Computer Simulation for Integrated Pest Management of Spruce Budworms

Paifi Southwest Forest and Range Experiment Station Researh Paper PSW 159 Computer Simulation for ntegrated Pest Management of Sprue Budworms Carroll B. Williams, Jr. Patrik J. Shea

Authors: CARROLL B. WLLAMS, JR., is a pioneer sientist studying integrated management systems for forest inset pests and diseases, with headquarters in Berkeley. Calif. He is a University of Mihigan graduate (B.S., 1955; M.S. 1957; and Ph.D., 1963, in forestry). He joined the Forest Servie in 1957. PATRCK J. SHEA is in harge of the Station's field evaluation of hemial insetiides res'arh unit, with headquarters at Davis, Calif. He joined the Forest Servie and the Station staff in 1967. He earned degrees (B.S., 1962; M.S., 1972) in entomology at the University of California, Berkeley. Aknowledgment: We are grateful to D. Gordon Mott. Northeastern Forest Experiment Station, Forest Servie, U.S. Department of Agriulture, for assistane in the development of the ideas expressed in this paper and for servies in omputer programming. Publisher: Paifi Southwest Forest and Range Experiment Station P.O. Box 245, Berkeley, California 94701 July 1982

Computer Simulation for ntegrated Pest Management of Sprue Budworms Carroll B. Williams, Jr. Patrik J. Shea CONTENTS ntrodution..................................... Components of the Pest Management System...... 2 Population Dynamis 2 Forest Stand Dynamis.................... 3 Eonomi mpat...... 3 Control Systems...... 3 Struture of the Model 4 Simulations...... 7 Variation in Parasite Searh Rate (a p )... 7 Variation in nsetiide Survival Rate (SC)... 7 Optimizing Pest Management...... 8 Referenes

N BREF... Williams, Carroll B., Jr.; Shea, Patrik J. Computer simulation for integrated pest management of sprue budworms. Res. Paper PSW-159. Berkeley, CA: Paifi Southwest Forest and Range Experiment Station, Forest Servie, U.S. Department of Agriulture; 1982. p. Retrieval Terms: sprue budworms, insetiides, parasites, integrated pest management System simulation an be used to develop a deision support system for sientists and forest managers in suppressing populations of forest inset pests. nformation from the literature desribing the effets of insetiides on the western budworm (Choristoneura oidentalis Freeman) and its major parasites, and models from population researh on the sprue budworm (C. fumiferana Clem.) were used in a trial of the method. A simple model was developed to desribe budworm-parasite systems whih differed aording to the hypothetial effetiveness of the parasites. Computer simulations desribed the survival ofthese systems when subjeted to different levels of ontrol by insetiides, and also desribed possible ostbenefits assoiated with different levels of ontrol for the various budworm-parasite systems defined in the model. The primary omponents of the model for the simulations were. Mathematial models of the population dynamis of the pest inset and its parasites. 2. Mathematial funtions for impat of different population levels of the pest inset on generalized forest produt yields or values. 3. Estimates of the effetiveness of various "ontrol" fators (parasites, insetiides) in suppressing and in preventing high populations of the pest inset. 4. The eonomi framework for ost-benefit analyses of the various ontrol options. Computer simulation of the model produes both stable and osillating average population densities over time, depending on the parasite's searhing effiieny or attak effetiveness. n general, as the parasite's effetiveness inreases, the budworm-parasite systems beome more stable, and the average or steady density of the budwornl dereases with inreased parasite effetiveness. n the simulations, when insetiide is applied to the osillating system, the amplitude of the density osillations inreases at the lowest levels (ontrol rates). However, at higher insetiide levels, amplitude dereases until a level of ontrol is reahed where the system beomes stable. The level of ontrol at whih the osillations attain maximum amplitude inreases with inreasing parasite effetiveness. The level of ontrol whih produes a steady system dereases with inreasing parasite effetiveness. Similarly, in stable budworm-parasite systems, as insetiide ontrol rates inrease, the host density inreases, then dereases at high insetiide rates. The ontrol rate whih produes the maximum density level inreases as parasite effetiveness inreases. The simulations revealed that the level of budworm population suppression in stable or steady density budworm-parasite systems is not proportional to the amount of ontrol applied in that inset generation. Only when very high ontrol rates (insetiide dosages) are applied is muh effet produed on the budworm population. Cost-benefit analyses showed that under these onditions, very high investments are worthwhile but moderate investments produe little effet. A steady density budworm-parasite system (budworm density of 2150 without insetiides) was simulated to illustrate through ost-benefit omparisons the most eonomial pest population level ahievable in ontrol efforts. A variety of linear and urvilinear relationships between pest density and the value of damage were depited for this system. f pest density was redued from 2150 to some smaller value, a variety of osts were inurred and a number of gains were possible, depending upon the initial relation between pest or budworm density and the value of the damage. Broadly, this study showed that the proess of onstruting a mathematial systems model serves to define the kinds of information required' for understanding the biologial struture and dynamis of the system. The study also demonstrated the usefulness of omputer simulation experiments with these models to predit system behavior under different onditions and the onsequenes of various management deisions.

