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Pesticide Resistance: Strategies and Tactics for Management. 1986. National Academy Press, Washington, D.C. F Computer Simulation as a Too} tor Pesticide Resistance Management BRUCE E. TABASHNIK Computer simulation may be usefulfor devising strategies to retard pesticide resistance in pests and to promote it in beneficials. This paper demonstrates the use of simulation to study interactions among factors influencing resistance development, describes efforts to test models of resistance development, and illustrates management ap- plications of computer models. Suggested guidelines for future tests of resistance models are to (IJ establish baseline data on suscepti- bility before populations are selectedfor resistance, (2) conduct tests under field conditions, (3J use experimental estimates of biological parameters in models, and (4J replicate treatments. Modelers of pesticide resistance must test models, explore the implications of polygenic resistance, and incorporate alternative controls such as biological control in models. INTRODUCTION Pest species have developed resistance to pesticides faster than beneficial organisms, limiting the integration of biological and chemical controls. Re- sistant strains of more than 400 insect and mite species have been recorded, but fewer than 10 percent are beneficial (Georghiou and Mellon, 1983; Croft and Strickler, 19831. The goals of resistance management are to retard re- sistance in pests and to promote it in beneficials. Models of pesticide resis- tance can be useful tools for working toward these goals. Various types of models have played an essential role in building a conceptual framework for resistance management (Table 1; Taylor, 19831. This paper emphasizes sim- ulation modeling as a component of management and identifies future di 194

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COMPUTER SIMULATION TABLE 1 Modeling Studies of Pesticide Resistance 195 Factors Emphasized Biological Operational Economic Studies Analytical MacDonald, 1959 X Comins, 1977a X Curtis et al., 1978 X X Gressel and Segel, 1978 X X Taylor and Georghiou, 1979 X Cook, 1981 X Skylakakis, 1981 X X Wood and Mani, 1981 X X Muggleton, 1982 X Simulation Georghiou and Taylor, 1977a,b X X Greever and Georghiou, 1979 X X Plapp et al., 1979 X Kable and Jeffrey, 1980 X Curtis, 1981 X X Taylor and Georghiou, 1982 X X Tabashnik and Croft, 1982, 1985 X X Levy et al., 1983 X Taylor et al., 1983 X X Knipling and Klassen, 1984 X Dowd et al., 1984 X X Optimization Hueth and Regev, 1974 X X Taylor and Headley, 1975 X X Guttierrez et al., 1976, 1979 X X Comins, 1977b, 1979 X X Shoemaker, 1982 X X Statistical/Empir~cal Georghiou, 1980 X Tabashnik and Croft, 1985 X SOURCE: The model classifications are based on Logan (1982) and Taylor (1983). The list of studies is expanded from Taylor (1983) but is not intended to be exhaustive. rections for modeling that can increase its usefulness as a resistance manage- ment tool. MODELING ASSUMPTIONS The key assumptions of the models discussed in this paper (Tabashnik and Croft, 1982, 1985; Taylor and Georghiou, 1982; Taylor et al., 1983) are as follows: 1. Resistance is controlled primarily by a single-gene locus with two

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196 POPULATION BIOLOGY OF PESTICIDE RESISTANCE alleles, R (resistant) and S (susceptible), with a fixed dose-mortality line for each genotype. 2. The dose-mortality line for RS heterozygotes is intermediate between the SS (susceptible) and RR (resistant) lines. At low pesticide doses RS heterozygotes are not killed, and the R gene is effectively dominant; at high doses RS heterozygotes are killed, and the R gene is effectively recessive. 3. The insect life cycle is divided into substages, with transition proba- bilities between substages determined by natural and pesticide mortalities. 4. Immigrants are primarily susceptible and have at least one day to mate and reproduce before being killed by a pesticide. INTERACTIONS There are four main classes of conditions for resistance development: (1) no immigration, low pesticide dose (R gene functionally dominant); (2) no immigration, high pesticide dose (R gene functionally codominant or reces- sive); (3) high immigration, low dose; and (4) high immigration, high dose. Initial modeling studies that focused on different subsets of these four main classes arrived at apparently conflicting results (e.g., contrast Georghiou and Taylor, 1977a,b, with Comins, 1977a, and Taylor and Georghiou, 19791. It was not clear whether contradictions arose from differences in modeling approaches or from differences in conditions among various studies. Tabashnik and Croft (1982) examined the influence of various factors on rates of resistance development under all four main classes of conditions. Results showed that the way certain factors influence the rate of resistance evolution depends on which of the four classes of conditions are present. In other words the same factor may have a different influence under different background conditions. One of the most striking examples of the interaction effect is the influence of pesticide dose on the time to develop resistance (Figure 1~. Without immigration resistance developed faster as dose increased. With immigration there were two distinct phases. At low doses resistance developed faster as dose increased, paralleling the case without immigration. At high doses, however, resistance developed more slowly as dose increased. These results are consistent with Comins (1977a). Without immigration the rate of resis- tance development is determined primarily by the rate at which S genes are removed from the population. As dose increases, S genes are removed more rapidly; resistance develops faster. The situation with low doses and immi- gration is similar. With immigration and doses high enough to kill RS het- erozygotes, however, pesticide mortality also removes R genes from the population. As dose increases in this range, more RS heterozygotes are killed, leaving relatively few resistant (RR) individuals. The RR survivors are ef

