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Simulations on the role of the egg parasite, Ooencyrtus kuvanae (Howard), in the population dynamics of the gypsy moth
Ecological Modelling, 18 (1983) 253-268 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands
253
SIMULATIONS ON THE ROLE OF THE EGG PARASITE, OOENCYRTUS KUVANAE (HOWARD), IN THE POPULATION DYNAMICS OF THE GYPSY MOTH
M.W. BROWN, F.M. WILLIAMS * and E. ALAN CAMERON
Department of Entomology, The Pennsylvania State University, University' Park, PA 16802 (U.S.A.) • Biology Department, The Pennsylvania State University, Universi O, Park, PA 16802 (U.S.A.) (Accepted for publication 24 March 1982)
ABSTRACT Brown, M.W., Williams, F.M. and Cameron, E.A., 1983. Simulations on the role of the egg parasite, Ooencyrtus kuvanae (Howard), in the population dynamics of the gypsy moth. Ecol. Modelling, 18: 253-268. Computer simulations were run to examine the effects of Ooencyrtus kuvanae (Howard) parasitism on gypsy moth populations. Two difference equation models were used, one, a simple theoretical model containing only a few important components, the other, a more comprehensive model with component functions based on field data. The simulations of the first model showed that O. kuvanae cannot control gypsy moth populations by itself. Egg parasitism was most important during the outbreak and collapse phase of the gypsy moth population cycle, and was of little importance in the endemic phase. The endemic phase was, however, lower and lasted longer with O. kuvanae parasitism than without. Simulations with the second model generally supported these conclusions. The second set of simulations also demonstrated that due to the non-linearity of the density dependence of O. kuvanae parasitism, the gypsy moth population could be forced into a chaotic regime (unstable, aperiodic population behavior). The variation in parasitism rate from the simulations was compared with that of field populations and found to be essentially the same, indicating that the simulation models are realistic.
INTRODUCTION T h e g y p s y m o t h , L y m a n t r i a dispar (L.) ( L e p i d o p t e r a : L y m a n t r i i d a e ) , is a serious pest of h a r d w o o d forests t h r o u g h o u t m u c h of the world. Its accidental e s t a b l i s h m e n t in N o r t h A m e r i c a in 1869 went virtually u n n o t i c e d until a b o u t 20 years later, when, in 1888, extensive d e f o l i a t i o n o c c u r r e d in M e d f o r d , M a s s a c h u s e t t s ( F o r b u s h a n d Fernald, 1896). D e s p i t e r e p e a t e d a t t e m p t s to e r a d i c a t e the g y p s y m o t h , its r a n g e in N o r t h A m e r i c a has 0304-3800/83/$03.00
© 1983 Elsevier Science Publishers B.V.
254 expanded as far as Virginia to the south and Ontario, Canada, to the north, with isolated infestations established in Michigan, Wisconsin, California, the state of Washington, and other locations in Canada and the United States. The severity of defoliation by this pest continues to increase; in 1980, over 2 million ha (5 million acres) of forest land was defoliated in the United States, and in 1981 over 5.2 million ha (almost 12.9 million acres) (personal communication, Robert Wolfe, USDA-Forest Service, Broomall, PA 19008). Early in the twentieth century, a large scale biological control effort was initiated against the gypsy moth and the browntail moth (Euproctis chrysorrhoea (L.), Lepidoptera: Lymantriidae), which was also introduced into New England at about the same time (Burgess and Crossman, 1929). Through this program, which is being continued to the present day on a reduced scale, over 40 species of parasites have been introduced, 10 of which have become established and are contributing to the control of the gypsy moth (Hoy, 1976). One of these parasites, Ooencyrtus kuvanae (Howard) (Hymenoptera: Encyrtidae), an egg parasite introduced from Japan, has become consistently one of the most abundant parasites of the gypsy moth in this country. No single natural enemy, or, for that matter, combination of natural enemies, has controlled gypsy moth populations at a subeconomic level. O. kuvanae removes a large portion of gypsy moth eggs from the population before there is any defoliation in the current generation. Because of its success in this country, it has also been introduced into North Africa and Europe to complement the native natural enemy complex. GYPSY MOTH--O. KUVANAE SYSTEM O. kuvanae is very prolific, with an average fecundity of 105 eggs per female and a generation time of 3-4 weeks (Crossman, 1925) under ideal conditions. There are 2-5 generations in late summer and fall, and another 1-2 in the spring, depending on the climate of the area (Dowden, 1961; Prota, 1966; Hitchcock, 1972). These attributes permit a rapid numerical response to changes in gypsy moth densities. Parasitism by O. kuvanae, however, is limited by the structure of the gypsy moth egg mass, which is composed of an average of 400-500 eggs as well as hair from the abdomen of the female (Forbush and Fernald, 1896). O. kuvanae, a small parasite, cannot penetrate deeply into the host egg mass, and is only able to parasitize the outer 2-3 layers of eggs (H6rard, 1978). In the larger gypsy moth egg masses, a lower proportion of eggs is in the outer layers; therefore percentage parasitism is low (Crossman, 1925; Tadi6, 1959; Dowden, 1961; Doane, 1968; Weseloh, 1972; H6rard, 1978; Brown and Cameron, 1979). This dependence of parasitism rate on egg mass size is very important in the interaction between populations of O. kuvanae and the gypsy moth.
255 The size of the gypsy moth egg mass, both in number of eggs and physical dimensions, is largely determined by the gypsy moth larval density in the preceding generation: high density gypsy moth populations produce small egg masses, low density populations produce large egg masses (Campbell, 1978). Combining the relationships between parasitism and egg mass size, and egg mass size and gypsy moth density, gives a strong density dependence of O. kuvanae parasitism (see Brown and Cameron, 1979). The restraints on O. kuvanae parasitism imposed by the egg mass structure severely limit the effectiveness of this parasite in controlling gypsy moth populations. This has led Bess (1961), Campbell (1967), Marcu and Tudor (1978) and others to conclude that O. kuvanae is not an important factor in gypsy moth population dynamics. However, parasitism by O. kuvanae does average in the 20-40% range, with some reports being as high as 80% in Sardinia (Prota, 1966) and Pennsylvania (Brown and Cameron, 1979). Maksimovic et al. (1972) claimed that the combined action of the two egg parasites, O. kuvanae and Anastatus disparis Ruschka (Hymenoptera: Eupelmidae) played an important regulatory role in gypsy moth populations in Eastern Europe; Crossman (1925) stated that O. kuvanae is important in Japan. Krnjaic (1967) agreed that the egg parasites can play an important role, but their effectiveness is dependent upon other factors affecting the gypsy moth population. This study was undertaken to evaluate the capabilities of O. kuvanae, and to determine how it interacts with gypsy moth populations in North America. MODEL FORMULATIONS A simple difference equation model was used to examine the effect of O. kuvanae on gypsy moth population dynamics. A flow diagram for this equation and its various components is given in Fig. 1. All simulations were done with the assumption that food was not limiting for the gypsy moth and that environmental factors remained at a constant, optimal level. The first simulation run included only a density dependent reproductive rate (from Campbell, 1978, fig. 1, p. 444) for gypsy moths, and parasitism by 0. kuvanae (from Brown and Cameron, 1979, fig. 1, p. 79). These two relationships produce a strong, non-linear density dependence (Fig. 2). Parasitism was allowed to vary from 0 to 99%. Simulations were run with additional factors in the model to mimic more closely actual gypsy moth population behavior. These factors were a nuclear polyhedrosis virus (NPV), vertebrate predation, and a density dependent mortality factor. The NPV component was set to trigger a population crash at ca. 107 gypsy moth eggs per ha, a figure based on data presented by Campbell (1967). Once the NPV epizootic threshold (inoculum index = 0.97) was reached, 99.999% mortality
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Fig. 1. Flow diagram of the simple gypsy moth population model, with all components.