The development of eologially aeptable management methods for forest inset pest populations is a omplex problem. t requires for its solution data from many investigations of the inset populations and the rops they affet, the effiaies of various ontrol methods, and the eonomi and soial systems in whih all of the ativities take plae. The urrently popular terms "integrated ontrol" and "systems approah" indiate an inreased awareness by biologists and resoure managers of the omplexities of pest-rop systems and the need to understand them in order to develop viable management tehniques. Many of these systems for forest pest management have been presented as generalized diagrams and flow harts (jig. 1), in whih the forests (rops), the pests and other system omponents, and their hypothetial relationships are illustrated (Campbell 1972, 1973; Waters 1976; Waters and Ewing 1976). Less ommonly, systems analysis and omputer simulation have been used to illustrate the struture and dynamis of the system, the linkages between system omponents and the onsequenes of various management deisions on the dynamis of the system (Watt 1959,1961,1964, 1968; Miller 1959; Holling 1963, 1964, 1966; Berryman and Pienaar 1974; Mott 1973). A thorough historial aount of the development of the onepts and realities in forest pest management was provided by Waters and Stark (1980). A great advantage of omputer simulation is that it permits experimentation with mathematial representations of real-world systems whih would be risky, diffiult, and expensive with atual systems. For example, a prime requirement in the development of most management sys~ tems for forest defoliating inset pests is the evaluation of the effets of insetiide appliations on these pest populations and their parasites, and of the amount of protetion suh appliations may offer to various forest produt yields and values. Field experimental programs designed to examine these interests are diffiult and expensive to run, but they provide quantitative estimates for various system parameters that allow us to evaluate the effets of insetiide treatments on the atual pest-forest system. Field studies of the effets of pestiides on the sprue budworms (Choristoneura sp.) and their parasites have shown severe suppression of host (budworrn) populations and inreased parasitism after treatment (Eaton and others 1949, MaDonald 1959, Williams and others 1969, Carolin and Coulter 1971). Parasite survival was enhaned by moderate redution (50-70 perent) of the host population; Agroforest eosystem Treatments Predition models r-------------, RESEARCH AND DEVELOPMENT nset population dynamis population L: d.:m~ Monitoring inset and plant populations Treatment strategies mpat Benefit/ost ---!,~ integration ~ Predition models m:~:~e., \ \ \ Total rop '> res;~re ment management system / Figure 1-Model struture of an inset pest management system, with re~ searh and development omponents and ation sequene (Waters and Ewing 1976).

inr~ased parasitism under these onditions lasted for several years (Williams and others 1979). n ontrast, reports of spray programs to ontrol agriultural inset pests have frequently desribed the initial severe suppression of the pest, but the virtual elimination of the natural enemies of the pests, followed by a resurgene of the pest populations; subsequent damage to rops is often higher than before pestiide treatments (Van den Bosh 1970, Kilgore and Doutt 1967, and Pikett and MaPhee 1965). The onfliting results of these two sets of studies are partly explained by the nature of the pest inset-rop system and the frequeny of insetiide appliations. Suh onflits indiate, however, a role for omputer simulations as an aid in foreasting the biologial onsequenes of applying different levels of insetiide ontrol on the pest populations and their parasites. This paper demonstrates the appliability of omputer simulation to researh and management through the onstrution and use of system models in integrated forest pest management. A mathematial systems model an indiate what kind of information is required for understanding the biologial struture of the system and predition of system behavior with and without regulation. We examine the interations among parasites and host (pest) densities and survival of host-parasite systems subjeted to different levels of ontrol by insetiides. We also examine ostbenefit funtions assoiated with different levels of ontrol. Although the onepts used in these simulation studies are taken from field insetiide trials on western sprue budworm (Choristoneura oidentalis Freeman), and data from population researh on the eastern sprue budworm (Choristoneura fumiferana Clem.) were used to desribe the interation; we do not suggest that the simulations mimi population dynamis of either budworm. Rather, we desribe a very simple and general proess that may pertain to other defoliators, with the aim of demonstrating the potential of simulation studies as aids in deisionmaking in forest inset pest management problems. COMPONENTS OF THE PEST MANAGEMENT SYSTEM deally a pest management system an be envisioned as a large model omposed of different omponents or submodels. These omponents desribe various biologial and soia-eonomi proesses and are linked in a manner to show the primary pathways of information flow that lead to deisionmaking. The nature of the linkages is important beause inputs from one submodel an be the parameters for another. The generalized forest pest management system model shown in figure 1 has two strutures-an inner researh and development ore and an outer "management" struture. OUf omputer simulations fous on four omponents of the researh and development ore: Mathematial models of the population dynamis of the pest inset and its parasites. Mathematial funtions for impat (usually damaging) of different population levels of the pest inset on generalized forest produt yields or values. o Estimates of the effetiveness of various ontrol fators (parasites, insetiides) in suppressing and in preventing high populations of the pest inset. An eonomi framework for ost-benefit analyses of the various ontrol options. Our simulations do not inlude the forest stand dynamis omponent beause it adds more omplexity, than we desire or need for our purpose. However, we will disuss this omponent below along with the others beause it provides the linkage between the pest population dynamis and impat omponents. The impat and ontrol omponents provide diret inputs into ost-benefit analyses requir~d for deisionmaking on pest management ativities within the forest resoure management system. A more detailed desription of these system omponents is given by Waters and Stark (1980). Population Dynamis Generally, models of population dynamis of pest inset speies show how inset mortality is affeted by population densities and forest onditions and identify key mortality agents. These models may indiate whih mortality agents have the greatest potential for biologial ontrol. Generally these agents-parasites, predators, or diseaseausing organisms-are density-dependent; that is, they respond to population hanges of the pest inset speies. Their potential an be enhaned oasionally by management ations, and although they may not adequately suppress epidemi pest populations, they may be effetive in regulating low or endemi pest populations. Models of population dynamis may indiate how natural enemies of the pest may be made more effetive. Perhaps some of the potentially more effetive parasites are themselves regulated by alternate hosts or hyperparasites. These models show whatever relationships may exist between inset survival and forest stand variables suh as size and age of host trees, forest omposition or habitat types, rown levels, stand densities and basal area, aspet, and topography. Consequently, the models serve to indiate the stand management or silviultural treatments that may produe forest onditions less favorable to population inreases of the pest inset. The models are also designed to mimi the effets of various kinds and dosages of, hemials. n partiular, they desribe the influene of these hemials on the effetiveness of parasites, predators, and disease-ausing organisms in ontrolling pest inset populations. 2

