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Proceedmgs of the 7th Iniernaiumal Wmkmg Conference all Stored-product Proteciuni - Volume 1
Models of stored-product pests:
Their relevance to biological control in traditional storage in
developing countries
C Stalk!' 3 , W van der Werf 2 , and A van HUlst
Abstract
Dunng the past decades, models that simulate the population
dynamics of stored-product pests have been developed Some
of these have been developed from an mterest m ecological
and evolutionary processes that shape populations Others
have been constructed with the ultimate aim of improvmg
control of these pests We diSCUSSboth approaches m
relation to biological control of stored-product pests m
developmg countries
Storage of food products in developmg countnes differs
from that m mdustnahzed countries Food ISoften stored at
a small scale, It ISmostly mtended for pnvate consumption,
and msect mcrdence IS hrgh Brologrcal control of these
msect pests IS considered an mterestmg alternative to
traditional and chemical control methods The situation of
control of bruchids m stored cowpea ISpresented as a case
Existing "apphed ' models do not answer the type of
questions that arise from the system of stored cowpea They
often do not mclude natural enemies, they are only vahdated
for relatively low msect densities and temperatures, they
assume control practices winch are not appropnate to
resource-poor farmers, and they often draw upon empmcal
relationships We suggest that a model that predicts WhICh
measures WIll Improve the biological control status of
tropical stored-product pests should combme the "ecological
reahsm ' of theoretical ecology WIth the accuracy of the
'pest management' models
Introduction
Storage of food products m developmg countnes differs from
that m mdustnalized countnes m many respects (Table 1)
Cereals and pulses, stored m traditional grananes, are often
1Laboratory for Entomology, Wagerungen Agncultural University, P
o Box 8031 ,6700 EH Wagenmgen, The Netherlands
2 Sub-department of Theoretical Production Ecology. POBox 430,
6700 AK Wagemngen, The Netherlands
3 Presenting author
senously mfested by msect pests (Compton et al , 1993,
Gahukar, 1994) Traditional methods of controllmg these
pests, such as the use of sand or wood-ash as protectants,
fall short m effectivity and efficiency for large quantities
(see Compton et al , 1993) Chemical control IS too
expensive and Imposes health risks, especially for illrterate
subsistence farmers For such systems, biological control of
stored-product pests ISan mterestmg option (Hames, 1984,
Van Huis, 1991, Van Huis et al , 1991), especially because
the tolerance for insect presence and cosmetic damage m
stored products IShigh (Hames, 1984)
A simulation model can be useful m selecting a natural
enemy for biological control, because It can predict the
effects of characteristics of mdividuals at the population
level SImulation models can also be used to study the
sensinvity of the system to changes m management or
changes m one of ItS parameters ThIS can be helpful in
determmmg
system
the best control strategy for a particular
A large number of models deal WIth the biology of
arthropod pests that occur m stored products (Throne,
1995, Longstaff, 1991) We examme the existing hterature
on these models for their relevance to biological control
situations m traditional storage of small-holders m
developmg countries The system of bruchids m stored
cowpea m West Africa ISused as an example
We start WIthan mtroducnon to bruchids m cowpea and to
the research questions that have ansen from preVIOUSwork
on this system Subsequently, we bnefly charactenze and
dISCUSSexisting models and evaluate their Importance to
stored-product protection m the trOPICS Fmally, we dISCUSS
future prospects for models of the type we have m mind
Biological Control of Bruchids in
Stored Cowpea in West Africa
West Africa, cowpea, and bruchids
Many countrIes m West-Mnca, espeCIally m the Sahel
region, have poor economies and a relatively low standard of
hvmg (measured by such cntena as Gross National Product
per capIta and hfe-expectancy at bIrth) (Barratt Brown,
1995 151, Michel, 1996 A87) ThiS regIOn, where
72

Proceedmgs of the 7th Internaiumol WOIklllg Conference on Stored-product Protection. - Volume 1
agnculture IS one of the mam actrvrties (FAO, 1986 16,
Ben Yahmed, 1993), IS a mam area of cowpea production
(FAOSTAT Internet database, Ben Yahmed, 1993, Nwokolo
& Ilechukwu, 1996) Cowpea (Vigna unquiculata Walp )
IS an Important source of protem for low income famihes
(Nwokolo , 1996, Van Alebeek, 1996) Cowpea, hke
sorghum, millet and maize, ISstored dunng the dry season
In rural areas, cowpea IS normally stored on-farm m
traditional granaries, which are made of natural matenals
such as wood, straw, and clay (Sagnia & Schutte, 1992,
Kone, 1993) Cowpeas are often stored as whole-pods, and
only when needed for consumption or for sale, they are
threshed and stored as grams m smaller contamers (e g ,
clay Jars) Typically, a subsistence farmer stores several
hundred kilograms of cowpeas (Sagrna & Schute, 1992)
Cowpeas are not only stored for home consumption but also
for the market, as the pnce of cowpea mcreases towards the
end of the storage season (Caswell, 1974, Sagma &
Schutte, 1992)
Unfortunately, stored cowpea ISoften heavily attacked by
bruchids, of which Collosobruchus maculatus Fab
(Coleoptera Bruchidae) ISthe most Important one (Jackal &
Daoust, 1986, Singh et al ,1990) The bruchid mfestation
starts m the field, where adult females lay smgle eggs on
npenmg pods Larvae that emerge from these eggs
penetrate the seeds, m which they develop and pupate The
adult emerges through an emergence hole m the bean The
total development time IS approximately three weeks at
32°C Adult females live for about a week, dunng which
they may lay some 100 eggs Populations of C maculaius
can grow rapidly m stored cowpea After several months of
storage, the stock may be totally destroyed due to the larval
feedmg
The nutritional value and the quality of stored beans
declme as a result of bruchid mfestation (Modgil & Mehta,
1994, 1996) Although It IS drfficul t to determme exact
losses (Boxall , 1991), quantitative losses are also severe
The loss to bruchids m northern Nlgena m terms of weight
has been estimated at 3 5 - 4% per year (Caswell, 1981)
This corresponds to approximately 20 - 30% of the beans
