Interference among insect parasitoids] a multi!patch experiment

Transcription

1 Ecology 0888\ 57\ 097Ð019 Interference among insect parasitoids] a multi!patch experiment MARCEL E[ VISSER\ T[ HEFIN JONES$ and GERARD DRIESSEN% Netherlands Institute of Ecology\ PO Box 39\ 5555 ZG Heteren\ The Netherlands^ $NERC Centre for Population Biology\ Imperial College at Silwood Park\ Ascot\ Berks[ SL4 6PY\ UK^ %Institute of Evolutionary and Ecological Sciences\ Leiden University\ PO Box 8405\ 1299 RA\ Leiden\ The Netherlands^ and $Department of Biology\ Imperial College at Silwood Park\ Ascot SL4 6PY\ UK Summary 0[ Interference among insect parasitoids leads to a reduction in the overall search rate "the population equivalent of searching e.ciency# with increasing parasitoid population density[ When this reduction is due to behavioural responses of individuals to increased intraspeci_c competition\ interference can serve as a stepping stone from individual behaviour to population phenomena[ 1[ Interference can take di}erent forms] "0# a direct within!patch reduction of searching e.ciency with parasitoid density "direct mutual interference#^ "1# a decrease in overall search rate with increasing parasitoid density if parasitoids have a non!uniform dis! tribution over patches where this distribution remains unaltered with increasing density "pseudo!interference#^ "2a# a decrease in the time spent on patches by each individual\ i[e[ more or longer travelling at higher parasitoid densities^ and "2b# a decrease in overall search rate due to a change in the distribution of parasitoid e}ort over patches with increasing parasitoid density[ These last two forms arise from behavioural responses to increased parasitoid density and are forms of indirect mutual interference[ 2[ We present an expression for the overall search rate in a patchy environment where individual parasitoids travel between patches[ We use this to show how the di}erent forms of interference a}ect the overall search rate\ contrasting environments with aggregated and uniform host distributions[ 3[ Using the data of Jones "0875# we explore the di}erent forms of interference in a multipatch experiment[ In these experiments\ di}erent numbers of parasitoids were introduced in an arena where the distribution of hosts over patches was either aggre! gated or uniform[ We show that both pseudo!interference and indirect mutual inter! ference play a role\ and that they have an opposite e}ect for a uniform host distri! bution\ but amplify one another for aggregated host distributions[ 4[ The indirect mutual interference arises from a shift towards a more uniform dis! tribution of parasitoid e}ort over patches with increasing parasitoid densities[ This shift is caused by a behavioural response to parasitoid density\ and is likely due to changes in the parasitoids patch arrival and departure decisions[ These decisions underlie the distribution of time spent on patches\ thereby linking individual behav! iour to a phenomenon at the population level[ 5[ Finally\ we put forward a more general framework for indirect mutual interference to also include behavioural responses in sex allocation\ clutch size and host acceptance to parasitoid density as forms of interference[ Key!words] interference\ overall search rate\ parasitoid\ population dynamics\ search! ing e.ciency\ Trybliographa rapae[ Ecology "0888# 57\ 097Ð019 Correspondence] Dr M[ E[ Visser\ Netherlands Institute of Ecology\ P[O[ Box 39\ 5555 ZG Heteren\ The Netherlands[ Tel] ^ fax] ^ e!mail] m[visserýcto[nioo[knaw[nl 097

2 098 M[E[ Visser\ T[ He_n Jones + G[ Driessen Introduction Behavioural interactions between insect parasitoid individuals can lead to a reduced rate of parasitism of host populations as parasitoid density increases[ Such interference a}ects the population dynamics of para! sitoidðhost systems^ when su.ciently strong\ it will stabilize otherwise unstable interactions "Hassell + Varley 0858^ Hassell + May 0862#[ Recently\ there has been a renewed interest in interference "Visser + Driessen 0880^ Cronin + Strong 0882^ Driessen + Visser 0882^ Driessen + Visser 0886^ Weisser\ Wilson + Hassell 0886# mainly because as a phenomenon it can serve as a stepping stone between individual behaviour and population dynamics[ This is par! ticularly true when the observed reduced rate of para! sitism is the consequence of the behavioural responses of parasitoid individuals to increased intraspeci_c competition[ Understanding the causation of inter! ference at the individual level helps explain population phenomena on the basis of natural selection[ Parasitoid behavioural interactions leading to inter! ference may take various forms[ Some parasitoids _ght or delay searching for hosts upon encountering a conspeci_c^ with increasing parasitoid density more of these encounters occur and more time is apparently {wasted "Hassell 0867#[ "Note that\ although time is wasted from a population viewpoint\ this behaviour may well be adaptive at an individual level] a para! sitoid spending time chasing intruders may gain future bene_t from reduced competition[# Other behaviour that may be in~uenced by parasitoid density include] guarding of a brood "Gri.ths + Godfray 0877# or patch "Waage 0871#\ decisions on superparasitism "Visser\ van Alphen + Nell 0889#\ sex allocation "Hamilton 0856# and clutch size "Rosenheim + Hong! kham 0885^ Visser 0885#[ While some of these behav! iours in~uence the rate of parasitism\ the latter two a}ect the sexual composition and density of the para! sitoid population in the next generation[ These latter e}ects fall outside the de_nition of interference\ but have obvious consequences on the population dynam! ics of the hostðparasitoid interaction "Hassell\ Waage + May 0872#[ For the main part of this study\ only the in~uence of within!generation behavioural inter! actions on the rate of parasitism is considered\ but we return to other forms of interference in the Discussion[ To assess what underlying behaviour is responsible it is important to di}erentiate between the various forms of interference[ These forms need to be de_ned in a way that points to the causal behavioural inter! actions[ First\ however\ we need to de_ne interference more formally[ In a habitat that is not subdivided into patches\ interference is