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occurred. The year after an epizootic, there was still 99% mortality from the NPV as a carry-over effect. Vertebrate predation was formulated as Type I functional response, Type II functional response, Type III functional response, a combined numerical and functional response, and how it acted based on actual data from Campbell (1969). An enzyme kinetics formulation of the density dependent mortality factor was used, with half saturation constants of 10, 100, and 1,000 gypsy moth eggs per ha. Each of these components was put into the model singly and in combination with one or more other factors. See Table I for the mathematical formulations for each mortality factor used in the model. A comprehensive gypsy moth population model (Picardi, 1973) was used to examine the effects of O. kuvanae in a more realistic system. A flow diagram of the Picardi model, including modifications, is presented in Fig. 3. The model was composed of a set of difference equations. Mortality factors, included as table functions, were: parasitism in the egg, larval, and pupal stages; late larval and pupal predation, by vertebrates and invertebrates respectively; NPV; sex ratio; and larval dispersal. Also included in the model was a forest sub-model that interacted with the gypsy moth model.
TABLE I Formulations of gypsy moth mortality factors used in the simple difference equation model Mortality factor Virus inoculum index Predation: Type I functional response Type II functional response Type lII functional response Numerical response
Formulation * loglo(X) log l0 ( x ) + 370,650 y ~ 25,000 y > 25,000 (100)(log,0 ( Y ) ) 6178 + loglo ( y )
(100)(log,0(y))2 (6178) 2 + (loglo ( y ))2 z~<25 z>25
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125 (2.471)(500)(z)
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k = 10, 100, 1000 * Constants used were selected arbitrarily to mimic most closely the real situation; x = gypsy moth eggs/ha, y = gypsy moth p u p a e / h a , z = number of gypsy moth pupae eaten per predator in the previous generation.
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This sub-model acted as a negative feedback on gypsy moth population growth through defoliation. The Picardi model was then modified to incorporate more recent data and to include several mortality factors not originally included, namely, pupal parasitism by Blepharipa pratensis (Meigen) (Diptera: Tachinidae), Parasetigena silvestris (Robineau-Desvoidy) (Diptera: Tachinidae), and Brachymeria intermedia (Nees) (Hymenoptera: Chalcididae); and larval parasitism by Apanteles melanoscelus (Ratz.) (Hymenoptera: Braconidae). Data for these factors were taken from Ticehurst et al. (1978). The reproductive rate and egg parasitism components were also changed to those used in the previous model. These modifications were made because the revised relationships had a better data base than the original model formulation. An analysis of variance was done on three of the model simulations, namely, the simple model with numerical and functional response formulation of predation, NPV, and a constant 40% mortality; the unmodified Picardi model; and the modified Picardi model. These analyses of variance were compared with analyses of variance on two data sets: one set was from the New Jersey Department of Agriculture permanent plots, 1971-79; the other from U.S. Forest Service permanent plots in Massachusetts, New Jersey, and New York, 1972-75. An arcsine of the square root transformation was used on the percent parasitism data.
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OF TREESl FOREST REGENERATIONI Fig. 3. Flow diagram of the Picardi model of gypsy moth populations, with modifications.
259 RESULTS
The base run simulation is shown in Fig. 4. (In all simulation graphs presented, the dashed line represents the gypsy moth population without O. kuvanae parasitism; the solid line, with parasitism.) O. kuvanae is capable of reducing gypsy moth egg density by two orders of magnitude. O. kuvanae in the model apparently changes the behavior of the gypsy moth population from a stable equilibrium to a two year oscillating cycle, but this is a result of the mathematics of the model and not a component of the interaction between the two species. The result of the simulation with the NPV component included is presented in Fig. 5. Due to the nature of the model, cyclic behavior is produced. Once the density rises above the epizootic threshold, mortality from the NPV reduces the population. No further mortality occurs after two years, and the population rebuilds to begin the next cycle. The addition of O. kuvanae parasitism has a drastic effect on the results of this simulation. The periodicity of gypsy moth population cycles is extended from four years in the absence of egg parasitism to six years with egg parasitism included, and populations fall to a level nearly four orders of magnitude lower when egg parasitism is present. All formulations of predation produced similar results: either the extinc-
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Fig. 4. Base run simulation of gypsy moth population model: with O. kuvanae parasitism ( ), without O. kuvanae parasitism ( . . . . . . ).
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tion of the gypsy moth resulted, or the population grew to a density near the level to which it grew in the base run simulation. The result of the simulation in which numerical and functional responses were combined was almost identical to the base run simulation. The addition of NPV to this simulation produced a result similar to that of the virus alone (Fig. 5) except that the periodicity of the cycle was five years without egg parasitism vs. seven years with egg parasitism. The addition of a constant mortality every generation had an interesting result on the model with the numerical and functional responses of predation and NPV. The periodicity of outbreaks was still five years (without O. kuvanae), but the outbreak lasted four years when egg parasitism was present (Fig. 6). Increasing the constant mortality from 40 to 90% each generation did result in control of gypsy moth density at ca. l0 s eggs per ha. Egg parasitism once again had a very insignificant effect on population behavior under these conditions. The density dependent mortality factor stabilized the gypsy moth population at just over 105 eggs per ha with a light density dependent mortality, at just under 105 eggs per ha with a moderate density dependent mortality, and at just under 10 4 eggs per ha with a heavy density dependent mortality. In all cases parasitism by O. kuvanae had a negligible effect (Brown, 1981). The simulation of the original Picardi model is presented in Fig. 7. The
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Fig. 6. Simulation of gypsy moth population model with combined functional and numerical responses of predation, virus, and a 40% constant mortality: with O. k u v a n a e parasitism ( ), without O. k u v a n a e ( . . . . . . ).