bemg mfested Weight losses m stored beans m Ghana after
five months of storage were as high as 20 or 45%,
dependmg on whether the beans were stored unthreshed or
shelled, respectively (Adams, 1977, Schulten, 1982)
Control methods
A large vanety of control methods agamst bruchlds m
stored cowpea IS known (Van HUls, 1991, Sagma &
Schutte, 1992, Llenard & Seck, 1994) They are aimed at
either preventmg bruchld mfestatlOn, ehmmatmg or
mmlmlzmg bruchld populations, or a combmatlon of these
effects. The control methods can be roughly dlVlded mto
three categones traditional methods, chemical methods and
73
alternative methods
Traditional methods compnse among others the use of
mert matenals such as sand and wood-ash, and the use of
plant matenals with insecticidal or msect-repellant action
(Javaid & Ramatlakapela, 1995, Apuuh & Villet, 1996,
Ofuya, 1986) Although these methods are often effective,
they are generally labonous and not suitable for large
quantities (e g Taylor, 1975, Compton et al , 1993)
Some methods require a lot of labour when labour demand IS
already high because of the harvest In addition, some
'natural msecticides ' may have chronic negative effects on
human health (Schulten, 1991, Compton et al , 1993)
Chemical control methods equally have several
disadvantages Some pesticrdes do not kill all the larvae and
pupae mside the seeds, wlule they do kill the natural
enemies of the bruchids, which are often more sensitrve to
msecncides (Caswell, 1973, Hames, 1984, Brower et al ,
1996) In addition, pesticides are expensive for subsistence
farmers, and not always available (Lienard & Seck, 1994)
Moreover, farmers are generally not tramed m the use of
pesticides, this results m a low efficacy of their use and an
mcreased health nsk (Schul ten, 1991, Dmham, 1993,
Compton et al , 1993, Schwab et al , 1995, Udoh, 1998)
Alternative methods of control, such as storage of beans
m hermetically closed plastic bags or 011 drums, have shown
prormsmg results (Caswell, 1974, Lienard & Seck, 1994)
Hermetically closed storage suffocates msects within a
relatively short time However, to most Sahehan farmers,
empty 011 drums or a sufficient number of strong plastic bags
are as yet not available or too expensive (S Sagrua, and A
Adandonon, personal commumcations, C Stolk, personal
observation, Gahukar, 1994) Another disadvantage of
plastic bags ISthat they have to be stored m such a way that
they cannot be damaged by e g rodents, as even a small
hole m the bag WIll nulhfy the suffocatmg effect ThIS IS
probably hard to achieve Even the bruchids themselves may
sometimes perforate plastic bags (Lienard & Seck, 1994) It
may also prove dIffIcult to prevent re-mfestatlon If the bags
are opened frequently for the purpose of sellmg beans
For many farmers no adequate method of control of
bruchld pests m cowpea IS therefore avatlable What IS
needed IS a sustamable method of control that IS (1)
effective, (2) practically and economIcally feasIble, (3)
environmentally safe, and (4) flexible Wlthm a changmg
SOCialand agncultural environment BIOlogicalcontrol of
bruchlds may meet all these reqUIrements
Biological control
The most Important natural enerntes of bruchlds of cowpea
are parasltOlds Larval parasltOlds (Dtnarmus basalzs and
EupelrH/8 spp ) and egg-parasltOlds (Uscana spp ) have
been proposed as candidates for biological control of bruchlds
m tropical storage (Monge & HUlgnard, 1991) We

Proceedmgs of the 7th Iniernatumal Workmg Cmlference on Stored-product Protectvm - Volume 1
concentrate on Uscana larwphaga Steffan (Hymenoptera
Tnchogrammatidae ) Egg parasitoids have the advantage
that they kill their host already before It has done any
damage (contrary to larval parasrtoids)
U larwphaga ISindigenous to West Africa In the field
and m storage It IS responsible for a substantial amount of
mortality of C maculaius (Lammers & Van HUlS, 1989,
Sagma, 1994) Its hfe-lustory, functional response and host
location have been mvestigated m the laboratory (Van
Alebeek, 1996) We are mvestigatmg possibilmes to
mcrease the Impact of U larwphaga on C maculaius
populations, usmg a 'conservation strategy' of biological
control Tlus strategy ISaimed at conservmg the populations
of natural enemies that are already present m the system
(rather than mtroducmg exotic natural enemies, or
producmg and regularly releasmg large numbers of natural
enemies) (Arbogast, 1984, Van HUlS, 1991, Van HUISet
al , 1991, Waterhouse, 1992) Conservation biological
control IS especially mterestmg for resource-poor farmers
(Waterhouse, 1992) In this particular case, prormsing
options are (Van Alebeek, 1996) ( 1) marupulatmg the
storage environment, such that conditions for U
larwphaga are optirruzed, (2) offenng food to the adult
parasitoids to enhance their longevity and fecundity, (3)
moculatmg the cowpea storage With Uscana from locally
available resources, and (4) addmg plants or plant extracts
to the stored beans which kill or repel the bruchids but do
not harm the natural enenues These strategies can of
course be combmed, for example, plant extracts (option 4)
and Uscana (option 3) could be added at the same time
The four options, and the possible role of simulation
modellmg, are discussed below
(1) Manipulation of the storage environment
Temperature IS one of the mam driving forces of msect
development and population dynanucs Insect species differ
m theIr temperature responses It IS therefore poSSiblethat
at certam temperature regImes, a natural enemy perfonns
relatively better, and ItS host worse, than at other
temperatures A SImulationmodel, based on experImentally
detennmed temperature-dependent development rates of
both host and parasltOld, could help establIsh whether such a
temperature regime eXIsts If It eXiSts, It would be
worthwhIle to mvestlgate whether such temperatures can be
achieved by SImple changes m the placement and
construction of tradItional grananes (Van HUIS et al ,
1994) For example, a granary can be placed m the shadow
or m the sunlIght (Van HUISet al , 1994), or a roof which
allows for mcreased ventilation m the granary could be
constructed (J Mumford, personal commurucatlon, see also
Hames, 1984) Meanwhile, Van HUISet al (1994) have
ShOWllthat, when U lanophaga IS offered an excess of
eggs, Its rm value at 35"C ISdouble the value at 20'C , whIle
the rm of C nmculatus remams constant and IS always
74
below that of U lariophaqa However, when the