de_ned as a decrease in searching e.ciency\ the area searched by an individual parasitoid per unit time\ with parasitoid density "Has! sell + Varley 0858#[ In a patchy environment\ however\ the overall search rate "the population equi! valent of searching e.ciency# is more relevant to the dynamics of a parasitoidðhost interaction[ The overall search rate\ s\ is calculated using the equation] s A PT ln N eqn 0 N N a where A is the total area "often taken to be 0#\ P is the number of parasitoids in the population\ T is the generation time "also often taken to be 0#\ N is the total number of hosts in the population and N a the number of hosts attacked[ Interference is then evalu! ated by regressing log 09 s against log 09 P^ the slope\ m\ is called the coe.cient of interference[ The forms of interference that can occur in an environment where hosts are patchily distributed and parasitoids can travel between patches include] "0# a direct\ within!patch reduction of searching e.ciency with parasitoid density increase "direct mutual inter! ference#^ "1# a decrease in overall search rate with increasing parasitoid density as a consequence of a non!uniform distribution of parasitoids over patches\ but where this distribution itself remains unaltered with increasing parasitoid density "pseudo!inter! ference^ Free\ Beddington + Lawton 0866#^ "2# inter! patch behavioural activities resulting in either "a# a decrease in the proportion of time spent on patches by each individual\ i[e[ more or longer interpatch trav! elling at higher parasitoid densities\ or "b# a change in the distribution of parasitoids over patches with increasing parasitoid density "indirect mutual inter! ference^ Visser + Driessen 0880^ Driessen + Visser 0886#[ Pseudo!interference only occurs when the para! sitoid population has a non!uniform distribution among patches[ Note that\ although this distribution might be the consequence of underlying parasitoid behaviour\ the parasitoids are not responding behav! iourally to increasing parasitoid density^ in this way pseudo!interference di}ers from indirect mutual inter! ference[ The di}erent forms of interference have di}erent underlying behavioural interactions[ For the population dynamics it makes no di}erence where the interference comes from\ but in order to relate population phenomena via interference to individual behaviour it is essential that there is a clear under! standing of the causal mechanisms[ Distinguishing between di}erent forms of interference therefore becomes a necessity[ To assess the contribution of the three forms of interference empirically necessitates\ ideally\ mul! tipatch experiments[ Such experiments are relatively rare "but see Hassell 0860^ Hubbard + Cook 0867^ Waage 0868^ and Jones + Hassell 0877 for examples#[ Usually studies have been restricted to single!patches which only allow the measurement of the degree of direct mutual interference "but see Visser + Driessen 0880 and Driessen + Visser 0882#[ One exception is a set of multipatch experiments conducted by Jones "0875#[ In these experiments\ di}erent numbers of parasitoids were released into an arena with patches

3 009 Interference among parasitoids of hosts\ which were distributed either uniformly or in an aggregated fashion[ All parasitoid patch arrivals and departures of parasitoids were recorded over the 7 h for which each of the experiments ran[ These data have been partially analysed by Jones + Hassell "0877#[ Their analysis was restricted to the aggregated host distribution and showed that female T[ rapae spent higher proportions of their time on high host density patches[ The overall search rate\ s\ declined at higher parasitoid densities "Fig[ 2a#[ They argued that this was {due both to behavioural interference "Hassell + Varley 0858# and to apparent\ or {{pseudo!inter! ference \ resulting from the uneven exploitation of hosts "Free\ Beddington + Lawton 0866#[ In this study we _rst formally de_ne the three di}erent forms of interference\ and secondly we re! analyse the data of Jones + Hassell "0877# for the aggregated host distribution and compare this to an analysis of the data from the uniform host distri! bution[ We then split the overall interference into its di}erent components\ assessing which of the potential underlying behaviours are of importance to the inter! ference patterns observed[ A model of interference Envisage a habitat where hosts are divided among M discrete patches of equal size A:M\ with a i denoting the proportion of the host population in patch i[ Hosts are con_ned to their patches[ The parasitoid time! budget has two components] "0# time spent on patches "on average\ T p time units#\ in which they search at random for hosts with searching e.ciency\ a "the area searched by an individual parasitoid per unit of time#^ and "1# time spent travelling between patches[ The proportion of the total search time on patches "PT p # that is spent on patch i is denoted by g i [ Host and parasitoid generations are discrete and synchronized[ We assume that handling times are negligible\ as they are in many _eld situations where encounter rates with hosts are usually very low "Janssen 0878^ Driessen + Hemerik 0881#\ and therefore use a Type I functional response "Holling 0848#[ Parasitoids are assumed to be time!limited[ Within patches hosts are assumed to have equal probabilities of being attacked[ In such a habitat\ the total number of hosts par! asitized in one generation\ N a \ is "see also Driessen + Visser 0886#] M amg N a N i00 $0 s a i PT p ie A eqn 1 1% Substituting equation 1 into equation 0 yields\ s A M amg PT ln i00 s a i PT p ie A eqn 2 1 By setting T p T and a?am:a\ equation 1 reduces to the well!known model of Hassell + May "0862^ model D#[ Furthermore\ setting M 0 yields the NicholsonÐBailey model] N a N"0 e a?pt # eqn 3 Substituting equation 3 into equation 0 yields s a^ within the assumptions of a classical NicholsonÐBai! ley framework the overall searching rate is therefore equal to the searching e.ciency of the individual[ Thus\ both s and a are often referred to as searching e.ciency[ This can lead to confusion as s refers to a population attribute "the e.ciency of a population of parasitoids in parasitizing their hosts#\ while a mea! sures a trait of an individual "the area it searches per