppositions in healthy hosts was 6 and the mean duration of the trials IS minutes), we neglected the possibility of rejection of self-parasitized hosts (Rogers, 1972). Second txpenrnmt The model predicts that under certain circumstances, parasitoids should show partial preferences of parasitized hosts. An experiment was performed to test whether partial acceptance was common in V. canactns. Three hours before the experiment, 21-day-old larvae were parasitized once by animals of our stock cultures. Ten parasitoids originated from the same strain, prepared in the same way as the first experiment and fed ad libitum were used in this experiment They were individually offered, first one healthy host, then 10 of the onceparasitized ones. Each parasitoid was offered a new host only when it had inserted its ovipositor in the previous one. For each parasitoid, we recorded the sequence of oppositions and rejections of parasitized hosts. Resold First txperrnmt In Figure 4, the SP values are plotted as a function of the egg load of each parasitoid. Figure 4a shows the results for the unfed parasitoids, Figure 4b those for the fed animals. Egg toad values were calculated for each parasitoid by adding the number of eggs counted in the oviducts and the number of ovipositions performed. The variances of the SP values for the two categories of animals are significantly different (Bartlett test for homogeneity of variances, x*=8.67, 1 df, p < 0.01). For the unfed parasitoids, the results show no influence of the egg load of the parasitoid on the tendency to superparasttize [Spearman rank correlation (two-tailed): p -.53]. The feet that the mean value for the variable measuring superparasitism (1.04) does not differ significantly from 1 indicates that starving parasitoids accept as readily healthy and parasitized ho*u. On the other hand, for low and moderated egg loads, the

5 230 Behavioral Ecology Vol. 8 No. 2 A) TUOe 1 nperparasldim SP cfgload Parasitoid number Proportion of hosts superparasitized 0J 0.4 0J J J"* J Si B) Each parasitoid was offered successively 10 parasitized hosts. "Paranoid number" identifies arbitrarily the animals. The probabilities correspond to the significance of a Mann-Whitney test performed to observe whether the oripositions were concentrated in a given part of the sequence. SP egg load Figure 4 The measure of superparasitism SP as a function of the mature egg loads of the pararitoldi. (A) Panuitoid* isolated for three day* without access to food. (B) Parasitoids isolated for three days with access to food. parasitoids that had being fed show a strong, but not perfect, avoidance of superparasitism. For higher egg loads, the tendency to superparasitize increases with egg load. The overall increase of superparasitism with egg load is highly significant [Spearman rank correlation (one-tailed): p.002]. Second txperimmt Table 1 shows the proportion of the 10 parasitized hosts offered that were superparasitized. All the parasitoids accepted at least five hosts and rejected at least one. No influence of the individual parasitoids or of the rank of host attacked was detected in a logistic regression of acceptance of superparasitism as a function of these two factors (x* " 8.41, 9 df, p >.25 for the first factor and x* = 7-92,9 df, p >.5 for the latter). A Mann-Whitney i/teat on the ranks of host rejections within the sequence reveals no aggregation of rejections at the beginning or at the end of the sequence. These results exclude the possibility that, within the sequence, the parasitoids might have twitched between acceptance and rejection of parasitized hosts or that processes such as learning or sampling might have played an important role. DISCUSSION In this paper, we present a model that predicts that, in solitary and proovigenic parasitoids, the tendency to superparasitize should be influenced both by the life expectancy and the egg load of the parasitoid. An experiment with the parasitoid V. canesctns explores the influence of these factors on superparasitism. In our model, we use a currency for fitness that is based on the rate of increase of the number of genotype copies. Hence, our approach is appropriate for animal* with overlapping generations (Sibty, 1991). In fact, if the population is not stable, the rate of increase of the number of genotype copies should be discounted by the population growth rate (Giske et al., 1993), but this is not necessary here. By using the absolute growth rate as fitness measure, our approach takes into account that natural selection operates on genotypes competing within a population (Cooper, 1984). In this work, we did not consider host depletion. It could be easily introduced, by changing the encounter rates with healthy and parasitized hosts (A t and A^). This would change the position of the [dr(t)]/(dir) curve and the actual value at which different behaviors