Forest Stand Dynamis Models of stand dynamis and biomass prodution portray the eologial impat of pest population density levels, and of the duration of feeding injuries, on a variety of forest onditions or habitat types. For example, defoliating insets onsume the leaves of forest trees. f this ativity is severe and sustained, it an lead to growth redution, stem diebak, stunted and deformed trees, and eventually tree mortality over small or large areas. Defoliation an also redue ompetition among surviving forest trees, however, and thus result in inreased tree growth. The residual stand may atually be more produtive than it would have been without the inset ativity. Defoliation an inrease the fall of nutrientrrih litter, stimulate the ativity of deomposer organisms, and inrease.light penetration to the forest floor, thereby inreasing the survival of seedlings, and the prodution of forage, or both. Defoliation an also inrease water yield from the area. Whether a partiular level of inset ativity is benefiial or injurious depends on the forest management objetives and plans of different ownership and user groups, the osts of effetive ontrol, the osts of alternative management plans if urrent plans are made unfeasible, and the vagaries of the market plae. Eonomi impat models serve to determine values (losses and gains) affeted by inset ativities within the forest stand in relation to speifi forest management plans. Eonomi mpat A model of eonomi impat desribes both the values produed by forests under speifi management plans and proedures and the influene of inset pest populations on this value prodution. Little or no eonomi damage may be aused by heavy defoliation over a short period of time, or severe damage may result from moderate defoliation over an extended period of time. The diret and indiret eonomi effets of defoliation by a forest inset pest speies may be immediately obvious or may not be measurable until the end of the rotation period. Under ertain onditions we may oasionally find that low to moderate pest population levels add value to forest stands by the end of the rotation period. Eonomi impat models guide deisionmaking for ontrol ativities by establishing a means of benefit-ost analysis, leading to more effiient use of resoures. The onept of "eonomi threshold" is a useful part of any benefit-ost analysis, and may be defined as the level at whih the loss aused by the pest inset population just exeeds in value the ost of the ontrol measures available (Geier and Clark 1961). Obviously, eonomi impat models must enompass the osts and effetiveness of various ontrol strategies, inluding no ontrol, and the short- and long-term value saved or lost by different ontrol strategies initiated at different population densities and different times during the outbreak. Control Systems The effetiveness of the various materials, organisms, and tehniques of vegetation management that either diretly suppress inset pest populations or inhibit further population inrease may be modeled as a ontrol system. Materials applied inlude insetiides, mirobials, and behavioral hemials. Computer simulation of the ontrol system an help in the evaluation of the effetiveness of various dosage levels of different materials on the pest inset and nontarget organisms. nsetiides differ in their uses, properties, advantages, and restritions. Preditions of the fate of eah insetiide in various environments and effets on target and nontarget organisms an be made on the basis of the orrelation of toxiologial, hemial, and physial properties for eah insetiide with the physial and biologial environment and the representative phylum and order of organism treated. Computer simulation an aid the development of ontrol systems that will allow the resoure manager to use those insetiides that are urrently available more intelligently and judiiously to avoid serious problems, and will help the researher to develop more eologially aeptable insetiides. Diret ontrol of inset pests by hemials tends to be least expensive in the short run ompared to other kinds of ontrols. f used repeatedly, however, hemial ontrol dereases in effetiveness as pest populations beome more resistant and eonomi and environmental osts inrease. Diret ontrol by ertain biologial organisms tends to be expensive in the short run, but if the organisms subsequently beome established and effetively keep pest population levels below the eonomi threshold, then this ontrol method beomes least expensive in the long run. Environmental osts assoiated with most forms of biologial ontrol are small. f we inlude the environmental osts in with the eonomi osts of ontrol, then some ombination of biologial and hemial ontrol ould be part of an optimal pest management program. To ahieve this, information on the interation of hemials and various biologial organisms suh as parasites would be required. Modeling these interations and the eonomi osts of ontrol may allow us to devise optimum ontrol strategies and poliies for use of hemials and other ontrols. An optimal pest management prnram would distribute available ontrols (singularly or in ombination) so that osts assoiated with forest produt damage, ontrols, and environmental damage due to ontrols are minimized. An example of how the methods of optimal ontrol theory an be applied to the problems of pest management and the results whih may be expeted has been desribed by Vinent (1975). 3