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model has a cycle of seven years with parasitism by O. kuvanae included, but only two years without O. kuvanae parasitism. The average gypsy moth density is nearly two orders of magnitude higher without egg parasitism than with it. A simulation of the modified Picardi model is presented in Fig. 8. The <
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263 T A B L E II
Analysis of variance tables for O. kuvanae parasitism from the New Jersey and U.S. Forest Service permanent plot data. Data transformed with the arcsine of the square root Source
Degrees of freedom
Sums of squares
F
p > F
1.350 0.197 0.293 0.001 1.350 3.191
3.31 2.30 13.65 0.03
0.0002 0.0686 0.0005 0.8709
20.37 1.82 2.55 6.02 70.51 0.01
0.0001 0.0121 0.0813 0.0153 0.0001 0.9367
New Jersey data Plot Year Egg mass size Gypsy Moth density Error Total
19 4 1 1 63 88
Forest Service data Plot Subplot nested within plot Year Height Egg mass size Gypsy Moth density Error Total
5 28 2 1 1 1 153 191
1.196 0.597 0.060 0.071 0.828 0.001 1.796 4.549
overall gypsy moth density is about the same with or without O. kuvanae. Parasitism by O. kuvanae does alter the gypsy moth population behavior: without egg parasitism the gypsy moth population cycles every two years; with egg parasitism no pattern is evident in the gypsy moth population. The result of a 90 year simulation of this model, with egg parasitism included, is presented in Fig. 9. Even over this period of time, the gypsy moth population does not settle into a pattern. The analyses of variance of data from New Jersey and from the Forest Service are presented in Table II; the analyses of variance for each of the three simulation models are included in Table III. In both the simulations and the actual data, egg mass size was very important in explaining variation in parasitism. Gypsy moth density was not a significant factor in explaining variation of parasitism in either the permanent plot data or in the modified Picardi model, but it was significant in the original Picardi and the simple model simulations,
264 TABLE III Analysis of variance of O. kuvanae parasitism data from the computer simulation outputs. Data transformed with the arcsine of the square root Source
Degrees of freedom
Sums of squares
F
p>F
Simple model * Gypsy Moth density Error Total
1 16 17
1.574 2.472 4.046
10.19
0.0057
2501.54 65.37
0.0001 0.0001
138.90 0.11
0.0001 0.7419
Original Picardi model Egg mass size Gypsy Moth density Error Total
1 1 15 17
0.376 0.010 0.002 0.388
Modified Picardi model Egg mass size Gypsy Moth density Error Total
1 1 15 17
0.013 0.001 0.001 0.015
* Included virus, combined numerical and functional responses of predation, and a constant 40% mortality components; the simulation is graphed in Fig. 6.
DISCUSSION
Ooencyrtus kuvanae alone is not able to m a i n t a i n low g y p s y m o t h p o p u lations. This does not m e a n that O. kuvanae does not play an i m p o r t a n t role in the p o p u l a t i o n d y n a m i c s o f the gypsy moth. High density gypsy m o t h p o p u l a t i o n s p r o d u c e small egg masses; therefore, egg parasitism significantly affects the p o p u l a t i o n . If, however, o n e or m o r e factors m a i n t a i n a low g y p s y m o t h density (ca. 10 5 eggs per h a or lower), parasitism b y O. kuvanae has an insignificant effect. N o r t h A m e r i c a n g y p s y m o t h p o p u l a t i o n s typically go t h r o u g h four stages: endemic, building, o u t b r e a k , and collapse ( C a m p b e l l and Sloan, 1978). This t y p e of b e h a v i o r was o b t a i n e d w h e n e v e r the N P V c o m p o n e n t was i n c l u d e d in a n y o f the m o d e l f o r m u l a t i o n s that otherwise resulted in a high gypsy m o t h equilibrium density; in these situations, parasitism b y O. kuvanae significantly affected the simulations. T h e r e are two m a j o r differences in simulations w h e n egg parasitism is present: first, the p e r i o d of o u t b r e a k is
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lengthened; and second, the collapse phase is more severe and the gypsy moth density is several orders of magnitude lower. Therefore, the model suggests that O. kuvanae is important during the outbreak and collapse phases of the gypsy moth population cycle. During the endemic and building phases, O. kuvanae is an insignificant factor. This is supported by the field observation of Bjegovi6 (1974) that O. kuvanae is most numerous during the outbreak and collapse of gypsy moth populations. One apparent adverse effect of O. kuvanae, according to the model, is that it has a tendency to prolong the duration of an outbreak. This was apparent in the simulation with the Type I functional response of predation, and especially with both predation and a constant 40% mortality (Fig. 6). If this were the case in reality, it could devastate the forest. It generally takes three years of heavy defoliation to kill deciduous trees (Knight and Heikkenen, 1980), so the effect of prolonging the outbreak to 3-4 years is obvious. We believe this prolongation of the outbreak phase is largely an artifact of the model, rather than a prediction of the real situation, because of the deterministic nature of the NPV component in the model. However, this may be a real manifestation of the interaction between these two species and deserves consideration in any manipulation of this system. The simulation of the original Picardi model gave similar results to the previous model. More specifically, O. kuvanae in the model both prolonged the time between gypsy moth outbreaks and produced a lower endemic density than when it was not present. This is surprising because the Picardi model is very different from the previous model, being much more comprehensive and including a food limitation component. Picardi also used a linear relationship between egg mass size and egg parasitism, which varied from only 38-55%. Even with these constraints, parasitism by O. kuvanae was important in the model's behavior. The simulations of the modified Picardi model showed no obvious effects of O. kuvanae parasitism on gypsy moth density. Egg parasitism does have a very significant effect on the gypsy moth population behavior: without egg parasitism the gypsy moth population cycles every two years; with egg parasitism there is no pattern to the population fluctuation. Results of the 90 year simulation (Fig. 9) suggest that the population acts in a chaotic manner. In such a regime the behavior of a set of differential equations is dependent upon the initial values used; the population can become cyclic or be completely aperiodic (May, 1975). Hassell et al. (1976) found this situation occurring most commonly in populations with discrete generations, and almost exclusively in laboratory populations. May (1975), though, has shown that chaotic behavior is produced from very simple difference equations with a high growth rate. An interesting aspect of our gypsy moth simulation is that the population fluctuates at a high density, whereas most chaotic
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populations are at very low densities with irregular outbreaks. The inclusion of a strongly non-linear density dependent equation in a deterministic model can produce chaotic behavior (Hassell et al., 1976). This is apparently what happened when we changed the egg parasitism/egg mass size relationship from the linear function Picardi used to the function of Brown and Cameron (1979), see Fig. 2. O. kuvanae may therefore be one of the factors responsible for the unpredictability of gypsy moth populations. The analyses of variance of the simulation data are comparable to those of the field data. A large amount of variability, especially in the Picardi models, was attributable to gypsy moth density a n d / o r egg mass size. This heavy dependence on egg mass size is a result of the dependence of egg parasitism on egg mass size in the models. The greatest variation in parasitism data was in the simple model. In this model, gypsy moth density varied over a range of nine orders of magnitude, resulting in parasitism varying from 0-99%. This is a much greater range than in the Picardi models. Once parasitism reached 99%, further increases in gypsy moth density had no impact on parasitism, thus explaining the comparatively low F value in the analysis of variance table. Overall, the analyses of variance suggest that the same relationships are present in the model as occur in the field data, but these relationships are not as rigid in the field as the models indicate, because of natural variation in the field. ACKNOWLEDGMENTS
We thank Drs. K.C. Kim and Robin Taylor, Department of Entomology, The Pennsylvania State University, and T. Evan Nebeker, Department of Entomology, Mississippi State University, for their comments and criticisms of the manuscript; Dr. Anthony C. Picardi, Development Analysis Associates Inc., Cambridge, Mass., for the unrestricted use of his model; and Mr. William Metterhouse, New Jersey Department of Agriculture, Division of Plant Industry, Trenton, New Jersey and Dr. Michael L. McManus, U.S. Department of Agriculture, Forest Service, Forest Insect and Disease Laboratory, Hamden, Connecticut, for the use of their data. Authorized as Paper No. 6385 in the Journal Series of The Pennsylvania Agricultural Experiment Station, this work was conducted under Experiment Station Project No. 2044, and supported in part by Regional Research Project NE-84 (revised). Based on a portion of a thesis submitted by MWB in partial fulfillment of the requirements of the degree of Master of Science. REFERENCES Bess, H.A., 1961. Population ecology of the gypsy moth Porthetria dispar (L.) (Lepidoptera: Lymantriidae). Conn. Agric. Exp. Stn. Bull. 646, 43 pp.