availabihty of bruchid eggs IS hmited. the I'm value of U
larwphaga may be lower
(2) Offenng food to parasrtoids Access to honey
mcreases the fecundity of Uscana larwphaga by three
times, and ItS longevity by five times, as compared to
parasitoids that are starved (Van HUISet al , 1991) If such
a result could be achieved m storage, It would probably exert
mfluence on the bruchid population (see Wakers, 1998,
Wakers, m prep) Whether enhanced pest control as a
result of additional food ISto be expected, and how much the
longevity and fecundity should be mcreased m order to
obtam an adequate effect, can be assessed usmg a computer
simulation model If simulations mdicate that feedmg the
parasitoids has a sufficient negative effect on the bruchid
populations, 'field' expenments could be set up in order to
test this prediction However, practically feasible ways of
adrrurustenng food to the parasitoids should be found
(3) Inoculating the cowpea storage With Uscana There
are many bruchid species which infest pulses of legummous
trees (e g Woegan, 1995) Those bruclnds are not
associated With cowpea, and many have only a few
generations per year The same bruchids are also hosts to
Uscana spp , which in turn are also capable of attackmg the
bruchids of cowpea (A Van HUlS, C Schutte & S Sagnia,
unpublished results) These resources of natural enemies
could be used m bruchid control by adding pulses of these
trees to cowpea stocks, at a time when the bruchid
population IS most vulnerable to an mcreased density of
parasitoids Farmers could even set up small temporary
reanngs of natural enemies, based on this leguminous plant
matenal, and release them mto their granary Legummous
trees are relatively abundant m the dry Sahel zone, and
farmers are fanuhar With these trees because they use the
leaves for medical purposes, flavourmg food, and as food
protectants, and the pulses are used as arumal feed (D K
Kossou, personal commurucatlon) Reanng of parasltOlds at
VIllage level IS feasible, as demonstrated by farmers m
MeXICOwho rear parasltOlds for the control of the coffee
berry borer (Galvez, 1992) Reanng of parasltOlds on
bruchlds m pulses from legummous trees IS currently under
mvestlgatlon m Togo (I A GlItho & S F Bolevane,
personal commumcatlon) Computer SImulations, together
With data obtamed from population-dynamics expenments,
could help decide at which time m the storage season
moculatlons With parasltolds are most lIkely to be effective,
and how many parasltOlds should be used These predIctions
can then be tested m expenmental grananes
(4) Dned leaves and other parts of many plants are used
m traditional control methods Some of these plant products
may not be hannful to the parasltOldsof bruchlds, dependmg
on the properties of the plant speCIeS The parasltOld
population that IS left behmd after treatment With these

Proceedmgs of the 7th Internatumal Work1lLgConference 011 Stored-product Protectum - Volume 1
products might be able to prevent resurgence of the beetle
population This can be tested with a model, based on
mortality data of both host and parasitoid This option IS
especially interesting m combmation With inoculation of
grananes With Uscana
Research questions
From the above, It appears that questions like, 'At which
moment during the storage season should grananes be
moculated with extra natural enemies m order to be effectrve
m biological control?' , and 'Can additional food to natural
enemies reduce the damage mfhcted by bruchrds" ' are of
practical relevance
However, other questions have also emerged from work
on tlus system These questions are more fundamental m
nature, but they are also Important for our understanding of
the level of control U lanophaga may offer For instance,
m the absence of food, U larwphaga has a very short
adult longevity and generation time compared to C
maculatus At 30'C and Without access to food, U
Iariophaqa has an adult longevity of 1 - 2 days and a
generation time of 8 days, while adults of C maculaius
live about a week, and their generation time IS
approximately 3 weeks ThiS Imphes that, If C rnaculatus
populattons would occur m age cohorts which are more than
two weeks apart, extmctton of Uscana m those
commumttes IS hkely to occur (Van Alebeek, 1996, Van
HUlset al ,submitted) Separate age cohorts may occur m
msect populattons as a result of actlVlty of larval parasltOlds
(Godfray & Hassell, 1987, 1989), or as a result of a
dlfferenttal response to relattvely low temperatures of
different Immature stages The questton IS whether thiS
occurs m C maculatns populatIOnsm stored cowpea Such
temporal separatton of generations would have Important
Imphcattons for the expected results of Uscana as a
bIOlogicalcontrol agent Another questton IS whether the
metabohc heat that IS developed by the beetles (larvae and
adults) IS of such a magmtude that It affects the
developmental ttme of the both the beetles themselves and
the parasltOlds There are mdlcattons that thiS might be the
case (Van HUls et al ,submitted) If It IS, It should be
taken mto account m predlcttons of the efftcacy of bIOlogical
control We Willget back to tlus m the fmal sectton
Models with a Theoretical and
with a Practical Aim
Models of stored-product pests have been developed from
two qUlte different backgrounds Theorettcal bIOlogistshave
used stored-product msects for studies of populatton dynamiC
phenomena and the mechamsms that are responSible for
those phenomena They have developed mathemattcal
models that descnbe these processes (Mertz, 1972)
75
Ouestions that are central to theoretical ecology are, 'What
causes oscillations m population density?' and' what causes
populanons of a host and a parasitoid to coexist?" Storedproduct
insects (especially Triboiium. and Callosobruchns
species) have often been used in ecological studies because
they show interesting population dynamics, they are easy to
rear, easy to handle, and because their biology IS welldescnbed
(Mertz, 1972, Hassell et al , 1989, Throne,
1995) Moreover, the larvae of many bruchid species use a
discrete food resource to feed upon, which IS selected by
their mother (as m parasitoids) This has provoked studies
on optimal foragmg and hfe-history evolution m these
species (Wilson, 1988, 1994, Messina, 1991, Sibly et al
1991, Colegrave, 1994, Horng, 1994) In this paper we
Willemphasize' ecological' and population dynamical models
because they are more relevant to the Issue of biological
