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1 Behavioral Ecology Vol. 7 No. 1: The influence of competition between foragers on clutch size decisions in an insect parasitoid with scramble larval competition Marcel E. Visser Department of Biology, Imperial College at Silwood Park, Ascot, Berkshire SL5 7PY, UK The effect of competition between ovipositing females on their clutch size decisions is studied in animals that lay their eggs in discrete units of larval food (hosts). In such species the effect of competition depends on the form of the larval competition within such units. In insect parasitoids, there might either be contest (solitary parasitoids) or scramble competition (gregarious parasitoids) between larvae within a host For gregarious parasitoids, a decreasing clutch size with increasing competition between foragers is predicted. This prediction is tested in experiments using the parasitoid Aphaertta minuta. Parasitoids were either kept alone or in groups of four before the experiment, in which they were introduced singly in a patch containing unparasitized hosts. Animals kept together laid on average clutches of.74 eggs smaller than females kept alone (average clutch is 5.3), thereby confirming the prediction. Clutch size decreased with encounter number, which might be due to the adjustment of the female's estimate of the encounter rate with hosts. Finally, the results are compared with those reported for solitary parasitoids (that have scramble larval competition), for which it is predicted that the clutch size will increase with increasing levels of competition between females. Key uwrds: competition, clutch size, parasitoids, superparasitism. [Behav Ecol 7: (1996)] FT almost half a century now, clutch size decisions have been studied from an adaptive point of view. Starting widi Lack (1947), the reproductive behavior of birds and mammals were explored (see review of Lessells, 1991). More recently, clutch size decisions in invertebrates have also been studied. There is a vast literature, both theoretical and experimental (see reviews of Godfray, 1987; Godfrey et al., 1991; Waage, 1986), showing that a large number of factors (like encounter rate with food patches, quality of food patches, and the egg supply of females) influence clutch size decisions in invertebrates. Many of these factors have received considerable attention from experimentalists, but one such factor, the degree of intraspecific competition, has not Intraspecific competition is, however, likely to be of importance in most natural environments, and it is therefore important to experimentally test the existing hypothesis on its effect on clutch size decisions. Theory Species that lay clutches in or on discrete units of larval food (like plants, insects, or fruits) leave these attacked units in the environment They can therefore be reencountered by other females which might add eggs. In that case, females, when laying a clutch of eggs in an empty unit of larval food, should take into account the probability of another female laying later in the same unit The optimal clutch size in both empty and already attacked units should therefore be calculated using game theory (Maynard Smith, 1974), taking the level of intraspecific competition (the number of females ovipositing in a unit) into account. The first to consider this situation were Parker and Courtney (1984) who assumed that there are two types of females, M. E. Visser is now at the Netherlands Institute of Ecology, P.O. Box 4, 6666 ZG Heteren, The Netherlands. Received 9 January 1995; revised 18 April 1995; accepted 24 April $5. O 1996 International Society for Behavioral Ecology one always encountering empty units, the other always encountering already attacked ones. Strand and Godfray (1989) modeled females that encounter both empty and already attacked units. They predict that the clutch size laid in an empty unit decreases with increasing likelihood of another female adding eggs later on. However, as Ives (1989) pointed out, whether such a first clutch should increase or decrease with increasing levels of intraspecific competition depends on the shape of the fitness curve: the relationship between the total fitness of the offspring from that unit of resource and the number of eggs in a unit Although Ives (1989) only considered the influence of the form of the fitness curve on the effect of competition on clutch size (without specifying the form of competition between the larvae within a unit of resource), his model can be interpreted as follows. When there is scramble competition between developing individuals (resources divided roughly equally between die competing larvae), a female should lay a smaller clutch with