Genetic variation in patch time allocation in a parasitic wasp

Journal of Animal Ecology 0888\ 57\ 010Ð022 Genetic variation in patch time allocation in a parasitic wasp ERIC WAJNBERG\ MARZIA CRISTIANA ROSI$% and STEFANO COLAZZA$ INRA\ Unite de Biologie des Populations\ 26\ Blvd[ du Cap\ 95599 Antibes\ France^ and $Agricultural Entomology Institute\ University of Perugia\ Borgo XX Giugno\ 95010 Perugia\ Italy Summary 0[ The intra!patch experience acquired by foraging parasitoid females has often been considered to have a strong in~uence on their tendency to leave a patch\ and thus on their total patch residence time[ Most studies that have been performed on this subject suggest that the patch!leaving rules observed are adaptive because they enable the females to adjust their patch residence time to local environmental conditions[ 1[ Considering a behavioural rule as being adaptive supposes that it has been pro! gressively settled by natural selection\ and thus that there is\ in the population\ genetic variation on which the natural selection could act[ 2[ Therefore\ this study aimed to discover whether there was indeed genetic variability in the patch!leaving decision rules in a population of the egg parasitoid species Telenomus busseolae\ which attacks patches of its hosts\ the eggs of Sesamia nonag! rioides[ Di}erent wasp families were compared using the isofemale lines method\ and the behavioural records were analysed by means of a modi_ed version of the Cox|s proportional hazards model proposed by Haccou et al[ "0880# and Hemerik\ Driessen + Haccou "0882#[ 3[ The results obtained show that T[ busseolae females increase their tendency to leave the patch after each successful oviposition[ Each host rejection also led to an increase in the tendency to leave the patch\ but this e}ect was smaller when host rejections were observed between two ovipositions occurring in rapid succession[ Subsequent visits to the patch also increased the patch!leaving tendency[ 4[ Genetic variability was found in both the global patch!leaving tendency and in the e}ect that successful ovipositions and host rejections have on this tendency[ 5[ The adaptive and evolutionary consequences of these results are discussed[ Key!words] Cox|s regression model\ genetic variability\ parasitoids\ patch time allo! cation\ Telenomus busseolae[ Journal of Animal Ecology "0888# 57\ 010Ð022 Introduction Patch time allocation in parasitoids "and predators# has been the focus of considerable theoretical and experimental work in the last few decades\ and has progressively become one of the main subjects in behavioural ecology and optimal foraging theory "see Stephens + Krebs 0875\ for a review#[ The starting Þ 0888 British Ecological Society %Present address] Agricultural and Forest and Zoology Insti! tute\ via delle Cascine\ 94010 Florence\ Italy[ Correspondence] E[ Wajnberg\ INRA\ Unite de Biologie des Populations\ 26\ Blvd[ du Cap\ 95599 Antibes\ France[ point is that hosts "or prey# usually occur in discrete patches "Godfray 0883#\ and foraging females are usu! ally time limited in the sense that they are unable to _nd enough hosts in which to lay all their eggs during their life time "Nelson + Roitberg 0884#[ Therefore\ the time allocated to each patch can be an important factor in the reproductive success of a parasitoid\ and can thus be the target of strong selective pressures[ A number of theoretical models have been proposed to predict the optimal residence time a female should allocate to each visited patch[ The most well!known one is Charnov|s "0865# marginal value theorem[ This theoretical approach\ and most of the subsequent ones\ make the implicit assumption that foragers 010 011 Genetic variation in patch time allocation Þ 0888 British Ecological Society Journal of Animal Ecology\ 57\ 010Ð022 know exactly the distribution and the quality of the patches within the habitat "Waage 0868^ McNair 0871^ van Alphen + Vet 0875^ Godfray 0883#[ Such an assumption is obviously unrealistic\ especially in a stochastic\ unpredictable environment "Oaten 0866^ Green 0879^ McNamara 0871^ Green 0873#[ In order to circumvent this problem\ it has been repeatedly proposed that animals\ while foraging on a patch\ are\ in fact\ continuously sampling their environment in order to obtain the information needed to trigger the patch!leaving decision "McNamara 0871^ Green 0873^ van Alphen + Vet 0875^ Yamada 0877^ Li\ Roitberg + Mackauer 0882#[ Simple patch!leaving decision rules\ based on intra! patch experience\ have been proposed^ for example\ Waage "0868# has suggested that female parasitoids enter a patch with a certain level of responsiveness that is determined by the concentration of contact kairomones\ and thus by the number of hosts avail! able[ Afterwards\ females are supposed to exhibit a turning response each time they encounter the edge of the patch "Waage 0867#[ When no hosts are enco! untered\ the level of responsiveness is assumed to decrease over time down to a threshold value at which the turning response is no longer elicited\ and the patch is left[ When a host is attacked\ the respon! siveness to the patch edge is increased by a given increment[ The size of the increment depends on the time elapsed since the preceding oviposition[ Such an incremental e}ect in response to each oviposition has been observed in several parasitoid species^ on the phycitid moth parasitoid Venturia canescens "Gra! venhorst# Waage "0867\ 0868#\ on several Drosophila parasitoids "van Lenteren + Bakker 0867^ van Alphen + Galis 0872^ Hemerik\ Driessen + Haccou 0882#\ on an aphid parasitoid "Cloutier + Bauduin 0889#\ on a leafminer parasitoid "Nelson + Roitberg 0884# and on a white~y parasitoid "van Roermund\ Hemerik + van Lenteren 0883#[ Using a mathematical approach\ Iwasa\ Higashi + Yamamura "0870# showed that this mechanism can lead to a result that closely approxi! mates the optimal strategy when the hosts exhibit a clumped distribution "i[e[ with a large variance in patch density#[ Therefore\ under some particular con! ditions\ such a patch!leaving decision rule is con! sidered to be adaptive "van Alphen + Vet 0875#[ In some cases\ successful ovipositions have been shown to have a decremental e}ect on patch residence time[ The most striking example has been observed on Cardiochiles nigriceps Vierick\ a parasitoid of the tobacco budworm\ which immediately leaves the patch after a single oviposition "Strand + Vinson 0871#[ Such a decremental e}ect\ sometimes called a {count!down| mechanism "Driessen et al[ 0884#\ has also been observed on a Lepidopterous larval para! sitoid "Wiskerke + Vet 0883#\ on an aphid parasitoid "van Steenis et al[ 0885#\ and on Venturia canescens "Driessen et al[ 0884#[ This patch!leaving mechanism is supposed to be adaptive when host patches are small "Strand + Vinson 0871# or when hosts are uniformly distributed "Iwasa et al[ 0870^ Driessen et al[ 0884#[ The general idea behind these patch!leaving decision rules is that an encounter with a healthy host provides\ not only a suitable place to lay an egg\ but also information[ In the case of an incremental e}ect\ the information may be that the patch is richer than had _rst appeared and therefore it is worthwhile to spend an additional amount of time foraging on it[ In the case of a decremental e}ect\ the information may be that the patch resources are depleting and it is becoming less and less interesting to remain on it[ The encountering of an already attacked host will also provide the forager with some information regarding the level of patch exploitation[ Thus\ encounters with parasitized hosts should have a decremental e}ect on patch residence time "van Alphen + Vet 0875^ van Alphen 0882#[ Indeed\ this has been veri_ed for several Drosophila parasitoids "van Alphen + Galis 0872^ van Alphen + Vet 0875^ Bakker + van