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COMPUTER SIMULATION Stable >10 `,, 1 0 _ 9 a) ~ 8 ce a', ._ , In a, a: o - a) i- 4 3 2 1 O 197 ~ , ~ I\ \\ 1 ~1 Air a, \\: Aim \~ ,~y "\ / " ~ No Immigration 0~ On --O .0003 .001 .003 .01 .03 .1 Dose (Log Scale) FIGURE 1 Effects of dose on the rate of evolution of resistance. Conditions: O or 100 grants daily, biweekly treatments of adults. Source: Tabashnik and Croft (1982~. fectively swamped out by susceptible immigrants, thereby retarding resis- tance development. The simulation results suggest that one of the most important factors influencing the rate of resistance evolution is the number of generations per year. Under all four classes of conditions, resistance developed faster as the number of generations per year increased. Field observations of resistance development in soil and apple arthropods (Georghiou, 1980; Tabashnik and Croft, 1985) are consistent with this prediction. A summary of the influence of various factors on resistance development (Table 2) highlights the interactions among factors. Increases in the opera- tional [actors (dose, spray frequency, and fraction of the life cycle exposed to pesticide) made resistance develop faster when there was no immigration (both low- and high-dose range) and when there was immigration and a low dose. The opposite occurred with immigration and a high dose. Some bio- logical factors (fecundity, survival, and initial population size) had little effect in the absence of immigration, but increases in these factors made resistance evolve faster when there was immigration. Two biological factors (genera- tions/year and immigration) had the same influence under all four classes of conditions.

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198 POPULATION BIOLOGY OF PESTICIDE RESISTANCE TABLE 2 The Influence of Operational and Biological Factors on Resistance Development under Four Main Classes of Conditions No Immigration High Immigration Low High Low High Factors Dosea Doseb Dosea Doseb Operational Dose + + + Spray Frequency + + + Life Stages Exposed + + + Biological Generations per Year + + + + Immigration Fecundity 0 0 + + Survivorship 0 0 + + Initial Population Size 0 0 + + Initial R Gene Frequency + 0 + + Reproductive Disadvantage - 0 - - DominanceC + O + + NOTE: + shows that increasing the listed factor speeds resistance development; - shows that increasing the listed factor slows resistance development; 0 shows little or no effect. aKills only SS, R gene functionally dominant. bKills SS and some RS, R gene functionally codominant or recessive. CBased on Comins (1977a), Georghiou and Taylor (1977a), Wood and Mani (1981), and Tabashnik (unpublished). SOURCE: Tabashnik and Croft (1982). The most important conclusion from this simulation approach is that the influence of certain factors will depend on the presence or absence of im- migration by susceptibles and on the functional dominance of the R gene (i.e., dose). Therefore, it is necessary to develop resistance management strategies that are appropriate for specific ecological and operational contexts. TESTING MODELS Experimental tests of pesticide resistance models are sorely needed (Taylor, 1983~. There have been more than 25 papers describing resistance models during the past 10 years (Table 1), but only two studies explicitly test such models (Taylor et al., 1983; Tabashnik and Croft, 19851. These two studies represent opposite types of validation. The following discussion summarizes results of the studies and suggests how elements of both approaches can be combined to produce an especially powerful test of resistance models. Taylor et al. (1983) used laboratory house fly (Musca domestica) popu- lations to test a model of evolution of resistance to dieldrin, an organochlorine insecticide. Resistance to dieldrin is due to a single gene, and three fly

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COMPUTER SIMULATION 199 genotypes are distinguishable by bioassay (Georghiou et al., 19631. Taylor et al. (1983) simulated five different treatment regimes, then compared the predicted resistance gene frequencies and population sizes with those ob- served in five corresponding experimental cages. All of the biological parameters used in the simulations were measured directly from laboratory fly populations. The initial conditions were alike for all cages (90 SS + 10 RS individuals of each sex per cage), and each cage received a different treatment: (A) control no insecticide and no im- migration, (B) slow insecticide decay and immigration, (C) fast decay and immigration, (D) no decay and no immigration, and (E) no decay and im- migration. Immigration was achieved by adding 25 individuals (24 SS + 1 RS) to the appropriate cages three times weekly. Dieldr~n was incorporated in the larval medium and acted only on larvae and newly eclosed adults. The initial dieldr~n concentration (40 ppm) was the same in treatments B to E, but decay rates corresponding to insecticide half-lives of 1.0 and 0.5 days were mimicked by using decreasing dieldr~n concentrations in successive treatments. Each cage was run for 57 days (about four generations). The results showed a strong correlation between predicted and observed values for the final R gene frequency in each treatment (Figure 21. Both the simulations and experiments support earlier predictions that immigration by susceptibles can retard the evolution of resistance, especially when the ratio of immigrants to residents in the treated population is high (Coming, 1977a; Taylor and Georghiou, 1979; Tabashnik and Croft, 19821. A 'to llJ o ~ 0.8 11 111 Z 0.6 L`J lo ~ 0.2 LL o.o C. _ MA B '/ 0.4 _ / BE / / / / D ,' o.o 0.2 0.4 0.6 0.8 1.0 OBSERVED R GENE FREQUENCY FIGURE 2 Predicted versus observed resistance (R) gene frequencies in caged house flies. Dashed line shows predicted = observed. Letters indicate treatments (see text) (Taylor et al., 1983~.