an increasing number of females in the patch. However, when there is contest competition between developing larvae (die larvae fight or are in other direct forms of competition), the size of the first clutch should increase. This makes intuitive sense: if offspring fight for possession of the food, die chance for an individual female diat one of her offspring wins this fight increases widi clutch size. Thus, when the likelihood that another female will lay in the same food patch increases, the first female should lay a larger clutch. On the other hand, if all larvae share the food, an increasing probability of other females laying is in fact the same as reducing the amount of food available for die offspring of die first female, and thus she should lay a smaller clutch. Note that diere is thus competition on two levels: (1) competition for a unit of resource between foragers and (2) competition between larvae widiin a unit of resource. The form of the latter determines die effect of die former on clutch size decisions. In parasitoids insects that lay Uieir eggs in or on other arthropods (hosts) bodi forms of larval competition are found (Godfray, 1994). In solitary parasitoids, there is contest competition within a host, and only one parasitoid will Downloaded from by guest on 17 December 218

2 11 Behavioral Ecology Vol. 7 No. 1 emerge from a host. In gregarious parasitoids, there is scramble competition, and in principle all eggs can develop into new parasitoids. With increasing clutch size however, smaller parasitoids emerge. The fitness of female parasitoids usually decreases with decreasing size, because smaller parasitoids have a lower fecundity, longevity, andor host-finding capacity (Visser, 1994). The precise shape of the fitness curve will strongly depend on this relationship between size and fitness. This is of importance because in the model of Ives (1989) a decreasing clutch size with increasing competition is only predicted when die scramble competition widiin a host is more severe than the form exp(-riv), with r > and N being die number of eggs laid in a host The insect parasitoids include species with both forms of larval competition, and diis group is therefore suitable for testing predictions on the influence of intraspecific competition on clutch size. In solitary parasitoids we expect females to lay larger clutches in unparasitized hosts (i.e., lay more dian one egg although only one offspring can emerge from a host) with an increasing level of intraspecific competition, and in gregarious parasitoids we expect die females to lay smaller clutches. Aim of the study There is some evidence diat solitary parasitoids lay, as predicted, larger clutches widi increasing levels of competition between parasitoid females (see Discussion). Here I will test the prediction for gregarious parasitoids diat smaller clutches are laid widi increasing levels of competition, using die parasitoid Aphaereta minuta. I will first calculate die fitness curve for this species when it attacks Drosophila hydei larvae, die host species used in die experiments. This fitness curve is then compared with die diree curves in Ives's (1989) model in order to predict die effect of competition between females on clutch size. Next an experiment is carried out in which die degree of competition is altered by keeping parasitoids eidier alone or in groups before the experiment Parasitoids are dien introduced singly onto a patch widi unparasitized hosts, and the clutch sizes laid are recorded. This setup has die advantage diat it alters the degree of competition widiout altering die rate of depletion and die amount of interaction between individuals while searching for hosts. The rationale behind it is diat females that have previously encountered conspecifics will behave as if diey are in an environment where it is likely diat odier females are going to encounter die same hosts. MATERIALS AND METHODS The parasitoid Aphaereta minuta (Nees) (Hymenoptera; Braconidae) is a gregarious, polyphagous endoparasitoid of Diptera larvae, which live in decaying plant and animal material (Evans, 1933). The host larva continues to grow after being parasitized and several adult parasitoids emerge from die host pupa. Female parasitoids search for hosts by vibrotaxis, detecting vibrations produced by die host. Once die ovipositor has been inserted into die host and die host paralyzed, die ovipositor is inserted more deeply. During oviposition, die last abdominal segments and die ovipositor sheadi undergo alternating periods of vibration and rest (Evans, 1933). The fitness curve To calculate die fitness curve, data are needed on die number, sex, and size of offspring emerging from a host, depending on