control in storage The models that are used m theoretical
ecology are mainly analytical, explanatory models that
contam biologically meaningful parameters which are
incorporated into mechanistic relatronships These models
mainly Yieldqualitative predictions
Researchers that are mterested m control of storedproduct
pests, on the other hand, have also developed
models that Simulate the development of msect populattons
m stored gram (Throne, 1995) However, these 'pest
management' models have been developed to answer
questtons hke, 'Can we expect a pest to develop m a gram
storage With these speCifiCImttal condlttons?' and 'When
should a storage manager start cooltng hiS gram?' (e g
Thorpe et al , 1982, Smclalr & Alder, 1985, Maler et al ,
1996, Flmn et al , 1997, Woods et al ,1997) These
models are mamly phenomologlcal, deSigned m order to
accurately and quantttattvely predict populatIOn
development, based on accurate sampltng and temperature
and hUlmdlty data from the gram store They are almost
always slmulatton models, and often draw upon empmcal
relattonshlps Temperature IS often mcluded as a dnvmg
vanable, and developmental rates depend on ambient
temperature. Models of thiS type can also be mcorporated
mto 'expert systems' or other 'deCISionsupport' tools (see
e g Norton & Mumford, 1993) These are software
products which help the storage manager deCide what he
should do to prevent or control msect mfestattons m the
stored product Models have been developed for most msect
pests that are of Importance m gram storage m mdustrlaltzed
countries
The models that have been developed m both dlsclplmes
(theorettcal and practtcal) are generally very different m
purpose and appearance Hlstoncally, both types of models
have been labeled 'strategic' and 'tacttc', respecttvely
(Nisbet & Gurney, 1982) In the next two secttons, we Will
diSCUSSthe models m both categones III more detail
Subsequently, we Willfocus on the relevance of the eXlstmg

Proceeunqs oj the 7th Internauonai Workmg Conference 011 Stored-product Protection - Yolume 1
models to the subject of our mterest The literature on
'theoretical' models of stored-product pests has also partly
been reviewed by Mertz (1972) and Throne (1995) The
literature on 'practical' simulation models has been
reviewed by Longstaff (1991) and Throne (1995) The use
of expert systems and decision support m stored product
protection has been discussed by Wilkin & Mumford (1994)
and Longstaff (1997) For an explanation of some baSIC
terms we refer to textbooks and general papers on modellmg
m biology (e g Rabbmge et al , 1989, Renshaw, 1991,
Brown & Rothery, 1994)
Models from Theoretical Ecology
Theoretical ecology models are here defmed as those that
deal With the question, 'What regulates the dynamics of
population densities?" Many different mecharusms have
been proposed to explam OSCillations m population densrties,
or the absence of them Three major ones can be
distinguished (either alone or m combmation ) Densitydependent
processes, mterations With natural enemies, and
spatial heterogeneity
Density-dependent reproduction and survival
Density-dependent reproduction or survival has been
mcluded in many models to account for the fact that
population growth IS not unlumted (Hassell, 1975) At high
population densities, mortahty rates mcrease and/or
reproduction rates decrease However, density dependent
processes can also create mterestmg OSCillations m
population Size These OSCillations tend to disappear after
some time, unless there IS a time-lag associated With the
density-dependent relationship (Hastmgs & Constantino,
1987, Shimada & Tuda, 1996) In such so-called delayed
density dependent systems, one life stage exerts at high
densities a negative effect on another life stage, rather than
on Its own life stage (e g adults eatmg juveniles when adult
densities are high) Tlus creates a time-delay m the effect
of high densrties, because It takes some time for the cohort
of affected life stages (e g , the juveniles) to develop mto
the cohort which can Itself produce denSity dependent effects
(e g , the adults) The OSCillations m delayed denSity
dependent systems typically have a penod of two to four
times the maturation penod (Gurney & Nisbet, 1985)
However, direct denSity dependence may m some cases also
produce strong fluctuations (Gurney & Nisbet, 1985) They
can be dlstmgUlshed from delayed denSity dependence
because they have a penod which approXlmately equals the
maturation penod We Will dtscuss m thiS section some
examples of both direct and delayed denSity dependence m
stored-product pests
Mathematically, denSity-dependent relatIOnships are often
of the form of the logistic dtfference equation, or
76
modifications of It (Utlda, 1967, Hassell, 1975, Shimada,
1989) However, the mechanism underlymg such densitydependence
IS not always specified These models do not
give a stnctly mecharustic explanation but rather a
phenomenological description of processes observed at the
population level (e g Utida , 1967, see Gordon et al ,
1988) Explicitly formulated mechamstic density dependent
processes mclude canrubalism, competition for energy,
nutnents and space, and a reduction m fecundity as a result
of crowdmg Note that these processes are not of the same
mtegration level (Fig 1), competition for energy, for
instance, may result m a reduced fecundity Canmbahsm
can be seen as a special form of competition
Fig. 1 Mecharusms that produce density-dependence III
stored-product insect populations (partly based on
Gurney & Nisbet. 1985) An astensk (* )
mdicates the methamsrns
text
which are treated III the
Canrnbahsm has mamly been studied m Tribolium ,
where mobile stages canrnbahze on rmmobile and/or younger
stages (Mertz, 1972, Desharnais & LlU, 1987, Hastmgs &
Constantmo, 1987) In Tribolium , cannibalrsm occurs
randomly, such that the nsk of bemg canrubahzed mcreases
at higher msect densities (Hastmgs & Constantmo, 1987)
There IS convmcmg eVidence that thiS IS mdeed respolllsble
for fluctuations m denSIties of laboratory populations of
TnbollUm, althought FUJll (1976) argued that food
renewal schedules also create CyCltClty, espeCially m the
mnnature stages
In the bruchld species Callosobruch ns chmenstS and C
macnlatns, whose larvae develop mSlde a smgle bean,
canlllbahsm does not playa role of any importance Instead,
denSity-dependent surVival through competition between the