267 Bjegovi6, P., 1974. Geographical distribution and reduction role of the gypsy moth egg parasites in Yugoslavia. (English Summary). Zast. Bilja, 25: 173-82. Brown, M.W., 1981. The role of Ooencyrtus kuvanae (Howard) (Hymenoptera: Encyrtidae) in the population dynamics of the gypsy moth. M.S. Thesis, The Pennsylvania State University, University Park, x+71 pp. Brown, M.W. and Cameron, E.A., 1979. Effects of disparlure and egg mass size on parasitism by the gypsy moth egg parasite, Ooencyrtus kuwanai. Environ. Entomol., 8: 77-80. Burgess, A.F. and Crossman, S.S., 1929. Imported insect enemies of the gipsy moth and the brown-tail moth. U.S. Dept. Agric. Tech. Bull. 86, 245 pp. Campbell, R.W., 1967. The analysis of numerical change in gypsy moth populations. For. Sci. Monogr., 15: 1-33. Campbell, R.W., 1969. Studies on gypsy moth population dynamics. In: Forest Insect Population Dynamics. Proc. of the Forest Insect Population Dynamics Workshop, 1967. USDA For. Serv. Res. Paper NE-125, pp. 23-27. Campbell, R.W., 1978. Some effects of gypsy moth density on rate of development, pupation time, and fecundity. Ann. Entomol. Soc. Am., 71: 442-48. Campbell, R.W. and Sloan, R.J., 1978. Numerical bimodality among North American gypsy moth populations. Environ. Entomol., 7: 631-36. Crossman, S.S., 1925. Two imported egg parasites of the gypsy moth Anastatus bifasciatus Fonsc. and Schedius kuwanai Howard. J. Agric. Res., 30:643 75. Doane, C.C., 1968. Changes in egg mass density, size and amount of parasitism after chemical treatment of a heavy population of the gypsy moth. J. Econ. Entomol., 61: 1288-91. Dowden, P.B., 1961. The gypsy moth egg parasite, Ooencyrtus kuwanai, in southern Connecticut in 1960. J. Econ. Entomol., 54: 876-78. Forbush, E.H. and Fernald, C.H., 1896. The Gypsy Moth, Porthetria dispar (Linn.). Wright and Potter, Boston, MA, 495 pp. Hassell, M.B., Lawton, J.H. and May, R.M., 1976. Patterns of dynamical behavior in single species populations. J. Anita. Ecol., 45: 471-86. H6rard, F., 1978. Ethology of the adults of Ooencyrtus kuvanae (Howard) (Hymenoptera: Encyrtidae), oophagous parasite of Lymantria dispar (L.) (Lepidoptera: Lymantriidae) in the Mamora Forest (Morocco). (English Transl.) Ann. Zool. Ecol. Anim., 10: 603-12. Hitchcock, S.W., 1972. Generation time of Ooencyrtus kuwanai on gypsy moth eggs in the field. J. Econ. Entomol., 65: 284-85. Hoy, M.A., 1976. Establishment of gypsy moth parasitoids in North America: An evaluation of possible reasons for establishment or non-establishment. In: J.F. Anderson and H.K. Kaya (Editors), Perspectives in Forest Entomology. Academic Press, New York, NY, pp. 215-232. Knight, F.B. and Heikkenen, H.J., 1980. Principles of Forest Entomology, 5th edn. McGraw Hill, New York, NY, 461 pp. Krnjaic, S., 1967. Survey of species and number of gypsy moth egg parasites in some localities of Yugoslavia. (English Transl.) Zast. Bilja, 18: 247-55. Maksimovic, M., Bejegovi~, P. and Vasiljevi6, L., 1972. Feeding and maintaining the density of the gypsy moth's enemies as a method of biological control. Proc. 12th Int. Congr. Entomol., 1968, Nauk., 3: 57. Marcu, O. and Tudor, I., 1978. Insectes parasite b. r61e destructif sur les populations de Lymantria dispar L. dans le p6rim~tre de la R6publique Socialiste Roumane. Zast. Bilja, 29: 111-18. May, R.M., 1975. Biological populations obeying difference equations: stable points, stable cycles, and chaos. J. Theoret. Biol., 51:511-24.
268 Picardi, A.C., 1973. Gypsy moth population simulation: system postulation, validation, analysis. Proc. 1973 Summer Computer Simulation Conf., Montreal, 73 CH0815-1 SMC: 1069-74. Prota, R., 1966. Contributi alia conoscenza dell'entomofauna della Quercio da sughero (Quercus suber L.) V. Osservazioni condotte in Sardegna su Ooencyrtus kuwanai (Howard) (Hymenoptera: Encyrtidae) nuovo per la fauna italiana. Stazione Sperimentale del Sughero, Tempio Pausania, Memoria 17 (English Summary), 26 pp. Tadi6, M.D., 1959. Incidence of gypsy moth egg parasites Anastatus disparis R. and Ooencyrtus kuwanai How. in some localities in Macedonia in 1958/1959. (English Transl.) Zast. Bilja, 10: 27-37. Ticehurst, M., Fusco, R.A., Kling, R.P. and Unger, J., 1978. Observations on parasites of gypsy moth in first cycle infestations in Pennsylvania from 1974-77. Environ. Entomol., 7: 355-58. Weseloh, R.M., 1972. Spatial distribution of the gypsy moth (Lepidoptera: Lymantriidae) and some of its parasitoids within a forest environment. Entomophaga, 17: 339-51.