Alphen 0877^ van Lenteren 0880^ Hemerik et al[ 0882# and for an aphid parasitoid "van Steenis et al[ 0885#[ However\ on other parasitoid species\ some investigations failed to show any e}ect "Waage 0868^ van Roermund\ Hemerik + van Lenteren 0883#\ or even showed the opposite e}ect "Nelson + Roitberg 0884#[ The di}erent patch!leaving rules discussed so far are a priori hypotheses that have to be investigated using laboratory experiments[ However\ the analysis of experimental data based on these simple models has generally been considered to be problematic "Haccou et al[ 0880^ Hemerik et al[ 0882#[ An alternative approach has been proposed in order to deduce the e}ect of females| intra!patch experience on their patch!leaving decision\ from experimental data with minimal prior assumptions[ The method used for this is a transposition to ecological problems of a statistical method widely used to analyse survival data in medi! cal research^ i[e[ Cox|s "0861# proportional hazards model "Haccou et al[ 0880^ van Alphen 0882^ Hemerik et al[ 0882#[ This model has the advantage of being stochastic\ in the sense that the deduced behavioural mechanisms are phrased in terms of probabilities instead of _xed rules\ like those proposed by Char! nov|s "0865# or Waage|s "0868# models\ and this appears to be more appropriate to analyse data on time allocation "van Roermund et al[ 0883#[ More! over\ it can be used to detect time!dependant mech! anisms and thus\ the timing of the di}erent events that occur during patch exploitation can be taken into account[ Supposedly\ such time!dependant processes have a strong e}ect on patch!leaving decisions "Waage 0868^ van Alphen 0882#[ Therefore\ this model seems appropriate to analyse the fact that a female para! sitoid may experience a continuous decrease in contact with healthy hosts on a depleting patch and must continually re!assess the changing value of the patch\ based on only its previous experience "Cowie + Krebs 0868^ McNamara + Houston 0874^ Li et al[ 0882#[ 012 E[ Wajnberg\ M[C[ Rosi + S[ Colazza Finally\ the use of this model permits the testing of any interactions between di}erent behavioural mech! anisms that are involved in the determination of patch residence time^ for example\ this model can be used to quantify the fact that the e}ect of encountering heal! thy hosts on patch!leaving decisions could change according to the number of hosts found that are alre! ady attacked[ Such interaction mechanisms are expected to a}ect patch!leaving decisions "Nelson + Roitberg 0884#[ The use of this statistical approach has shown that female parasitoids are managing their patch residence time according to the experience they acquire while foraging on the patch[ At least qualitatively\ most of the patterns that have been revealed are usually in agreement with the prediction of optimal foraging theory "Haccou et al[ 0880^ Hemerik et al[ 0882^ God! fray 0883#\ and are thus thought to be adaptive[ There! fore\ behaviours have probably been progressively set! tled by natural selection over the course of generations "Iwasa et al[ 0870^ Pyke 0873#[ This is conceivable only if the biological traits of the wasp that are involved are genetically determined and if there is variation on which natural selection could act[ However\ such genetic variation has never been demonstrated[ The aim of the present study is thus to look for genetic "i[e[ polygenic# variability in the e}ect of intra!patch experience on patch time allocation by females of Telenomus busseolae Gahan "Hym[^ Scelionidae#\ which attack patches of one of their hosts\ the eggs of Sesamia nonagrioides Lefebvre "Lep[^ Noctuidae#[ To achieve this\ the results obtained on di}erent wasp families were compared using the isofemale lines method "Parsons 0879^ Ho}mann + Parsons 0877#[ Experimental data were analysed using a modi_ed version of the Cox|s proportional hazards model that was used by Haccou et al[ "0880# and Hemerik et al[ "0882#[ First\ the results have given a comprehensive insight into the mechanisms used by T[ busseolae females to manage their patch time allocation[ Then\ an analysis of the inter!family variation was used to identify strong genetic variability in these mechanisms in the population analysed[ The evolutionary conse! quences of these results are discussed[ Material and methods PARASITOIDS AND HOSTS Þ 0888 British Ecological Society Journal of Animal Ecology\ 57\ 010Ð022 Telenomus busseolae is a solitary egg parasitoid of various lepidopteran species belonging to Noctuidae and Pyralidae "Polaszek\ Ubeku + Bosque!Perez 0882#[ Its geographical distribution covers several African countries\ the middle East and India[ In Europe\ it has been found only in Greece "Polaszek et al[ 0882# and in Portugal "C[ Meierosse\ unpub! lished data#[ Host egg!masses attacked by this species can vary greatly in size\ both within a species "e[g[ the egg!mass size of the Noctuidae Sesamia nonagrioides can range from about 19 eggs to more than 059 eggs# and between species "from a few hosts up to several tens of eggs per egg!mass#[ Moreover\ the hosts of T[ busseolae are often present in the same period of the year in the _eld[ The T[ busseolae strain used in this experiment was reared from ¼ 09 parasitized egg!masses of S[ non! agrioides\ provided by Dr S[ Kornosor "University of C ž ukurova\ Adana\ Turkey#[ These egg!masses were collected from corn _elds located in Adana in Sep! tember 0883[ From the time of capture onwards\ the strain was maintained on S[ nonagrioides under lab! oratory conditions for ¼ 29Ð21 generations\ at 15 2 0 >C\ 54 2 4) RH\ L ] D 05 ] 7 h "see Colazza\ Rosi + Clemente 0886#[ The S[ nonagrioides strain\ originating from pupae collected in central Italy\ was reared on a diet based on milled corn stalks and cobs as described by Giacometti "0884#\ and was main! tained under the same laboratory conditions[ Adult moths were kept in an oviposition cage with a wet cardboard cylinder covered spiralwise with para_lm strips to provide suitable oviposition sites "Giacometti 0884#[ The moth colony has been refreshed\ at irregu! lar intervals\ by wild material collected from corn _elds[ EXPERIMENTAL SET!UP Ten mated T[ busseolae females\ taken at random from the mass!reared population\ were used to establish 09 isofemale lines "i[e[ families#[ All of these females were reared under highly standardized conditions\ some of them even developed in the same vial[ Furthermore\ the host eggs that were used for rearing these females "and also those used for the experiment# originated from several S[ nonagrioides females and were ran! domly distributed over the 09 families compared[ Thus\ any variation that may be observed between families cannot be explained by variation in the environmental conditions of the developing founding mothers[ Experiments were performed on the next generation[ On average 7=2 "range] 5Ð09# daughters were observed per family and were randomly dis! tributed over all the days of the experiment[ Therefore\ a total of 72 females was analysed[ The statistical test of the variation observed between families indicates whether or not the behavioural mechanisms studied can be considered to be family features[ If this is the case\ this would indicate the existence of a signi_cant genetic variation in the patch!leaving decision mech! anisms that were identi_ed "i[e[ isofemale lines method\ Parsons 0879^ Falconer 0870^ Ho}mann + Parsons 0877#[ It should be noted that the isofemale lines method that was used here provides information on broad sense genetic variability\ that is to say\ it does not distinguish between additive and non!addi! tive components of the genetic variation observed[ Any kind of genetic determinism\ including domi! nance and maternal e}ect\ may also be revealed[ A 013 Genetic variation in patch time allocation Þ 0888 British