STRUCTURE OF THE MODEL The basi struture of the model used for the present simulation is in whih Nt + == number of pest insets at time t + SC t = survival rate for the exposed population, Nt. from insetiidal appliations during the interval from t to t + SC t = survival rate for the exposed population, Nt> from other fators during the interval t to t + 1 RP t = mortality rate for Nt from parasitism during the time interval F t = reprodutive rate for Nt during the time interval. The following general assumptions are made:. The pest host inset-parasite system is losed, with neither immigration nor emigration. 2. Generation survival (SG) is a onstant. These assumptions are unrealisti. Many unonsidered fators affet system dynamis. For example, death results from weather and from predation, disease, and aident. n real systems, many of these mortality agents are density dependent. Also, the intensity of many of them is determined by extrinsi or aidental events whih affet population levels at various stages of an inset generation. 120 - ~ u "~ 80. 2 ~ ~ u, - e 40. ~ '" ol_.l-.-----:-~--.c~~"""""!!... o 1000 2000 Pest density, N Figure 2-Feundity funtion F= C, exp( - a,n); C, = 100. These two assumptions are neessary, however, beause our intention here is to study ertain simple effets. Our main rationale is that these merit attention before studies of ompound effets. 3. SC-survival of pest inset under insetiidal ontrol-is a onstant in eah simulation run, for a given ase (set of system values), but varies from ase to ase. 4. F-reprodutive rate-varies in response to density, N. t is assumed (fig. 2) that F has an upper limit (C r ) when density approahes zero, and that F diminishes exponentially at a rate a r as N inreases, suh that F = Crexp( - arn) F is not permitted to derease at very low population density as a result of mating failure or other phenomena affeting the reprodutive proess. The general form of this relation losely resembles natural events, however, and it is an aeptable approximation for our present purpose. 5. Parasite attak and adult parasite population dynamis are as defined by Watt (1959): in whih NA( = number of host insets attaked in generation t P "" number of adult parasites present in generation t apand bp = onstants for parasite effetiveness K = maximum attaks per parasite For a omplete disussion of the derivation of this model, see Watt (1959); for examples of its appliation see Miller (1959) and figure 3. The onstant a p desribes the parasite's searhing ability in the absene of ompetition, and b p desribes ompetition among parasites for opportunities to attak hosts. Briefly, the attak rate per parasite, NAP, an attain a maximum, K, and diminishes as the ratio of hosts per parasite, NP, diminishes. We assume that parasite attak ours early in the host's generation, that the survival of the parasite and that of the host are identially affeted by the mortality fators, exept for the insetiide applied, and that, after emergene, parasites are subjet to an additional mortality fator (C p, see assumption 7) before attaking the next generation of host insets. 6. Natural ontrol of the pest host inset population results from redutions in reprodutive rate (F) and from the effets ofparasites, RP. When some insetiides are applied against some forest pests, partiularly immature stages of the sprue budworms ontaining developing parasites, differential mortality ours among parasitized and nonparasitized insets (Eaton and others 1949; MaDonald 1959; Carolin and Coulter 1971; Williams and others 1969, 1979). The sur- 4

.. <- z 100 K and SC E(PP + PN) = LN LPPP RP=- SC " Co -" uo < a 400 Host insets BOO Figure 3-Number of attaks per parasite, NA/P as host~parasite ratio varies. NA, ~ P,K[1 - exp( -apn,p,' - bp)] vival rate of the relatively inative, moribund parasitized larvae is higher beause they are less exposed than the nonparasitized insets to other mortality fators, suh as the insetiide spray droplets. This interpretation is partiularly relevant for 5th and 6th instar western sprue budworm larvae parasitized by Apanteles fumiferanae Vierek and Glypta fumiferanae Vierek (Williams and others 1969, 1979). These parasites attak the 1st and 2d instars of the budworm, and exept for some early emergene of A. fumlferanae from the 4th instar, their progeny emerge from 5th and 6th instars. A 5th- to 6thinstar budworm ontaining a fully developed parasite about to emerge is usually inative and moribund. These host larvaeare probably not as muh exposed to insetiide droplets and residues as normal, highly mobile, atively feeding 5th to 6th instars. We inluded this phenomenon in our model by making the insetiide more effetive, by fator E, against nonparasitized than parasitized insets (fig. 4). The following relationsthen hold: f then pp = proportion of insets parasitized before spraying PN = proportion not parasitized before spraying RP = proportion parasitized after spraying SC = survival rate oftotal inset population from spraying LP = survival rate of parasitized insets from spraying LN :::: survival rate of nonparasitized insets from spraying E = ratio of LP to LN LP - (E LN) = 0 (LP PP) + (LN PN) = SC Solving for LP, LN, and RP yields LN RP SC + (E - LP = ELN EPP + (E - )PP )PP The relation between RP and PP for various values of E is shown infigure 4A. Analyses ofdata from Williams and others (1979) support our ontention that E is dependent on SC. f this relation is valid, E is ertainly dependent on the timing, method and quality of insetiide appliation, the type and physial properties of the insetiide, and the speifi host-pest-parasite system under onsideration. We hose the relation E = e"s (fig. 48) beause it is based on observed fat (Williams and others 1979) and logial reasoning. Experiments to test this hypothetial relation are partiularly needed beause the phenomenon has a profound effet on the results of simulation of insetiide appliations in an integrated ontrol program. 7. Our model omponent for hanges in parasite populations subjeted to insetiide treatments while in the host budworms reflets the differential survival of parasitized budworms over nonparasitized budworms, as well as other fators previously desribed. in whih CpN,SC RP CpN,SC(1 C p == parasite mortality in adult stage, and pp = NA[ N, EPP ) + (E - )pp 8: An element in the system to be simulated is the degree of damage to the resoure. We assume that eah year the pest population produes some damage to the resouredamage that will our either in the year of attak, or in some future year-for example, growth redution in a perennial rop; or proportional mortality in an annual rop_ Several ases are disussed below. 9. The following relations were used to derive the ost funtion: First, a relation usually exists between the dos- 5