clutch size. Also die relationship between size and fitness of females needs to be known. To diis end, parasitized hosts were collected by observing a female A. minuta searching for and ovipositing in Drosophila hydei larvae of 6 days old. Clutch size was determined by counting die movements of die abdomen by the ovipositing female. The number of bouts of vibration correlates very well widi die clutch size actually laid (observed versus found at dissection: n = 4, r 2 =.94, p <.1; see also Vet et al., 1994; observed versus found at dissection: n = 131, I s =.87, p <.1), and can dierefore be used as an estimate of die clutch size laid. The parasitized hosts were reared individually in vials widi a tomatoyeast medium (5 ml tomato juice, 4 g dry yeast, 1 g agar, and die antifungal nypagine). After emergence of the offspring, die number of males and females were counted and dieir head widdi measured. From these data die relationships between clutch size and (1) the probability for an egg to survive to an adult parasitoid, (2) die size of the females emerging, and (3) die sex ratio of die offspring can be determined. Data on the relationship between size and fitness in female A. minutawere obtained by Visser (1994), and will also be used in diis study. The effect of competition on clutch size The A. minuta were cultured on D. hydei Parasitized pupae were isolated (in a vial widi a layer of vermiculite) and die emerging parasitoids were mated on die day of emergence and then kept alone or in groups of four in a vial with an agar layer and honey. The wasps were used 4 days after emergence, and were kept togedier until 1 h before die experiment. As far as possible, parasitoid size was kept constant. The patches consisted of tomato juice widi agar and nypagine (2 ml tomato juice, 3 g agar, and die antifungal nypagine) and had a diameter of 8.7 cm. The hosts used were 2 D. hydei larvae of 6 days old, put in die patch 24 h before die experiment. Parasitoids were always introduced onto a patch singly and observed continuously. A full behavioral record (walking, piercing, handling host, standing still, preening, off patch, laying an egg) was made, using a Psion Organizer running The Observer (version 3.; Noldus Information Technology, Wageningen, The Netherlands, 199). Parasitized hosts were removed from the patch immediately after being parasitized and stored individually. There were four criteria on die basis of which die experiment was halted: (1) no hosts parasitized for 1 s, (2) female escapes, (3) female rejects a host (ovipositor in die host for less than 5 s), and (4) female has parasitized five hosts. After die experiment die size of die parasitized hosts and of die parasitoid (head widdi) were measured and die number of eggs in die parasitoid's ovarioles counted. For each of die two treatments 12 replicates were carried out Analysis Clutch size was initially determined by counting die movements of die abdomen by die ovipositing female. In 43% of die ovipositions die movements could, however, not be seen clearly for die entire oviposition bout. For diis reason, die handling time (die time die ovipositor was inside die host), which could be measured accurately in nearly all cases, is used as a measure of clutch size. In a simple regression model handling time explained 63% of die variation in clutch size (clutch size = handling time (s), n = 58). The main explanatory variable in die analysis of handling time is die treatment (kept alone or in groups of four). Anodier variable of interest is die number of hosts previously encountered (encounter number). When searching a patch, a parasitoid will encounter hosts and may use diat information Downloaded from by guest on 17 December 218

3 o.1 t E 2.5 ' CO CO <D B \ \. CO 9 7 X V s i T 1 1 f : ". X " Ss ''- 4 Ss ' - i 5 :,, Clutch size? Encounter number 5 Figure 2 Figure 1 The fitness curve [s(n), the relationship between the total fitness of the offspring from a host and the number of eggs laid in that host (iv)] for A. minuta attacking D hydei larvae (). Also plotted are the three curves from Ives's (1989) model (see also his Figure 1): dotted line, s(n) = JJL(1 - aiv), with (j. =.124 and a =.15; dashed line, s(n) = iie~m, with \L =.167 and r =.3; solid line, s(n) = u, (1 + on)- with p. =.175, a =.35 and b = 9.5. to estimate die encounter rate. After a number of encounters widi hosts, die female's estimation of die encounter rate is expected to converge toward die real value. Optimal clutch size depends strongly on encounter rate, when hosts are encountered frequendy, travel time between oviposition opportunities is short, and animals should lay small clutches. Due to changes in die female's estimation of die encounter