larvae, and decreased reproductIOn as a result of crowdmg
has received more attention m models of these species
(Bellows, 1982a,b, Shimada, 1989, Tuda & Shimada,
1993, Tuda, 1993, Kuno et al , 1995, Shimada & Tuda,

Pmceedmgs of the 7th Iniernatumai Workmg Canference an Stored-product Protechor~ - Volu:me 1
1996) At high larval densrties. the larvae compete for
nutrients, energy and space (direct density dependence)
At high adult densities, females lay fewer eggs, and eggs
are damaged by trampling adults and because of tOXICeffects
of the oviposition marker pheromone (delayed density
dependence) (Bellows, 1982b, Oshima et al m Kuno et
al , 1995) Although both processes contribute to damped
osciiiations or a monotonic approach towards a stable
eqtnhbnum density, only the increased egg mortality as a
result of large numbers of old adults m overlappinggeneation
systems of C chrnensis prolonged the
OSCillations(Shimada & Tuda , 1996)
Gurney & NISbet (1985) have shown that, If the effect of
larval competition IS expressed directly on the larvae
themselves (direct density dependence), strong fluctuations
Witha penod approximately equal to the maturation time can
anse In other words, separate generations may occur m
populations whose larvae suffer an mcreased death rate or
maturation time at high larval densrties Discrete
generations m msect populations can therefore be an
mtnnsic property of the system, they are independent of
external cues (such as food renewal schedule) or nutial
conditions They have been observed m expenmental
populations of the Indian meal moth, Plodia mterpunciella
(Gurney et al , 1983 m Gurney & NISbet, 1985), and m
models and expenmental systems of Ca llosobnu:h us spp
(Bellows, 1982a, Hassell et al , 1989)
Most of the models mentioned so far are capable of
producing chaotic dynamics at certam parameter values
However, Hassell et al (1976) have shown that m most
smgle-species cases denSity-dependence Will probably
produce monotomc dampmg, rather than chaotic or unstable
OSCillations Indeed, the models discussed m thiS sectIon,
usmg realIstic bIological parameter values, show either a
monotomc or OSCillatory approach towards a stable
eqUIlIbnum, or stable lImit cycles Constantino et al
(1995, 1997) have shown that quasipenodic cycles and
chaos, which IS predIcted by their model of Tl'1bolmm for
certam parameter values, can be achieved by artifiCIally
Imposmg certam adult recrUItment and death rates m
laboratory population of Tr1bohurn
Nuttall (1989) developed a very detailed model of the
population dynamiCs of the stored product beetle Ptmus
tectu,:" HIS model Illustrates the dynamiC processes that
have been treated m thiS section, mcludmg denSity
dependence, delayed denSIty dependence, and all types of
fluctuations m population numbers
Interaction with a parasltOid or predator
Numerous studies have been devoted to the dynamiCSof
systems With one or more herbivores and one or more
natural enemies In contrast to the denSity-dependence
lIterature, the question that IS behmd most herblvore-
77
natural enemy models IS .how can hosts and natural enemies
coexist, or how can their populations become stable?' rather
than 'how can population oscillations anse? ' (Hassell &
May, 1973, Reeve, 1990) Reviews of the literature on
host-parasitoid models have recently been published
(Godfray & Hassell, 1994, Jones et al , 1994, Mills &
Getz, 1996) Although many of these models have not been
developed specifrcaily for stored-product systems, the theory
ISso general that It can be applied to such systems as well
Here we WIllrefer mainly to the reviews, in addition we Will
CIte some examples from work on stored-product msects
Numerous mechamsms that promote stability have been
Identified (Reeve, 1990, Godfray & Hassell, 1994, Jones et
al , 1994, Mills & Getz , 1996) For convemence we have
combmed the most Important mto four groups In general,
stability or long-term coexistence of hosts and parasitoids IS
promoted by the following mechamsms
1 A relatively low efficiency of the parasitoid at low host
densrties (Godfray & Hassell, 1994) Thrs can be
related to learning behaviour of the parasitoid, or to
refuges for the host Learmng behaviour imphes that
parasrtoids search more efficient at higher host
densities, because they become fanuhar With this
particular host Such parasitoids search less efficiently
at low host densities Physical refuges provide shelter
for a number of hosts, which also results m a reduced
attack rate at low host densities However, host
refuges need not be only physical Phenological and
physiological refuges are also possible (Godfray &
Hassell, 1994) Phenological asynchrony (the host
emerges before or after the penod m which parasltOlds
are active) results m a temporal refuge, and the term
phYSiologicalrefuge ISused to mdlcate that some hosts
may escape parasItism as a result of e g encapsulation
of the parasltOld eggs These mechamsms, too,
promote stabilIty Low parasltOld effiCiency at low
denSities of the host IS graphically represented by a
SigmOIdalfunctional response curve
2 A relatively low effiCiency of the parasltOld at high
parasltOld denSIties (Hassell & May, 1973, Godfray &
Hassell, 1994) At mgh parasltOld denSities the
encounters between parasltOldsbecome more frequent,
and thiS results m relatively fewer hosts bemg
parasItized Even Without phySical encounters, many
paraSltOlds notice the presence of conspeClflcs by
chemical cues (Godfray & Hassell, 1994) It has been
observed that thiS leads to a reduced net effiCiency
3 InclUSionof more species Oones et al , 1994) The
mtroductlon of an extra parasltOld or host speCIesmay
contribute to stabilIty Competition between a
speclaltst and a generalIst parasltOld, for mstance, can
result m a stable eqUIlIbnum where the mteractlOn
between the host and the generalIst alone wnld not be

Proceedmqs of the 7th Iniernaiumal Workmg Conference on Stored-product Protectum. - Volume 1
stable. Similarly, a system of two hosts and a host themselves Tuda & Shimada (1995) mvestigated the
parasrtoid which switches to the host which IS most persistence of the host-parasitoid system at different
abundant at any particular time IS potentially stable temperatures Persistence of host and parasitoid appeared to
4 Spatial heterogeneity m host density, combmed With depend very precisely on ambient temperature
environmental
attack (Reeve.
variation or
1990, Jones
variation m
et al 1994.