" ~ o ""0!::! _ -= 0 'Vi ell o U C Ui 0..E: 0- ='" _ Ol ~.. 40,..!: _ 0 o " :: :;- ent. For the pnrposes of this study we will exlude any environmental or soial ost of using insetiides. The funtion for ost was obtained as follows: in whih ( - SC) = e - "NS a ::: onstant whih establishes proportionality bet ween units-that is, numbers or perent of in sets killed and pounds of insetiide applied NS = amount of insetiide. Solving the above for NS, we obtain n SC NS =-- - a, 40 80 Host insets parasitized before spraying, PP (perent) or solving for mortality ( - NS 1- SC =- a, sq, we obtain ""0 N - o "o 0. ~w ~i ""0 0. " N_ ::: 0 ';;;;.:: o > ; 0. o,. - o 0. ~ '" - For applying insetiide, as in aerial spraying, the osts inurred are fixed osts (FX) plus a variable amount proportional to the amount of insetiide applied (inluding appliation ost, ost of insetiide and so forth). Thus in whih C = 4000!, \'\ COST, = FX + C,( : ~~) variable ost per unit of insetiide. oo!-----''-----;4';;o,-------'-------;8~o,------' Spray survival rate, SC (perent) Figure 4-{A) Relationship between RP and PP as fator E varies. E is the ratio of the survival rate of the parasitized insets from spraying to that of the nonparasitized insets from spraying. (B) Relationship between E and Be for various values of Be' a onstant representing rates of inrease (E = eaa se). z \.rlimits of osillation \............,..-_\~ age of any insetiide and the proportional mortality seured. Conventionally, a probit mortality, logarithmi dosage transformation produes an approximately linear relationship (Goldstein 1964, Finney 1971). We assumed a simpler relationship, that of an asymptoti exponential. The result assumes a greater effetiveness for insetiides at low dosages than is ordinarily obtained, and thus, a lower ost for any speified level of ontrol below 50 per- Os illat in g----....--stabe----" o ~2;-1-----:2':6----;3':1----:3:':6----4':1,------;-f Parasite searh rate, a p (perent) Figure 5-Result of varying parasite effetiveness onstant ap after 200 generations. 6

SMULATONS To demonstrate the appliability of system simulation in integrated pest management in forestry, we onduted simulation runs using data drawn from the literature and analyti proedures developed from our study of the problem. The results of these simulations serve to illustrate ertain basi points:. ntelligent multiple-use forest resoure management (with respet to pest ontrol) requires the development and early appliation of analyti methodology suh as that represented by the simulations. 2. Forest inset population biologists must provide information in the form required by the analyti methodology referred to in, above. 3. The nature of the pest-forest interation, and the estimated value of the damage aused to speifi forest produts by different population levels of the pest inset, must be known if the simulation is to be useful. The values used in the experimental simulations were obtained from Miller (1959): SO (generation survival from fators other than insetiides) = 0.4 C r (upper limit of reprodutive rate) = 0.100 af (rate that F diminishes exponentially) = 0.001 K (maximum attaks per parasite) = 0.70 b p (onstant for parasite effetiveness) = 1.8 C p (added mortality fator for parasite after emergene) = 0.1 FX (fixed ost of insetiide) = 0.50 C (variable ost per unit of insetiide) = 0.50 a (onstant for proportionality between units of insets killed and amounts of insetiide applied) = 0.001 Variation in Parasite Searh Rate (a p ) The model produes both stable and osillating population densities after 200 generations, depending upon the value of a, the onstant representing the parasite's p searhing effiieny. Figure 5 depits these results. n general, as a inreases, the system beomes more stable, p and the average or steady density dereases with inreased parasite attak effetiveness. These results demonstrate that pest management an be obtained by improving parasite effetiveness, either by inreasing the vulnerability of the host inset or the searhing effetiveness of the parasite, or by finding new parasites with more effetive searhing abilities. Studies are needed, however, to test the feasibility of suh efforts. The osts and benefits of the studies themselves must be investigated, with referene to their net effets on the host-parasite system. The auray of,the model must also be tested, by examination of the effets of varying its parameters. Subsequently, additional biologial studies are needed to estimate the osts of modifying promising parameters. Variation in nsetiide Survival Rate (SC) The results of modifying both SC and a p are shown.in figure 6A. First, the interept values on the y axis represent the values plotted infigure 5. Note that there is a separate urve for eah value of "p, relating pest density to SC. SC dereases from left to right-that is, mortality due to insetiide inreases from left to right. Two types of ases are possible. The first type inludes those in whih a p has values whih permit the system to osillate. n these ases, a two-branhed urve shows the limits of the osillation. The seond type inludes those in whih the values of a p produe a stable system. n the osillating system, as insetiide is applied at inreasing levels, the amplitude of the osillations hanges. At the lower insetiide levels, amplitude inreases; at higher levels, it dereases until a level is reahed where the system beomes stable. The level at whih the osillation attains maximum amplitude inreases with inreasing parasite effetiveness. The level whih produes a steady system dereases with inreasing parasite effetiveness. Similarly, in steady density systems, as insetiide levels inrease, the steady density inreases, then it dereases. The level whih produes the maximum density inreases as parasite effetiveness inreases. These results illustrate the need for a relevant framework for the development of methods for ontrolling inset population and minimizing forest pest impat. From the ases desribed by these simulations, it is evident that sine damage is related to inset density, it may be more profitable to leave the system alone than to attempt ontrol with low insetiide dosage rates. A partiularly important result is shown in figure 6B. The degree of steady density redution obtained by inreasing levels of ontrol is plotted against the mortality rate. Clearly, the level of population suppression obtained is not proportional to the amount of ontrol applied in the generation. Only when very high ontrol rates or insetiide dosages are applied is muh effet produed in the population. t appears that very high investments are worthwhile but moderate investments produe little effet. A final important result from these simulations is the indiation that parasites beome extint when suffiient insetiide is applied (SC = 0.13) to ause 87-perent mortality. At this point eah host-parasite system behaves in the same way in response to the insetiide dosage, and all urves in figure 6A oalese. n a real system, the presene of alternate hosts and invasion of parasites from surrounding untreated areas may maintain or reestablish the parasite population. 7