253
SIMULATIONS ON THE ROLE OF THE EGG PARASITE, OOENCYRTUS KUVANAE (HOWARD), IN THE POPULATION DYNAMICS OF THE GYPSY MOTH
M.W. BROWN, F.M. WILLIAMS * and E. ALAN CAMERON
Department of Entomology, The Pennsylvania State University, University' Park, PA 16802 (U.S.A.) • Biology Department, The Pennsylvania State University, Universi O, Park, PA 16802 (U.S.A.) (Accepted for publication 24 March 1982)
ABSTRACT Brown, M.W., Williams, F.M. and Cameron, E.A., 1983. Simulations on the role of the egg parasite, Ooencyrtus kuvanae (Howard), in the population dynamics of the gypsy moth. Ecol. Modelling, 18: 253-268. Computer simulations were run to examine the effects of Ooencyrtus kuvanae (Howard) parasitism on gypsy moth populations. Two difference equation models were used, one, a simple theoretical model containing only a few important components, the other, a more comprehensive model with component functions based on field data. The simulations of the first model showed that O. kuvanae cannot control gypsy moth populations by itself. Egg parasitism was most important during the outbreak and collapse phase of the gypsy moth population cycle, and was of little importance in the endemic phase. The endemic phase was, however, lower and lasted longer with O. kuvanae parasitism than without. Simulations with the second model generally supported these conclusions. The second set of simulations also demonstrated that due to the non-linearity of the density dependence of O. kuvanae parasitism, the gypsy moth population could be forced into a chaotic regime (unstable, aperiodic population behavior). The variation in parasitism rate from the simulations was compared with that of field populations and found to be essentially the same, indicating that the simulation models are realistic.
INTRODUCTION T h e g y p s y m o t h , L y m a n t r i a dispar (L.) ( L e p i d o p t e r a : L y m a n t r i i d a e ) , is a serious pest of h a r d w o o d forests t h r o u g h o u t m u c h of the world. Its accidental e s t a b l i s h m e n t in N o r t h A m e r i c a in 1869 went virtually u n n o t i c e d until a b o u t 20 years later, when, in 1888, extensive d e f o l i a t i o n o c c u r r e d in M e d f o r d , M a s s a c h u s e t t s ( F o r b u s h a n d Fernald, 1896). D e s p i t e r e p e a t e d a t t e m p t s to e r a d i c a t e the g y p s y m o t h , its r a n g e in N o r t h A m e r i c a has 0304-3800/83/$03.00
© 1983 Elsevier Science Publishers B.V.
254 expanded as far as Virginia to the south and Ontario, Canada, to the north, with isolated infestations established in Michigan, Wisconsin, California, the state of Washington, and other locations in Canada and the United States. The severity of defoliation by this pest continues to increase; in 1980, over 2 million ha (5 million acres) of forest land was defoliated in the United States, and in 1981 over 5.2 million ha (almost 12.9 million acres) (personal communication, Robert Wolfe, USDA-Forest Service, Broomall, PA 19008). Early in the twentieth century, a large scale biological control effort was initiated against the gypsy moth and the browntail moth (Euproctis chrysorrhoea (L.), Lepidoptera: Lymantriidae), which was also introduced into New England at about the same time (Burgess and Crossman, 1929). Through this program, which is being continued to the present day on a reduced scale, over 40 species of parasites have been introduced, 10 of which have become established and are contributing to the control of the gypsy moth (Hoy, 1976). One of these parasites, Ooencyrtus kuvanae (Howard) (Hymenoptera: Encyrtidae), an egg parasite introduced from Japan, has become consistently one of the most abundant parasites of the gypsy moth in this country. No single natural enemy, or, for that matter, combination of natural enemies, has controlled gypsy moth populations at a subeconomic level. O. kuvanae removes a large portion of gypsy moth eggs from the population before there is any defoliation in the current generation. Because of its success in this country, it has also been introduced into North Africa and Europe to complement the native natural enemy complex. GYPSY MOTH--O. KUVANAE SYSTEM O. kuvanae is very prolific, with an average fecundity of 105 eggs per female and a generation time of 3-4 weeks (Crossman, 1925) under ideal conditions. There are 2-5 generations in late summer and fall, and another 1-2 in the spring, depending on the climate of the area (Dowden, 1961; Prota, 1966; Hitchcock, 1972). These attributes permit a rapid numerical response to changes in gypsy moth densities. Parasitism by O. kuvanae, however, is limited by the structure of the gypsy moth egg mass, which is composed of an average of 400-500 eggs as well as hair from the abdomen of the female (Forbush and Fernald, 1896). O. kuvanae, a small parasite, cannot penetrate deeply into the host egg mass, and is only able to parasitize the outer 2-3 layers of eggs (H6rard, 1978). In the larger gypsy moth egg masses, a lower proportion of eggs is in the outer layers; therefore percentage parasitism is low (Crossman, 1925; Tadi6, 1959; Dowden, 1961; Doane, 1968; Weseloh, 1972; H6rard, 1978; Brown and Cameron, 1979). This dependence of parasitism rate on egg mass size is very important in the interaction between populations of O. kuvanae and the gypsy moth.
255 The size of the gypsy moth egg mass, both in number of eggs and physical dimensions, is largely determined by the gypsy moth larval density in the preceding generation: high density gypsy moth populations produce small egg masses, low density populations produce large egg masses (Campbell, 1978). Combining the relationships between parasitism and egg mass size, and egg mass size and gypsy moth density, gives a strong density dependence of O. kuvanae parasitism (see Brown and Cameron, 1979). The restraints on O. kuvanae parasitism imposed by the egg mass structure severely limit the effectiveness of this parasite in controlling gypsy moth populations. This has led Bess (1961), Campbell (1967), Marcu and Tudor (1978) and others to conclude that O. kuvanae is not an important factor in gypsy moth population dynamics. However, parasitism by O. kuvanae does average in the 20-40% range, with some reports being as high as 80% in Sardinia (Prota, 1966) and Pennsylvania (Brown and Cameron, 1979). Maksimovic et al. (1972) claimed that the combined action of the two egg parasites, O. kuvanae and Anastatus disparis Ruschka (Hymenoptera: Eupelmidae) played an important regulatory role in gypsy moth populations in Eastern Europe; Crossman (1925) stated that O. kuvanae is important in Japan. Krnjaic (1967) agreed that the egg parasites can play an important role, but their effectiveness is dependent upon other factors affecting the gypsy moth population. This study was undertaken to evaluate the capabilities of O. kuvanae, and to determine how it interacts with gypsy moth populations in North America. MODEL FORMULATIONS A simple difference equation model was used to examine the effect of O. kuvanae on gypsy moth population dynamics. A flow diagram for this equation and its various components is given in Fig. 1. All simulations were done with the assumption that food was not limiting for the gypsy moth and that environmental factors remained at a constant, optimal level. The first simulation run included only a density dependent reproductive rate (from Campbell, 1978, fig. 1, p. 444) for gypsy moths, and parasitism by 0. kuvanae (from Brown and Cameron, 1979, fig. 1, p. 79). These two relationships produce a strong, non-linear density dependence (Fig. 2). Parasitism was allowed to vary from 0 to 99%. Simulations were run with additional factors in the model to mimic more closely actual gypsy moth population behavior. These factors were a nuclear polyhedrosis virus (NPV), vertebrate predation, and a density dependent mortality factor. The NPV component was set to trigger a population crash at ca. 107 gypsy moth eggs per ha, a figure based on data presented by Campbell (1967). Once the NPV epizootic threshold (inoculum index = 0.97) was reached, 99.999% mortality
256
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Fig. 1. Flow diagram of the simple gypsy moth population model, with all components.