unit of time#[ Using equation 2\ the di}erent forms of interference "m# can be de_ned by showing how the overall search rate "s# is altered when parameters values are a}ected by parasitoid density "P#[ Because of the analytical intractability of equation 2\ we solve it numerically using speci_c parameter values of similar order of magnitude as those derived from the experiment pre! sented later[ Furthermore\ note that although A\ M and a i do in~uence the value of s\ these parameters are set by the environment and cannot\ therefore\ be sources of interference[ DIRECT MUTUAL INTERFERENCE Direct mutual interference occurs when the presence of conspeci_c parasitoids on a patch reduces the searching e.ciency of an individual parasitoid "a# on that patch "Hassell + Varley 0858#[ In this case\ searching e.ciency depends on local parasitoid den! sity^ for a patchy environment this can be incor! porated in equation 2 as a i f "g i P#\ where a i is the searching e.ciency on patch i[ One possible mech! anism to explain such a reduction in a with increasing parasitoid numbers on a patch is that encounters between females lead to various non!searching activi! ties "e[g[ _ghting#[ This reduces the actual time spent searching\ and thereby the amount of area searched per unit of patch time[ PSEUDO!INTERFERENCE For patchy environments in which time spent search! ing patches by the parasitoid population is not uni! formly distributed "i[e[ g i 0:M#\ increasing para! sitoid density decreases s "Fig[ 0#[ Pseudo!interference is an appropriate term to describe this phenomenon "Free et al[ 0866# as the parasitoids exhibit no real behavioural response to increased parasitoid density "no change in T p or in the distribution of gi in equation 2#[ Pseudo!interference plays a role in both uniform and aggregated host distributions[ For both host dis! tributions the amount of pseudo!interference increases with increasing aggregation of patch times[

4 000 M[E[ Visser\ T[ He_n Jones + G[ Driessen Log 10 overall search rate (a) (b) Log 10 parasitoid density Fig[ 0[ A model of interference "see equation 2#] log 09 overall search rate "s# versus log 09 parasitoid density when only pseudo! interference plays a role[ The value of the searching e.ciency a is 9=990 "log 09 a Ð 2#[ Other parameters] generation time T equals the time spent on patches T p 49\ the total area A 0 and the number of patches M 4[ Hosts are either in an "a# aggregated "distribution according to a geometric distribution^ a i z ið0 "0!z#:"0!z M ## with shape parameter z 9=38# or "b# uniform "a i 0:M# distribution[ Total time spent searching on patches by the parasitoids is aggregated and also follows a geometric distribution[ The value of the shape parameter z varies and is indicated "low values correspond to strong aggregation\ values close to unity to weak aggregation#[ This is illustrated in Fig[ 0[ Total time spent searching on patches by the parasitoids is aggregated and fol! lows a geometric distribution ðg i z ið0 "0Ðz#:"0Ðz M #Ł[ The value of the shape parameter z determines the degree of aggregation] highly aggregated for low values of z and almost uniform for values close to unity "with g i 0:Mfor z 0#[ For highly aggregated patch times there is a strong decrease in s with P for both aggregated and uniform host distributions[ The value of s relative to a however\ di}ers[ When the host distribution is uniform\ s will always be smaller than a "Fig[ 0b\ a 9=990\ thus log 09 a Ð 2# because the parasitoid population parasitizes fewer hosts com! pared to when the parasitoids e}ort is uniformly dis! tributed over all patches "for which s a#[ This can be shown analytically by replacing g i by 0:M in equa! tion 2[ When the host distribution is aggregated and the parasitoids spend more time on patches which are initially the more pro_table ones\ s will be larger than a when parasitoid densities are low[ When parasitoid densities increase\ s will decrease and eventually become less than a "Fig[ 0a\ again log 09 a Ð 2#[ For highly aggregated patch times "low values of z in Fig[ 0a# s becomes smaller than a at low parasitoid density[ For more uniform distributions of patch times "values of z close to 0 in Fig[ 0a# this occurs later\ for para! sitoid densities outside the range indicated in Fig[ 0a[ The reason why the overall search rate\ s\ becomes smaller than the searching e.ciency\ a\ is that when few parasitoids aggregate on the high host density patches s will be higher than when they distribute themselves uniformly "for which s a#[ However\ if many parasitoids search only the high host density patches\ and ignore the low host densities ones\ the overall search rate s will decline[ The hosts in the low host density patches escape parasitism causing the overall search rate to decrease even below a[ With increasing aggregation of parasitoid e}ort\ the value of s at low parasitoid densities increases\ but so does the rate at which s decreases with P\ i[e[ the amount of pseudo!interference "Fig[ 0a^ see also Free et al[ 0866#[ Increasing either T p or a has similar e}ects[ INDIRECT MUTUAL INTERFERENCE!TIME SPENT ON PATCHES "T P # AS A FUNCTION OF P A decrease in the total time spent on patches per parasitoid "T p #\ as the number of parasitoids in the environment increases can be a consequence of more frequent or longer!lasting interpatch movements[ As the overall search rate s is calculated using the total time available to a parasitoid "T#\ the consequence is a decrease of s with increasing parasitoid density ðt p f"p# in equation 2Ł[ The decrease in the patch time per parasitoid "T p # arises from real behavioural responses by the para! sitoids to parasitoid density[ It cannot therefore be considered as pseudo!interference[ However\ as it has no e}ect on individual searching e.ciency "a# it also cannot be referred to as direct mutual interference "sensu Hassell + Varley 0866#[ Thus\ we follow Visser + Driessen "0880# and refer to this\ and the inter! ference described in the next section\ as indirect mut! ual interference[ INDIRECT MUTUAL INTERFERENCE! DISTRIBUTION OF PATCH TIME "g i # AS A FUNCTION OF P The distribution of time spent on patches may change in response to increasing parasitoid density "g i f"p##

