Complexity, Evolution , and Persistencein Host-Parasitoid Experimental Systems
With Callosobruchus Beetles as the Host
MIDOR I T UDA AND MASAKAZU SHIMA DA

I. Summary . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
II. Genera l Introd uctio n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
III . Persistence of a Simple Host-Parasitoid System . . . . . . . . . . . . . . . . . .

Bottom-Up Control Factors . . . . . . . . . . . . . . .
B. Top-Down Control Factors

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TV. Persistence of Complex Host-Parasitoid Assemb bes .
. . , . ... ,V. Population Dynamics in a Three-Species System: At the Interface.........
Between Simplicity and Complexity. . . . . . . . . .
A. Experiment. . . . . . . . . .. . . .. . .. . . . . . . . . . . . . .. . . . . . . . . . .
B. Detection of Chaos by a Non- Mecha nistic Model . . . . . . . . . . . .
C. Par ameter Estima tion and Reconstruction of Population
Dynamics by a Semi-Mechanistic Model
D . Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
VI. Host-Parasitoid Interaction and Beyond . . . . . . . . . . . . . . . . . . . . . . . .
Ackn owledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Appe ndices. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Append ix 1. Basic Ecology of the Experimental O rganisms. . . . . . . .
Appendix 2. Selection of Model.
Appendix 3. Assumption of N oise and Parameter Estimation . . . . . .
References . . . . . . . . . . . . . . . .
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I. S UMM ARY
Experimental labora tor y systems of bruchid beetles, Callosobruchus in particular, and their parasitoids have been used as models to study population
dynam ics of single species and host-parasitoid interactions since the early
1940s. First, this paper reviews the recent advances in ecological studies onlaborat ory systems of bruch id ho sts and their parasitoids as represented bybotto m-up and top-d own controls. Factors con trolling the persistence ofsimple host-parasitoid systems that can be modified by an evolutionarychange in a host beetle are demonstrated with reference to local carrying
capacity, vulnerab le time window of hosts to parasitism, and functional
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M. T UDA AND M . SHI MA DA

HOST-PARASITOTD SYSTEMS WITH CA L I.OSOBRUCIlUS BEETLES

respon se of par a sitoid s. Second , we p resent exper imen tal result s o n persis-

systems. Their basic ecology is well studied and described in Appendix 1. In
this pa per, we review recent advances in ecological studies of br uchid hosts
and their pa rasitoids in laborator y systems. Bott om-up (compe tition overreso urce) an d top-down (pa rasitism) con trols on the persistence of simple
host-parasitoid systems, which can be modified by the evolution ary cha nge inreso urce competition in a host beetle, are reviewed . Particular reference ismade to local carr ying capacity, vulnera ble time window of hosts and function aI respo nse of parasitoids as the control factors. We also present findings
from experimental rests on persistence of large r species assemblies ana lyzed in
the light of these con tro l factors as well as number of species. Finally, at theinterface between simple an d complex assemb lies, we asked how ad dition ofa
second parasitoid species to a simp le host-pa rasitoid system affects stabi lity,
As a measure of sta bility, we used both persiste nce time and resilience.

tence of larger species assem blies analyzed in the light of the simple 1\"0species host-parasitoid co ntro l factors. The mos t persisten t asso ciatio n of
species showed that both host and parasitoid con tro l factors in the simp lehost-parasitoid system were consistently effective in the la rger species complexes. There was also a genera l loss of persistence of host-pa rasitoid associa tions as species richness increased . Fina lly, at the int erface be tween simple
an d com plex assemblies. we asked how an addit ion of a third species to asimple host-parasitoid system affects resilience and dur ation of transients.
with the Cailosobruchus beetles as the host and two parasitoids (the pteromalid Anisopteramalus calandrae and braconid Heterosp ilus pro sopidis).
Semi-mecha nistic mod els pa ra meterized by fining to the pop ulation data
were constructed to help understan d the driving forces that govern the
behavior of interacting po pulations. The population dynamics of the threespecies system was ascribed to cyclictchaotic transient dynamics towa rds anattractor that has potentia l of no t only a sta ble equilibrium but also achaotic one. By comparing the three-species dynamics to the stable twa.
species (one host-one parasitoid) dynamics before H. prosopidis was intra.
duced. the instability that lead s to chaos was revealed to be induced bydensity-de pendent host-feeding by A. calandrae. Although the destabilizing
host -feeding was under the control of a stabi lizing effect of mutual interference, the effect was estima ted to be weakened by the introd uction of thesecond parasitoid, H . pr osopidis.

II. GENERAL INTRODUCfIOi'I
Followi ng Pearl's (1927) seminal work, lab oratory experime nts under co ntro lled environmenta l co nd itions have played a key role in test ing ecolog ical
hypotheses. In the late I930s, Syunro Ut ida was the first to initiat e studies onlaboratory experi men tal systems, using Callosobruchus beetles and theirparasitoi ds: a series of publica tions followed in the 1940s (e.g.. Utida
1943a.b, 1944a,b ). Since then, the biology of intraspecific and interspecificdensity dependence and the co nsequences on dynamic behavior in the bruchid and pa rasitoid populat ions have pro vided a useful model for testing
theories in ecology an d for the development of new theoretical perspectives.
T hus, these host-parasitoid mod el systems play a similar role to tha t ofmod el organ isms such as Drosophila (Pimentel an d Stone , 1968) and Plodia
Hegon et al., 1995) as the host.
Beetles of the genus Caltosobvuchu« (Coleopte ra: Chrysom eloidea :Bruchidae) an d their parasitoids. A. calandrae (Hymenoptera : Pteromalid ae)an d H. prosop idis (H ymenoptera: Braconidae), are the model organ isms weused in the series of experiments on pop ulation dyna mics of host -par asitoid

Ill. PERSI STEl'O CE O F A S IM I'LE
HOST-PARASITOID SYSTEM
To examine life history and beha vioral cha rac ters that prom ote persistenceof host-parasitoid associations, the simplest possib le host-parasitoid systems
were studied with different combi na tion s of resou rce an d host species, each
assembled with the same species of parasitoid {Tuda, 1996b). The resources
used were the mung bean , Vigna radiata , an d azuki, V. angularis; the hosts
were the cowpea beetle. Callosobruchus macula/us and C. phaseoli, an d theparasitoid was H. prosopidis. V. radiate is more suitable for the develop mentof the two bruchids, and the bruchid s differ in the degree of scramblecom petition; C. phaseoli exhibits a higher degree of scramble compe tition(many individ uals share a bean ) than C. macula/us. It should be noted that
C. maculatus, exhibits an extreme va riat ion in larval competition between
geogra phical pop ulations; the populatio n used here as well as the one in thefollowing sectio n was of the scram ble type in that mu ltiple ind ivid uals
survive in a single bean but closer to the co ntest type (a single individual
dom inat es a bean) in that survivors are close to one.

A. Bottom-Up Control Factors
1. L ocal Carrying Capacity or Larval Comp etition TypeTwo life history characters have proven to be the causes of persistence ofhost-parasitoid systems: local/global carrying capacity and duration of vulnerability to para sitoid attack s (Tuda, 1996b). Local carrying capacity in40

M , T UDA AN D M. SHIMA DA

HOST-PARASIT OID SYSTEMS WITH CA L L OS OBRVC If US BEETL ES

bruc hids on the bean scale is a direct result of density-dependent compet ition
oflarvae in a con fined (bean) resource (Ap pendix 1); a popula tio n of con test
type competitors, beca use o f its higher reso urce req uirement, has a lower
local carr ying cap acity, and consequentl y a lower global carrying capacity at
the popu la tion level.
Lower local/global carrying capa city of the host C. maculatus thanthat of C. phaseoli significantly promoted persistence of the bost-parasitc id
system (Fig. I) (Tuda, 1996b). Simula tion of a Nicholson -Bailey type mod el
wit h age structu re also supported the effect of loca l ca rry ing ca pa city,with parameter values esti ma ted independently of the long-term experiments. Th is result is consistent with the prediction of the par adox of enrichment. in which the increase in (global) carrying 'ca pacity red uces
sta bility (Rosenzweig. 197 1). O n the contra ry. when the global carrying
ca pacity is increased by the add ition of a grea ter resource for the host .
longe r coex istence was achieved (T ud a. 1999 . un pu blished da ta) . Therefo re.
parallel inc reases in local and globa l ca rrying ca pacities or increases inglob al carrying ca pacity by cha nging the degree of densi ty dependence (o rnonli nea rity) rather tha n by increasing resource pa tches, is the key to thepa rad ox of enr ichment. which may oft en be imp licitly vio la ted in the field(T uda, 1999, unp ubl ished data).
In a compet ition system, the intraspe cific contest-type of C. maculatus isalso a su perio r interspecific compe titor (Toquena ga a nd Fujii, 1991 ) tha t ca ncompe titively exclude other bruchid species in assemblies of bea n resource
a nd herbivores.
Bruch id beetles tha t utilize small beans o f wild legumes a re the contest
type . tha t is. only a single ind ivid ual that domi na tes (bea n) resou rce ca nsurvive in each gra in of bea ns, whereas pest species such as the azuki bea nbeetle. ColJosobruchus chinensis a nd Zabrates subfasc iatus. a re (or evo lved tobe) the scra mble type. with mu ltiple individuals sha ring single grai ns ofbean s. This would predict tha t population dynamics of pest species. tha ta re likely to ha ve high carrying ca pacit ies beca use of resource sha ring. ca n bedesta bilized by introductio n of a pa ras itoid for control. which allows bo th
ou tbrea ks a nd extinctio n of the pests. Selection fo r eithe r the scramble orcontest competition types will be discussed furt her in the subsection on
evolutiona ry c ha nge.