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257
occurred. The year after an epizootic, there was still 99% mortality from the NPV as a carry-over effect. Vertebrate predation was formulated as Type I functional response, Type II functional response, Type III functional response, a combined numerical and functional response, and how it acted based on actual data from Campbell (1969). An enzyme kinetics formulation of the density dependent mortality factor was used, with half saturation constants of 10, 100, and 1,000 gypsy moth eggs per ha. Each of these components was put into the model singly and in combination with one or more other factors. See Table I for the mathematical formulations for each mortality factor used in the model. A comprehensive gypsy moth population model (Picardi, 1973) was used to examine the effects of O. kuvanae in a more realistic system. A flow diagram of the Picardi model, including modifications, is presented in Fig. 3. The model was composed of a set of difference equations. Mortality factors, included as table functions, were: parasitism in the egg, larval, and pupal stages; late larval and pupal predation, by vertebrates and invertebrates respectively; NPV; sex ratio; and larval dispersal. Also included in the model was a forest sub-model that interacted with the gypsy moth model.
TABLE I Formulations of gypsy moth mortality factors used in the simple difference equation model Mortality factor Virus inoculum index Predation: Type I functional response Type II functional response Type lII functional response Numerical response
Formulation * loglo(X) log l0 ( x ) + 370,650 y ~ 25,000 y > 25,000 (100)(log,0 ( Y ) ) 6178 + loglo ( y )
(100)(log,0(y))2 (6178) 2 + (loglo ( y ))2 z~<25 z>25
Density dependent
y-10 25,000
125 (2.471)(500)(z)
(z)+200
loglo(X) loglo(X) + k
k = 10, 100, 1000 * Constants used were selected arbitrarily to mimic most closely the real situation; x = gypsy moth eggs/ha, y = gypsy moth p u p a e / h a , z = number of gypsy moth pupae eaten per predator in the previous generation.
258
This sub-model acted as a negative feedback on gypsy moth population growth through defoliation. The Picardi model was then modified to incorporate more recent data and to include several mortality factors not originally included, namely, pupal parasitism by Blepharipa pratensis (Meigen) (Diptera: Tachinidae), Parasetigena silvestris (Robineau-Desvoidy) (Diptera: Tachinidae), and Brachymeria intermedia (Nees) (Hymenoptera: Chalcididae); and larval parasitism by Apanteles melanoscelus (Ratz.) (Hymenoptera: Braconidae). Data for these factors were taken from Ticehurst et al. (1978). The reproductive rate and egg parasitism components were also changed to those used in the previous model. These modifications were made because the revised relationships had a better data base than the original model formulation. An analysis of variance was done on three of the model simulations, namely, the simple model with numerical and functional response formulation of predation, NPV, and a constant 40% mortality; the unmodified Picardi model; and the modified Picardi model. These analyses of variance were compared with analyses of variance on two data sets: one set was from the New Jersey Department of Agriculture permanent plots, 1971-79; the other from U.S. Forest Service permanent plots in Massachusetts, New Jersey, and New York, 1972-75. An arcsine of the square root transformation was used on the percent parasitism data.
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OF TREESl FOREST REGENERATIONI Fig. 3. Flow diagram of the Picardi model of gypsy moth populations, with modifications.
259 RESULTS
The base run simulation is shown in Fig. 4. (In all simulation graphs presented, the dashed line represents the gypsy moth population without O. kuvanae parasitism; the solid line, with parasitism.) O. kuvanae is capable of reducing gypsy moth egg density by two orders of magnitude. O. kuvanae in the model apparently changes the behavior of the gypsy moth population from a stable equilibrium to a two year oscillating cycle, but this is a result of the mathematics of the model and not a component of the interaction between the two species. The result of the simulation with the NPV component included is presented in Fig. 5. Due to the nature of the model, cyclic behavior is produced. Once the density rises above the epizootic threshold, mortality from the NPV reduces the population. No further mortality occurs after two years, and the population rebuilds to begin the next cycle. The addition of O. kuvanae parasitism has a drastic effect on the results of this simulation. The periodicity of gypsy moth population cycles is extended from four years in the absence of egg parasitism to six years with egg parasitism included, and populations fall to a level nearly four orders of magnitude lower when egg parasitism is present. All formulations of predation produced similar results: either the extinc-
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tion of the gypsy moth resulted, or the population grew to a density near the level to which it grew in the base run simulation. The result of the simulation in which numerical and functional responses were combined was almost identical to the base run simulation. The addition of NPV to this simulation produced a result similar to that of the virus alone (Fig. 5) except that the periodicity of the cycle was five years without egg parasitism vs. seven years with egg parasitism. The addition of a constant mortality every generation had an interesting result on the model with the numerical and functional responses of predation and NPV. The periodicity of outbreaks was still five years (without O. kuvanae), but the outbreak lasted four years when egg parasitism was present (Fig. 6). Increasing the constant mortality from 40 to 90% each generation did result in control of gypsy moth density at ca. l0 s eggs per ha. Egg parasitism once again had a very insignificant effect on population behavior under these conditions. The density dependent mortality factor stabilized the gypsy moth population at just over 105 eggs per ha with a light density dependent mortality, at just under 105 eggs per ha with a moderate density dependent mortality, and at just under 10 4 eggs per ha with a heavy density dependent mortality. In all cases parasitism by O. kuvanae had a negligible effect (Brown, 1981). The simulation of the original Picardi model is presented in Fig. 7. The
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model has a cycle of seven years with parasitism by O. kuvanae included, but only two years without O. kuvanae parasitism. The average gypsy moth density is nearly two orders of magnitude higher without egg parasitism than with it. A simulation of the modified Picardi model is presented in Fig. 8. The <
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263 T A B L E II
Analysis of variance tables for O. kuvanae parasitism from the New Jersey and U.S. Forest Service permanent plot data. Data transformed with the arcsine of the square root Source
Degrees of freedom
Sums of squares
F
p > F
1.350 0.197 0.293 0.001 1.350 3.191
3.31 2.30 13.65 0.03
0.0002 0.0686 0.0005 0.8709
20.37 1.82 2.55 6.02 70.51 0.01
0.0001 0.0121 0.0813 0.0153 0.0001 0.9367
New Jersey data Plot Year Egg mass size Gypsy Moth density Error Total
19 4 1 1 63 88
Forest Service data Plot Subplot nested within plot Year Height Egg mass size Gypsy Moth density Error Total
5 28 2 1 1 1 153 191
1.196 0.597 0.060 0.071 0.828 0.001 1.796 4.549
overall gypsy moth density is about the same with or without O. kuvanae. Parasitism by O. kuvanae does alter the gypsy moth population behavior: without egg parasitism the gypsy moth population cycles every two years; with egg parasitism no pattern is evident in the gypsy moth population. The result of a 90 year simulation of this model, with egg parasitism included, is presented in Fig. 9. Even over this period of time, the gypsy moth population does not settle into a pattern. The analyses of variance of data from New Jersey and from the Forest Service are presented in Table II; the analyses of variance for each of the three simulation models are included in Table III. In both the simulations and the actual data, egg mass size was very important in explaining variation in parasitism. Gypsy moth density was not a significant factor in explaining variation of parasitism in either the permanent plot data or in the modified Picardi model, but it was significant in the original Picardi and the simple model simulations,