Ecological Society Journal of Animal Ecology\ 57\ 010Ð022 thorough analysis of the genetic variation in the behavioural traits studied\ using the isofemale lines method\ would have necessitated the design of some accurate way to avoid the e}ect of environmental in~uence on the variation observed "e[g[ by splitting each family and rearing them in independent repli! cates\ and:or by repeating the experiment over suc! cessive generations#[ However\ this design would have resulted in an experiment that would have been too large to handle[ So\ all sources of variation "e[g[ rear! ing vials\ host eggs used for rearing and experiments\ etc[# were randomly distributed over all the 09 families compared[ Freshly emerged T[ busseolae females were kept with males for 13 h for mating[ They were then indi! vidually isolated with a drop of honey solution and used in experiments when they were 1Ð2 days old[ Experiments were carried out during the daytime at 15 2 0 >C and 59 2 4) RH[ At the beginning of each replicate\ a single female was introduced into an arena "diameter] 07 mm\ height] 3 mm# with a circular patch of _ve freshly laid S[ nonagrioides eggs in the middle[ Females were not allowed to contact any hosts before the experiment "i[e[ inexperienced females# and were used only once[ Attacked hosts were not replaced\ so the patch su}ered a continuous depletion[ As soon as the female was introduced into the arena\ she exhibited a succession of patch!entering and ! leaving behaviours[ While foraging on the patch and as soon as a suitable host was encountered\ she adopted a characteristic oviposition posture and star! ted to drill the egg chorion with her ovipositor[ This behaviour lasted\ on average\ "2 SD# 79=8 2 25=4 s[ Then\ after a successful oviposition\ the female adopted a typical marking behaviour\ sweeping the surface of the host several times with her ovipositor[ This marking behaviour\ which lasted\ on average\ 5=8 2 1=3 s\ probably corresponds to the deposition of a chemical compound that indicates to other females and to herself that the host has already been attacked[ When an unsuitable host was encountered\ the female adopted the oviposition posture\ but did not show any marking behaviour thereafter[ This event was con! sidered to be a so!called host rejection behaviour[ In order to increase the number of replicates per unit of time\ six females\ each on a separate arena with a single host patch\ were simultaneously videotaped\ leading to a cumulative video recording of continuous observation of more than 20 h[ The videotapes were then analysed with an event recorder and\ for each female\ the beginning and the end of the following behaviours were recorded with an accuracy of 9=0 s] "i# entering or "ii# leaving the patch^ "iii# adopting an oviposition posture or "iv# showing a marking behav! iour^ "v# standing still or "vi# preening[ Patch entering was considered to be the point when the female had at least four legs on the egg mass\ and patch leaving was recorded when the female had all her legs on the substrate[ Observations started as soon as the female entered the patch for the _rst time and stopped when she left the patch for more than 59 s[ After analysing all the videotapes\ it appeared that the preening behaviour was observed only when the female was o} the patch[ Therefore\ since only intra! patch residence time was studied\ the duration of this behaviour was not taken into account[ The behaviour of {standing still| was also mostly observed when the female was o} the patch[ In this case\ it was also not taken into account[ In only six out of 281 patch visits studied\ was this behaviour observed while the female was on the patch\ but its duration was only about 1=4) of the corresponding patch residence time[ Thus\ in these cases\ the duration of this behaviour was included in the total intra!patch foraging time[ On some occasions\ the female left the patch and walked a few millimetres away for a short excursion before returning to the hosts[ The patch was thus considered to be left when the female spent at least 0=9 s o} the patch[ Such an arbitrary criterion is com! monly used in studies on patch time allocation by parasitic wasps "Waage 0867\ 0868^ Driessen et al[ 0884#[ However\ to check whether the criterion had any artefactual e}ect on the results\ all computations were also performed with a threshold value of 4=9 s[ The results led qualitatively to the same conclusion in both cases[ In order to have a su.cient number of replicates\ the females were con_ned within the experimental arena[ Despite the fact that the patch:arena surface ratio was less than 9=902\ these experimental con! ditions may induce an increase in the patch!returning tendency of the females[ Therefore\ in order to reduce the possibility of this artefact\ only the patch!leaving tendency was studied\ and only the _rst _ve visits to the patch were taken into account[ However\ when the data were available\ computations were also made with the _rst 09 or 04 visits to the patch[ The results obtained led qualitatively to the same conclusion in all cases[ Therefore\ con_ning the females does not seem to have any e}ect on the results obtained[ DESCRIPTION OF THE MODEL The data were analysed using a Cox|s proportional hazards model\ also called a Cox|s regression model[ A detailed description of this model can be found in the literature on survival analysis "e[g[ Kalb~eisch + Prentice 0879^ Collett 0883#[ Such a model enables the correct handling of censored data "see Bressers et al[ 0880^ Haccou + Meelis 0881\ for a discussion on this#[ It is formulated in terms of hazard rate\ which is the probability per unit of time that a female leaves the patch\ given that she is still on it[ Thus\ this represents the tendency for a female to leave the patch[ In sur! vival analysis terminology\ entering the patch cor! responds to a renewal point and leaving the patch to a failure[ It is assumed that the hazard rate function is the product of a basic tendency to leave the patch 014 E[ Wajnberg\ M[C[ Rosi + S[ Colazza "baseline hazard#\ which is reset after each renewal point\ and a so!called hazard ratio\ which gives the joint e}ect of all the explanatory variables taken into account "covariates#[ The general form of the model is] 6 p h "t#  h9"t# exp s bi zi Þ 0888 British Ecological Society Journal of Animal Ecology\ 57\ 010Ð022 i0 7 eqn 0 where h"t# is the hazard rate\ h9"t# the baseline hazard\ t the time since the latest renewal point\ and bi the coe.cients that give the relative contribution of p covariates[ These coe.cients can be interpreted through the hazard ratio\ which is the exponential term[ A joint e}ect of the covariates leading to a hazard ratio greater than one will be interpreted as having an increasing e}ect on patch!leaving tendency\ while a hazard ratio lower than one will be interpreted in the opposite way[ Covariates can be time!dependent or _xed[ The baseline hazard\ which is the hazard rate when all the covariates are equal to zero\ is left unspeci_ed[ All observable behavioural events that occur during the exploitation of a patch cannot be considered because the resulting data set would be too large[ Therefore\ optimality theory can be used to restrict the set of relevant features of intra!patch experience that should be taken into account "Haccou et al[ 0880^ Hemerik et al[ 0882#[ The model that was used was derived from the one proposed by Haccou et al[ "0880# and Hemerik et al[ "0882#[ As in their model\ in the present study _rst the number of successful ovi! positions that were observed during the current patch visit was considered[ The analysis of the cor! responding hazard ratio will indicate whether each oviposition had an incremental or decremental e}ect on patch residence time[ The number of host rejections during the current patch visit