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Figure 1 Population dynamics and persistence of host-p arasitoid systems:(a) V. rodtata -C, mocutaue-H. prosopidis, (b) V. angulons-C maculatus-H. prosopidis, (c) V. radiata-C. phascoli-H. p rosopidis, and (d) V. angulo ns-C. phaseoli-H.

prosopidis. Both resource (V. radtata or V. anguluris) and host (C rnoculatus or
C phasco/i) effects are significant (Tuda, I996b). The closed circles show the numbersof host adults emerged during the preceding 10 days. and the open circles show thoseof parasitoid adults emerged during the same periods as the hosts. The arrows
indicate the times of extinction of either the host or the parasitoid in replicatedsystems. Modifi ed from Tude (l 996b).

It has been shown t hat the d ura tio n of the vulnera ble developmental sta ges
in the ho st to parasitism is one of the factors tha t ha ve the great est effec t
on the persistence of host-pa rasito id dynami cs (Tuda a nd Shimada. 1995;
Tuda, 1996b ). The longer the vulnerable period . the less persistent the ho stparasitoid system. which was obser....ed in host-parasitoid systems with azu ki
as the resou rce tha t elongates developmental t ime in both C. maculatus a nd
C. p haseoli (Fi g. I ). Feed ing on po or-qu ality pla nts hinders development of
herbivoro us insects. increasing the time window of susceptibility to natura lenemies an d leads to higher mo rtality o f the herbivores (Johnson a nd G ould.
1992; Benrey a nd Denno. 1997). H owever. th is slow-growth-high-mortality
rela tion is not always observed in na ture beca use of confoun ding inter act ions (C lancy and Price, 1987; Benrey and Denno. 1997 ). Slow de velopme nt ca n also be associated with low fec undi ty. Model simu la tions totest this possibility, howeve r, showed that the effect of such low fecun di ty is
minor compared to that of a vulne rab le time window for a par asitoid withhigh sea rching efficiency as in H. prosopidis (Tud a. 1996b ). Resource is not
the only fac tor tha t affects the vulnerable time window of the host. Increasein temperatu re elongated the vulnerable time window of C. chinensis
to 11. prosop id is, which reduced persistence . or time 10 extinction, of t hehost-pa rasitoid system (Tuda and Shimada, 1995).

42

HOST-PARASIT OID SYST EMS WIT H CALL OS OBRUCHUS BEET LES

M . TUDA AND M . SH I M A D A

43

3. Evolut ionary Change

We often assum e characters that play an impo rtant role in deter mining
persistence of host-parasitoid systems are constant over time. T his assumption, however. can be violated as obse rved in the host C. maculatus durin g along-term experiment of a host -pa rasitoid system. Larval com petition of
C. maculatus was initially the scramble type, and two to three individuals
survived from a small V. radiata seed (Fig. 2a) . When the experiment wasterm inated on day 800. only single ad ults emerged indicating the larva lcompe tition was of the contest type (Fig. 2a) (Tuda . 1998). Th is po pulationof C. maculatus was brough t into the laboratory relatively recently (twoyears prior to experi mentation), unlike the ot her po pula tio ns of bruch ids
and parasitoids in our lab oratory. There was no difference in the attack rates
between pre- and post -experiment of the parasitoid H. prosopidis, which has
been maintained in the laboratory for about 20 years. The cha nge in the
population dyna mics occu rred approximately at 20 generations of the host(Fig. 2b), and the po st-experimental host and parasito id after 800 days ofcoexistence showed stable population dynam ics unlike the initial oscillatio ns
when they were return ed to initial densities (Fig. 2c). Th is confirms thechange was not temp ora L
With a parameterized game-theoretical mod el, Tuda and lwasa (1998)
showed that the evolution ary change in larval competitio n towards thecontest type can induce a large shift in the po pulation dynam ics of hostand pa rasitoid as observed in the experimental system. For such ra pid
evolutionary change to occur, 20 generations was shown to be sufficient by
the model with the following assumptions: l) a small fraction of initial
populati on was a contest-type competitor, in which the phenotype is generically determined: and 2) the co ntest compe tito r consumes a certain volume
of bean and kills othe r individua ls in that volume, enabling a scramble
competitor to survive only when bean s are lar ge eno ugh. It is wort h no tingtha t ran do m pa rasitoid attacks did not alter the evolution towards contest
type but ca n slow the evolution .
T his explains the results of experiments on a single-species C. macidatus
pop ulation by Toq uenaga et 01. (1994), in which competi tion type wasestimated based on the resemblance of dynam ical trajectories. T heir study
also indicated tha t the tr ansition from scramble to co ntest type occurred ona time scale consistent with the prediction of the present model (i.e., 20
generati ons). Th e time scale required for such a change also corresponds tothe one observed in Nicho lson's laboratory blowfly populat ion (Nic holson,
1957; Stokes et al., 1988). T his similari ty may arise not only from the stable
labora tory conditions but also fro m a common biological mechan ism, e.g.,density-dependent proc esses in the insects.

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Figure 2 (a ) Evolutionary change in the number of emer ged adults that survived
from larval competit ion of the host C. maadatus in the replicate shown in Figure Ia.
Redrawn from T ud a (1998). (b) Temporal change observed in population dynamics
of the C. ma cula/us-H. prosopidis host-parasitoid system (the rep licate shown in
Figure l a). Red rawn from Tuda and Iwasa (1998). (e) A representative replicate of
popu latio n dynamics of post-experimental host and parasitoid populations collected~fte~ 800 days from the replicate shown in Figure 2b. The open and closed circles asm FIgur e I.

45

M. T U DA AN D M . SHIM A DAHOST-PAR ASITOID SYSTEMS WITH CALLOSO BRUCH US BEET LES

Because the co ntest type in the host is stabilizing in host-parasitci ddynamics, this bottom-up herbivore evolut ion enh anced the persi~tence .of
the host-parasitoid (c. macuknus- H. prosopidis) system. Genetic van abilit y retained in the host proba bly facilitated the evolutionary cha n ~e .
Recently, the effect of genetic variability was directly tested on the persrstence of the C. chinensis-H. prosopidis host-parasito id system (Imura el a/.,2003). Th e system with an F 1 generation derived fro m a cross of two
different strains of host as a foun der pers isted longer than those with single
strai ns as founders . What is not known is bow general th is is and whether
genetic variability in the parasitoid pop ulation has the same effect. The
model prediction is that genetic varia bility that exhibits a trad e-off in theparasitoid population does not have a critical effect, whereas that in the hostpopulation enables coexistence when the pa rasitoid att ack rate is moderate
which allows host-parasito id coexistence in the early phase (T uda andBo nsall, 1999).
Such evolutionary change in host -parasitoid dy namics ma y not be
rare, especially when the insect po pulations are brou ght recently into thelaborato ry or a new environ ment. The po pulation dyna mics of C. chinensisH. prosopidis system studied by Utida (1957a,b) appears to change overtime (Utida, 1957a,b; Royama, 1992). Parameterization of a subset oft he three-species mod el. by fitting to the time-series, ind icated that there
was indeed a decrea se in the attack rate of the parasitoid as time windows
for fitting are shifted gra duall y from the onset of the experiment to the endof the time series (Tuda, 2003, unpu blished data). Evolu tion ary flexibility
and phenotypic plasticity as a modification force on th e food -web has been
discussed theoretically and emp irically (Pimentel, 1968; Pimentel and Stone,
1968; Thompson, 1998; Abrams, 2000; Agrawal, 2001; Kondoh, 2003).
What we observed in the bruchid-parasitoid system illustra tes how evolution
can promote persi stence of species coe xistence that. in the first place. is
att ained ecologically. Although evolution can also reduce persistence of ahost-pa rasitoid system, it is more difficult to capture once coexistence isterm inated by extinction . For this reason. biological assemblies we see inna ture ma y be biased examples of selection 'towards coexistence'. Experimental tests on the possibility of evolution 'against coexistence' are
intr iguing future challenges.

C. chinensis affected variability of populat ion dynam ics of one of the twoparasitoids, A. calandroe and H. prosopidis. The differential effect of pa tchi-

44

4. Spatial and Temporal Heterogeneity

Distribu tion of resou rces or plants for herbivores, which is often determinedby enviro nmental factors, is also crucial for host-parasitoid interact ions topersist. Shimada (1999) showed t hat the degree of patchiness of resource forness between the two pa rasitoids is ascribed to their different searching
beha vior (Shimada , 1999). By comparing spat ial to temporal heterogeneityof resou rces using two species of legumes, Mitsunaga and Fujii (1997)
concluded tha t temp oral heterogeneity or alter ing two resources in sequencecontributed to the persistence of a two hosts-one pa rasitoid system. The
conclus ions of the two studies cannot be com pared as they are because of thedifferent st ructures of the assembli es. The host-par asitoid systems withdifferent architectures have potent ial to be subjected to further testing for
genera lity of the conclusions on the effect of heteroge neity, with a different
combination of species.