6000 A OPTMZNG PEST MANAGEMENT Z.~ ~ ~ ~ 0. 4000 2000 80.~ o ~ 40 :;; o.0026.0021.0031.0041 1L,,~-L_-,J,-,Jo--,J-,J-"60~---,-~,,,=o----,--~,,,o--L---'oo B Spray survival role, SC (peren') Diret proportionality J 6 i.,. i~ 1,1.,. 1.1 '1' 1./ ',' i!;,! ', iii ;' ii./. i,. /../.0031./,/ i... /....,.' / :~:~:::::=::::::~::':';;:;~'~':::::7""';'::r"'"'''''''''' -.-.-.-.- _ -:0036...,. ---l---.j,10- --::.O:.:O::..:4:..:1-.J L;_ -----;l,;-----.j -20 ~." o 40 80 Control applied (perent) Figure 6-{A) Relationships between pest density and SC for vari w QUS values of a p ' (8) Relationship between perent ontrol applied with insetiides and atual redution in population level for various values of a p after 200 generations. The preeding disussion suggests that the behavior of the pest-parasite population system under insetiidal ontrol is omplex; suppression of the pest is not proportional to insetiide dosage rate.. The most eonomial pest population level ahievable through ontrol an only be determined through ost-benefit analyses of the impat of pest inset populations on forest produt values. First onsider a simple example of the relation between damage value and pest density. We know that without insetiidal ontrol our pest population has a density that depends on the parameters of the model, and that if a p = 0.0031, the steady density is 2150. n figure 7A three similar ases are depited in whih there are simple linear relationships between the value of damage to different forest produt values and pest density. Consider ase A with pest density 2150 and value of damage about 350 units. f pest density is redued to 0, all of this value will be gained. A linearly proportional gain ours at intermediate pest densities. n ase B, the maximum gain is greater-about 50 units, and in ase C, a very high gain is possible. nfigure 78 these three gain urves are desribed as a funtion of pest density. The ost of obtaining this pest density, alulated as explained above, is also shown. Clearly, in ase A, any insetiidal ontrol operation will yield a net loss-the gain funtion is always less than the ost funtion. n ase B, pest ontrol does not beome profitable until pest density is redued to about 700; then there is a region of inreasing net gain to a maximum, followed by a region of dereasing net gain to a point beyond whih ontrol rates that result in very low densities are again unprofitable. n ase C, in whih there is a very rapid inrease in gain as pest density delines, it will be maximally profitable to pratie the highest possible rate of ontrol beause the point at whih the gain funtion urve exeeds the ost funtion urve the most (point of maximum net gain) is in the viinity of the interept. Otherwise, some lower rate of population suppression is maximally profitable. This simplified example demonstrates several fundamental points:. The- ost and gain funtions are neessary to determine optimal ontrol rates. 2. The ost funtion annot be derived without a thorough knowledge of the onsequenes of attempting population ontrol. Results may not be those expeted. n more realisti ases-where there are ompound interations among the mortality soures, or where integrated ontrol through manipulation of several fators of mortalities or ontrol methods is to be attempted-it will be neessary to observe and analyze system response in far greater detail than an be shown here. 8