was also added\ because they could also have an e}ect on the leaving tendency[ Moreover\ whereas Haccou et al[ "0880# and Hemerik et al[ "0882# considered the instantaneous oviposition and host rejection rates up to eight or four ovi! positions backwards in time\ the present study only looked at these rates up to the three preceding ovi! positions in order to reduce the number of parameters to estimate "see below#[ These rates\ expressed in timeÐ0\ were assumed to change with patch depletion and their study allowed the analysis of the corresponding consequence of this on the patch!leaving tendency of females[ All these covariates were time!dependent[ In addition to this\ two _xed covariates were also con! sidered] the rank of subsequent visits to the patch and the family to which each female belonged[ The rank of visits to the patch can also be considered to be the number of times females were o} the patch "as in Haccou et al[ 0880^ Hemerik et al[ 0882#\ or\ equally\ the number of times females cross the edge of the patch[ Finally\ in order to quantify the genetic varia! bility in each of the behavioural mechanisms studied\ the interaction between the {family| e}ect and all the relevant covariates was also considered[ Table 0 gives a list of all of these covariates with their dimensions[ To _t the model with a categorical covariate "i[e[ a factor#\ such as the {family| e}ect\ the _rst family was arbitrarily assumed to be the reference level cor! responding to the baseline hazard with a parameter set to zero[ Thus\ only nine parameters need to be estimated for this factor[ The same procedure was used for all the corresponding interactions "see McCullagh + Nelder 0878^ Collett 0883\ for a detailed explanation#[ Parameters were estimated from the data by the maximization of the {partial likelihood| function proposed by Cox "0864#[ The procedure gives the estimated coe.cients of the model with their esti! mated varianceÐcovariance matrix\ which\ in turn\ can be used to compute con_dence intervals of hazard ratios "see Appendix 1#[ All computations were carried out in S!Plus\ using the package developed by T[ Ther! neau "Venables + Ripley 0883#[ Several statistical procedures are available for test! ing the signi_cant e}ect of the covariates\ all of which take into account the existence of possible correlations between the corresponding parameters[ In general\ a Wald!test has been used "Haccou et al[ 0880^ Hemerik et al[ 0882^ van Roermund et al[ 0883^ Ormel\ Gort + van Alebeek 0884#\ however\ for the study reported here\ a standard likelihood ratio test was preferred "Collett 0883^ see McCullagh + Nelder 0878\ for a general description of this test#[ The procedure that was used to _t the model is described in Appendix 0[ The name {proportional hazards model| stems from the assumption that\ for di}erent values of a _xed covariate\ the hazard rates described in eqn 0 are pro! portional "Kalb~eisch + Prentice 0879^ Collett 0883#[ The most simple and e.cient method to test this assumption is to plot the log!cumulative hazard\ logð! log S"t#Ł\ against log"t#\ where t is the patch time dur! ation and S"t# is the KaplanÐMeier estimate of the survivor function\ for each value of the _xed covari! ates "Andersen 0871^ Collett 0883#[ If the curves can be taken to be parallel\ the proportional assumption is justi_ed[ Figure 0 gives the log!cumulative hazard plots for the two _xed covariates studied[ Hazard rates for the _rst visit to the patch do not appear to be proportional to those obtained for the subsequent visits[ In this case\ the model can still be _tted by means of strati_cation between the _rst and the subsequent visits to the patch\ leading to a new model with di}erent baseline hazard functions[ For the isofemale lines\ however\ the proportional assumption appears to be justi_ed[ Finally\ the adequacy of the _tted model can be assessed by making residuals plots[ The most com! monly used residuals in the analysis of survival data are those proposed by Cox + Snell "0857# "e[g[ Hemerik et al[ 0882^ van Roermund et al[ 0883#[ For the present study\ it was preferred to use the deviance residuals proposed by Therneau\ Grambsch + Flem! 015 Genetic variation in patch time allocation Table 0[ List of the explanatory covariates used in the Cox|s regression model[ The indicated dimensions correspond to the number of parameters that should be estimated to test them "see text# Covariates Dimension Time!dependant Number of successful ovipositions during the visit to the patch Number of host rejections during the visit to the patch Oviposition rates up to the three preceding ovipositions Rejection rates up to the three preceding ovipositions Rank of successive visits to the patch Family each female belongs to "i[e[ female|s genotype# Interaction {family|Ð{number of ovipositions| Interaction {family|Ð{number of host rejections| Interaction {family|Ð{oviposition rates\ three steps backwards| Interaction {family|Ð{rejection rates\ three steps backwards| Interaction {family|Ð{rank of visit to the patch| 0 0 2 2 0 8 8 8 16 16 8 Yes Yes Yes Yes No No Yes Yes Yes Yes No Fig[ 0[ Log!cumulative hazard plots for the two _xed covariates used in the Cox|s regression model[ The curve on the right in the left panel "successive visits to the patch# corresponds to the _rst patch visit[ Both axes are in log scale[ ing "0889#\ because they have the same properties of residuals used to check the adequacy of linear models and are thus easiest to interpret[ Indeed\ they are uncorrelated with one another and are symmetrically distributed around zero with an expected value of zero\ when the _tted model is correct[ Figure 1\ which gives the corresponding plot for the _nal model _tted\ shows that nothing is amiss[ Therefore\ the _nal model seems properly to describe the patch!leaving tendency of T[ busseolae females[ Results Þ 0888 British Ecological Society Journal of Animal Ecology\ 57\ 010Ð022 The _tting procedure\ described in Appendix 0\ has led to a _nal model with 21 parameters[ Table 1 gives the estimated e}ect of all the covariates that have a signi_cant in~uence on the patch!leaving tendency of T[ busseolae females[ Each successful oviposition signi_cantly increased the patch!leaving tendency by a factor of 3=05[ This result indicates that T[ busseolae females are using a decremental mechanism to manage their residence time on patches of _ve S[ nonagrioides eggs[ Fur! thermore\ the rejection of a host also led to an increase in the patch!leaving tendency "here\ by a factor of 1=26#[ Despite these highly signi_cant e}ects\ the instantaneous oviposition rates\ up to the three pre! ceding ovipositions\ have not shown any e}ect on the patch!leaving tendency "all x1 at P × 9=94#[ However\ there was a signi_cant e}ect of the rejection rates up to two ovipositions backwards in time[ The cor! responding hazard ratios were both less than unity\ suggesting that they have a decreasing e}ect on the patch!leaving tendency[ Therefore\ when host rejec! tions appeared between two ovipositions that were in rapid succession\ and this up to two ovipositions 016 E[ Wajnberg\ M[C[ Rosi + S[ Colazza Fig[ 1[ Plot of the deviance residuals against the rank order of patch time duration[ These residuals were computed after the _nal model had been _tted to the data "see text#[ backwards in time\ the corresponding rejection rates increased and the e}ect of each host rejected on the patch!leaving tendency is reduced or possibly reversed[ In fact\ according to eqn 0\ and taking into account the host rejection rate r0 only one step back! wards in time\ the hazard ratio after one host rejection was exp "9=75Ð74=53 r0#[ Thus\ the increasing tendency to leave the patch after each host is rejected will be cancelled or reversed as soon as r0 × 0=993 × 09Ð1 "i[e[ as soon as the hazard ratio decreases below