are optimal but not the overall outcome of the model. The model predicts that egg-limited parasitoids will spare eggs to use them later in healthy hosts, whereas time-limited animals will accept superparasitism. Comparable predictions were drawn by dynamic programming models, where the currency maximized was total lifetime progeny (Iwasa et al, 1984; Mangel, 1989a, Weisser and Houston, 1993). According to this prediction, the optimal behavior should reduce both egg- and time-limitation in the population. The proportion of egg- and time-limited animals, as a result of each individual's behavior, depends on the richness of the environment (VTsser, 1994), but as shown by Driessen and Hemerik (1992) both kinds of parasitoids may coexist in the same population. These authors suggested that, if parasitoids behave optimally, according to their internal state, then some will osculate between egg- and time-limitation, and because of this, partial preferences for parasitized hosts will be observed. Our model provides a theoretical support to that hypothesis. Though our prediction is only qualitative, it suggests that a certain proportion of parasitoids will be at the borderline between egg- and time-limitation, and thus we expect that a non-negligible proportion of parasitoids will show partial preferences for parasitized hosts. Experimental results indicate that partial preferences do occur in parasitoids (van Dijken et al., 1986; this paper). Different explanations have been proposed for the eoaswneo ef partial preferences in foraging animals. Apart from the mislrariing calculation of a mean behavior for different animals (Stephens, 1985), the other explanations are compatible with adoption of the optimal behavior. Partial preferences might arise if the animals discriminate imperfectly between prey

6 Sirot et al State dependent superparasituin 231 type* (Kreb* and McQeery, 1984; Yoccoz et al, 1993), if they respond to some changes in their internal state (Courtney et al, 1989; Mangel, 1989b; McNamara and Houston, 1987), or to changes in the characteristics of the environment (Visser, 1993,1995). Partial preferences might also arise if, depending on their distances from the predator, similar items take different energetic values (Waddington and Holden, 1979), or if, because of nutritional constraints, the an ima1t must consume different kinds of items (PulHam, 1975). The present work ^rplain partial preferences by the necessity to maintain a high rate of offspring production, but not to the complete expense of future reproduction. Depending on ecological conditions, the predicted behavior inayimft>n the total lifetime progeny of the animal (Prediction 1), both the instantaneous reproductive rate and the total lifetime progeny of the animal (Prediction 2), or a compromise between the two of them (Prediction 3). This reflects the fact that our approach combines the rate-maximizing and the state-dependent approaches. Mangel (1989b) already suggested a possible convergence in the predictions of the two kinds of models. We must stress that these approaches can also yield very different results. For example, using the second approach, Iwasa et al (1984) predict, in a model for the host diet of parasitoids, that "if an instantaneous mortality on a type of host is negligible, the optimal parasitoid should oviposit on that host even if it gives only a small fitness gain at the cost of long handling time." A model such as the one presented here would certainly predict the rejection of lowranking hosts with a long handling time, even if mortality is low, because the reproductive rate would suffer from that. The comparison between the experimental results and the predictions of the model calls for some qualification. First, V. cantsctns is a paithenogenetic parasitoid, with every individual being a good, though imperfect, copy of its mother's genotype (Slobodchikoff, 1983). This justifies the identification of the individual and the genetic levels in the model (Nur, 1984; Stenseth, 1984). Second, in France, V. cantsctns, mainly breeds on moths in granaries. As it has a short and variable development time (Harvey et al, 1993), we can reasonably assume that in these sheltered conditions it has several overlapping generations per season. Nevertheless, also in France the same animal has been recorded in natural conditions (Daumal J and Marro JP, personal communication), in which it seems to be univoltine. Third, our model assumes that the parasitoid is pro-ovigenic. In fact, the predictions of the model remain valid if the egg maturation rate of the parasitoid is low enough that egg-limitation may occur. In V. cantsctns, each individual emerges with a certain complement of eggs and is immediately ready to oviposit but keeps maturing new eggs (Trudeau and Gordon, 1989). However, the egg maturation rate of this species is very low, compared