B. Top-Down Control Facto rs
Functional respo nse, or the number of attacked hosts as a function ofhost density, of parasitoid can be an impo rtant top-down con trol on host(Ha ssell, 1978). The att ack rate of A. calandrae is chara cterized by thefollowing: first, the number of attacked hosts increases gra dually with increas ing host density. specifically per -bea n density. which itself is destabilizing (Utida, 1943b; Utida, 1957a; Kistler, 1985, unpublished data: Shimadaand Fujii. 1985; Mitsunaga and Fujii, 1999); second , at a high density of
A. calandrae, strong mutual interference stabi lizes its po pulatio n dyna mics
with the host. Th e C. chinensis-A , calandrae system with azuki beans ( Vigna
angularis). for example, exhibits mild oscillations with a sma ll amplitude(Utida, 1948b, 1957a; Fuj ii, 1983). O n the contrary, with blackeye bean ,V. unguiculata as the resource, A. calandrae is able to attack more effic iently
even when the density of host beetles is low, because the thin seed coat of thebean allows easier penetrati on of the ovipositor of the parasitoid . Eventua lly. host-par asitoid interaction ended with extinction probably because thedestabilizing effect of host-feeding was greater than the sta bilizing effect ofmutual interference.
H. prosopidis has a high attack rate independent of host density but
is limited by the number of eggs, which results in sat uration in the numberof attacked hosts as host den sity increases {Utida, 1957a). A C. chinensis- H,
prosopidis system with azuk i beans fluctuat es with large amplitudes. sometimes showing po pulatio n cycles o f 100 days or longer (Uti da , 1957a,b;
Fuji i, 1983; Tud a and Shimada, 1995). Du ring the low-density phase, thesystem is likely to become extinct ( Fujii, 1983; Tu da and Shimada, 1995),
altho ugh it does pers ist for a fairly lon g time in some experimental rep licates(Ut ida, 1957a,b).

46

47

M. TU DA AND M. SH IMADAHOST-PARASITOID SYST EMS WITH CA L L OS OBR UCHU S BEETLES

IV. P ERSISTENCE OF CO M P LEX
HO ST-PARASITOID ASSEM BLIES(mut ual inte rference of A . calandrae) co ntrol facto rs pro ved critical in theprevious section, stay effective in the larger species assemblies (Tuda, 1996a).
The experiment on the large species assembly in this section illustrated that it is
not on ly the number of species itself but also the characteristics of species
intera ctions that determin e the persistence or sta bility of a host-parasitoid
assembly.

The re is co ntroversy ove r the rela tion between co mplexity an d sta bility in abiological community. Random assembl y models predict that comp lexity (interm s of species rich ness) reduces local stabi lity and con nectance (May,1972), whereas Elto n ( 1927) suggested that complexity enhances stability.
In terms of global sta bility and perman ence, which guarantee persistentcoexistence of species, sta bility decreases with inc reas ing complexity, whichis consistent with Ma y' s prediction (Chen an d Cohen, 200 1b). Recent studies
ind icat e that adaptive evolutionary cha nges in compo nent species can eith er
incr ease or decrease diversity (Abrams, 2000; Kondoh , 2003). Studies using
micro-orga nisms supported May' s prediction (Ha irston et ai.; 1968; Lawler,
1993; La wler and Morin, 1993). Accumula tion of so un d em pirical evidence
is required for assemb lies of higher orga nisms. Here, we review recent
advances in empirical tests on the complexity-stability hypothesis in theexperimental assem bly o f bruch id ho sts a nd their pa ras itoids.
Tuda (l996a) and Tuda and Kondoh (2003, unpublished da ta) a nalyzed
experimental result s that tested the complexity-stab ility hypo thesis by using
bruchid beetles and their pa rasitoid (Ohdate, 1980; Fujii, 198 1, 1994). The
experim ental design was as follows: each of the four compa rt ments of a petri
dish was filled with 5 g ofazu ki beans, then bruchids, followed by parasitoids .
Th e maximum num ber of the initial com ponent species was 5, i.e., three
bru chid species (c. maculatus, C. chinensis a nd Z. subfascia /us) an d two parasitoid species (A. calandrue and H. prosopidis), and the minimum was 2, i.e., twobruchid species (Fujii, 1994). Initial assemblies were replicated up to threetimes. As each species becomes extinct, different initial assem blies ca n end up
with the same assembly, a nd replicated assemblies can lose different species.
Each such tra nsient assembly is treated as an additional replicate. Bean supply
was contin ued un til t he assembly reached stable sta tes. or sta ble species compos itions. Persistence, or time to extinction of a species, of each assembly typewas recorded . Th e origina l records were tra nsfonned to mean proba bility ofextin ction per generation of a com ponent species (Tuda and Kondoh , 2003,
unpublished da ta). The results indicate that extinction probability increased as
the number of species increased (Tuda a nd Kondoh , 2003, unpubli shed data),
and persistence decreased with the incre asing number of species (T uda, 1996a).
Wh ile this suppor ts May's complexity-insta bility relationship found from ra ndo m combinat ion of species, there was somet hing beyond the prediction: aclear pattern in the composition of species in the final experimental assemblies(Ohd ate, 1980; Fujii, 1983, 1994). The fina l assemblies were composed ofeither
single br uchid, C. macukuus. or single hos t-single par asitoid, C. maculatusA . calandrae. This shows that the bottom-up (contest competition or resultan t
low local carrying capacity of C. macula/ us) and self-regulating to p-down

V. POPULATION DYNAMICS IN A THR EE-SPECIESSYSTE M: AT T HE INTER FACE BETW EENSIMPLICITY AND COM P LEXITY
Recen t studies of insect a nd animal po pu lations dem onstrat ed com plex
nonlinear dyna mics (including cha os) a re ub iquitous in single - as well as
paired - species populat ions (Nicho lson , 1954; Han ski et al., 1993; Cos ta ntino
et al., 1995, 1997; Ellner an d T urchin, 1995; Falck et al., 1995; Turchin, 1996;
T urchin a nd Ellner, 2000). In nature. almost all popula tion s a re concurre ntlyinteracting with m ultiple species, as predator and prey or as host and pa rasite/parasitoid. Three-species systems are on e of the simplest and mo st intriguing
ca ndidates to allow a n understanding of irr egular. complex population
dynamics of multi- species assemblies, with emerging effects of indirect inter act ions (Ho lt, 1977; Sih et 01., 1985; Briggs, 1993). An example is a laboratory
experim ental syste m with a seed beetle ho st an d two parasitoid wasps th at
persis ted for a fairly long time with irr egula r populat ion fluctu at ion s of thethree component species (Utida, 1957a).
Detection of mecha nisms by pa ra meter ized models from population timeseries has becom e a prom ising approac h in eco logy in recent years with theap plication of extensive stat istical tools (e.g., Denn is et al., 1995, 1997, 200 1;
Kendall et al., 1999; Jost a nd Arditi, 200 1; Kristoffer sen et 01., 2001; Turchin
and lI anski , 200 1).
With parameterized semi-mechanistic mod els, thi s pape r aims to: I) characterize persistent population dynamics of the same three species as Utida(1957a); 2) detect any change in the dynamic property and effect induced by
the addition of the third species, by comparing the three-species dynamics withthe two-species dyn amics; a nd 3) clarify which characteristic(s) of the three
species induced alteration of dynamic behavior.

A. Experiment
All of the experim ents were conducted a t 30°C . 65% rela tive hum idity an d
16: 8· ho ur light: dark cycles. Our system was first designed with on ly thehost , C. chinensis, in a square plastic case (15 em x 15 em x 4 em) in which

48

fou r ro und dishes (diameter 6 em), each with 10 g of azuk i beans ( Vigna
angularis) were set as resource patches . Live an d dead adult insects were
censused in each of three replicate systems at each lO-day interval, the oldest
resou rce patch being replaced with uninfested azuki bean s. T he two pa rasi taid species were introduced sequentially int o the system aft er the hostpopulation had converged to the equ ilibri um dens ity: A . calandrae on days
130 a nd 140, then H. pro sopidis on days 440 and 450. Populatio n censuses were
continued un til the extinction of the host on da y 1550. The num ber of adults
that emerged during the preceding 10 days was calculated as: (number of thelive ad ults at t) + (number of the dead adults at t) - (number of the live ad ults
at t - 1) in each species.
In the host-only phase, C. chinensis reached the equi librium po pu lat ion
size of about 350 between day 50 and day 100 (Fig. 3). Afte r adding the firstparasitoid , A. ca/andr ae, on day 130 the host-a . calandrae system showedstab le pop ulation dynamics with sma ll oscillations around the equi libri um
population sizes of the host (70 to 90) and A . calandrae ( ISO to 180) in all
three replicate systems . However, afte r introd uctio n of the second parasitoid, H . prosopidis, on day 440, the stable dynamics of the host andA. calandrae were disr upt ed and changed to irr egular fluctuat ion s with alarge amplitude (Fig. 3).
Pers istence of the three-species system ranged from 100 da ys (replicate
C, not shown) to longer than 800 day s (replicate B, F ig. 3b). Repl icate C
collapsed after one peak of H. p rosopidis po pu lation outbreak because thewasp parasitized all the hosts. In replicates A and B, however, the threespecies assembly persisted for 450 and 860 da ys (Fig . 3). Since H. p rosop idis
went essentially extinct in replicate A on day 890 (all emergen ts were males),
4 ma les and 8 females of newly emerged H. prosopidis were introduced , theeffect of which was sma ll on the time-series of the host an d A. ca/andr ae
in com parison with usual demographic stochasticity. Replicate A con tinued
there afte r until da y 1,230, when finally H. prosop id is went extinct again,
which was followed by rapi d convergence to the original host-A. ca/andrae
equilibrium states (F ig. 3a). The coexistence of the host and A. ca/andrae
persisted thereafter until day 1,550 when we ended the long-term exper iment ,In replicate B, on the other hand , the three-species assembly per sisted for
longer than 800 da ys from day 440 to day 1,300, during which po pulation
fluctuations were much larger in the host and A . calandrae after introduct ionof H. p rosop idis than befo re (Fig. 3b). Both parasitoids went extinct simultaneously on da y 1,300 after very low pop ulat ion densities of the host. Whenthe host po pul at ion had recovered, we re-introduced H. p rosopidis only
int o the system to ob serve populat ion dynamic s of the host-H. p rosop idis
assembly. After an ou tbreak of host and H. prosopidis po pula tions, all of thehost s were pa rasitized and the system collapsed on da y 1,450 (no t shown).