unity#[ Only nine out of 876 "i[e[ 9=8)# rejection rates esti! mated were over this threshold value[ Therefore\ the host rejection rate one step backwards in time only had a reducing\ but not reversing\ e}ect on the increas! ing tendency to leave the patch that was induced by each host rejected[ The same conclusion was obtained when the host rejection rate two steps backwards in time was considered\ but in this case\ the e}ect was less signi_cant[ As can be seen in Fig[ 2\ the _rst visit to the patch was always much longer than the subsequent ones[ Up to 59) of all the successful ovipositions were observed during this _rst patch visit[ Afterwards\ the patch!leaving tendency signi_cantly increased by a factor of 0=10 for each subsequent visit\ leading to a decrease in the corresponding average residence time "see Table 1#[ Finally\ no signi_cant interactions were observed between the rank of patch visit and the e}ect of each successful oviposition\ host rejection and rejec! tion rates up to two steps backwards in time "all x1 at P × 9=94#[ Thus\ the patch!leaving rules that have been discussed so far "e[g[ decremental e}ect of each oviposition\ etc[# seem to remain constant over the successive visits to the patch[ The results also have shown that there is a signi_cant variation in the patch!leaving tendency between the isofemale lines that were compared "see Table 1#[ Within the T[ busseolae population that was studied\ some families showed a signi_cantly stronger patch! leaving tendency than others[ This suggests that the variation in the behavioural traits involved may be under genetic control[ The genetic variation quanti_ed in this manner can either be transmitted to the fol! lowing generation according to Mendelian mechanisms or can be maternally inherited[ Both mechanisms can have an important ecological meaning and can be the target of strong selective pressures\ leading the females to adapt their patch!residence time to local environ! mental conditions[ Besides this global genetic variation\ there was also a signi_cant interaction between the isofemale lines and the e}ect of each oviposition[ As can be seen from Fig[ 3a\ each oviposition has led\ globally\ to hazard ratios above unity\ con_rming the associated decremental e}ect on the patch!residence time described above[ However\ the present results indicate that this e}ect is not the same among the di}erent lines compared[ This suggests the existence\ within the population\ of signi_cant genetic variation in the intensity of the decremental e}ect on the patch residence time[ Finally\ a signi_cant interaction was observed between the isofemale lines and the e}ect of each host rejected "see Table 1 and Fig[ 3b#[ Within the Table 1[ Estimated regression coe.cients "b#\ standard errors "SE# and hazard ratios ðexp"b#Ł for only those covariates that had a signi_cant e}ect "P ³ 9=94# on the patch!leaving tendency of T[ busseolae females[ x1 corresponds to the likelihood ratio tests[ All of them were computed with all other signi_cant terms present in the model[ For each covariate including the {isofemale lines| e}ect\ nine parameters were estimated[ They are not provided here b Þ 0888 British Ecological Society Journal of Animal Ecology\ 57\ 010Ð022 Ovipositions "0# Host rejections "1# Rejection rate one step backwards Rejection rate two steps backwards Rank of patch visit Isofemale lines "2# Interaction "0# × "2# Interaction "1# × "2# 0=32 9=75 Ð74=53 Ð89=05 9=08 Ð Ð Ð SE 9=06 9=29 23=91 36=11 9=94 Ð Ð Ð exp"b# 3=05 1=26 5=32 × 09Ð27 5=84 × 09Ð39 0=10 Ð Ð Ð x1"d[f[# P!value 068=95 "0# 10=41 "0# 6=09 "0# 3=93 "0# 01=70 "0# 06=80 "8# 10=41 "8# 14=41 "8# ³ 9=990 ³ 9=990 9=997 9=933 ³ 9=990 9=925 9=900 9=991 017 Genetic variation in patch time allocation Fig[ 2[ Average patch residence times for each isofemale line and for each visit to the patch[ Additional upper limits correspond to standard errors[ Both averages and standard errors are computed from the KaplanÐMeier estimator of the corresponding survivor functions[ population analysed\ the decremental e}ect of each host rejected on the patch!residence time also appears to be a family feature[ This result suggests that this variation is also genetically determined[ Discussion Þ 0888 British Ecological Society Journal of Animal Ecology\ 57\ 010Ð022 As pointed out by Haccou et al[ "0880#\ the use of a Cox|s regression model to describe patch!leaving strategies has the advantage of providing quantitative results that indicate the importance of each tested e}ect on the patch!leaving tendency of females[ Using this method\ the results presented have revealed that the intra!patch experience of T[ busseolae females which attack eggs of S[ nonagrioides\ has a strong in~uence on their decision to leave the patch[ The e}ect of several behavioural events that appeared dur! ing the intra!patch foraging process were quanti_ed[ Most of them were shown to have a signi_cant in~u! ence on the tendency of females to leave the patch\ and thus on their patch!residence time[ The strongest e}ect was related to successful ovi! positions\ each of them leading to a signi_cant increase in the patch!leaving tendency[ This indicates that T[ busseolae females were using a decremental mechanism similar to the {count!down| mechanism proposed by Driessen et al[ "0884# for the larval para! sitoid Venturia canescens[ As stated by these authors\ such a mechanism\ also observed on other parasitoid species "Strand + Vinson 0871^ Wiskerke + Vet 0883^ van Steenis et al[ 0885#\ may be adaptive when hosts are uniformly distributed across patches "Iwasa et al[ 0870# or host patches are small "Strand + Vinson 0871#[ In both cases\ each host that is attacked will provide information regarding the loss of the future value of the patch and may thus promote readiness to leave[ In the present study\ patches of _ve hosts were o}ered to the females and these patches were much smaller than those usually encountered under natural situations[ This could be the reason why each ovi! position was found to have a decremental e}ect on patch!residence time[ In order to verify this hypoth! esis\ complementary experiments were performed using the same experimental set!up\ but with patches of 09 "07 females# or 04 "10 females# hosts[ In both cases\ a Cox|s regression model led to the same con! clusion] each successful oviposition signi_cantly increased the patch!leaving tendency by a factor of 0=75 "on patches of 09 hosts# or 1=38 "on patches of 04 hosts#[ Thus\ the decremental mechanism appears to be a _xed rule which does not seem to depend on the size of the host patch[ This mechanism is probably an adaptive behaviour for females that attack hosts which are uniformly distributed across patches in the prospected environment[ Each successful oviposition was followed by a typi! cal marking behaviour\ which probably corresponds to the deposition of a contact pheromone on the attacked host[ Therefore\ the decremental e}ect associated with each oviposition may be related to the increase in the amount of pheromone deposited and this may lead to a stepwise decrease in the respon! 