parasitoid
Godfray &
Spatial processes in single-species systems
Hassell. 1994) Spatial heterogeneity or patchmess Compared to spatial aspects of the interaction between
may contnbute to stabrhty of a system. because If the hosts and parasitoids, relatively little attention has as yet
host and/or the parasrtoid become extmct m one been paid to spatial aspects of smgle-species systems of
patch. the same patch can be colomzed agam m the storage pests Hassells et al ( 1989) investigated the
next time step Of the four muchamsms mentioned. stability of patchy systems WIth C maculaius or C
this one IS also a very powerful persistence-promoting chmensts m an expenmental and model context Stability
mechamsm (Jones et al 1994) It may be the most appeared to depend on the reproduction rate and the spatial
Important force behmd coexistence m successful distnbunon of the females A high reproduction rate,
biological control SItuations (Beddmgton et al 1978. combmed With little aggregation (low patchiness) results m
MIlls & Getz, 1996)
mstabihty of the system A high degree of patchiness can
A general cntenon for stabrlrty. based on these cause the system to stabilize (and also results m a smaller
mecharusms, could be heterogeneity or vanabihty m the risk population SIZe due to unequal resource utihzation combined
of bemg parasitized (Godfray & Hassell, 1994) It should be With density-dependent effects) However, the
noted. however, that stability also depends on the model expenmental systems were all in the zone of damped
context Some of the mechamsms mentioned abouve do not oscillations, the degree of patchiness m tills case had little
create stability m discrete-time models (Nicholson-Bailey), effect on stability
willie they do so for contmuous-ume models (Lotka- Tuzmkevich (1991) developed a model which could
Volterra) (Reeve, 1990. Godfray & Hassells, 1994, MISS& quantitatively predict the results of an expenment wich
Getz , 1996) ThIS IS due to the time-delay WhIChIS inherent Newman. Park & Scorr had carred out m 1956 In tlus
to the discrete-time models As was concluded m the expenment, the spatral dIstrIbution of Trtboltum beetles m
preVIOUSsection. delayed denSIty dependence often creates a CUbIC contamer. fIlled With flour. was studied The
mstabilIty
hIghest concentrations of beetles occurred near the walls of
Ecologral theory concermng host-parasitOied relatIonshIps the contamer. and near the surface of the flour mass The
IS Illustrated by several examples WIth Callosobruchus model of Tuzmkevich (1991). of willch baSIC features were
chmensu; and C mnculatus Hassell et al (1985) showed mortaity as a result of competition With nearby mdlvlduals,
that Amsopterornalus calandrae and Heteros]nlus and random movement of beetles. descnbed the
prosopulu; both show mverse denSIty dependence m an expenmental data well He also dIscussed other models
enVIronment With patchIly distrIbuted hosts (the fraction of WhICh had been developed to explam the observations
host larvae paraSItIZed m a patch decreased With mcreasmg There are many models that do not fIt mto any of the
host denSIty m a patch) Tills was due to a lack of denslty- categones that have been dIscussed so far (e g Joneset
dependent aggregation of the parasitoid and a relatlvely low al 1990) However, the models descnbed m tlus sectlon
maxImum attack rate per parasltold WIthm a patch show WhICh aspects of storage pest ecology have receIved
Accordmg to Hassell et al (1985), thIS mechamsm, lIke most attention
normal denSIty dependence m a patchy enVIronment. can
contrIbute to perSIstence of the system Hassell & May 'Pest Management' Models
( 1988) mention that A calandrae and C chmenstS
coexIsted m a patchy expenmental system. whereas the Pest management models have been developed pnmanly by
homogeneous system was unstable The dynamICS of both research teams m AustralIa, North-Amenca and the Umted
brucilld speCIes and the larval parasitOid Larwphagus Kmgdom (Throne, 1995) They deal mamly With storage of
dlSttnguendUS were mvestIgated m a model context by wheat. but also With storage of maIze (Subramanyam &
Bellows (1988) Tuda & ShImada (1995) dId the same for Hagstrum. 1991, SmIth. 1994, Throne. 1994, Maler et
C chtnenstS and H prosopults In both studIes. age- al 1996) or nce (Ryoo & Cho. 1988) Models that deal
structured models were used The model of Bellows (1988) With other types of stored produce, such as frUit (Jang,
predIcted erratic fluctuations WhICh were SImIlar to those 1996). are not conSIdered here because the system IS very
found m laboratory systems These fluctuations were the different from cereal storage
result of the age structure and complex mteractIons between Most attentIon has been paId to frve coleopteran pests,
parasitOid attack of host stages and competition between the namely Oryptolestes ferrugtneus , Oryzaephtlus
78

Prcceeduuu. of the 7t11 lutes uatiouo! WOIhlllg Conteience 0/1 Stcn ed-prodnct Protection - Volume
'1011I1/(l/ilell'I. (Smith. 199.:1) and
Cepluilouonnu uutei stuu, against Ci uptolesie-;
Models to Storage in Developing
Countries, Particularly Stored
fl'l I uotuetu ( Fhnn & Hagstrum , 1995)
Cowpea in West Africa
Temperature IS included Ii1 most models .h the mam
vanable drr, mg insect development Many ot these models Aspects considered essential to tropical storage are (1) the
can therefore be used for prediction of insect population specific pest organisms involved. (2) high temperatures and
growth based on actual temperatures measured m the sometimes high humidity. which create an Ideal
granary In addition, some models also predict the environment for many pest msects (Jones et al 1993.
temperature inside the granary (e g . at the center of the Hames. 1995), (3) socio-econormc constraints. due to
gram mass) based on ambient temperature and solar which gram coolmg , the apphcation of pesticides, and other
Irradiation The latter models mclude physical sub-models techniques commonly used m mdustnahzed countnes are not
wluch descnbe the conduction ot heat through a gram mass teaslble. (.:I) the Impact of natural enemies on pest
(e g Thorpe et al , 1982, Flmn et al 1992. Maler et populations All these aspects should be taken mto account
al , 1996, V-v'oodset al . 1997) These phYSical models are m a relevant model that can be used to develop a sound
not mcluded m thiS overView, for a review see Jayas bIOlogICal control strategy for stored-product pests m
(1995 )
developmg countlles
Models which predICt populatIOn size as a functIOn of
temperature normally mcorporate models which predICt rates
Pest orgamsms
of development. mortality. and OViposItion as a functIOn of In pest management models. most attention has been
temperature These models are sometimes pubhshed gl\ en to bve coleopteran storage pests However. the
sepalatelv (e g Hagstrum & Mllhken. 1991) They are msects willch cause most problems m developmg countnes
only mcluded If It IS clear that they were developed to be are not necessanly the same (see Allotey. 1991. Khan &
used m pest-management models
Mannan. 1991, Gahukar. 199.:1. Hames. 1995) For
Most models predict vanables such as the number of mstance. after ItS mtroductlOn from Central amenca m the
msects present per kilogram of gram In general, the 1980s. PlVl>tep!lll/lIUo tllllicatw, (Coleoptera
practical' models are sm1UlatlOn models whICh are Bostnchldae) has become a se\ere pest of stored maize m
charactenzed by empmcallelatIonshlps Some exceptIOns to Atnca (Boxall. 1Y91 Gahukar, 199.+) Smlliarly.