5 001 Interference among parasitoids by becoming either more or less aggregated[ This change may be su.cient to a}ect the overall search rate "s#[ Again\ this type of indirect mutual inter! ference is di}erent from pseudo!interference as in the latter the decrease in overall search rate is due solely to an increase in P^ the distribution of patch times remains unaltered[ The behaviour causing these chan! ges in the distribution of patch times may be the para! sitoids patch arrival and departure decisions[ For instance\ if parasitoids avoid landing on patches alre! ady occupied by a number of conspeci_cs\ patch time distribution will become less aggregated as parasitoid density increases[ Changes in the distribution of patch times\ g i \ a}ect s\ but in a di}erent way for the two host distributions[ This is illustrated in Fig[ 1\ where total time spent searching on patches by the parasitoids is aggregated\ but where this distribution becomes more uniform at higher parasitoid densities[ The values of log 09 s are plotted against log 09 P "the solid lines in Fig[ 1#^ the changes in s with P are due to the combined e}ect of pseudo! and indirect mutual interference arising from changes in g i [ At six points on the solid line\ the change in overall search rate due solely to pseudo!interference in the environment of these points is indicated "dashed lines in Fig[ 1#[ These changes are calculated by vary! ing P\ but not g i for these points in equation 2[ The angle between the tangents to the solid and dashed lines represents the impact of indirect mutual inter! ference[ For both host distributions s will approach a "log 09 a Ð 2 in Fig[ 1# when the distribution of patch times becomes more uniform as parasitoid density increases "for g i 0:M\ sa#[ For the uniform host distri! bution\ this results in a weaker decrease in s than expected from pseudo!interference "Fig[ 1dÐf#\ with even an increase in s for high parasitoid densities[ This arises because in the uniform host distribution s is smaller than a "Fig[ 0b#[ Thus\ for uniform host dis! tributions\ pseudo!interference and indirect mutual interference a}ect the overall search rate in opposite directions[ For the aggregated host distribution "where the parasitoids spent more time on the highest host density patches#\ the more uniform distribution of patch times at higher parasitoid densities will result in a stronger decrease in s than expected from pseudo! interference alone "Fig[ 1aÐc#[ This arises because for aggregated host distributions\ with more patch time 2.65 (a) 2.65 (b) 2.65 (c) Log 10 overall search rate (d) (e) (f) Log 10 parasitoid density Fig[ 1[ A model of interference "see equation 2#] log 09 overall search rate "s# versus log 09 parasitoid density "P# when both pseudo!interference and indirect mutual interference play a role[ The value of the searching e.ciency a is 9=990 "log 09 a Ð 2#[ Other parameters "see legend Fig[ 0#] T T p 49\ A 0\M 4[ Hosts are either in an aggregated "distribution according to a geometric distribution^ a i z ið0 "0!z#:"0!z M # with shape parameter z 9=38\ Fig[ 1aÐc# or uniform "a i 0:M\ Fig[ 1dÐf# distribution over patches[ Total time spent searching on patches by the parasitoids is aggregated and also follows a geometric distribution[ The value of the shape parameter z is a function of parasitoid density such that the distribution becomes more uniform at higher densities^ Fig[ 1a and d] z 9=29 9=917 P\ Fig[ 1b and e] z 9=49 9=919 P and 1c and f] z 9=69 9=901 P[ Solid lines] the change in overall search rate due to the combined e}ect of pseudo! and indirect mutual interference "as calculated with equation 2#\ interrupted dashed lines] the change in overall search rate solely due to pseudo!interference in the environment of the intersection point[ These lines are calculated using equation 2 by varying P\ but not g i for any given point on the solid line[ The angle between the tangents to the solid and dashed lines at each intersection point represents the impact of indirect mutual interference[

6 002 M[E[ Visser\ T[ He_n Jones + G[ Driessen being spent on the high density patches\ s will be above a "Fig[ 0a# and therefore pseudo!interference\ which always leads to a decrease in s\ and indirect mutual interference\ which for a more uniform distribution of patch times with increasing P leads to s approaching a\ work in the same direction[ Thus\ the decrease in s with increasing P derived from pseudo!interference is enhanced by indirect mutual interference[ In Fig[ 1\ it is assumed that the distribution of patch times becomes more uniform with increasing para! sitoid density[ If\ on the other hand\ the distribution of patch times becomes more aggregated with increasing parasitoid density\ s will diverge from a and the overall search rate will decrease when the host distribution is uniform and increase when it is aggregated "where parasitoids spent more time on the patches with a large number of hosts#[ Methods EXPERIMENTS Standardized parasitoids were obtained by removing adult female Trybliographa rapae Westw[ "Hymen! optera] Cynipoidae# from a laboratory culture 9Ð01 h after emergence[ The females were placed for 01 h in small plastic containers with two males\ a carbo! hydrate nutrient source and an excess of Delia radicum L[ "Diptera] Anthomyiidae# larvae for host!contact experience "see Finch + Coaker "0858# and Jones + Hassell "0877# for culturing details#[ Second instar D[ radicum larvae were used as hosts in all experiments[ Five swede discs "Brassica napus var napobrassica L[^ 24 mm diameter^ 4 mm depth# were arranged within a plastic arena " cm# so as to be equidistant from each other and the centre of the arena[ The ~oor of the arena was covered with a 9=4! cm layer of dry\ washed sand and closed with a tightly _tting lid[ Aggregated distributions of hosts per swede disc " patch# were established by inoculating each disc with 1\ 3\ 7\ 05 or 21 second instar larvae "total hosts per arena 51#[ Uniform distributions were established by inoculating each swede disc with 01 second instar hosts "total hosts per arena 59#[ They were left for 13 h prior to the start of the experiments[ The experimental procedure involved introducing 0\ 4\ 09\ 04 or 19 standardized female parasitoid wasps into the arena[ The time spent by the parasitoids on each disc was continuously recorded for 7 h\ enabling the