49

HOST-PAR ASITOID SYSTEMS WITH CA L L OS OBR UCH US BEETLES

M . TUD A A N D M . SH IMAD A
(.(

~

i ~[
~i. ,
o

«

100

«
200

'
300

, ~, , ~~·~·~I

400

500

600

70 0

800

900

1000

1100

1200

1300

1400

1500

Time in days"'

~ ~'~'""'"i ~[ ~.~,,~.
~~[:::: : : :~H _~"
o

100

200

300

400

500

600

700

800

900

1000

1100

1200

Time in days

Figure 3 Observed population dynamics of C. chinensis (host), and its twoparasitoid s, A . calandrae and H. prosopidis . (a) replicate A and (b) replicate B. The
numbers of adults are as explained In Figure L Redrawn fro m Kristoffersen et al.
(200 1).

Po pu latio n fluctua tion of the host became abruptl y larger after a low-density
ph ase of A . calandrae between day !,l 80 and 1,210, so we omi tted the timeseries after day 1,200 of replicate B from later analyses in the host andA. calandrae .

50

M. TUDA AND M. SHIMADAHOST. PARA SITOID SYSTE MS WITH CALLOSOBRUC H US BEET LES

B. Detection of Chaos by a Non-Mechanistic M odel
Th e com puter programs LENNS (Lyapunov Expon ent of Noisy No nlinear
Systems) an d RSM (Response Surface Method ology) were applied to estimate the dominant Lyapunov expo nent (LE) , used as a measure of chaotic
d yna mics (Ellner et 01.• 1992; T urch in and Taylo r. 1992). The 10 best fits by
LENNS and the single best-fit estimates by RSM were selected to computet he LEs. Using LENNS, they were either positive (host in replicate B), zero
(host in replicate A), or slightly negative CA. calandrae in both replicates)(Fi g. 4a). Using RSM . the LEs in the thre e-species system were either
positive (host population in both replicates and A . calandrae in replicate B)or slightly negat ive (A . calandrae in replicate A) (F ig. 4b). T hese estimatesindicate that the o ne host-two parasitoid system can be cha otic but the result
is not consistent among component species and replica tes.
For comparison, the program s were also applied to the po pulation
dynamics of the two-species, or host-A. calandrae system (F ig. ac, d) . Bothmethods estimated large negative LEs for all four time-series except a
positive exponent for the host in replicate A by LENNS.
By comparing the estimates between the two-species and three-species
time series, the following characteristic differences were found: I) the
three-species system is less stab le than the two-species system (F ig. 4);2) the lag tends to be shorter in the three-species system (LENNS resultin Table I); an d 3) the dimension is higher in the three-species system(fable 1).

C. Para meter Estimation and Reconstruction of P opulat ion
Dynamics by a Semi-Mechanistic Model
1. Deterministic M odel

The deterministic mod el is formulated with a Mor en-Ricke r equation for hostdensity-dependent growth (Moran, 1950; Ricker, 1954) and a NicholsonBailey type equation for escape from parasitoid attack (Nicholson.
1933; Nicholson an d Bailey, 1935). The selected mod el, based on thelikelihood ratio test (Appendix 2), includes host rep rod uction followed
by density-dependent survival of eggs according to adult density, densitydependent larval survival, and recru itment of adults from the previou stime step in the host (Tuda, 2003, unpublished).
For generation time, two time units for the host and A. calandrae and on etime unit for H. p rosopidis were selected based on the time required fordevelopment fro m the egg to the reprod ucing female adult that is elon gatedby synergistic host feeding in A . catandrae (Append ix I).

•

•

J

"

.

•

1

•

<

•

J
<

•

J
•
•

e

1

•

••

"

<

1

~

,
"

J

"'

<

s

j
• I

51

52

HOST.PARASITOID SYSTEMS WITH CALLOS OBR UCHUS BEETLES

M . T UDA AND M . SH IMADA

53

Tab je I Best fit pa ra met ers and t he coefficie nt of determ ina tio n (? ) in L ENNS a nd Ta ble 2; Definitions of variables and parameters
RSM . LENNS-estimated Lya punov expo ne nts, A's. are the means of the 10 best fill
Definitiona nd I (th~ la g), d .(the num ber
lag s o r embe dd ing d imen sions), a nd k (t he nu mber VariableslParamelersof nod es In the hl~den layer), based on GCV (generalized cross valid a tio n) cri terio ll
number of host larvae( ElI n~r and Tu rchin, 1995). Numbers In parent heses indicate the second frequent I. d
Xu
number of host adults
or k In the 10 best fits. The RSM -estimated A's are, on the other han d, the best fi t a.;numbe r of larvae of par asitoid A. calandrae
the best /.(the time lag = 1), d (nu mber of lags or dimensions), and q (the order of a YI .,number of adu lts of parasitcid A. calandrae
po lynomial), ba sed on cross-validat ion criterion (Turchin and Taylor . 1992). The Y...,number of ad ults of parasitoid H . prosoptdis

or

x.,

number at the head of each lime series corresponds to th e number in Figure 4. The Z,
range of days shows the time series that Wd S used for calculation
x
bO
LENNS
RSM
hi
d

Host-A. calandrae
Replicate A (dayJ4l>-44O)' Host2A. calandrae

Replicate A (day1,220--1,550)
lHost
4 A. calandrae

Replicate B (day14Q-440)' Host
6A . cakmdrae

k - InGCV

d

s

q

a,
f
m

2
4 (1, 3, 2)

0.996
0.935

3
I

I (2, 3)
I (3)

I
3

0.687
0.500

0.433
0.801

az

'z

0.468
0.747
(XI. X,,) and pa rasitoids, A . calandrue (YI , Y..) and H . prosopidis (Z), at time

2 (4, I)
I

1.07
0.427

I

2

1
2

0.624
0.696

t are thus described as:

Xl" = ).X",I_tex. p{-!Jo X..,I_1 - b l)'xa,t_ lexp(-!JoXa,f- I) }Ix.. ,

Hcst-z parasiloids
Replicate A (da y440-1 ,230)
7Host

aA . calanarae

3 (4, 2)
4 (2)

2
2

- 0.319- 0.44 623

2 0.818
2 0.788

4 (3)
4

2
1

-0.486- 0.3222
3

2 0.801
2 0.689

Replicate B (da y 440--- 1,190)

9Host
lOA.

number of eggs deposited by a female host x 0.5
density dependence in egg mortality in hostdensity dependence in larval mortality in hostsurvival rate of host adults from 1-1 to t
searching efficiency of parasitoid A. calandrae
coefficient for host-feeding by A . calandrae that
contributes to egg production
mutual interference in A. calandrae
searching efficiency of parasitoid H. prosapidis
handling time (or inverse of number of eggs) inparasitoid 1I. prosop idis

cotanarae

Multiparasitized {i.e., co-parasitized) hosts were assumed to prod uce
each parasitoid with an equa l cha nce (Appendix. I) , thus the pro bab ility of p roducing A. calandrae is the sum o f the p ro bability o f being
att acked a t least once by A . calandrae but not by H. prosoptdis. whichis ex p( -dz Z;_t ){ l - exp ( - a'y Y:~ tl } and the probability of being attacked by both parasitoids and only A. calandrae surviving, tha t is{l - ex.p( -dZZ;_I) }{ I - exp ( - a'y l )} / 2. T he sum is reduce d to theform : {I + exp(-a'z Z;_1 )}{ I- exp(- a'Y Y:_tl}/2. The same can be donefor H. prosopidis. Popul ation sizes of each developmenta l stage of the host

Y:-

( I)

= X l l.texp(-ay'Y't.I-a Z'Z \ . I) + S X..1.1(2)

Yt,l -= Xt,1_1{I + exp( - dZZ;_l )} { I - exp ( - d y Y:_l )} / 2(3)

Y" ,I = Yt.I- 1(4)

2/ =:: XI,I- d I + exp ( - d y Y:_l )}{ I - exp ( - a'ZZ; _l )} / 2.