rate, reflected in die clutch size, die clutch size laid is expected to change over the first encounters widi hosts and dien remain constant Such a pattern in change of clutch size widi encounter number has indeed been found by Ikawa and Suzuki (1982). Odier variables diat might influence clutch size are parasitoid size, parasitoid egg load at encounter, host size, and interval since last encounter. These variables were kept as constant as possible in die experiments, and indeed there were no differences in these four variables between die two groups (kept alone or kept togedier, t test, all p >.15). The results were analyzed using generalized linear modeling techniques (Aiddn et al., 1989; Crawley, 1993), using GLIM (version 3.77; Numerical Algoridims Group, Oxford, UK, 1985). RESULTS The fitness curve In total, 45 parasitized hosts were collected. T h e probability for an egg to develop to an emerging adult decreased widi clutch size: probability of emerging = clutch size (Aiop = 1, r = , i =.29, n = 45). T h e sex ratio (proportion males) did not significandy decrease widi clutch size (^.lop,. =.35, n = 45). This is because from small clutches (two to diree eggs) often only females emerged. The size of emerging females (head widdi) decreased widi clutch size: Mean time spent handling a host (bars indicate SE, plotted in only one direction to avoid overlap) versus encounter number for female A. minuta kept in groups of four (open symbols) or kept alone (closed symbols) before the experiment The lines connect the fitted values (see Table 1). head widdi (mm) =.6-.2 clutch size ( ^ =.4, r =.48, J2 =.23, n = 35). In order to calculate die fitness curve, die relationship between size of a female and her fitness needs to be known. I used die data in Visser (1994) on die sizedependent constraints in longevity, fecundity and searching efficiency in A. minuta. These are combined into one fitness measure, using a dynamic programming model (see Visser, 1994, for details). This model was used by Visser (1994) for a different host species, so I recalculated this relationship widi D. hydei as a host species: fitness 9 = head widdi (head widdi 9) 2. The fitness curve can now be calculated using die equation: fitness clutch = clutch size X probability of emerging X fitness 2 (head width 9) (The sex ratio of die emerging parasitoids is left out because diere was no relationship between sex ratio and clutch size.) This fitness curve is plotted in Figure 1 togedier with die diree curves from Ives's (1989) figure. It is clear diat die fitness curve falls below die larval-competition curve for which Ives's model predicts no change in clutch size widi increasing competition between foragers (fitness = (ie"'", widi u. >, r >, and N = clutch size). Thus, for A. minuta attacking D. hydei, clutch size is predicted to decrease widi increasing competition between female parasitoids. The effect of competition on clutch size The degree of intraspecific competition, as altered by keeping parasitoids eidier alone or in groups of four before the experiment, was found to have an effect on clutch size (Table 1 and Figure 2) in die predicted direction. Females kept togedier before die experiment handled hosts on average 16.6 s shorter dian females kept alone, which corresponds widi a decrease in clutch size of.74 eggs (using die equation, clutch size = handling time). The encounter number also had a significant effect; clutch size decreased over die first diree encounters. There is no Downloaded from by guest on 17 December 218 o ndling time britrary unit Visser Competition and clutch size

4 112 Behavioral Ecology Vol. 7 No. 1 Table 1 Generalized linear model on handling time (n = 19), which is highly correlated to clutch size Null model Residual Treatment Encounter number 6 Not in model (treatment X encounter number) Change in deviance 12,252 78, , Change in df P <.5 <.1 =.7 1st 2nd 3rd to 5th Alone Together The two variables of interest are treatment (parasitoids kept alone or kept together before the experiment) and the number of previously encountered hosts (encounter number). Estimates for the linear model; for example, a female kept alone encountering the second host is estimated to handle that host for = 1.8 s. b Encounter number ranges from 1 to 5. Lumping the third, fourth, and fifth encounter does not significantly decrease the deviance explained (8 deviance = 1119, 8 df = 2); therefore, encounter number is included in the model in three categories; first encounter, second encounter, third to fifth encounter. significant change in clutch size from the third to the fifth encounter (Figure 2). An explanation for this decrease in clutch size widi encounter number is presented in the