018 E[ Wajnberg\ M[C[ Rosi + S[ Colazza Fig[ 3[ Graphical representation of the interaction between the isofemale lines and the e}ect of "a# each successful oviposition or "b# host rejection[ Hazard ratios "2 SE# are computed according to the explanation provided in Appendix 1[ Isofemale lines are labelled as in Fig[ 2[ Þ 0888 British Ecological Society Journal of Animal Ecology\ 57\ 010Ð022 siveness of females to the patch[ This mechanism appears to be similar to the one described for several leaf!miner parasitoids by Sugimoto and his colleagues "Sugimoto\ Murakami + Yamazaki 0876^ Sugimoto + Tsujimoto 0877^ Sugimoto et al[ 0889#[ Using a mathematical approach\ these authors have shown that\ while searching for host larvae on a leaf\ foraging females deposit a marking chemical compound[ They found that a patch!leaving decision was triggered as soon as the amount of this marking cue reached a critical threshold[ In the results presented here\ however\ the marking pheromone was only deposited at particular discrete time intervals\ i[e[ when hosts were successfully attacked[ 029 Genetic variation in patch time allocation Þ 0888 British Ecological Society Journal of Animal Ecology\ 57\ 010Ð022 Each host rejection also led to a signi_cant increase in the patch!leaving tendency[ As stated by van Alphen + Vet "0875#\ van Lenteren "0880# and van Alphen "0882#\ such a mechanism could be adaptive because the rejection of a host provides the female with some information regarding the decreasing value of the patch on which she is currently foraging[ Besides this\ instantaneous oviposition rates\ up to three pre! ceding ovipositions\ do not have any signi_cant e}ect[ A similar result was obtained on the Drosophila larval parasitoid Leptopilina clavipes "Hemerik et al[ 0882#\ whereas L[ heterotoma appears to react to these rates more signi_cantly "Haccou et al[ 0880#[ In this case\ the most recently experienced oviposition rates were shown to have the strongest e}ect[ These instan! taneous oviposition rates are likely to change as a result of patch depletion[ Therefore\ the results obtained here suggest that T[ busseolae females are not using the rate of patch depletion as a way to decide when the patch should be left[ On the other hand\ there was a signi_cant e}ect of the host rejection rates\ up to two ovipositions backwards in time[ These rates have a reducing e}ect on the increasing tendency to leave the patch associated with each host rejection[ These rejection rates can only be estimated if host rejections are followed by at least one successful ovi! position[ Thus\ this result suggests that any successful oviposition that occurs after one or several host rejec! tions will restore\ to a certain extent\ the wasp|s motiv! ation to remain on the patch\ and this mechanism will be all the stronger as this new successful oviposition occurs rapidly after the previous one[ In such a case\ the wasp acquires new information\ indicating that healthy hosts are still available on the patch and it therefore becomes worthwhile to remain on it for an additional amount of time[ Thus\ this mechanism may be considered to be adaptive[ Finally\ there was signi_cant variation in the patch! leaving tendency between subsequent visits to the patch[ In particular\ the _rst visit was always much longer than the subsequent ones[ A similar result has been observed for several other parasitoid species "e[g[ van Lenteren + Bakker 0867^ Waage 0868^ Strand + Vinson 0871^ Haccou et al[ 0880#[ Furthermore\ Haccou et al[ "0880# demonstrated that\ after the patch has been visited once\ the patch!leaving tend! ency of L[ heterotoma females increases\ but in a non! monotonic way[ Here\ the patch!leaving tendency was also found to increase with each subsequent visit to the patch\ but this e}ect was considered to be linear[ The fact that the _tted model appeared to describe correctly the observed data seems to con_rm such a hypothesis[ Several mechanisms can be proposed to explain this result[ First\ it may be possible that for! aging females have used their past experience\ acquired during preceding visits to the patch\ to adjust their current patch!residence time[ Such a mechanism could explain why the _rst visit was much longer than the subsequent ones\ because females were only naive in the _rst case when they have to discover a new environment[ Second\ after the patch has been visited once\ females may recognize some landmarks or patch marking\ or may experience a reduced motivation to search because of egg depletion\ habituation or tir! edness "van Alphen + Galis 0872#[ Under such a hypothesis\ the most important mechanism would be the recognition of a marking pheromone that is deposited after each successful oviposition[ A third hypothesis can be related to the rate of patch depletion and thus\ indirectly\ to the rate of superparasitism "i[e[ oviposition in a host that has already been attacked#[ Indeed\ under the experimental conditions used here\ some cases of superparasitism did occur^ for example\ in two out of 72 "i[e[ 1=3)# _rst visits to the patch that was studied\ six or seven successful ovipositions were observed on the patch of _ve hosts[ Even though the timing of such events was not recorded\ their fre! quency would be likely to increase during subsequent visits to the patch[ This\ in turn\ could lead to a corresponding increase in the patch!leaving ten! dency[ In all theoretical and experimental studies per! formed on patch time allocation\ the patch!leaving decision rules\ under a given environment\ have always been considered to be _xed species!speci_c mechanisms "Driessen et al[ 0884#[ However\ the results obtained by the present study indicate that there was strong genetic variability in the cor! responding mechanisms\ within the population stud! ied[ Using the isofemale lines method\ di}erent genetic variations were observed and quanti_ed[ First of all\ there was a signi_cant global genetic variation in the patch!leaving tendency between the di}erent families compared[ This indicates that\ within the studied population\ some genotypes result in females remain! ing on the patch for a longer period of time than others[ According to Waage|s "0868# model\ the patch residence time will depend on] "i# the initial degree of responsiveness to the patch edge\ which is assumed to be related to the number of hosts available^ and "ii# the decreasing rate of this responsiveness during the foraging process\ leading to a decreasing tendency to exhibit a turning response each time the patch edge is encountered "Waage 0867\ 0868#[ Thus\ the inter! family variability observed in this study could be the consequence of genetic variation in the initial response to the number of hosts available in the patch and:or in the rate of habituation to the patch edge[ Irres! pective of the mechanism involved\ such genetic vari! ation is likely to be the characteristic of a polyphagous species like T[ busseolae\ which is known to attack\ over successive generations\ several host species show! ing strong di}erences in patch size\ quality and dis! tribution[ Aside from the global genetic variability\ there was also\ within the analysed population\ signi_cant gen! etic variation in the intensity of the decremental e}ect of each oviposition on the patch!residence time "see 020 E[ Wajnberg\ M[C[ Rosi + S[ Colazza Þ 0888 British Ecological Society Journal of Animal Ecology\ 57\ 010Ð022 Fig[ 3a#[ The decremental "or even incremental# e}ect of each oviposition has always been considered to depend only on the time between successive ovi! positions "Waage 0868# or on the number of past ovipositions "Driessen et al[ 0884#[ The results pre! sented here show that it also depends on the genotype of the females[ As suggested above\ the observed dec! remental e}ect may be related to the response to a deposited pheromone on each successfully attacked host[ Therefore\ the genetic variability in the intensity of this decremental e}ect may correspond to genetic variation in the amount of pheromone deposited and:or in the response level to such a marking cue[ A decremental e}ect is usually considered to be an adaptive behaviour for females which attack hosts with a uniform distribution across patches "Iwasa et al[ 0870#[ The observed genetic variability in the intensity of the decremental e}ect could thus be con! sidered to be a characteristic of a wasp population that consists of females which experience some variation in the distribution pattern of their hosts[ Finally\ there was also signi_cant genetic variability in the