tl1lS rule mclude the parasltOid-host mteractlOns m Smith llposcehds (Psocoptera) seem to be a much bigger problem
( 199.:1) and Fhnn & Hagstrum ( 1(95) which ha\ e teatures of m tropICal gram stores than m temperate zones (Hames.
mechamstlc models, phYSICal submodels, which are 19(5) Fmallv. bruchlds are knowledge. no pest
mechamstlc and often also analvtlc. and models of Longstaff management model that deals With bruchlds has yet been
(1981. 1(88) and Thorpe et al (191\2). m whICh an developed However. a number of models that deal With
analytical approach to mvestIgate pest-management Issues bruchlds have been developed m theoretical ecology (e g
was used In additIOn. some models of msect development Bellows. 1982a. b. 191\8)
rate employ bIOchemically
rendel s them mechamstlc
meanmgful parameters
(e g Rvoo & Cho,
which
19S5,
High temperatures and high denSIties of msects
Subramanyam & Hagstrum. 1991. I(93)
Many of the models that have been developed m
79

Pvoceedruq- 0/ tin' Til: Iutei uatiouo! Wl!lhlllg Coutevence Oil Sttn ed-proli«t Protect ion - Yoiun,« 1
theoretical ecology take into account high densities of
insects Tlus IS not surpnsmg , because theoretical
ecologists au, inu rested m the tactors wluch regulate the
dynamic size ot a population However, in these studies the
densities of insects are generally so high that they are not
relevant tor (tropical) gram stores ( see e g Hassell et al .
19t;9. Jones et al 1990) Moreover, in the studies on
Tllbo!1II1Ji and Callowbl uclut--, the tood source IS tvpicallv
renewed at regular intervals (e g Fuju , 1976. Hassell e-t
al 1989) Tlus does not resemble a normal storage
situation the storage manager. on the other hand. wants to
control pest populations below levels which are of interest of
theoretical ecologists As a consequence. the tvpical pest
management model deals pnmarily wtth msects at \ery low
densttLes where populattOn dvnanuc processes ate
qualtatt\-elv dttferent from those at htgher densttLes
Temperatures m cowpea grananes m West Afnca (an
exceed -iOe (Van Huts et al . submttted. C Stolb. et al
unpubltshed results) These temperatures need not be lethal
for the adult brucluds (see e g Hemtlch. ILJLJ3) but
mortaltty of the larvae may mcrease Tuda & ShImada
(1993) have shown expenmentally and theoretIcally that a
rather small mcrease m ambIent tempetatute (trom 30°C to
32°C) lesults m a stgmftcant decltne m the equtltbtlum
populatton stze ot Chllo,obl III II/Ii) dllllCII;"lb Tlus may be
due to a decreased lanaI suntval at 302C compared to 30°C
(Tuda. 1993) Tuda & Shtmada ( 1095) ha\ e shown ( both
expenmentallv and m a model context) that the perststence
of a larval parasttOld of thts bruchtd. Hetcm\pil u\
PI'ObOP/(ZI\ IS gleater at 3WC than at 32'C AddttLonally.
their model predtcted that the parastt01d would go e"tmct
ear Iter at 28°C than at 32C These results suggest that
relatt\-ely small dtfferences m temperature may hm-e a
stgmflcant eflect on btOlogtcal control. as we reterred to m
the secon secttOn of thiS paper Most practIcal pestmanagement
temperatures
models. howe\er. are not valtdated for htgh
50('10-1'(01101111(' lO/l\fiWIl t\
Compton et al (1992) and Jones et al (1993) ha\e
develped an expert system for pest control m bagged matze
m the troptcs Tlus computer-based model tS mtended fO!
large-scale stores Oones et al . 1903) and tS not applOpnate
for Saheltan subststence falmers who store thetr cereals and
beans prt\-ately The lack of tmanctal means and the poor
state of mfrastructute (electncttv. lOads) tmposes
constramts on the methods that can be used to control
st01age pests m thess systems The control methods that are
constdered m most pest management models are not
applOpnate m tlus case
Rather than a dectstOn support tool tor farmers. we want
to develop a model that enables lesearchers and posstbley
extenStOn workers to e g select a natural enemy 01 a yearly
'release date' for the natural enemy whtch wtll prove most
80
ettectr, e m supressing the pest popula tions
Natural enemies
While a large pat t ot theoretical ecology deals with natural
enenues , the type of questions that tS treated there are often
not appropnate to storage condrtions For instance. the
paradigm ot an ecological equthbrium has dormnated for the
past decades (Mtlls & Cetz , 1096) However. it tS
questionable whether the 'search for stabihty ' can be
justified from the viewpoint of pest control m stored
product It may be benefrcal if the natural enemy and its
host CoeXIStat a very low equihhnum density in storage. but
a high equilibnum densitv tS obviously destructive to the
stored product Nonetheless. concepts and techniques which
hm-e been de\ eloped m theoretLcal ecology may be used m
deternunmg wluch aspects of a storage sYstem need to be
mcluded m a sunulattOn model For mstance. Godfray &
Hassell ( 1987. 10t;LJ) show how natural enenues may cteate
sepatate generattOns m troptcal tIlsect spectes As menttOned
III the second secttOn of tiltS paper. such dlstmct genera ttOns
may lumt the abtltty of U
populattOns
lclilOplwga to suppress bruchld
:-.Jatural enemtes have only been constdered m a pestmanagement
model m two cases ( Table 2) However. there
tS now mcreased attenttOn for btologtcal control m stored
products m mdustnaltLed countnes (Arbogast, 198-i.