Materials and Methods section. Animals that just arrived on a patch might have to estimate die encounter rate with hosts, an estimate diat will convert to die real value. As a result, the clutch size decisions will be adjusted. In dieory, die clutch size could also go up: when an animal's estimation of die patch quality is higher than the actual value. In die experiments, as well as in diose of Ikawa and Suzuki (1982) and of Rosenheim and Hongkham (in press), die clutch size decreases widi encounter number, which might indicate diat die patches used are of a higher quality than initially estimated by the parasitoid. DISCUSSION Intraspecific competition is predicted to influence clutch size decisions. In solitary parasitoids, females should lay a larger first clutch at a high level of competition. In gregarious parasitoids, a smaller clutch is predicted, provided that die scramble competition widiin a host is more severe dian die form exp(-riv), with r > and N being die number of eggs laid in a host (Ives, 1989). I have shown diat diis is die case for A. minuta attacking D. hydei larvae, and hence diat a decreasing clutch size widi increasing competition between foragers is predicted. This prediction is tested, and met, in die experiments: animals kept togedier before die experiment lay clutches diat are on average.74 eggs smaller (mean clutch size is 5.3) dian females under die same conditions, but kept alone before die experiment This is a decrease of 14% in clutch size, even widiout direct competition between searching females widiin die patch. It is clear diat A. minuta responds to preexperimental encounters widi conspecifics. This indicates diat the opposition decisions of die parasitoid can be adjusted to die level of competition. This is to be expected if in die natural environment die level of competition varies on a spatial andor a temporal scale. In a field site in Modanio (Greece; Visser, 1994) diis was indeed die case. There were sites widi very few parasitoids, and sites where eight to ten parasitoids could be seen searching simultaneously on a rotten tomato widi Diptera larvae. There also seems to be a clear build-up of die parasitoid population over die season, widi initially low densities (G. Driessen, personal communication) There are no clear alternative explanations for die smaller clutch size laid by females stored togedier. Keeping animals togedier in a vial might decrease dieir longevity due to encountering odier females. A shorter longevity, however, is predicted to increase clutch size, not decrease it. Evidence in solitary parasitoids In some solitary parasitoids, females sometimes lay two eggs in one oviposition bout [see Rosenheim and Hongkham (in press) for a review]. Aldiough at most one offspring can emerge from a host in solitary parasitoids, having two eggs in a host is advantageous when die probability of superparasitism by another female is high (Visser, 1993; Visser et al., 199). A parasitoid female encountering a parasitized host will reject diat host more often when it contains two eggs than when it contains a single egg (Bakker et al., 199), and even if she lays anodier egg, die first female still has two eggs in die host instead of one. Such a strategy of defense pays because diere is strong contest competition in solitary parasitoids, and diis hypodiesis can be viewed widiin die framework oudined in die introduction [based on die model of Ives (1989)]. There are two studies diat explicidy test, and confirm, die prediction diat whedier a clutch size of two eggs is laid depends on die level of competition between female parasitoids. In experiments widi Asobara tabula (see Table 2 for experimental protocol), M. E. Visser and A. R. Kraaijeveld (unpublished data) found diat females diat were kept togedier before die experiment always laid one egg in unparasitized hosts when searching a patch widi eidier only or 5% unparasitized hosts (die odier 5% were already parasitized by a conspecific before die experiment). In such patches parasitized hosts are always rejected. When females were, however, searching a patch widi only 25% unparasitized hosts (and hence 75% already parasitized hosts), diey superparasitized hosts previously parasitized by odier females. But what is more, diey also laid two eggs in unparasitized hosts (Table 2). Superparasitism of hosts parasitized by a conspecific (causing larval competition widi an unrelated individual) is more profitable dian laying two eggs in die same host (causing competition widi a sib) as a defense against superparasitism by odier females. Therefore, diis pattern is expected under die hypodiesis. Rosenheim and Hongkham (in press) used die same experimental setup as used in diis article when studying clutch size decisions in die Downloaded from by guest on 17 December 218