(5)

The variables and pa rameters are defined in T ab le 2. T he gender ratios ofparasitoid was approximated by 0.5, so that the numbers of females aredescribed as Y; = YIl ,d 2 and Z; = Z,f2 for each respective parasitoid .
Female A . caiandrae feeds on hosts and this increases the number of her
ma tu re eggs. Therefore, h ost-feedin g by adult females tha t contributes exponent ially to the att ack rate was incorporated . It is obse rved that the fema le A .
calandrae interrupt with parasitizing conspecifics on encou nter by jump ing
upon them (Tuda , 2003, personal observat ion), while female H. p rosopidis
do not sho w interference behavior, altho ugh pseudo-interference appears
at extremely high density (Fig. 4 in Shimada, 1999). For A . calandrae,
mutual interference (Hassell and Varley, 1969) was incorp orat ed that

54

HOST-PAR ASITOID SYSTEMS WITH CA LL OS OBR UCH US BEET LES

M. TUDA AND M. SH IMADA

reduces the att ack rate as ad ult densities of A . calandrae increase (Shimada,1999). H. prosopidis searc hes and para sitizes hosts efficiently but soo n depletes its eggs by doing so, as in a typical type II funct ional response(Ho lling, 1959; Royama, 1971; Rogers. 1972). And it does not host-feed.
Thus, the attack rates of the parasi to ids are formulated as:
(6)
a'z =

az/Cl + oZ CZ X1,l _I ).

(7)

Not a ll o f the dev elo pmen ta l sta ges in eq ua tions 1 to 5, however . can beobserved. Larval sta ges of the host and pa rasitoid are invisible from outside
the beans. The equations for the larval stages (equations 1 and 3) areembedd ed into equa tion s 2 and 4, respect ively. T hus, the determinis tic
model is represented by three state variables:

X..,l = H,_2exP( - a'y I- I Y:_ I - a'ZI_IZ:_I) + SX o.l _ I

55noise is as follows:'I'(

x a.1 = {h,_2exP - d YY,' _I -dZ-'" I ) +SXa.l_l JI /2 + EX.I

( 14)

( 15)
z; /l = [h _2{1 + exp ( -a'Y}~_ I) }{ 1 - exp( -dZ~_ I)}j2] 1/2 + E:.1.

(16)'
Fo r the assumption s on the noise and parameter estima tion , see Appendix 3.
Numbers of ad ults of each species from da y 430 to 870 in rep licate A andday 430 to 1270 in replicate B were used as time series to fit the model.

3. Two-Species Dynam ics(8) The host-A. calandra e dynamics before the introd uction of H. prosopidis
were fit by a subset of the three-species model to see if any factor was
modified by the presence of H. prosopidis. The dete rministic mod el for thehost (X a ) an d A . calandrae ( Ye) was a modi fied version of equation s 8 and 9:

X..,1 = H ,_2e x p ( - a'Y,1_ 1 Y:_1) +SX..,I_ I

(17)

where
(18)

d Y,I-I = a yexp(JH,_i_l ) 1";: ;"(II )aZ,r_i = az j (1 + az cz Hr_l_d(12)

A stocha stic mod el for the two species with no rm ally-d istrib uted demograp hic noise was modified from equation s 14 and 15:

Hr_i = I:XO,l-i exp{ - bOXa,,_i - blAXa.t-Iexp(- bOXa,,_I) }.

(13)

x~:/ = {ht _ 2exp(- d y 1- IYr- l ) + SX a.I_ I}1 / 2 + Ex.,(19)

y~~2 = [ht3 {l - exp(- a'y t _ 2-Yr_ 2)} ]1/2 + EY,I'(20)

2. Stochastic M odel and Fill ing to Time-Series Data

O bserved po pulation sizes of each replicate were used for the initi al values
in the simulations: replica te A; XI = 80, X2 = 6 1, X 3 = 57, Y2 = 169, Y3 =142, 2 2 = 12, and 2 3 = 13; and replica te B; XI = 85, X2 = 55, X 3 = 42, Y2 =218, Y3 = 96, 2 2 = 12, and 2 3 = 17 for the three-species system (day 430 to450). Replicate A; XI = 4 10, X2 = 274 , X 3 = 212 , Y2 = 8, an d Y3 = 158 andreplicate B; X I = 351, X 2 = 343, X3 = 140, Y2 = 8, and Y3 = 132 were used
for the two-species system (day 130 to 150).

In the observed time series, no ise is added to the deterministic dynamics.
Demograp hic noise pr esum ably dominates, relat ive to env ironmental
noise in our controlled grow th-cham ber environ men t. Host reprod uction isassumed to follow a Poisson distribution with mean AXa. I _ I _ Survival
through density-dependent competitio n and pa rasitism can be described asa bino mial distribution. A binomially distributed variab le with Poissondistributed mean n and probability p is known to follow Poisson distribution
with mea n JiP, where 11 is the mean of the Poisson distribution of n (Boswell 4. Estima tion of Dominant L E
et al., 1979). The refore, all the variab les on the left ha nd of equations I to 5
can be approximated by a Poisson distribution . The numbers in the present Th e dominant LE was estimated from a time-series of time unit (I)da ta set a re square-roo t transformed to normalize the Poisson distribution 1,00 1- 2,000 (l tim e unit = 10 days), om itti ng the first 1,000 points to remove(Denni s et al., 200 1). Stochastic realization of the model with demographic any transient phase. The Jacobian matrix of part ial derivati ves of equations

56

M . T U DA AND M . SHIMADAHOST_PARAS ITOID SYST EMS WIT H CA LLOSOBRUCHUS BEETL ES

1 to 5 was used to estim at e LE by a pp lying th e chai n rul e and then a vera gingth e exponential divergence rates of init ial perturbation over time. Boot,
stra ppe d dat asets were constructed to estimate the confidence int ervals ofLEs, following Dennis et al. (2001). The error terms of the three populations
as a set were resampled 1,000 times with replacement after standa rdization.
Except for the first th ree da ta poi nt s, the boo tstrap ped erro rs were ad ded to(squa re-roo ted) po pu la tion densities generate d by determin istic simulationof the models with ma ximum likelihood (ML) estimates, an d squared. Whenthe population densities with added noise were < 0, they were set to 0.5
before squ are d . The resultant data with the first three observed data ineach replicate were fitte d by the model to estima te LE . T he 2.5t h and
97.5th percentiles of th e LE distribution were considered as 95% confidence
lim its of the LE.

D. Results and Discussion
1. Three-Species Pop ulation Dynamics
The results of the fit by the model a nd stochastic simulation are shown in Fig. 5.
The ML estimates and 95% confidence intervals (CI) were as shown in Table 3.
The dominant LE estima ted from a determ inistic sim ula tion of the modelwith the ML esti m ates wa s sligh tly negative, - 0.0510 (bootstra p 95% CI ,- 0.684, 0.00 14 for lo wer and upper confidence limits (CL) F ig, Sa).
Simu late d po pula tio n dynamics with ML estimate s had tr ansients to sta ble
equi librium (Table 3) reached at time unit 472 (bootstrap 95% CI for
duration of tra nsient dynamics, 46, 2000 < ). The eq uilibrium may not bereached in the experim ents that per sisted for to, 45, and 86 time units.
Among estimate s for all the bootstra pped data, 9.3% exhi bited complex
d yna mics (Fig. 6b) (a bo ut 8% were either cha otic or qu asiperiodi c andabo ut 1% were lo ng cha otic transien t dynam ics). The LE s were also estim ated with th e 95% CL of the par ameters a nd were either pos itive o r 0 at thelower limits of para meter s a y and m for A . calandrae (equ atio n 11), whereas
at the othe r lim its the LE s were all nega tive but with small a bsolute values(Ta ble 3; Fig. 7 for o ne-dimension al bifurca tion diagrams). The LE can beused as an index of resilience (i.e., a bility to reco ver from a small perturbatio n; G underso n, 2000) beca use the la rger absolut e va lues of nega tive LE,th e more rapid convergence to an equ ilibr ium (a strong positive correlation
between inverse of the duration of transients and absolut e va lues of negat ive
LE , r = 0.992, n = 128,p < 0.0001). In m ulti-dimensional bifurcation, wherea ll parameters wer e estima ted for each value of a pa rameter changed within
its co nfidence interval, LEs mo not onically increas ed with dec reas ing a y an d

57

' 00

(c) :/

600' r-~-~-~--~-~,~-~--~-~-­

i

400

I

00

'e

"

'"

m tha t can ind uce comp lex popul a tion d ynamics (i.e., chaos and qu asiperiodici ty) .
With in the confidence inte rval of LE, these chaotic, quasiperiodic, o rchaotic tra nsien t behaviors resem bled cycles of periods that varied from
3--4 to 18-1 9 tim e steps (typically 4 and 11 tim e steps, that is, 2 and 5.5
host genera tio ns). When the att ractor is a point equilibrium, lo ng transientsof q uasi- per iod of 10-25 (about 5- 12.5 hos t generations) were seen before
reac hing the equilib rium state . During low-density ph ases of such periods, ap0r.ula~ion is vulner a ble t o extinction especia lly with demogra phic noise.
Extincti o ns that occurred at time units to (replicate C), 45 (replicate A), and86 (replicat e B) in the three experim ent al replicates may co rrespond to suchlow densities in quasi-cycles. Inco rpo ration of demo graphic sto chast icity