to its oviposition rate (Trudeau and Gordon, 1989). In addition, we have shown, by dissecting 1-day-old fed and host deprived parasitoids, that the mature egg load in the oviducts is positively correlated to the mean number of ovocytes in each ovariole [Spearman rank correlation (two-tailed): n = 15, p».02]. Provided the number of ovarioles in each ovary is not negatively correlated to the number of ovocytes they contain, we can assume that the egg load of our wasps during the experiment is a good indicator of their total lifetime egg complement and compare the results with the model predictions. Finally, our model assumes that the payoff from superparasitism is small, compared to the payoff from an oviposition in a healthy host In our experiment, we did not control the number of eggs in already-parasitized hosts. However, the assumption that the mean number of offspring is smaller for an oviposition in an alreadyparasitized host than for an oviposition in a healthy host, is met in V. cantsctns (Sirot, 1996). In accordance with the predictions of the model, parasitoids with a very short life expectancy always superparasitize, whereas parasitoids with a longer life expectancy superparasitize more if they have a large egg load (first experiment). In this experiment, the host larvae are concealed in the host food, as it is the case in natural conditions. In these conditions, it is not possible to assess whether the parasitoid has effectively attacked a host when it inserts its ovipositor in the semolina. The second experiment was designed to solve this problem. It shows unambiguously that partial preference exists in V. cantsctns and that the parasitoids don't change their strategy within a short sequence of encounters with hosts. In our model partial preferences stem from the fact that it is assumed that oviposition decisions are taken for a short but discrete time interval. This is justified by the fact that host finding and ovipositions are discrete processes. Taking the limit AT >0 is a highly useful, but unrealistic, mathematical approximation. Our approach leads only to qualitative predictions and this precludes more stringent tests, for instance of the egg load value above which the parasitoids should superparasitize. A recent paper (Fletcher et al, 1994) describes an experiment with V. cantsctns where the tendency to superparasitize of respectively fed and unfed wasps was measured as a function of their egg load. In this experiment, the acceptance of superparasitism increased with egg load both for starved and fed parasitoids. For a given egg load, unfed animals accept also more readily superparasitism. There are two main differences between their experiment and the present one: (1) Fletcher et al's experiment was performed with 1-day-old wasps and ours with 3-day-old animals, and (2) In Fletcher et al.'s experiment, wasps were not given the choice between parasitized and unparasitized hosts, as it was done here. It is quite possible that only one day of deprivation or access to food has a small influence both in the nutritional state of the animal and in the way it perceives food availability in the environment In our experiment, fed animah had a much longer life expectancy than unfed animals, because the former had an ad libitum access to food for three days, while the latter were deprived of food for the same period. It is plausible that this not only changes the state of the animal but also its perception of food availability in the environment, two factors that determine its life expectancy. In Fletcher et al's experiment, wasps did not have the choice between parasitized and unparasitized hosts. This could lead to a larger acceptance of superparasitism, So, more stringent conditions in our experiment allow a more appropriate test of the predictions of our model. Nevertheless, despite an experimental setup less dose to the assumptions of our model, Fletcher et al. showed that the proportion of parasitized hosts accepted varies continuously with the egg load, thus highlighting the transient phase of partial preference predicted by the model The experimental part of this work and Fletcher et al's experiment support the predictions of the model and in particular the prediction that partial preference should exist We are aware that this convergence is not a proof that our model provides the correct explanation to the behavior of the parasitoids, but it provides one possible explanation, which is coherent with behavioral data. We are most grateful to Jacques van Alphen, Jerome f»"f p Dotnitien Debouzie, Emmanuel Deiouhant, Gerard Drienen, Lia Hemerik, Bernard Roltberg, and Marcel VUser for helpful comments on previous venioru. Batter K, van Alphen JJM, van Baoenburg FHO, van der Hoeven N, Nell H, van Strien-van Llempt WITH, Turlings TJ, The func-

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