5 Visser Competition and clutch size 113 Table 2 The number of eggs laid by Asobara tabida Nees (Hymenoptenu Braconidae) when accepting either an unparasitized or a parasitized host (larvae of Drosophila mdanogaster) Patch consists of All unparasitized hosts 5% unparasitized 5% parasitized hosts 25% unparasitized 75% parasitized hosts Number of eggs laid on one oviposition bout when accepting Unparasitized hosts 1 egg eggs 7 Parasitized hosts 1 egg SO 2eggs Females were kept together before the experiment and were given a patch together on the day before the experiment. In the experiment all females were introduced singly into a patch, and all hosts (super)parasitized were immediately replaced and dissected (Visser ME and Kraaijeveld AR, unpublished data). solitary parasitoid ComperieUa bifasdata. They showed that females kept in groups of three laid larger clutches when introduced singly to an unparasitized host than females kept alone before the experiment. Thus, these data sets both confirm the prediction for solitary parasitoids: a larger clutch is laid with increasing levels of intraspecific competition. Females of some solitary species have never been observed laying two eggs in one oviposition bout. Females, however, sometimes do lay an additional egg upon reencountering a host, an act referred to as self-superparasitism. In both solitary and gregarious parasitoids self-superparasitism can be viewed as a clutch size adjustment (van Alphen and Visser, 199). In the solitary parasitoid Leptopilina heterotoma the influence of competition on self-superparasitism has been shown by Visser (1993) and Visser et al. (199). Using the same experimental setup as used in this article it was shown that individuals that were kept alone before the experiment did not self-superparasitize, whereas those that were kept in a group self-superparasitized 1% of the hosts. Evidence in other taxa Wilson (1994) found no effect of competition (females were kept alone, with two or with five before the experiment) on clutch size in a bruchid beetle (Callosobruchus maculatus). The clutch size laid was, however, as predicted for the situation in which five to seven other females laid on the same food patch (a bean). He concluded that there is a response of the beetles to future ovipositions on the same bean, but that it is fixed and not, as in the case of A. minuta, dependent on previous encounters with conspecifics. In species that do not lay their clutches in discrete units of food, intraspecific competition can also be important- Power et al. (1989) explained why the most frequently found clutch size in the starlings (Sturnus iwlgaris) in their study site was smaller than the most productive one with the occurrence of intraspecific brood parasitism. Because there is scramble competition between the young within a nest, this explanation seems to fit in with the framework outlined in the introduction. There is, however, a pitfall, as pointed out by Rothstein (199). When there is extensive parental care, as in the starlings but also in some parasitoids (Hardy et al., 1992), another strategy to deal with brood parasitism is possible. The parent could remove eggs after another female has laid additional eggs in the nest (host). Even when animals cannot distinguish between own and conspecific eggs this might be a better option than laying a smaller clutch, leaving "space" for intraspecific brood parasitism. Concluding remarks There are also some practical implications of die results reported here. When carrying out experiments on reproductive decisions, one needs to pay attention to how the animals are treated before the experiment. Storing them under a certain light regime might influence their decisions because of an "end-of-season" effect (Roitberg et al., 1992), and storing them with other individuals might lead to different host acceptance decisions (Visser, 1995) or smaller clutch sizes. This might be part of an explanation why so very often a smaller clutch size than predicted is found in insects (Godfray, 1994; Hardy et al., 1992; Lessells, 1991). Intraspecific competition will very often play an important role in natural environments. Its effect on reproductive decisions is quite well studied from a theoretical point of view for clutch size (Ives, 1989; Strand and Godfray, 1989), prey acceptance (Mitchell, 199; Visser, 1991; Visser et al., 1992), and sex ratio decisions (Local Mate Competition, Hamilton, 1967). It is, however, only for the latter type of decisions that a reasonable body of experimental studies exist I think that the effect of competition on reproductive decisions is a topic