total time spent on each disc to be determined[ The wasps were then removed and 13 h later the D[ radicum larvae were dissected to determine the num! ber of hosts parasitized in each swede disc[ Each combination of parasitoid density and host distribution was replicated _ve times\ resulting in 49 experiments\ and carried out at >C and ) r[h[ OVERALL PATTERN OF INTERFERENCE For each experiment the overall search rate\ s\ was calculated using equation 0[ Log 09 s was then plotted against log 09 P\ the total number of parasitoids in the arena[ The slope of the regression line indicated the strength of the overall interference[ This relationship is often not linear "and is\ indeed not expected to be linear\ Royama 0860#^ to allow for non!linearity\ both log 09 P and its square were used as explanatory vari! ables[ ANALYSIS OF THE COMPONENTS OF INTERFERENCE 0[ Direct mutual interference[ An increase in the num! ber of parasitoids on a patch causes a decrease in searching e.ciency within that patch "a#[ To test whether direct mutual interference occurs\ searching e.ciency must be calculated for each patch using] a i A N i ln eqn 4 Mg i PT p N i N a\i where g i PT p is the total time spent on patch i and A:M is the size of the patch[ Direct mutual interference occurs when a is dependent on the density of para! sitoids on a patch ða i f "g i P#Ł[ In this experiment a total of 149 patches "14 experiments\ each with _ve patches\ for each of the two host distributions# can potentially be analysed[ However\ to avoid unrealistic estimates of a\ we only included the 028 patches on which the parasitoids spent at least 4 min and found at least one host[ The multipatch set!up allows the parasitoids to distribute themselves freely and there! fore there is no logical single value for local parasitoid density[ As a measure of local parasitoid density we used the maximum number of parasitoids sim! ultaneously on a patch[ In the statistical analysis we used a generalized lin! ear model with log 09 a as a response variable and log 09 maximum number of parasitoids\ log 09 total time spent on the patch\ the log 09 number of parasitoids in the arena\ the type of host distribution "aggregated or uniform# and the number of hosts on the patch as explanatory variables[ We also investigated further the interactions between these latter two variables and the other explanatory variables[ The interactions and main e}ects were omitted from the model in a step! wise fashion\ starting with the interactions[ Sig! ni_cance was evaluated using an F!test[ As the total time spent on the patch and the maximum number of parasitoids on the patch are correlated we also tested their signi_cance without the other correlated explanatory variable included in the statistical model[ This way we addressed the potential problem of col! inearity[ 1[ Pseudo!and indirect mutual interference[ First\ we determined whether a relationship existed between the total time spent on patches per parasitoid "T p # and the

7 003 Interference among parasitoids parasitoid density ðp\ i[e[ T p f "P#Ł[ If T p does not decrease with increasing parasitoid density we can conclude that any indirect mutual interference does not arise from more\ or longer\ travelling periods[ We then focused on pseudo!and indirect mutual inter! ference[ To separate these we used the same graphical method as applied in Fig[ 1\ but _rst it was necessary to establish whether the distribution of patch times "g i # is a}ected by parasitoid density[ As a measure of the aggregation of parasitoid e}ort over patches\ we used the coe.cient of variation "CV standard deviation:mean# of the patch time distribution[ This enables changes in g i to be expressed in a single value[ If parasitoids aggregate more with increasing density\ the CV will increase\ if they aggre! gate less\ the CV will decrease[ The aggregation index\ m "Hassell + May 0862#\ is less suitable because it cannot be used for uniform host distributions[ Quan! tifying the changes in g i by estimating the parameter of the geometric distribution "as used in Fig[ 1# gives the same results as the CV method\ but has the dis! advantage that for uniform host distributions there is no logical ordering of patches[ In separating pseudo!and indirect mutual inter! ference we _rst calculated the overall search rate\ s\ for each experiment\ using equation 2 with a value for T p averaged over all experiments and a value for a averaged over all patches[ In this way\ we excluded both direct and indirect mutual interference arising from more or longer travelling[ The values of log 09 s are then plotted against log 09 P "for the uniform and aggregated host distributions separately#[ Any nega! tive slope arising is due to the combined e}ect of pseudo! and indirect mutual interference due to chan! ges in g i [ Next\ we calculated the e}ect of pseudo! interference for each parasitoid density[ This is done as in Fig[ 1 by calculating the value of s\ using equa! tion 2 and varying P\ but not g i [ For each point _ve lines are calculated^ there are _ve replicates for each parasitoid density with each having a distribution of patch times g i [ The mean "2 SD# of these _ve lines is given[ At each of the parasitoid densities\ the angle between the tangents to both lines represents the impact of indirect mutual interference[ Results OVERALL PATTERN OF INTERFERENCE The overall search rate\ s\ decreased with parasitoid density "Fig[ 2#[ For the aggregated host distribution not only was log 09 parasitoid density signi_cant "F 0\ 12 06=7\ P 9=9992#\ but also its square "F 0\ 12 46=4\ P ³ 9=9990#[ For the even host distribution there was no signi_cant deviation from a linear relationship^ only log 09 parasitoid density was sig! ni_cant "F 0\ 12 10=0\ P 9=9990#[ ANALYSIS OF THE COMPONENTS OF INTERFERENCE 0[ Direct mutual interference[ In analysing searching e.ciency\ a\ only the number of hosts on the patch and the total patch time explained signi_cant amounts of the variance when all explanatory variables were _tted "Table 0a and Fig[ 3b#[ The maximum number of parasitoids searching simultaneously on the patch had no signi_cant e}ect[ Because of the experimental set!up\ the total patch time and the maximum number of parasitoids are correlated "Pearson s r 9=76\ n 028#[ To overcome this problem