intensity of the decremental e}ect associated with each host rejection "see Fig[ 3b#[ For some famil! ies\ each host rejection led to a strong increase in the patch!leaving tendency\ while for others\ the increase appears to be less pronounced[ As stated by van Alphen + Vet "0875#\ encounters with parasitized hosts\ and thus host rejections\ could a}ect patch time\ either because they impart information to the para! sitoid about the decreasing value of the patch or because they decrease the forager|s host!searching motivation[ The genetic variation observed in the intensity of the decremental e}ect associated with each host rejected could thus correspond to genetic varia! bility in the quality of the information acquired on the decreasing value of the patch\ and:or in the associated decreasing level of the host searching motivation of females[ The genetic variation observed in the intensity of the decremental e}ect associated with each oviposition or host rejection indicates that there is\ within the analysed population\ genetic variability in the response to the information acquired by the foraging females during their intra!patch foraging experience[ Patch time allocation is considered to have a strong in~uence on the spatial distribution of parasitoids\ and thus on the population dynamics of parasitoidÐ host systems "van Alphen 0882#[ Thus\ it would be interesting to include such an inter!individual genetic variability in models that take into account individual behavioural decisions in order to estimate its conse! quence in terms of population dynamics[ To accomplish this\ the models developed by Bernstein\ Kacelnik + Krebs "0877\ 0880# and Krivan "0886# could provide a good starting point[ Finally\ patch! residence time is known to be in~uenced by the num! ber of females foraging on a patch "Visser\ van Alphen + Nell 0889^ Visser + Driessen 0880#[ Therefore\ experiments are now being performed in order to see whether there is some interference between T[ bus! seolae females foraging on a patch and if\ within the population studied\ there is genetic variability in this behavioural mechanism[ Acknowledgements We thank C[ Bernstein and G[ Driessen for their con! tinuous encouragement and criticisms and for their precious patience\ and C[ Bernstein\ G[ Driessen\ J[C[ van Lenteren\ O[ Pons\ J[S[ Pierre and X[ Fauvergue for their critical reading of the manuscript[ S[ Fuller kindly read the English version of the manuscript[ This work was supported by CEE grant number AIR2!CT83Ð0322 and by the CNR {Program for Ital! ian and Foreign Research Institution Ð Short!term mobility| number 006841[ References van Alphen\ J[J[M[ "0882# Patch residence time and encoun! ters with parasitised hosts] A reaction[ Netherlands Journal of Zoology\ 32\ 239Ð238[ van Alphen\ J[J[M[ + Galis\ F[ "0872# Patch time allocation and parasitization e.ciency of Asobara tabida\ a larval parasitoid of Drosophila[ Journal of Animal Ecology\ 41\ 826Ð841[ van Alphen\ J[J[M[ + Vet\ L[E[M[ "0875# An evolutionary approach to host _nding and selection[ Insect Parasitoids "eds J[ Waage + D[ Greathead#\ pp[ 12Ð50[ Academic Press\ London[ Andersen\ P[K[ "0871# Testing goodness of _t of Cox|s regression and life model[ Biometrics\ 27\ 56Ð66[ Bakker\ K[ + van Alphen\ J[J[M[ "0877# The in~uence of encounters with parasitized hosts "larvae of Drosophila subobscura# on the time spent searching on a patch by Leptopilina heterotoma "Hym[\ Cynip[#[ Parasitoid Insects\ Proceedings of the European Workshop "eds M[ Bouletreau + G[ Bonnot#\ pp[ 28Ð39[ Les Colloques de l|INRA\ Vol[ 37\ Paris[ Bernstein\ C[\ Kacelnik\ A[ + Krebs\ J[R[ "0877# Individual decisions and the distribution of predators in a patchy environment[ Journal of Animal Ecology\ 46\ 0996Ð0915[ Bernstein\ C[\ Kacelnik\ A[ + Krebs\ J[R[ "0880# Individual decisions and the distribution of predators in a patchy environment[ II[ The in~uence of travel costs and structure of the environment[ Journal of Animal Ecology\ 59\ 194Ð 114[ Bressers\ M[\ Meelis\ E[\ Haccou\ P[ + Kruk\ M[ "0880# When did it really start or stop] the impact of censored observations on the analysis of duration[ Behavioural Pro! cesses\ 12\ 0Ð19[ Charnov\ E[L[ "0865# Optimal foraging] the marginal value theorem[ Theoretical Population Biology\ 8\ 018Ð025[ Cloutier\ C[ + Bauduin\ F[ "0889# Searching behavior of the aphid parasitoid Aphidius nigripes "Hymenoptera] Aphi! diidae# foraging on potato plants[ Environmental Ento! mology\ 08\ 111Ð117[ Colazza\ S[\ Rosi\ M[R[ + Clemente\ A[ "0886# Response of egg parasitoid Telenomus busseolae to sex pheromone of Sesamia nonagrioides[ Journal of Chemical Ecology\ 12\ 1326Ð1333[ Collett\ D[ "0883# Modelling Survival Data in Medical Research[ Chapman and Hall\ London[ Cowie\ R[J[ + Krebs\ J[R[ "0868# Optimal foraging in patchy 021 Genetic variation in patch time allocation Þ 0888 British Ecological Society Journal of Animal Ecology\ 57\ 010Ð022 environments[ Population Dynamics "eds R[M[ Anderson\ B[D[ Turner + L[R[ Taylor#\ pp[ 072Ð194[ Blackwell Sci! ence Ltd\ Oxford[ Cox\ D[R[ "0861# Regression models and life tables[ Biometrics\ 27\ 56Ð66[ Cox\ D[R[ "0864# Partial likelihood[ Biometrika\ 51\ 158Ð 165[ Cox\ D[R[ + Snell\ E[J[ "0857# A general de_nition of residuals[ Journal of the Royal Statistical Society\ 29\ 137Ð 164[ Driessen\ G[\ Bernstein\ C[\ van Alphen\ J[J[M[ + Kacelnik\ A[ "0884# A count!down mechanism for host search in the parasitoid Venturia canescens[ Journal of Animal Ecology\ 53\ 006Ð014[ Falconer\ D[S[ "0870# Introduction to Quantitative Genetics\ 1nd edn[ Longman\ New York[ Giacometti\ R[ "0884# Rearing of Sesamia nonagrioides Lefebvre on meridic diet "Lepidoptera Noctuidae#[ REDIA\ 67\ 08Ð16[ Godfray\ H[C[J[ "0883# Parasitoids[ Behavioral and Evol! utionary Ecology[ Princeton University Press\ Princeton\ New Jersey[ Green\ R[F[ "0879# Bayesian birds] A simple example of Oaten|s stochastic model of optimal foraging[ Theoretical Population Biology\ 07\ 133Ð145[ Green\ R[F[ "0873# Stopping rules for optimal foragers[ The American Naturalist\ 012\ 29Ð39[ Haccou\ P[ + Meelis\ E[ "0881# Statistical Analysis of Behav! ioural Data[ an Approach Based on Time!Structured Models[ Oxford University Press\ Oxford[ Haccou\ P[\ de Vlas\ S[J[\ van Alphen\ J[J[M[ + Visser\ M[E[ "0880# Information processing by foragers] e}ects on intra! patch experience on the leaving tendency of Leptopilina heterotoma[ Journal of Animal Ecology\ 59\ 82Ð095[ Hemerik\ L[\ Driessen\ G[ + Haccou\ P[ "0882# E}ects of intra!patch experiences on patch time\ search time and searching e.ciency of the parasitoid Leptopilina clavipes[ Journal of Animal Ecology\ 51\ 22Ð33[ Ho}mann\ A[A[ + Parsons\ P[A[ "0877# The analysis of quantitative variation in natural populations with iso! female strains[ Genetic Selection Evolution\ 19\ 76Ð87[ Iwasa\ Y[\ Higashi\ M[ + Yamamura\ N[ "0870# Prey dis! tribution as a factor determining the choice of optimal foraging strategy[ The American Naturalist\ 006\ 609Ð612[ Kalb~eisch\ J[D[ + Prentice\ R[L[ "0879# The Statistical Analysis of Failure Time Data[ John Wiley + Sons\ New York[ Krivan\ V[ "0886# Dynamic ideal free distribution] E}ects of optimal patch choice on predatorÐprey dynamics[ The American Naturalist\ 038\ 053Ð067[ van Lenteren\ J[C[ "0880# Encounters with parasitized hosts] To leave or not to leave a patch[ Netherlands Journal of Zoology\ 30\ 033Ð046[ van Lenteren\ J[C[ + Bakker\ K[ "0867# Behavioural aspects of the functional responses of a parasite "Pseudeucoila bochei Weld# to its host "Drosophila melanogaster#[ Nether! lands Journal of Zoology\ 17\ 102Ð122[ Li\ C[\ Roitberg\ B[D[ + Mackauer\ M[ "0882# Patch resi! dence time and parasitism of Aphelinus asychis] a simu! lation model[ Ecological Modelling\ 58\ 116Ð130[ McCullagh\ P[ + Nelder\ J[A[ "0878# Generalized Linear Models\ 1nd edn[ Chapman