important enough to justify further experimental exploration. Charles Godfray is gratefully acknowledged for his support and for stimulating discussions. Gerard Driessen collected the A. minuta to initiate the culture and Jane Hodgson assisted with keeping the cultures alive. Lex Kraaijeveld is acknowledged for the use of unpublished data. Kate Lessells, Tony Ives, Jay Rosenheim and Bart Kempenaers provided constructive comments on the manuscript This study was supported by the EC Science Grant ERB41GT91445 and Human Capital and Mobility Programme Grant ERBCHBICT REFERENCES Aitkin M, Anderson D, Francis B, Hinde J, Statistical modelling in GUM. Oxford: Oxford University Press. Bakker K, Peulet Ph, Visser ME, 199. The ability to distinguish between hosts containing different numbers of parasitoid eggs by the solitary parasitoid Leptopilina heterotoma (Thompson) (Hym., Cynip.). NethJ Zool 4: Crawley MJ, GLIM for ecologists. Oxford: Blackwell Scientific Publications. Evans AC, Comparative observations on the morphology and biology of some hymenopterous parasites of carrion-infesting Diptera. Bull Entomol Res 24: Godfray HCJ, The evolution of invertebrate clutch size. Oxford SurvEvol Biol 4: Godfray HCJ, Parasitoids, behavioral and evolutionary ecology. Princeton, N.J.: Princeton University Press. Godfray HCJ, Partridge L, Harvey PH, Clutch size. Annu Rev Ecol 22: Hamilton WD, Extraordinary sex ratios. Science 156:477^88. Hardy ICW, Griffiths NT, Godfray HCJ, Clutch size in a parasitoid wasp: a manipulation experiment J Anim Ecol 61: Ikawa T, Suzuki Y, Ovipositional experience of the gregarious parasitoid, Apantdes glomeratus L. (Hymenoptera: Braconidae), influencing her discrimination of the host larvae, Pieris rapae crudvora. Appl Entomol Zool 17: Ives AR, The optimal clutch size of insects when many females oviposit per patch. Am Nat 133: Lack D, The significance of clutch size. Ibis 89: Lessells CM, The evolution of life-histories. In Behavioural ecology, an evolutionary approach (KrebsJR, Davies NB, eds.). Oxford: Blackwell Scientific Publications; Downloaded from by guest on 17 December 218

6 114 Behavioral Ecology Vol. 7 No. 1 Maynard Smith J, The theory of games and the evolution of animal conflicts. J Theor Biol 47: Mitchell WA, 199. An optimal control theory of diet selection: the effects of resource depletion and exploitative competition. Oikos 58: Parker GA, Courtney SP, Models of clutch size in insect oviposition. Theor Popul Biol 26: Power HW, Kennedy ED, Romagnano LC, Lombardo MP, Hoffenberg AS, Stouffer PC, McGuire TR, The parasitism insurance hypothesis: why Starlings leave space for parasitic eggs. Condor 91: Roitberg BD, Mangel M, Lalonde RG, Roitberg CA, van Alphen JJM, Vet LEM, Seasonal dynamic shifts in patch exploitation by parasitic wasps. Behav Ecol 3: RosenheimJA, Hongkham D, in press. Optimal clutch size in an obhgately siblicidal parasitoid wasp. Anim Behav. Rothstein SI, 199. Brood parasitism and clutch size determination in birds. Trends Ecol Evol 5: Strand MR, Godfray HCJ, Superparasitism and ovicide in parasitic Hymenoptera: a case study of the ectoparasitoid Bracon hebetor. Behav Ecol Sociobiol 24:421^432. van Alphen JJM, Visser ME, 199. Superparasitism as an adaptive strategy for insect parasitoidj. Annu Rev Entomol 35: Vet LEM, Datema A, van Welzen K, Snellen H, Clutch size in a larval pupal endoparasitoid: 1. Across and within host species variation. Oecologia 95: Visser ME, Prey selection by predators depleting a patch; an ESS model. Neth J Zool 41: Visser ME, Adaptive self- and conspecific superparasitism in the solitary parasitoid Leptofnlina heterotoma. Behav Ecol 4: Visser ME, The importance of being large: the relationship between size and fitness in females of the parasitoid Aphaereta minuta (Hymenoptera: Braconidae). J Anim Ecol 63: Visser ME, The effect of competition on oviposition decisions of Leptopilina heterotoma (Hymenoptera: Eucoilidae). Anim Behav 49: Visser ME, van Alphen JJM, Hemerik L, Adaptive superparasitism and patch time allocation in solitary parasitoids: an ESS model. J Anim Ecol 61: Visser ME, van Alphen JJM, Nell HW, 199. Adaptive superparasitism and patch time allocation in solitary parasitoids: the influence of the number of parasitoids depleting a patch. Behaviour 114: Waage JK, Family planning in parasitoids: adaptive patterns of progeny and sex allocation. In: Insect parasitoids (Waage JK, Greathead D, eds.). London: Academic Press; Wilson K, Evolution of clutch size in insects. II. A test of static optimality models using the beetle Callosobruchus maculatus (Coleoptera: Bruchidae).J Evol Biol 7: Downloaded from by guest on 17 December 218

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