58

M. TUDA AND M. SHIMADAHOST-PARASITOID SYSTEMS WITH CALL OSO BRU CHUS BEETL ES

T abl e 3 Estima ted values and their 95% co nfidence in tervals o f pa ram eters,
a nd p ropert y of attr acrors a t the co nfidence limits o f the three -species system,
C. chinensis (ho st) a nd two pa rasitoids, A . calandrae a nd H. prosopidis. An ast erisk
indica tes a significant d ifference from the pa ra meter value estima ted fro m the 1"""0_la)

400 ,----,- - -,-- - -,-- ---, 0.4300

0 2 species

species system. The Lyapunov exponent for ML estimate was -0.0510 (bootstrap

e asceces

950/. C I, - 0.684, 0.(014) and simulated dynamics showed chao tic tra nsients to stableeq uilibrium ( X... Y... Z) = (30.33, 42.83, 87.92). The absolute of eigen values a t theeq uilibriu m were all <1. Estimated elemen ts in varia nce-covariance ma trix were c u= 10.38. 0"22 = 12.40, U n = 6.899, O"l 2 = a 2 1 = 0.1411, alJ = 0"31 = 1.292.0"2) = Un
= - 1.719

Parameters'"b,

ML Estimate(95% e ll
7.580 (5.726, 11.52)s

0.004658 (0.002584,
0.(06560)
0.00 1168 (0.0006660,
0.00 1529)
0.09774(0.03996,0.1723)

Q,

0.07 168(0.02517, 0.1 796)f

0.002082 (0, 0.(05473)

m

0.4480 °(0.2684, 0.6024)b,Qz

0.1580 (0.04885, 1.0)'z0.1891 (0.1156, 0.2545)

Lyapunov Exponent
Wit h 95% C L(- 0.02 19,- 0. 143)(- 0.0325,-0.( 24)(-0.0 192,
- 0.14 1)(-0.0502,- 0.0655)(0.0003,-0.0780)( -0.0704,- 0.0370)(-0.0003,- 0.0903)(- 0.0546,- 0.0223)(-0.0257,- 0. 152)

Attracto rWith 95% ( L(eq uilibrium,
eq uilibrium)(eq uilibrium,
equ ilibriu m)(eq uilibrium,
eq uilibrium)(eq uilibriwn .
eq uilibrium)(cha os,eq uilibrium)(eq uilib rium,
eq uilibrium)(q uasiperiod,
eq uilibrium)(equ ilibrium,
equilibrium)(equ ilibrium,
equilibrium)

59

",•

0.'

0

I

200

100

0.1

oL . _--'.d..l.ill.l.J...O
-2
-1
-a

0 - - - '1 0.0

l yapunov expo nen1

(b)

....
...-..

-- ,-'"

4-poirTl°~_.,.,.1.
2.5%

Ie)

.....
'4%

..ecs
5.7%

100%

aquilibfUr\

86.7%

was likely to termina te the system. The dyna mics ofthe three-species assembly Figure 6 Estimated property of bootstrapped data sets. (a) F req uency distri butionof Lya punov expo nen ts of determ inistic three- a nd two-species d ynam ics. Po pula tionis concluded to be long cyclic/chaotic transients towards an attractor that is dynamic Properties of auracto rs for (b) three-species system and (c) two-species
either point equ ilibrium, cycles, quas i-cycles, or chaos, judging on a realistic system.
time scale. In summary , complex population dynamics in th e three-species
assembly are likely either when the searching efficiency of H. prosapidis is high(Fig. 7a), when the searching efficiency of A . calandrae is low (F ig. 7b) that it
associates with the high rate of synergistic host feeding, or when the mutual model with a generat ion time of A . calandrae of I time unit instead o f 2 had ainterference of A. calandrae is low (Fig. 7c). Both synergistic host feeding and ~ow~r ML (-992.770), which was also declined. Our semi-mecha nistic model
low mut ual interference are generally destab ilizing (May and Hassell, 1973, IS dlff~rent from the non-paramet ric (or non-mechani stic) model proposed
1981; Briggs et af. , 1995).
?y. Kristoffersen et al. (2001), in tha t mult iparasitism (i.e.• co-parasitism)
The model that assumes differen t host develop ment al stages are vulnera- IS incorporated and mut ual interference is present in A . calandrae In their
study
I.
..
.
ble to the two parasito ids (with H. pr osopidis attac king the host first), had a, mu l1~araslhsm was assumed negligible based on experimental
lower ML (-948.972) and, therefore, was declined des pite its simplicity. The results by Shimada (1985). Our explicit sta tistical comparison o f models

60with and without multiparasitism showed tha t m ultipar asitism by the two
pa rasitoid s is not negligib le. We inte rpret the experimental result on theniche modification by the two coe xisting parasitoid species (Shimada andF ujii, 1985) as fo llows: The sepa ratio n of the host stages tha t the twoparasitoids ut ilize was only pa rtia l, which probably ena bled the coexistenceof the pa rasitoids for more than 100 days (7-9 generations) even when the
single stage of hosts was pro vided (Shimada, 1985). Previou s experiments
showed tha t mutu al interference is present in A . calandrae (Shimada. 1999)
which is consistent wit h our result. In H. prosopidis, on the ot her hand. theeffect of mu tual in ter ference beco mes ma nifest only when its density isextremely high (Shima da, 1999), whic h ma y be the cause of exclusion ofm utu al interference by the present a nalysis. The time series used for a nalysis
in K ristoffersen et al. (200 1) was different from the one used here (i.e., theformer excluded the initial pa rt of bo th replicates and the last pa rt of
replica te B and included the last part of replicate A), which might exp lain
the different density-de pendence structures. Furthermore, mutua l interference that remains constan t along its density (i.e., a constant negative slope
along logged den sities), as in A . calandrae (Shima da, 1999), is more likely to
be detected in funct ion al response, embedded in Ni cholson -Bailey typemodel (our model), than in to ta l de nsity (Kristoffe rsen et al. [2001] mod el).
Th e estimated parameter set at the confidence intervals indicated somecorrelat io ns between param eter s; po sitive correla tions am ong J.., boo and hI(between Aand bu, r == 0.823, n == 19. p < 0.001; between A and hJ, r == 0.863,
p < 0.(01 ) and between az a nd cz (r == 0.690, p < 0.05), and a nega tivecorre lat ion between a r a ndf (r == - 0.743, p < 0.01).

2. Two-Species Popu/arion Dyn amics

61

HOST-PARASITOID SYSTEM S WITH CA L LO S OBRUCIIUS BEETL ES

M. TUDA AN D M. SHIMADA

5..• [ 2"'• • .'_~--~~., ! . _.~. -: - :J
o

0.1

0.2

~

, .

.

~

,

•

"" ~_2

0.1

02

0.3

0.4

0.5

0.6

0.1

08

0.9

~

U

U

M

V

OB

~

1

''-~----- --------~

1b)

!

i
-s

s

. 11111",

a 111111....... ..•.................. ................. .. ....... .. ....... . .....,111111

I·

Th e ho st-A . calandrae dyna mics before introd uction of H. prosopidis were fil
5
by a subset of the three-species mod el (Eq uations 19 an d 20) to determ ine if
any factor was modified by the presence of H. prosopidis (F ig. 8). Th e ML
estimates and 95% confidence intervals are given in Ta ble 4. Th e LE with
ML estimat es was negative, - 0.889 (bootstra p 95% CI, - 1.692, - 0.585).
The bootstrapped LE for the two-species system was significa ntly smaller
than that for the three -species (Fig. 6a) (Bartlett's test fo r homogeneity ofvaria nce, F == 14 1.5, d.f. == I, P < 0.0001; Welch' s ANOVA, F == 4,533.2.
nume rat or d.f. == I, denominator d.f == 1,764.8, P < O.OOO I) and thesimulated dynamics for all the bootstra pped data qu ickly converged to astable equilibrium at the time un it, 35 (bootstrap 95% CI, 19, 49 time unit s) Figure 7 (colltil1ued )(F ig. 6c, Table 4). Among the estima ted paramete rs, III for m utual

1

.

62

M . T UDA AND M. SHIMA DA

HOST-PAR ASITOID SYST EMS WITH CALLOSOBRUCHUS BEET LES. ~~-------~--~---~(0)

Ta ble 4

,

. •

~

difference from the pa~ame ter val~e estimated from the three-spec1;S system. The· nov exponent with ML esnm a te was - 0.889 (bootstrap 95Yo CI, - 1.692,
L)~u. .
'I'bnum'-0.585)
and.. simulated dynamics
showed quickconvergence to ~ta ble equm
(X = 81.56. Y = 147.32). Estimated elements III vanance-covan ance matnx were........
.., ..... ......
I,· ·· ······· ··· ········ ·· ·····························: •........... .. . . .

i

J

a

!

Q

0 11

,

l~~
t. ':' ?:;;;~'" . "'~.•. •. ':' ~m
~
°i' '
0.3

O.