of co!linearity the e}ect of the maximum number of parasitoids on the patch was tested when patch time was not included\ and shown to be signi_cant "Table 0b and Fig[ 3a#[ As a consequence\ we cannot disentangle the e}ect of direct mutual interference and the e}ect of patch depletion on the reduction of searching e.ciency[ The e}ect of patch depletion on the search! ing e.ciency may come about if not all hosts are equally accessible\ or if hosts become less accessible when disturbed often[ Because a is calculated from the number of parasitized hosts and the patch time\ it will decrease with increasing host depletion[ In the present study\ depletion does occur\ but not to a large extent[ In most patches less than 14) of the hosts were parasitized\ in only a few were more than 49) of the hosts attacked[ The level of depletion increases with both the total time spent on the patch ðx 1 "0# 34=45\ P ³ 9=990\ Fig[ 3cŁ and the number of hosts on the patch ðx 1 "0# 3=61\ P 9=92Ł[ This lends support to the suggestion that the decrease in search! ing e.ciency is due to depletion and not behavioural interactions between parasitoids[ Such a _nding is in agreement with the experimental observations] para! sitoids did not seem to interrupt their searching when they encountered one another "Jones 0875#[ However\ we can not show conclusively that direct mutual inter! ference does not play a role in the experiments[ We want to stress that single patch experiments with con! tinuous observation of the parasitoids and their encounters with hosts are a more appropriate way to analyse direct mutual interference[ 1[ Pseudo!and indirect mutual interference[ To test whether the time budgets of the individual parasitoids were a}ected by the number of parasitoids in the arena we considered the relationship between the time spent on patches by individual parasitoids and parasitoid density[ We found no signi_cant relationships "uni! form host distribution] F 0\12 0=92\ P 9=21^ aggre! gated host distribution] F 0\12 9=27\ P 9=44#[ We conclude that the number of parasitoids in the arena did not a}ect the time spent on patches "i[e[ travelling and escape behaviour are neither more frequent nor longer#[ Next\ we calculated whether the distribution of patch times changed with parasitoid density[ For both uniform and aggregated host distributions\ the CVs

8 004 M[E[ Visser\ T[ He_n Jones + G[ Driessen Fig[ 2[ Log 09 overall search rate "s# versus the log 09 number of parasitoids in the arena with hosts arranged in "a# an aggregated "data from Jones + Hassell 0877# or "b# uniform distribution[ The lines are _tted relationships as found by a statistical model "see text#[ The numbers in the graph indicate the number of overlapping points[ Table 0[ Analysis of the log 09 searching e.ciency\ a\ on a patch using all 028 patches on which the parasitoids spent at least 4 min and found at least one host[ As a measure of local parasitoid density\ both the log 09 maximum number of parasitoids simultaneously on a patch "log 09 max[ parasitoids# as well as the log 09 total time spent on the patch "log 09 total patch time# were used[ Other explanatory variables are the number of hosts on the patch "no[ hosts#\ the log 09 number of parasitoids in the arena "log 09 no[ parasitoids arena# and the type of host distribution "aggregated or uniform] type distribution#[ None of the interactions explained a signi_cant part of the deviation[ "a# Model including all explanatory variables\ "b# model in which log 09 total patch time was not included "see text# Change in deviance change in d[f[ F!ratio P!value Estimate A Log 09 total patch time 1= =46 ³9990 Ð9=72 No[ hosts 9=67 0 3=85 9=92 9=90 Not in model Log 09 max[ parasitoids 9=92 0 9=07 Log 09 no[ parasitoids arena 9=20 0 0=75 Type distribution 9=96 0 9=39 B Log 09 max parasitoids 1= =11 ³9=990 Ð9=87 Not in model No[ hosts 9=19 0 0=00 Log 09 no[ parasitoids arena 9=34 0 1=15 Type distribution 9=90 0 9=96 for the distribution of patch times decreased with the number of parasitoids in an arena "Fig[ 4\ uniform host distribution] F 0\12 02=0\ P 9=990^ aggregated host distribution] F 0\12 05=38\ P ³ 9=990#[ The dis! tribution of patch times becomes less aggregated as parasitoid density increases[ Surprisingly\ the CV for the distribution of patch times for aggregated and uniformly distributed hosts were very similar "Fig[ 4#[ Parasitoid aggregation on high host density patches is often used to explain aggregated patch times and in the aggregated host distribution the parasitoids did aggregate on the high host density patches "see Jones + Hassell 0877#[ It is unclear why some patches were searched longer then others at the uniform host dis! tributions[ The combined e}ect of pseudo! and indirect mut! ual interference was determined by calculating the overall search rate\ s\ from the observed distribution of patch times "g i # using the mean a over all patches in that habitat "log 09 mean a for uniform host dis! tribution Ð 4=44\ and aggregated Ð 4=88# and a mean value for T p over all experiments "T p for the uniform host distribution s\ for aggregated s#[ These values of s were calculated for each of the _ve di}erent parasitoid densities[ A decrease in overall search rate with increasing parasitoid density

9 Log 10 searching efficiency (a) 4.20 (b) (c) Log 10 max parasitoids on patch Log 10 searching efficiency Log 10 total time spent on patch 5 6 Proportion of hosts parasitized (Thousands) Total time spent on patch Fig[ 3[ Log 09 searching e.ciency "a# on a patch for all 028 patches on which the parasitoids spent at least 4 min and found at least one host\ versus "a# the log 09 total time spent on the patch and "b# the log 09 maximum number of parasitoids on the patch[ "c# The proportion of hosts parasitized versus the total time spent on the patch for the same 028 patches[ Patches from arenas with a clumped host distribution are indicated with a ž\ patches from arenas with a uniform host distribution with a R[ 2.50 (a) 2.50 (b) CV Parasitoid density Fig[ 4[ The CV "standard deviation:mean# of the distribution of patch times vs[ the number of parasitoids in the arena[ Higher CV values indicate stronger aggregation of parasitoids e}ort[ Arenas have either "a# an aggregated host distribution or "b# a uniform host distribution[ 