264 TABLE III Analysis of variance of O. kuvanae parasitism data from the computer simulation outputs. Data transformed with the arcsine of the square root Source
Degrees of freedom
Sums of squares
F
p>F
Simple model * Gypsy Moth density Error Total
1 16 17
1.574 2.472 4.046
10.19
0.0057
2501.54 65.37
0.0001 0.0001
138.90 0.11
0.0001 0.7419
Original Picardi model Egg mass size Gypsy Moth density Error Total
1 1 15 17
0.376 0.010 0.002 0.388
Modified Picardi model Egg mass size Gypsy Moth density Error Total
1 1 15 17
0.013 0.001 0.001 0.015
* Included virus, combined numerical and functional responses of predation, and a constant 40% mortality components; the simulation is graphed in Fig. 6.
DISCUSSION
Ooencyrtus kuvanae alone is not able to m a i n t a i n low g y p s y m o t h p o p u lations. This does not m e a n that O. kuvanae does not play an i m p o r t a n t role in the p o p u l a t i o n d y n a m i c s o f the gypsy moth. High density gypsy m o t h p o p u l a t i o n s p r o d u c e small egg masses; therefore, egg parasitism significantly affects the p o p u l a t i o n . If, however, o n e or m o r e factors m a i n t a i n a low g y p s y m o t h density (ca. 10 5 eggs per h a or lower), parasitism b y O. kuvanae has an insignificant effect. N o r t h A m e r i c a n g y p s y m o t h p o p u l a t i o n s typically go t h r o u g h four stages: endemic, building, o u t b r e a k , and collapse ( C a m p b e l l and Sloan, 1978). This t y p e of b e h a v i o r was o b t a i n e d w h e n e v e r the N P V c o m p o n e n t was i n c l u d e d in a n y o f the m o d e l f o r m u l a t i o n s that otherwise resulted in a high gypsy m o t h equilibrium density; in these situations, parasitism b y O. kuvanae significantly affected the simulations. T h e r e are two m a j o r differences in simulations w h e n egg parasitism is present: first, the p e r i o d of o u t b r e a k is
265
lengthened; and second, the collapse phase is more severe and the gypsy moth density is several orders of magnitude lower. Therefore, the model suggests that O. kuvanae is important during the outbreak and collapse phases of the gypsy moth population cycle. During the endemic and building phases, O. kuvanae is an insignificant factor. This is supported by the field observation of Bjegovi6 (1974) that O. kuvanae is most numerous during the outbreak and collapse of gypsy moth populations. One apparent adverse effect of O. kuvanae, according to the model, is that it has a tendency to prolong the duration of an outbreak. This was apparent in the simulation with the Type I functional response of predation, and especially with both predation and a constant 40% mortality (Fig. 6). If this were the case in reality, it could devastate the forest. It generally takes three years of heavy defoliation to kill deciduous trees (Knight and Heikkenen, 1980), so the effect of prolonging the outbreak to 3-4 years is obvious. We believe this prolongation of the outbreak phase is largely an artifact of the model, rather than a prediction of the real situation, because of the deterministic nature of the NPV component in the model. However, this may be a real manifestation of the interaction between these two species and deserves consideration in any manipulation of this system. The simulation of the original Picardi model gave similar results to the previous model. More specifically, O. kuvanae in the model both prolonged the time between gypsy moth outbreaks and produced a lower endemic density than when it was not present. This is surprising because the Picardi model is very different from the previous model, being much more comprehensive and including a food limitation component. Picardi also used a linear relationship between egg mass size and egg parasitism, which varied from only 38-55%. Even with these constraints, parasitism by O. kuvanae was important in the model's behavior. The simulations of the modified Picardi model showed no obvious effects of O. kuvanae parasitism on gypsy moth density. Egg parasitism does have a very significant effect on the gypsy moth population behavior: without egg parasitism the gypsy moth population cycles every two years; with egg parasitism there is no pattern to the population fluctuation. Results of the 90 year simulation (Fig. 9) suggest that the population acts in a chaotic manner. In such a regime the behavior of a set of differential equations is dependent upon the initial values used; the population can become cyclic or be completely aperiodic (May, 1975). Hassell et al. (1976) found this situation occurring most commonly in populations with discrete generations, and almost exclusively in laboratory populations. May (1975), though, has shown that chaotic behavior is produced from very simple difference equations with a high growth rate. An interesting aspect of our gypsy moth simulation is that the population fluctuates at a high density, whereas most chaotic
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populations are at very low densities with irregular outbreaks. The inclusion of a strongly non-linear density dependent equation in a deterministic model can produce chaotic behavior (Hassell et al., 1976). This is apparently what happened when we changed the egg parasitism/egg mass size relationship from the linear function Picardi used to the function of Brown and Cameron (1979), see Fig. 2. O. kuvanae may therefore be one of the factors responsible for the unpredictability of gypsy moth populations. The analyses of variance of the simulation data are comparable to those of the field data. A large amount of variability, especially in the Picardi models, was attributable to gypsy moth density a n d / o r egg mass size. This heavy dependence on egg mass size is a result of the dependence of egg parasitism on egg mass size in the models. The greatest variation in parasitism data was in the simple model. In this model, gypsy moth density varied over a range of nine orders of magnitude, resulting in parasitism varying from 0-99%. This is a much greater range than in the Picardi models. Once parasitism reached 99%, further increases in gypsy moth density had no impact on parasitism, thus explaining the comparatively low F value in the analysis of variance table. Overall, the analyses of variance suggest that the same relationships are present in the model as occur in the field data, but these relationships are not as rigid in the field as the models indicate, because of natural variation in the field. ACKNOWLEDGMENTS
We thank Drs. K.C. Kim and Robin Taylor, Department of Entomology, The Pennsylvania State University, and T. Evan Nebeker, Department of Entomology, Mississippi State University, for their comments and criticisms of the manuscript; Dr. Anthony C. Picardi, Development Analysis Associates Inc., Cambridge, Mass., for the unrestricted use of his model; and Mr. William Metterhouse, New Jersey Department of Agriculture, Division of Plant Industry, Trenton, New Jersey and Dr. Michael L. McManus, U.S. Department of Agriculture, Forest Service, Forest Insect and Disease Laboratory, Hamden, Connecticut, for the use of their data. Authorized as Paper No. 6385 in the Journal Series of The Pennsylvania Agricultural Experiment Station, this work was conducted under Experiment Station Project No. 2044, and supported in part by Regional Research Project NE-84 (revised). Based on a portion of a thesis submitted by MWB in partial fulfillment of the requirements of the degree of Master of Science. REFERENCES Bess, H.A., 1961. Population ecology of the gypsy moth Porthetria dispar (L.) (Lepidoptera: Lymantriidae). Conn. Agric. Exp. Stn. Bull. 646, 43 pp.