0,35

0 .5

0e

O~

0,5

m

h"
b,
.s
Q,

f
m

(')

~

o

•

t a
J

i

Q

0.8513. (J' 22 - 2.965, (J'12 = a l l = - 0.2112

Parameters

5aEstimated pa ra meter values a nd their 9 5%confide~ce .in(~rvals ro ~ th~ two -. system, An asterisk indicatesspecies.. , C. chinensis (host) and A . cakmdror.
. a Significant

o

a

a

s

c

t
1
I

- 20.•

63

ML Estimate(95% CI)6.776 (5.157,
9.529)
0.003654 (0.00 1540,
0.005352)
0.001398 (0.001013,
0.001585)0(0,0. 1506)
0.2473 (0.08347,
0.6547)0.006286 (0.003209,
0.01107)1.005 • (0.8636,
1.154)

Lyapuncv Exponent
With 95% CL

Auractor With(- 1.06,- 0.843)(-0.986,- 0.8 17)(-LI S,- 0.708)(-0.888,- 0.698)(-0.670,- 0.74 1)(- 1.01,- 0.546)(- 0.638,- 0.470)(equilibrium,
equilibrium)(equilibrium,
equilibrium)(equilibrium,
equilibrium)(equilibrium,
equilibrium)(equilibrium,
equilibrium)(equilibrium,
equilibrium)(equilibrium.
equilibrium)

95%CL............ ....
....
......
..........

i'..

.. ...

i i· · ····

I'.

(

u

' .'

0.$

06

interference that can stabilize the system was significantly larger in the twospecies system than in the three-species system with H. prosoptdts (Welch's
t = - 4.93, P < 0.001) (Tables 3 an d 4). A bifurca tion diagram showed that a
reduction in In results in chaotic dyna mics (F ig. 7d).
Th e larger values of III in the two-species system can be explained by thehigher density of A . calandrae relative to the host density, in the ab sence of
11. pr osopidis. With the addition of th e third species (or the second parasitaid), hOSIS, on average, became less availabl e and consequently A . ca landrae
did nOI increase to the pop ulation level that t riggers mut ual interference
behavior because of limited host-feeding on a less abundant host. However,during chaotic tr ansient s the host can become tempo rally super-abundantfollowing low density of parasitoids, which may be the cause of the reduced
self-regulatio n effect of mutual interference among A. calandrae .
O n the other hand , the C. chinensts-H, prosop idis system was diag nosed as a long chao tic transient, and there were no significant cha nges in
the pa rameter values from those in the three-species system, indicating
asymmetric interspecific interactions between the two parasitoids (Tud a,
2004, unpublished).

. ~ '.' 1

u
0.7

08

0.11

1

1.1

m

Figure 7 Bifurcation diagrams and cor,responding ?o ~ inant Lyapunov ~xponen"for (a ) or - (b) {/ y, a nd (c) m in three -species.system wlth.1ll95% confidence l~t~rval o~respective pa rameter and (d) III in t WO-SPCCICS system wIth. extended lower limit of It.
95% con fidence interval to co mpa re to that of three species.

64

M . TU D A AND M . SH I M A D AHOST _PARAS ITO ID SYSTE MS WIT H CALLOSOBRUCH US BEET LES

65system. H. prosapidis. has a higher
popu lat iton behav ior in our three-species. .
hing efficiency and a pnon ty effect, both of them contribute to com:::~~~ve superiority of H. pro sopidis to A. colandr~e, which explains the larger
influence of H. prosopidis to A. calandrae than vice versa .
.
eoAnother th ree-species system (Bega n et 01. , 1996c, 1997) showed multipleneration cycles, compared to the generat ion cycles wit h smaller maggo. (host only) or any com binati'~~
nitudes of either single-species
manon 0 f two
component species. T hree-, or more, species systems are likely to have'~ O'
indir ect interactions besides direct interactions, which can generate irregular,(b)o~,--;,,"-;o--;s----.i
0
10
20
30
un predictable dynamic s (Holt, 1 9~7) . Several prey an d predator species ~a ybe involved in the In-year populat ion cycles ofthe hare-Lynx system (Keith,.
1983). Many natural systems con tain large num bers of interactions. some
200 ,' , . , ' ,..destabilizin g, some stabilizing, and their combined effects almost always
1~ ~include an indi rect interaction that could not be predicted fro m independent
2d
Old
o
20
40
60
eo
pa irwise interactions (Hassell and Anderson, 1989; Begon et al .• 1996a.b).
{el l! .oo.----~-~-_--~-~-~-_--~-~-,The dynamics of interact ing po pula tion s that we observe may often dis~ 300
play transient behavior because it is likely that they ha ve been d riven away~""from intrinsic at tractor s by recent natural as well as human -induced cha nges.
~ 100 . •','~,The cha racteri stics of at tractors themselves may be altered by evolution of
z o
I!IO
100
120
component
species in the assemblies (e.g.• Tuda and lwasa, 1998). Unde r~ l"10daysJ
standing no n-equilibrium (i.e., transient and/o r evolutiona ry) dynamics isfigu re 8 (a) One-step-ahead predictions by the model (+), superimposed 0 0
po pula tion dynamics of adult numbers of two species (square-roo t tran sformedt crucial for the prediction on dynamics of biological assembly under cha nging(connected by lines). (b) Observed popula tion dynamics of the two species (nOl environments. Laboratory experimental host-parasitoid systems will provide
transformed). (e) Stochastic simulation of the three-species model with maximum us with too ls for further testing of ecological an d evolution ary top ics.

"[

i§r
k
~
~ ol
I:'. .:

"

"'"
""'~

I

"

"

'"

likelihoo d est imates. Demographic noise and enviro nmen ta l noise (standard
deviation of the environmental noise = 0.15) are incorpora ted. The lines andsymbols arc as indicated in Figure 5.

3. Changes in Dynam ical Behavior From Two- toThree-Spe cies A ssemblies

Com plex host-parasit oid dynamics in the three-species system were generated when self regulations in the host an d the parasitoid A . catandrae were
low and when the searching efficie ncy of t he non-self-regu lating parasitoid
H. prosop idis was high. This is induced by the introd uction of a no n- sellregulating parasitoid tha t also may have reduced the self-regulat ion in theother parasitoid ind irectly throu gh reduced host densi ty. It is also impo rtantto realize that the observed po pulation dynamics correspond to initialtransients toward s such an attractor. A long tra nsient phas e is known for
high-dimen sional physical and biological models (Crutchfield and K aneko.
1988; Kaneko, 1990; Hast ings and Higgins, 1994; Chen and Cohen, 2001a),
The asymmetric stronger effect of a destabilizing species (N. prosop idis) on astab ilizing species (A . calandraev is the key to generating complex transient

VI. HOST-PARASITOID INTERACfI01\ AND BEYOND
In brief, ecologica l rules on po pulation dynam ics of interacting species
discovered from host-parasitoid experimental systems with br uchid beetles
as the host are as follows:
Trans ient dynamics: The au rac tor of the three-species system has both
stable and chaotic features. In the chaotic region of the an ractor, quasicycles of a period of multiple (an d, in some ca ses, partial) genera tions of hostand parasitoids appeared in the simulat ion . Even when the att racto r is apoint equi librium , a long transient phase of quasi-cycles of multiple generauo ns preceded, and the time required to reach equilibrium states is beyond
the time of observed coexistence. The population dynamics of th ree-species
host-para sitoid dynamics, therefore, is ascribed to a chaotic tr ansient to astable/chaotic at tract or. Such int rinsically long transients can easily be elongated by demographic and enviro nmental noise that con stantly excites
the population dynamics away from an equilibrium sta te (Bauch andEarn, 2003).

66

M. T UDA AND M. SHIMA DA

Botto m-up cascade control: Species of bean resources (plant) can control
persistence of interactions of herbivores and parasitoids. In the simple Callosa,bruchus- parasi toid systems , the wind ow o f vulnerability was elongated by hosj.
plant shift , which resulted in termination of the Callosobruchus-parasitoid
interaction because of increa sed vuln erability of the host Callosobruchus topa rasi tism .
Evolutionary cascade effect: Evo lut ionary cha nge occurred in the Callose:bruchus beetle withi n a relat ively short time spa n, as it shifted to a new bean
resource tha t differs in size from its original bean . This change not only
affected its own popu lat ion dynamics but also modified host-parasitoid
dynamics. An imp lica tio n of the result for agricult ural selecti on of la rger
and nutrient-rich crops is that pests can become more scramble-type corn,
petito rs that allow mo re serious outb reaks of a pest pop ulation even under acon trol of par asitoid . It should be noted that the biology of evolution of
con test/scramble compe tition ca n be more profound than shown in thepresent paper; the selection background of different geographical pop ulations constra ins artificial selection in the laborat ory (Takano et al.. 200 1;
Kawecki and Mer y, 2003; Tuda , 2005 , unpublished) .
In the future, how evolutiona ry chan ges modify beh avio r of interacting
species and eventually sta bility/persistence of overall assem bly of hosts andparasitoids will be one of the nex t themes to pursue. As described in thesection on bottom-up control, experimental tests on the possibility of evolution 'against coexistence' are intriguing fut ur e challenges. Does evolutionary
capacity of species tend to vary between trophic levels? D oes it depend on
the num ber of interacting species (generalist vs. specialist, herbivore vs.
carn ivore, intraguild preda to r vs. non-intraguild predator, and so on)?
These are some of the questions tha t do not yet ha ve concrete empiricalanswers, however , they are crucial for the prediction of possible outcomes on
the whole assem bly when a species either is introduced or goes extinct.
Evolutionary scheme of ecological sta bility/persistence of biological interactions may also be extended to includ e a lower troph ic level (i.e., producer orplant) which could be mu ch more complex. Wha t is known from the investigati on on insect faun a associated with legumino us plants, however, suggeststhat it may not complicate our understandings but rather simplify them:ecological characteristics of legume species such as their distributional range(similar to islan d-size effect), morphology (tr ee or herb), and historicalbackground (introduced, native or endemic) are found to be excellent predicto rs of species richn ess of their seed predators, including bruchid beetles.
an d consequently their para sitoids (Tuda et al., 1998, un pu blished). The
process of accumulation of insect herbivores , followed by parasitoids on
introduced plants or that of parasito id on invading insect herbivores is notwell understood (Tuda et al., 200 1); this sho uld include learning and evolutionary processes in insect s. Patterns of species richness in nature such as thi s

HOST.PARASITO ID SYSTEMS WITH CALL OS OBRUCHUS BEETLES

67'11 b readily tested for their ecological an d evolutionary proce sses, using~~or:tory experimental systems of bruchid beet1e~ an d their parasitoid (fora list of new candidates of Callosohruchus species for future laborat ory
exper iments on species richness, see T uda et 01., 2005, and Tuda, 2003).