Brower et al . 1l)LJ6) Thts may accelerate the deYelopment
of pest management whtch mcorporate natural enenues
Conclusions and Perspectives
for the Future
Thele tS a dtstmcttOn between models from theoretLcal
ecologv and pest management models m terms of the type of
questLons and the methods they employ (Ftg 2) both
approaches ha\-e prO\ en to be vet y useful and fruttful areas
of lesearch. and m order to be able to develop gutdelmes for
btOlogKal contlOl m tradtttonal storage m mdustnaltzed
countnes. we need to combme the' ecologtcal realtsm' of
theoretLcal ecology wtth the accurate. quantLtatlve
predtcttOns of pest management models Extstmg pestmanagement
models have mamly been constructed for use m
mdusttlaltzed counttles They do mostly not entad natural
enenues. wlule these are tmportant for stored-product
protecttOn m developmg countnes Natural enemies of
stored-product pests are ftrmly embedded m ecologtcal
the01 y. however. the type of research questLons and
predtcttOns that are ytelded by these models do not meet the
needs of people who are mterested m practtcal btologtcal
control m developmg countnes The same tS true for othel
aspects
counttles
that are spectftc to tladtttOnal storage m developmg

Pvoceediuq« of tile 7t11 lutei natuntu! WUlhllltj Couiereuce Oil SfOled-]JI'(x/nd Piotection - VO/IIllle 1
THEORETICAL PEST
mass. metabolic heat production sornetnnes results m so-
MODEL AIM
fEATURES
•
..
~
-NATURAL ENEMIES
-HIGH INSECT
DENSITIES
ECOLOGY
QUALITATIVE
PREDICTIONS
MANAGEMENT
QUANTITATIVE
PREDICTIONS
RELEVANT
FOR
called 'hot spots' 111gram (Howe. 19··[\. 1962. Sinha &
Wallace 1966) In such hot spots. insects and fungi
develop more rapidly. causing severe deterioration of the
gram quahtv the amount of metabolic heat production under
different Circumstances has been measured m several storedproduct
pests (e g Cofie-Agblor et al 1995. 1996)
-MECHANISTIC
RELATIONSHIPS
-NO -NATURAL- - - - - -
ENEMIES
-LOW INSECT
TROPICAL
STORAGE
------------~--------------
,
I,
(LIJ
Longstaff ( 199 J 1997) and Throne (1995) have both
pointed out the need to incorporate the mfluence of
metabolic heat production on gram temperature models of
stored-product protection Nevel theless, a robust model
DENSITIES
-EMPIRICAL
expoIlIfIII8l
growth)
that pi edicts insect population
based on ambient temperature
growth and heat production
and nunal gram conditions IS
RELATIONSHIPS
not yet available Such a model would both be useful for the
A model that qu.mut.rrrvelv piedic h the ie--ult uf
development of pest-management models. and mterestmg
dt ffcrent m.magcme nt pi.u ucc«. .umed at from a theoretical point of View It would be useful because
con-ervmg the n.uui II enenuc- III d n opn al ~tordge It could hep decide whether the heat generation for a grven
-v-u m h nut "",dctbk Requu cuu nt-, dIe msect species and climatic range IS such that It should be
111lrctt!ono{ I1ct(11lctlenemle~. vcthdd 1

PWCf'e(//lf(j, of the Tth Iutei uution«! \TO/hilf(} (()J/frlel/((' ()/I "t()/erl-jJJ'(x/lict Protection -Volllllle I
also possible Filed' mdiv iduals regularly enter storages and
interbreed there with storage' mdividuals Knowledge
about the evolution of storage pests and their natural
enenues could give Important mforrnation concerning
(bilogical i control of storage pests
Several insects develop easily on stored cereals and
pulses. For that reason. they are both a nuisance to the
storage manager. and an opportunitv to the SCientist who
seeks to understand population ecologv Storage managers
and theoretical ecologists need collaborate for safe and
effective control ot those insects m storage As haines
(1995) has pointed out. a thorough analvsis ot the ecology
ot tropical stored-product pests IS needed If we want to
control those pests Natural enenues will hav e to be included
111 such an analysis for the development of biological control
of stored-product pests m developing countries
Acknowledgements
nuiculai u-: (Coleoptera. Bruchidae ) Joumal of Animal
Ecology 51 263 - 2l'.7
Bellows. JI, T S 1982b Simulation models for laboratory
populations ot Cal/ovAn uclt u-; cluuenu» and C
nuu.ulat u« Journal of Animal Ecologv 51 547-623
Bellows J I. T S and Hassell. M P 19l'.8 The dynanucs ot
age-structured host-parasitoid 111teractions Journal of
Animal Ecology 57 25Y - 268
Ben Yahmed , B (ed ) 1993 L'atlas du contment africam
Ieune
175p
Atnque and Les Cdrtions du Jaguar. Pans. France
Boxall, R A IY91 Post-han est losses to msects a worled
overview In H W Rossmoore (ed ). Biodetenoration
and biodegrada non 8 160 - I75
Brower. J H and Tilton. E W 1975 Potential for control
of Cadra cautella (Walker) by release of fully or partially
stenle males Interational Journal of Applied Radiation and
Isotopes 26 no - 725
Brower. J H Smith. L . Vail. P V and Flmn , P W
We thank Frank van den Bosch. Ioop van Lenteren and 1996. BIOlogical control In B Subramanyam and D W
PhD students ot the Laboratory for Entomology for valuable Hagstrum (eds ). Integrated management of insects 111
comments on previous versions ot this paper Many of the stored products Marcel Dekker. Inc New York (etc )
Ideas presented m this paper have emerged from the work of pp 223 - 286
Frans van Alebeek We thank Felix Wackers tor mterestmg Brown. D and Rothery. P 1994 Models m biology
discussIOns Gerard Pesch assisted With the literature Mathematics. statistics and computll1g John Wiley and
reterences Use was made of a literature database whICh was Sons. Chlcester. England 688p
prevIOusly mall1tamed by Frans van Alebeek
Campbell, A and Sll1ha. R N 1990 AnalYSIS and
sll11UlatlOn modelling of populatIOn dynamiCs and
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