267 Bjegovi6, P., 1974. Geographical distribution and reduction role of the gypsy moth egg parasites in Yugoslavia. (English Summary). Zast. Bilja, 25: 173-82. Brown, M.W., 1981. The role of Ooencyrtus kuvanae (Howard) (Hymenoptera: Encyrtidae) in the population dynamics of the gypsy moth. M.S. Thesis, The Pennsylvania State University, University Park, x+71 pp. Brown, M.W. and Cameron, E.A., 1979. Effects of disparlure and egg mass size on parasitism by the gypsy moth egg parasite, Ooencyrtus kuwanai. Environ. Entomol., 8: 77-80. Burgess, A.F. and Crossman, S.S., 1929. Imported insect enemies of the gipsy moth and the brown-tail moth. U.S. Dept. Agric. Tech. Bull. 86, 245 pp. Campbell, R.W., 1967. The analysis of numerical change in gypsy moth populations. For. Sci. Monogr., 15: 1-33. Campbell, R.W., 1969. Studies on gypsy moth population dynamics. In: Forest Insect Population Dynamics. Proc. of the Forest Insect Population Dynamics Workshop, 1967. USDA For. Serv. Res. Paper NE-125, pp. 23-27. Campbell, R.W., 1978. Some effects of gypsy moth density on rate of development, pupation time, and fecundity. Ann. Entomol. Soc. Am., 71: 442-48. Campbell, R.W. and Sloan, R.J., 1978. Numerical bimodality among North American gypsy moth populations. Environ. Entomol., 7: 631-36. Crossman, S.S., 1925. Two imported egg parasites of the gypsy moth Anastatus bifasciatus Fonsc. and Schedius kuwanai Howard. J. Agric. Res., 30:643 75. Doane, C.C., 1968. Changes in egg mass density, size and amount of parasitism after chemical treatment of a heavy population of the gypsy moth. J. Econ. Entomol., 61: 1288-91. Dowden, P.B., 1961. The gypsy moth egg parasite, Ooencyrtus kuwanai, in southern Connecticut in 1960. J. Econ. Entomol., 54: 876-78. Forbush, E.H. and Fernald, C.H., 1896. The Gypsy Moth, Porthetria dispar (Linn.). Wright and Potter, Boston, MA, 495 pp. Hassell, M.B., Lawton, J.H. and May, R.M., 1976. Patterns of dynamical behavior in single species populations. J. Anita. Ecol., 45: 471-86. H6rard, F., 1978. Ethology of the adults of Ooencyrtus kuvanae (Howard) (Hymenoptera: Encyrtidae), oophagous parasite of Lymantria dispar (L.) (Lepidoptera: Lymantriidae) in the Mamora Forest (Morocco). (English Transl.) Ann. Zool. Ecol. Anim., 10: 603-12. Hitchcock, S.W., 1972. Generation time of Ooencyrtus kuwanai on gypsy moth eggs in the field. J. Econ. Entomol., 65: 284-85. Hoy, M.A., 1976. Establishment of gypsy moth parasitoids in North America: An evaluation of possible reasons for establishment or non-establishment. In: J.F. Anderson and H.K. Kaya (Editors), Perspectives in Forest Entomology. Academic Press, New York, NY, pp. 215-232. Knight, F.B. and Heikkenen, H.J., 1980. Principles of Forest Entomology, 5th edn. McGraw Hill, New York, NY, 461 pp. Krnjaic, S., 1967. Survey of species and number of gypsy moth egg parasites in some localities of Yugoslavia. (English Transl.) Zast. Bilja, 18: 247-55. Maksimovic, M., Bejegovi~, P. and Vasiljevi6, L., 1972. Feeding and maintaining the density of the gypsy moth's enemies as a method of biological control. Proc. 12th Int. Congr. Entomol., 1968, Nauk., 3: 57. Marcu, O. and Tudor, I., 1978. Insectes parasite b. r61e destructif sur les populations de Lymantria dispar L. dans le p6rim~tre de la R6publique Socialiste Roumane. Zast. Bilja, 29: 111-18. May, R.M., 1975. Biological populations obeying difference equations: stable points, stable cycles, and chaos. J. Theoret. Biol., 51:511-24.
268 Picardi, A.C., 1973. Gypsy moth population simulation: system postulation, validation, analysis. Proc. 1973 Summer Computer Simulation Conf., Montreal, 73 CH0815-1 SMC: 1069-74. Prota, R., 1966. Contributi alia conoscenza dell'entomofauna della Quercio da sughero (Quercus suber L.) V. Osservazioni condotte in Sardegna su Ooencyrtus kuwanai (Howard) (Hymenoptera: Encyrtidae) nuovo per la fauna italiana. Stazione Sperimentale del Sughero, Tempio Pausania, Memoria 17 (English Summary), 26 pp. Tadi6, M.D., 1959. Incidence of gypsy moth egg parasites Anastatus disparis R. and Ooencyrtus kuwanai How. in some localities in Macedonia in 1958/1959. (English Transl.) Zast. Bilja, 10: 27-37. Ticehurst, M., Fusco, R.A., Kling, R.P. and Unger, J., 1978. Observations on parasites of gypsy moth in first cycle infestations in Pennsylvania from 1974-77. Environ. Entomol., 7: 355-58. Weseloh, R.M., 1972. Spatial distribution of the gypsy moth (Lepidoptera: Lymantriidae) and some of its parasitoids within a forest environment. Entomophaga, 17: 339-51.