ACKNOWLED GM EN TS
We ar e grate ful to R. F . Cost antino, J. M . C ushing, B. Denn is a nd R.A.
Desharnais for the opportunity to prese nt this paper. Thank s are also
extended to J.E. Cohen, B. De nnis , H . H a koyama, T . Ikegami, Y. Iwasa,
G .J. Kenicer, T . Yanagawa, an d two anonymous referees for their valuab lead vice. Disc ussions a t the Complex Population Dynamics workin g grou p a t
the Nat io nal Cen ter for Ecological Analysis a nd Synthesis, Santa Barba ra,and at the Centre for Population Biology, Silwood Pa rk, stimu lat ed thiswork . Th is stu dy was supported in part by Grant-in-Aid fo r Scientific
Resea rch (08640798 and 09640747) a nd for Internationa l Scientific Research(07044180 and 09044202) from MESC and by JSPS fellowship (08389 5).

APPENDICES
Appendix 1. Basic Ecology of the Experimental Organisms
Beetles of the genus Callosobruchus (Chrysom eloidea: Bruchidae) utilize
beans or seeds of leguminous plan ts as the resource for their larvae. Adults
deposit eggs and hatching la rvae bore into not on ly imm ature, soft seeds
but also mature, dried one s. Consequently , the beetles are stored bea npests. Since Callosobruchus larv ae, except those a t the late fourth (last)sta ge, can not survive once they ar e remo ved from bean s, the beans they
bore into are the only resource they cons ume. D uring development, therefore , the la rvae can suffer from competi tion with other individual s in thebeans when the densi ty of the beetles is high rela tive t o the resou rce requirement. There a re two parasito ids of Callosobruchus that are well studied forhost-parasitoid populat ion dynamic s. They are Anisopteromalus calandrae(Hymenoptera : Pteromalidae) a nd Heterospilus prosoptdis (Hymenoptera:
Braconidae), which a re solitary ectopa rasitoids of la te stages of la rvae andpre/pupae of Bruchidae. The fann er widely ut ilizes coleop terous pests ofstored.pro.ducts such as grain weevils (Curc ulion oidea : Rhynchophoridae)
and biscui t beetles (Bostrychoidea: An obiidae) as its hosts (Ghani a nd
~weet.man, 1955). These parasitoids dep osit a single egg on the host by
mse r~mg their ovip ositor int o beans. Whe n they superpara sitize (i.e., deposit
multiple eggs) a host , only a single wasp individual can survive an d emerge
as an adu lt.

68

M. TU D A AND M . SH I MA D A

HOST-PARASlT OID SYSTEMS WITH CALLOSOBRUCH US BEET LES

C. chinensis

accordin g to the likelihoo d ra tio sta tist ic:

I

L

Lv

7

A

7

A. caland ratl

L

L

A/"

H. prosopidis

I

69

L

7

A

7

Figure 9 Life cycles of t he host beet le C chinensis, and t he two pa rasito id
A . cakmdrae and H. prosopidis. L: larval stage, Lv: larval vulnerab le stage of host,
A: adult stage.
.

Developmenta l times from the egg deposition to adu lt emergence offemales ar e 22 days (ra nge 20 to 24) for the host and abo ut 12 da ys (range
12 to 13) an d 15 days (ra nge 13 to 20) fo r H. pr osopidis and A . calandrae,
respectively, und er ou r growth-chamber cond itio ns (Utida. 194 1, 1944a.b,
1948a; Tuda an d Shimada, 1995; Tuda, 1999, unpublished data ) (Fig. 9).
Duration s of the repro ductive adu lt sta ge a re a pp ro ximat ely one week in allt hree species (U tida, 1944a.b, 1948; Tuda and Shimada. 1995), which can beextended under high popula tion density (Shimad a a nd Tuda , 1996). Fecundity of a female C. chinensis is a bo ut 80 (Utida , 194 1; T ud a a nd Shimada,1995). Fecundi ty of H. prosopidis is about 35 (U tida, 1948a) and of A.
co/ant/rae it can increase up to 260 (Utida, 1943b) by synergistic host feedingat higher host density. H ost-feeding in the latter species also elongates
longevity (U tida and Nagasawa, 1949; Gh a ni an d Sweetm a n, 1955). Eachpa rasito id has an equal c hance of surv ival on mult ipa rasitized (i.e., coparasitized) hosts (Wai, 1990).
The host popula tion und ergoes two density-dependen t p rocesses: first, theeggs suffer from mo rtality cau sed by mechan ical injury by adult tra mpling:
second, density-dependent mortality is indu ced by compet ition a mong larvae over a limited (bea n) resource. The int egra tion of these two processes
exhibits wea k overcompensa tio n. so a single-species system converges to an
equilibrium with sho rt-damped oscillations (Fujii . 1968; Shimad a, 1989;
Shimada and Tuda, 1996).

G2 = - 2(lnL..... - lnL A ) _1. 2,(a2. 1)h
L and L A are the likelihoods of null a nd alt erna tive mod els, respecwere.v statistic approximat ely follows a c hi -square distribu
ti n. A. Iy Thisism unoliverameter
.
.
.
"
1
h
'
ith tht e
was removed when the likelihood ra tio IS ess t an 1.0.05 WIt~ ree offreedom set at 1, which is a di fference in the num bers of pa ra meters
be~ween the two models that a re compa red . where ;d,05 is the 95th percentile
of a chi-sq uare distribution (Dennis et 01.• 1995).
For A. calandrae, we incorporat ed m ut ual interference but not ha ndlingtime. based on the result of the likelihood ratio test . A ho st-feeding parameter of the pa rasitoid was incorporat ed despite its insignifica nce in the threespecies model but because of its stat istical significa nce in the two-s pecies
mod el [Tuda, 2003, unpublished).
For H. prosopidis, a simple type II functional respon se was applied since
the likelihood ratio test indicated the model with mutual interference that iseither constan t or increasing with its density was not significa ntly differen t
from that without it (Tuda, 2003, unpublished).

A ppendix 3. Assumption of Noise and Pa rameter Es ti mation
The noise is assumed to follow a mu ltiva riate normal distribution withmu ltiple parameters in the model and elements in varia nce-covariancema trix I: in maximum likelihood function to be estimated (Denn is et aJ.,

1995, 200li
L(O, I ) ~IT• p (w,lw,_,},(a3.1)

l=i + 1

where p (w,lw/_,) is the joint trans ition proba bility density function for WI
cond itional on W /_ 1 = w/_;, q is the length of time series and 6 is the vecto r of
unknown parameters of functions :][hr_2exp( - a r}~_1 - aZ;_I ) + S."((I)_ I )112
g(w' _I) = [hH { I + exp( -aZ~_2)}{ 1 - exp ( -aY}~_2)}/2J I12[[hr_2{1 + exp ( - a r}~_ I ) } { 1 - exp(- az; _I )} /21112(a 3.2)a nd

Appendix 2. Selection of ModelA mechan istic model was tirst designed inco rporating functions that are
maximally complex, regar ding the real biolog y we know about the component species. Th en pa ra met ers in the model were remove d one by one.

p (W,jW1_1) = (21t)d/21:I-1 112exp( _ c; I - let/2),(a3.3)

where e, = W , - hw t _ i ) , e~ is the tra nspose of the vector e, a nd d is the num ber of dimensions or state variables. The distribution of the no ise is assumed
uncorrela ted through time but correla ted with each other between species

70

M . TU DA AN D M . SHIM ADA

at time t. T he latter assum ption requ ires estimation of three cova ria nce
elements in addit ion to three va riance elements in the vari a nce-covariancematrix . Log-likelihood was maximized by Ne1der-Mead 's simplex method,
implemented in M ATLA B 6.5.1 for Windows. Th e 95% co nfidence intervalsof parameters were calculated based on pro file likelihood that uses a likelj,
hood ratio test (Venzon and Moolgavkar, 1988; McCullagh and Neider,
1989; Lebreton et al., 1992; Dennis et aI., 1995).

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