3. The best ontrol deision is based on the form of both the gain funtion and the ost funtion. The gain funtion depends on the relation between damage value and pest density in this ase. This relationship, of ourse, is an important problem in inset impat studies. n this example we are onerned with the relation between inset densities and damage values. More generally, we must be onerned about relationships whih depend on density, time of attak relative to the development of values in the tree speies, physial loation of attaks in timber, the interation between pest ontrol ativities and the yield of other forest resoure values, and so forth. Ultimately, we must be able to ompute real ost and real gain in the system. Consider an additional fator whih ompliates the simple linear density example. n figure 8A a threshold effet has been added to the previous linear ase. Two different threshold densities, below whih no damage ours, are introdued. The onsequenes (fig. 88) are that the point of maximum net gain is always less than omplete ontrol. n additional simulation runs, we added more omplexity to our examples by showing a urvilinear relationship between the amount or value of damage and pest density in order to represent a situation where low inset populations or densities provide some benefit in forest value prodution. nfigure 8C, the lower urve represents a situation in whih there is atually some gross gain (a negative damage) from a low pest density. Clearly (fig. 8D), high ontrol rates would not be seleted. On the other hand, the upper urve infigure 8C would indiate a very"high ontrol rate. n summary, we have learly shown the kinds of data required for determining inset ontrol strategies in timber management. The primary requirements are o A thorough knowledge of the pest system, inluding effetiveness of natural ontrol agents, and the onsequenes of introduing various degrees or rates of ontrol into that system. o The effetiveness and osts of alternative methods of ontrol required to obtain various degrees of population redution. o An understanding of the relationship between pest population levels and units of damage. o Knowledge of the value of the resoure and units of damage. o Ability to develop the ost and gain funtions neessary to determine optimal ontrol rates. 600 A 600 Cost funtion Gain funtion.~ 400,, 400 ~ 0 '" 0,'" E 0 0.0 u " 200 200. 0p = 0.0031 1000 2000 2150 Pest density / N Figure 7-{A) Unear relation between the amount or value of dam~ age and pest density for three ases of the parasite-hast-pest system, with a p = 0.0031. The steady density of the pest population is 2150. (B) Relationships between the gain urves of three ases or 0;;-----'------;;;S;---..L----;;;~"'---' o 1000 2000 Pest density, N situations and pest density for the parasite-pest system: a =.0031, and ost urve for the amount of ontrol required to redue the pest density from 2150 to O. 9

700 A B Cost funtion _Gain funtion 600, \ \\ 500, 0> o E 0300 C :> 400 '0 0> ;;. o U \ \ \. A "...... 200-100 o o!;----;:5~0~0----''--------;,-;:50!0;:---l--;:'-;:5:-:00 Pest density, N 0~0---.L--';-;0!:;0-;:0-----l---:'-;:0::!0-;:0-:'!!':"50:;-.J Pest density, N 600 - D 600 H...--_.. \ Cosl funtion _ Gain funtion, 0> o E o :;; ::J 400 '.0> ;;.o u '00 o ~--L-~o_--L.-:::~~C-..-l o 1000 2000 Pest density, N Figure 8-(A) Relationships between the amount or value of dam~ age for the parasjte~pest system (a p =.0031) where no damage ours until the pest population density reahes 500 (ases A and B) and 1000 (ase C), The steady density for the pest population is 2150. (B) Relationship between the gain funtions of ases A and B with a pest density threshold of 500 and ase C with a pest density threshold of 1000, and ost U/vas for the amount of ontrol required to redue pest density of the parasite-pest system (a p :;;;;;,0031) from 2150 to 0, (e) Curvilinear relationship between the amount or value of the damage and pest density for the parasitepest system: 8 p =:.0031. The steady density of the pest population is 2150. Situation A represents small gains (negative damage) at pest densities from 0 to 800. (D) Relationship between the gain funtions of ases A and S, pest density for the parasite-pest system: a p :;:;;:.0031, and ost urve for the amount of ontrol required to redue the pest density from 2150 to O. 10