and Hall\ London[ McNair\ J[M[ "0871# Optimal giving!up time and the mar! ginal value theorem[ The American Naturalist\ 008\ 400Ð 418[ McNamara\ J[M[ "0871# Optimal patch use in a stochastic environment[ Theoretical Population Biology\ 10\ 158Ð177[ McNamara\ J[M[ + Houston\ A[I[ "0874# Optimal foraging and learning[ Journal of Theoretical Biology\ 006\ 120Ð138[ Nelson\ J[M[ + Roitberg\ B[D[ "0884# Flexible patch time allocation by the leafminer parasitoid\ Opius Dimidiatus[ Ecological Entomology\ 19\ 134Ð141[ Oaten\ A[ "0866# Optimal foraging in patches] A case for stochasticity[ Theoretical Population Biology\ 01\ 152Ð174[ Ormel\ G[J[\ Gort\ G[ + van Alebeek\ F[A[N[ "0884# Ana! lysing host location in Uscana lariophaga "Hymenoptera] Trichogrammatidae#\ an egg parasitoid of bruchids "Coleoptera] Bruchidae# using Cox|s proportional hazards model[ Bulletin of Entomological Research\ 74\ 002Ð012[ Parsons\ P[A[ "0879# Isofemale strains and evolutionary stra! tegies in natural populations[ Evolutionary Biology\ Vol[ 02 "eds M[ Hecht\ W[ Steere + B[ Wallace#\ pp[ 064Ð106[ Plenum Press\ London[ Polaszek\ A[\ Ubeku\ J[A[ + Bosque!Perez\ N[A[ "0882# Tax! onomy of the Telenomus busseolae species!complex "Hymenoptera] Scelionidae# egg parasitoids of cereal stem borers "Lepidoptera] Noctuidae\ Pyralidae#[ Bulletin of Entomological Research\ 72\ 110Ð115[ Pyke\ G[H[ "0873# Optimal foraging theory] A critical review[ Annual Review of Ecology and Systematics\ 04\ 412Ð464[ van Roermund\ H[J[W[\ Hemerik\ L[ + van Lenteren\ J[C[ "0883# In~uence of intrapatch experiences and temperature on the time allocation of the white~y parasitoid Encarsia formosa "Hymenoptera] Aphelinidae#[ Journal of Insect Behavior\ 6\ 372Ð490[ van Steenis\ M[J[\ El!Khawass\ K[A[M[H[\ Hemerik\ L[ + van Lenteren\ J[C[ "0885# Time allocation of the parasitoid Aphidius colemani "Hymenoptera] Aphidiidae# foraging for Aphis gossypii "Homoptera] Aphidae# on cucumber leaves[ Journal of Insect Behavior\ 8\ 172Ð184[ Stephens\ D[W[ + Krebs\ J[R[ "0875# Foraging Theory[ Prin! ceton University Press\ Princeton\ New Jersey[ Strand\ M[R[ + Vinson\ S[B[ "0871# Behavioral response of the parasitoid Cardiochiles nigriceps to a kairomone[ Entomologia Experimentalis et Applicata\ 20\ 297Ð204[ Sugimoto\ T[\ Minkenberg\ O[P[J[M[\ Takabayashi\ J[\ Dicke\ M[ + van Lenteren\ J[C[ "0889# Foraging for patch! ily!distributed leaf miners by the parasitic wasp\ Dacnusa sibirica[ Research in Population Ecology\ 21\ 270Ð278[ Sugimoto\ T[\ Murakami\ H[ + Yamazaki\ R[ "0876# For! aging for patchily!distributed leaf!miners by the para! sitoid\ Dapsilarthra ru_ventris "Hymenoptera] Bracon! idae#[ II[ Stopping rule for host search[ Journal of Ethology\ 4\ 84Ð092[ Sugimoto\ T[ + Tsujimoto\ S[ "0877# Stopping rule of host search by the parasitoid\ Chrysocharis pentheus "Hymen! optera] Eulophidae#\ in host patches[ Research in Popu! lation Ecology\ 29\ 012Ð022[ Therneau\ T[M[\ Grambsch\ P[M[ + Fleming\ T[R[ "0889# Martingale!based residuals for survival models[ Biome! trika\ 66\ 036Ð059[ Venables\ W[N[ + Ripley\ B[D[ "0883# Modern Applied Stat! istics with S!Plus[ Springer!Verlag\ New York[ Visser\ M[E[\ van Alphen\ J[J[M[ + Nell\ H[W[ "0889# Adapt! ive superparasitism and patch time allocation in solitary parasitoids] The in~uence of the number of parasitoids depleting a patch[ Behaviour\ 003\ 10Ð25[ Visser\ M[E[ + Driessen\ G[ "0880# Indirect mutual inter! ference in parasitoids[ Netherlands Journal of Zoology\ 30\ 103Ð116[ Waage\ J[K[ "0867# Arrestment responses of the parasitoid\ Nemeritis canescens\ to a contact chemical produced by its host\ Plodia interpunctella[ Physiological Entomology\ 2\ 024Ð035[ Waage\ J[K[ "0868# Foraging for patchily!distributed hosts by the parasitoid\ Nemeritis canescens[ Journal of Animal Ecology\ 37\ 242Ð260[ Wiskerke\ J[S[C[ + Vet\ L[E[M[ "0883# Foraging for solitary and gregariously feeding caterpillars] A comparison of two related parasitoid species "Hymenoptera] Braconidae#[ Journal of Insect Behavior\ 6\ 474Ð592[ 022 E[ Wajnberg\ M[C[ Rosi + S[ Colazza Yamada\ Y[ "0877# Optimal use of patches by parasitoids with a limited fecundity[ Research on Population Ecology\ 29\ 124Ð138[ Received 16 October 0886^ revision received 16 April 0887 Appendix 0 Usually\ all the parameters of a Cox|s regression model are estimated and tested simultaneously[ How! ever\ if we consider the 88 parameters listed in Table 0 and the possible pairwise interactions between all the covariates\ except for the {family| e}ect\ the model presented here can have more than 029 parameters that need to be estimated and cannot be _tted that way[ Therefore\ the _t of the model was performed using the iterative procedure described in the fol! lowing steps "Collett 0883#[ 0[ The model was _rst _tted with only one of the covariates "except the {family| e}ect# at a time[ 1[ All the covariates that gave a signi_cant likelihood ratio test at the preceding step were _tted together[ In the presence of certain covariates\ others may cease to be important[ So\ the e}ect of each covariate was tested again by sequentially omitting each of them from the set[ Only those that still showed a signi_cant e}ect were retained in the model[ Once a covariate was dropped\ the e}ect of omitting each of the remain! ing ones in turn was re!examined[ 2[ Covariates which were not important on their own\ and so were not under consideration in the previous step\ may become important in the presence of others[ Thus\ they were added to the model built in step 1 one at a time\ and those leading to a signi_cant e}ect were retained in the model[ This process may result in some terms in the model that was built in step 1 ceasing to be signi_cant[ In this case\ the terms were removed and the process was resumed at step 1 above[ 3[ A _nal check was made to ensure that all covariates in the model were signi_cant by omitting and testing them one at a time\ and that any covariate which was not included did not have a signi_cant e}ect once it was added[ Þ 0888 British Ecological Society Journal of Animal Ecology\ 57\ 010Ð022 4[ Finally\ the {family| e}ect was added and tested with the corresponding interactions[ The total covari! ates selection procedure was performed with a sig! ni_cance level of 09)\ in order to avoid rejecting an e}ect that would appear to be signi_cant in the following steps[ Appendix 1 The _tting procedure of the model leads to the esti! mation of coe.cients with their estimated varianceÐ covariance matrix[ In return\ these di}erent par! ameters can be used to estimate speci_c hazard ratios with their standard error[ Let us consider the result shown in Fig[ 3a that presents the interaction between the isofemale lines and the e}ect of each oviposition in terms of hazard ratios and their standard error[ For these e}ects only\ the model contains 09 parameters\ ai\ i  0\ 1\ [ [ [\ 09\ with a0  9 "i[e[ baseline hazard# and nine estimated parameters corresponding to the isofemale lines compared^ one term\ d\ corresponding to the e}ect of each oviposition\ and 09 parameters\ gi\ i  0\ 1\ [ [ [\ 09 "with g0  9#\ corresponding to the interaction between these two e}ects[ Thus\ the hazard function for a female belonging to family i\ and that has already attacked j hosts is] h"t#  h9"t# exp "ai ¦ j"d ¦ gi ##[ eqn A0 So\ the hazard ratio for this female\ relative to a female of the same family that has not yet shown any ovi! position is] ðexp "ai ¦ j"d ¦ gi #Ł:ðexp "ai #Ł eqn A1 which reduces to exp "j "d ¦ gi ##[ The standard error of the log!hazard ratio is thus] jzðvar"d# ¦ var"gi# ¦ 1 cov "d\gi #Ł eqn A2 For the _rst family\ both a0 and g0 are set to zero\ and the standard error of the log!hazard ratio is modi_ed accordingly[ The same procedure is used for the inter! action between the family e}ect and the number of host rejections "Fig[ 3b#[