20 was evident in both uniform and aggregated host dis! tributions "Fig[ 5#[ For each parasitoid density the change in overall search rate due to pseudo!interference only was then calculated[ For both host distributions there is a clear di}erence between the decrease in overall search rate attributable to pseudo!interference and the total amount of interference observed[ This di}erence is caused by the decrease in aggregation of patch times with increased parasitoid density and thus to indirect mutual interference[ The variation around the cal! culated lines is substantial[ This arises from the vari! ation in the observed distribution of patch times between replicates[ If these are strongly aggregated\ pseudo!interference will be the stronger component "see also Fig[ 0#[ For the aggregated host distribution\ pseudo! and indirect mutual interference enhances one other] the decrease in overall search rate is stronger than expected from pseudo!interference alone[ For the uniform host distribution the opposite is true^ pseudo! and indirect mutual interference have an opposite e}ect[ To summarize\ for T[ rapae the decrease in the overall search rate with increasing parasitoid density "Fig[ 2# can be partly attributed to a reduction in searching e.ciency a[ This arises either from an increasing level of host depletion with an increasing number of parasitoids in the arena or from behav! ioural interactions between parasitoids[ Another com! ponent of the total interference can be explained by the contributions of pseudo!interference and indirect mutual interference arising from a behavioural response of the parasitoids to increased parasitoid density[ While for the uniform host distribution\ pseudo!interference and indirect mutual interference have opposite e}ects for the aggregated host dis! tributions they ampli_ed one another[

10 006 M[E[ Visser\ T[ He_n Jones + G[ Driessen Fig[ 5[ Log 09 overall search rate "s 2 SD\ solid symbols and solid line# versus log 09 parasitoid density[ To exclude direct mutual interference and indirect mutual interference due to more or longer travelling\ s is calculated with mean values for the searching e.ciency\ a\ and the time spent on patches\ T p \ that thus not vary with parasitoid density[ Arenas have either "a# an aggregated or "b# a uniform host distribution[ The open symbols and the interrupted dashed lines indicate the change in overall search rate solely due to pseudo!interference in the environment of the intersection point[ These lines are calculated using equation 2 by varying parasitoid density "P#\ but not the distribution of patch times "g i # for any given point on the solid line[ For each point _ve lines are calculated as there are _ve replicates for each parasitoid density which each have a distribution of patch times g i [ The mean "2 SD# of these _ve lines is given[ The angle between the tangents to the solid and dashed lines at each intersection point represents the impact of indirect mutual interference[ Discussion Interference between parasitoids can potentially con! tribute to the stability of parasitoidðhost interactions in a spatially heterogeneous environment[ Interference can be caused solely by an increase in parasitoid den! sity "pseudo!interference#\ but can also be caused by a change in the behaviour of individual parasitoids with increasing parasitoid density[ This leads to mut! ual interference[ In this study\ we have discussed inter! ference in a realistic habitat] patches with non!migrat! ing hosts\ but with parasitoid transitions between patches[ The role of travel among patches by para! sitoids has only recently been considered in popu! lation models "Rohani\ Godfray + Hassell 0883^ Jones\ Godfray + Hassell 0885#[ Incorporating trav! elling\ and consequently\ the continuous redis! tribution of parasitoids over patches in population models\ is of great importance when linking individual decision making to population dynamics[ For instance\ whether the distribution of patch times becomes more or less aggregated with increasing para! sitoid density depends on the parasitoids arrival and departure rules[ There will be strong natural selection on these rules and these decisions determine the dis! tribution of parasitoid e}ort over patches[ In turn\ this distribution greatly in~uences the dynamics of the hostðparasitoid interaction[ To determine why the distribution of parasitoid e}ort over patches becomes more uniform with increasing parasitoid density\ patch arrival and depar! ture rules should be investigated at the individual level[ Specially designed experiments are required to estimate the rules "see Driessen et al[ 0884#[ From such experiments\ there is evidence that parasitoid density a}ects these rules[ Departure probabilities might decrease with increasing parasitoid numbers on the patch because the pro_tability of superparasitism increases with parasitoid number "Visser et al[ 0889^ Visser\ van Alphen + Hemerik 0881^ Cronin + Strong 0882#[ Arrival probabilities might be a}ected by para! sitoid density because in some species females can detect conspeci_cs from a distance\ and avoid already occupied patches "Janssen et al[ 0884#[ The avoidance of patches with parasitoids will decrease the aggre! gation "lowering the CV#\ while the reduced prob! ability to leave such patches will enhance the aggre! gation of patch times[ Experiments quantifying these e}ects of local parasitoid density on patch arrivals and patch departure probabilities are needed to explain the less aggregated distribution with increasing parasitoid density[ The role of mutual interference in population dynamics has received little attention since Free et al[ "0866# showed that when populations are at equi! librium the value of m will be about t w :T "where t w is the time wasted upon an encounter with a conspeci_c#[ They concluded that m would be too small to have a stabilizing e}ect on the population dynamics[ This conclusion\ however\ only holds when direct mutual interference is the only form of behavioural inter! ference present[ In a multi!patch environment\ indirect mutual interference may account for an important part of the interference[ It is therefore important to distinguish between the di}erent types\ measure the magnitude of the interference and com! pare this with the amount needed to contribute to the stability of the hostðparasitoid interaction[ Unfor! tunately\ there are only few data sets in the literature on which such an exercise can be attempted[