Perhaps the most important points that we have demonstrated are the analytial methodology neessary to determine the relationship between ertain kinds of information required in deisionmaking for pest ontrol, and the usefulness of omputer simulation in experimenting with mathematial representatives of real world systems to predit the onsequenes of various management deisions. REFERENCES Berryman, A. A.; Pienaar, L. V. Simulation: a powerful method of investigating the dynamis and management of inset populations. Environ. Entomal. 3(2): 199-207; 1974 April. Campbell, Robert W. Developing a pest population management system. Proeedings of the Tall Timbers onferene on eologial animal ontrol by habitat management; 1971 February 25-27; Tallahassee, FL. Tallahassee, FL: Tall Timbers Res. Stn; 1972; 9-20. Campbell, Robert W. The oneptual organization of researh and development neessary for future pest management. n: Stark, R. W.; Gittens, A. R., eds. Pest management for the 21st entury. Nat. Res. Series 2. Mosow, D: daho Res. Found., n.; 1973: 23-38. CaroHn, V. M.; Coulter, W. K. Trends of western budworm and assoiated insets in Paifi Northwest forests sprayed with DDT. J. Eon. Entomol. 64(1):291-297; 1971 February. Eaton, C. B.; Beal, J. A.; Furniss, R. L.; Speers, C. F. Airplane and heliopter spraying with DDT for sprue budworm ontrol. J. For. 47(10):823-827; 1949 Otober. Finney, D. J. Probit analysis. 3d ed. London: Cambridge University Press; 1971. 333 p. Geier, P. W.; Clark, L. R. An eologial approah to pest ontrol. Proeedings of the 8th tehnial meeting of the nternational Union for Conservation of Nature and Natural Resoures, 1961; Warsaw, Poland. 1961; 10-18. Goldstein, Avram. Biostatistis. An introdutory text. New York: Mamillan Publishing Co., n.; 1964. 272 p. Holling, C. S. An experimental omponent analysis of population proesses. Memoirs Entomol. So. Can. 32:22-32; 1963. Holling, C. S. The analysis of omplex population proess. Can. Entarnal. 96(1-2):335-347; 1964 January-February. Holling, C. S. The funtional response of invertebrate predators to prey density. Memoirs Entomol. So. Can. 48:3-86; 1966. Kilgore, W. V.; Doutt, R. L. Pest ontrol, biologial, physial and seletedhemialmethods. New York: AademiPress; 1967.447p. MaDonald, D. R. Biologial assessment of aerial forest spraying against sprue budworm in New Brunswik : Effets on two overwinteringparasites. Can. Entomol. 91(6):330-336; 1959June. Miller, C. A. The interation of the sprue budworm, CllOristoneura jumiferana (Clem.), and the parasiteapantelesjum,iferanae Vier. Can. EntomoL 91(8):457-477; 1959 August. Mott, D. Gordon. Future pest management systems. n: Stark, R. W.; Gittens, A. R., eds. Pest management for the 21st entury~ Nat. Res. Series 2. Mosow, 10: daho Res. Found., n., 1973; 73-92. Pikett, A. D.; MaPhee, A. W. Twenty years experiene with integrated ontrol programs in Nova Sotia apple orhards. Proeedings of the 12th nternational Congress on Entomology. London; 1971.597p. Van den Bosh, R. Pestiides: presribing for the eosystem. Environment 12(3):20-25; 1970 April. Vinent, Thomas L. Pest management programs via optimal ontrol theory. Biometris 31:( 1)1-10; 1975 Marh. Waters, William E. Evaluation of inset impats on forest produtiv~ ity and values. Proeedings of the XV UFRO World Congress, Group 6; 1976 June 24; Oslo, Norway. Mosow, D: University of daho; 1976; 15-18. Waters, William E.; Ewing, Bland. Development and role of predi~ tive modeling in pest management systems-insets. Tummala, Ramamohan L.; Haynes, Dean L.; Croft, Brian A., eds. USAUSSR Symposium on long-term and short-term predition models of insets, phytopathogens, and weed populations as they relate to rop loss; 1974 July 16-18. East Lansing, M: Mihigan State Univ.; 1976; 19-27. Waters, William E.; Stark, Ronald W. Forest pest management: on~ ept and reality. Ann. Rev. Entomol. 25:479 509; 1980. Walt, K. E. F. A mathematial model for the effet of densities of attaked and attaking speies on the number attaked. Can. En~ tomol. 91(3):129-144; 1959 Marh. Wau, K. E. F. Mathematial models for use in inset pest ontrol. Can. Entomol. Supp!. 19; 1961. 62 p. Watt, Kenneth E. F. Computers and the evaluations of resoure management strategies. Amer. Si. 52(4):408-418; 1964 Deember. Watt, Kenneth E. F. Eology and resoure management. New York: MGraw Hill Book Co.; 1968. 450 p. Williams, Carroll B., Jr.; Walton, Gerald S.; Tiernan, Charles F. Zetran and naled affet inidene of parasitism of the budworm Choristoneura oidenta/is in Montana. J. Eon. Entomol. 62(2):310-312; 1969 April. Williams, Carroll B., Jr.; Shea, Patrik J.; MGregor, Mark D. Effets of aerially applied mexaarbate on western sprue budworm lar~ vae and their parasites in Montana. Res. Paper PSW-144. Ber keley, CA: Paifi Southwest Forest and Range Experiment Station, Forest Servie, U.S. Department of Agriulture; 1979. 14 p. 11

r-----------------------, Williams, Carroll B. Jr.; Shea, Patrik J. Computer simulation for integrated pest man~ agement of sprue budworms. Res. Paper PSW 159. Berkeley, CA: Paifi Southwest Forest and Range Experiment Station, Forest Servie, U.S. Department of Agriulture; 1982. p. Some field studies of the effets of various insetiides on the sprue budworm (Choristoneura sp.) and their parasites have shown severe suppression of host (budworm) populations and inreased parasitism after treatment. Computer simulation using hypothetial models of sprue budworm-parasite systems based on these field data revealed that (1) effetive para sites produe greater stability in budworm populations than ineffetive ones and are more resistant to hanges indued by insetiides; and (2) the level of budworm population suppression in most budworm parasite systems is not proportio~al to the amount of insetiide applied. Only high insetiide dosages produe any effet on the budworm population. Cost-benefit analyses showed that very high investments are worthwhile, but moderate investments produe little effet. The study demonstrated that the omputer simulation pmess helps to define kinds of information needed for understanding the budworm-parasite system, and an predit system behavior under varying onditions. Retrieval Terms: sprue budworms, insetiides, parasites, integrated pest management - - - -- ----'