11 007 Interference among parasitoids In the Trybliographa dataset we explored\ indirect mutual interference modi_es the reduction in overall search rate arising from pseudo!interference "Fig[ 5#[ It is di.cult to assess the relative strengths of pseudo! and indirect mutual interference as these changes with parasitoid density "Fig[ 5#[ Although pseudo! and indirect mutual interference are additive\ for both forms their strength depends on the distribution of patch times[ If there is little aggregation of patch times at low parasitoid densities\ pseudo!interference will be weak "Fig[ 0#\ but there will also be weak indirect mutual interference simply because the distribution of patch times cannot become much more uniform[ If the distribution of patch times is highly aggregated at low parasitoid density there will be strong pseudo! interference[ This\ however\ does not imply that indirect mutual interference will also be strong[ It might be that the distribution of patch times is only weakly a}ected by parasitoid density and that there! fore indirect mutual interference "via a change in the distribution of patch times# is weak[ Other studies have incorporated indirect mutual interference as part of pseudo!interference[ For instance\ Hassell "0867#\ when discussing his mul! tipatch experiment with Venturia canescens "Hassell 0860#\ distinguishes three components of interference] an increase in direct mutual interference\ a decrease in the proportion of the total time that is spent search! ing on patches "indirect mutual interference# and an increase in pseudo!interference with an increasing number of parasitoids in the experiment[ The reduction in overall search rate attributed to pseudo! interference is partly due to the increase in the number of parasitoids and partly due to a decrease in the aggregation of the time spent on patches "see Hassell 0867\ _g[ 4=04#[ In Hassell s "0867# study the host dis! tribution was aggregated and\ therefore\ this pseudo! and indirect mutual interference ampli_ed each other "see Fig[ 1#[ Other laboratory studies that show a relationship between the aggregation of parasitoid e}ort and para! sitoid density\ indicating that indirect mutual inter! ference occurs\ are those of Pallewatta "0875# and Tregenza\ Thompson + Parker "0885#[ In the latter\ a two!patch system was studied[ Parasitoid density was varied from 5 to 13^ there was a linear decrease in the percentage of parasitoids on the better patch "from 79 to 44)# as parasitoid density increases\ thus the distribution changed from aggregated to almost uniform[ In a _eld study of the parasitoid Leptopilina clavipes attacking Drosophila larvae in stinkhorns\ Driessen + Hemerik "0880# found that the CV value of patch times over patches was lower during the part of the season in which parasitoid density was highest "low density period] mean number of parasitoid per stinkhorn was between 2 and 3\ and the CV of patch times over patches was 9=77^ high density period] mean number of parasitoid per stinkhorn was between 5 and 7\ and the CV of patch times over patches was 9=43#[ These data indicate that under _eld conditions also a higher parasitoid density might lead to a less aggregated distribution of parasitoid e}ort[ Occasionally\ the overall search rate of a population increases with parasitoid density[ All reported exam! ples are within!patch studies[ Parasitoids might search a larger area per unit of time "increase their a^ Pijls et al[ 0885# or handle hosts for a shorter time "van Dijken + van Alphen 0880# when there are con! speci_cs in the patch[ If these behavioural changes do not have long!term costs in terms of the number of hosts attacked in the future "which is unlikely#\ they lead to an increase in the overall search rate[ No conclusions on interference can be drawn from such changes that are measured on a patch for a limited amount of time[ Another phenomenon that causes {positive interference is systematic search[ Many parasitoid species mark the area they have explored^ such marking can lead to deviations from random search "Bernstein + Driessen 0885#[ Equation 2 is based on random search within patches and thus is not the most appropriate equation for parasitoids that avoid areas searched by themselves or conspeci_cs[ In these cases the de_nition of interference\ and the equation used to calculate the overall search rate "equation 0#\ can still be used but will lead to an increase in s with parasitoid density[ This emphasizes the limitations of the classical approach to inter! ference[ Indirect mutual interference includes a far wider range of e}ects than those considered here[ To include these we need to expand our framework of inter! ference[ So far\ we have assumed that each attacked host gives rise to a new female parasitoid in the next generation] P t 0 cn a\t with c 0 "Nicholson + Bai! ley 0824#[ Normally\ c is considered to be a species! speci_c constant\ depending on the overall sex ratio\ the clutch size and the host defence system[ It is clear that c might also depend on the parasitoid density\ P[ If\ for instance\ the overall sex ratio increases "becomes less female!biased# with increasing para! sitoid density\ as was found for Nasonia vitripennis "Jones + Turner 0876#\ the value of c will decrease with P[ This decrease in sex ratio can be explained at the individual level "local mate competition^ Hamilton 0856# and is thus due to behavioural interactions[ The decrease in the parasitoid population s e.ciency in producing mated daughters with increased parasitoid density can be considered as indirect mutual inter! ference[ That this can have consequences on the stab! ility of interactions was shown by Hassell et al[ "0872#[ A similar exercise could be done for host acceptance and clutch size decisions\ which also may depend on parasitoid density "Visser 0885#[ This is a direction that should be explored further[ We have chosen to de_ne interference as a reduction in the overall search rate\ a population attribute rather than an individual character\ with increasing para! sitoid density[ By incorporating other density!depen!