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200 POPULATION BIOLOGY OF PESTICIDE RESISTANCE This validation study shows that in a highly defined situation, model predictions may correspond well with reality. Because virtually all of the biological and operational parameters were either measured or controlled, the correspondence between predictions and observations is no accident. The model appears to incorporate the essential processes affecting evolution of resistance in the system studied. The system studied, however, was highly artificial, and its relationship to field systems is unclear. Validation in an artificial system probably cannot adequately address the question of whether model predictions apply to field situations. Tabashnik and Croft (1985) tested a resistance model by comparing sim- ulated times versus historically observed times to evolve resistance to azin- phosmethyl in the field for 24 species of apple pests and natural enemies. Azinphosmethyl is an organophosphorous insecticide that has remained a major apple pest-control tool in North America for almost 30 years. The long-term patterns of evolution of resistance to azinphosmethyl among the diverse apple orchard insects and mites constitute a unique data set for testing predictions about resistance. To represent 24 different apple arthropod species in the simulation, the following population ecology parameters were estimated independently for each species: generations/year, fecundity, immigration, natural (nonpesti- cide) mortality, initial population size, development rate, sex ratio, pesticide exposure in orchards, and percent of time spent in orchards by adults. Pa- rameter values and historically observed times to evolve resistance for each species were based on a survey of 24 fruit entomologists (Croft, 19821. Operational and genetic factors were held constant for all 24 species. All species were subjected to the same simulated pesticide dose, spray schedule, and pesticide half-life because all species were present in the same habitat and were exposed to a similar treatment regime in the field. The genetic basis of resistance, dose-mortality lines, and initial R gene frequency were assumed to be the same for all species because these parameters are virtually impossible to estimate for most species. Further, Tabashnik and Croft (1985) sought to determine how much of the variation in rates of evolution of resistance could be explained by differences among species in population ecology, with all other factors being constant. The results show a significant rank correlation between predicted and historically observed times to evolve resistance for the 12 pest species and the 12 natural-enemy species (Figure 31. Thus, ecological differences among apple species are sufficient for explaining observed variation in rates of resistance development among pests and natural enemies. There was no consistent bias in the predictions for pests, but predicted times were consistently less than observed times for natural enemies, sug- gesting that the original assumptions may omit factors that slow resistance development in natural enemies. The original assumptions about natural

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COMPUTER SIMULATION 1 ~ a Tp. P.b ~25 25 - % c' ~,1 0 o o3_ - E F 2 1 cL 0.5 , ~ Put Ap, - ,' , Rptn 0.25 , . . ... . . Dp Tt' 1 2 5 201 Hh Crr b | y sr ~ ,' Aa Cc|lAm ,," Sp ,' iAf 'To . I I I l,,,,l 10 25 >25 10 25 > 25 1 2 Observed Time (years-log scale) 5 FIGURE 3 Predicted versus observed times to evolve resistance to azinphosmethyl for apple arthropods. Predicted time (~) = simulated time to evolve resistance using means of estimates of population ecology parameters. Observed time = years after 1955 (first widespread use of azinphosmethyl) to first report of resistance. Vertical bars show range of predicted times from sensitivity analysis. Dashed lines show predicted = observed. A. Pests: n = 12. Spearman's rank correlation coefficient, rS = 0.652, p < 0.05. Key: Aa = Archips argyrospilus, Ap = Aphis pomi, Av = Argyrotaenia velutinana, Cn = Conotrachelus nenuphar, Dp = Dysaphis plantaginea, Lp = Laspeyresia pomonella, Pb = Phyllonorcyter blancardella, Pu = Panonychus ulmi, Qp = Qua~lraspidiotus perniciousus, Rp = Rhagoletis pomonella, Tp = Typhlocyba pomccria, Tu = Tetran- ychus urticae B. Natural enemies: n - 12. rS = 0.692, p c 0.025. Key: Aa = Aphidoletes aphidimyza, Ae = Anagrus epos, Af = Amblyseiusfallacis, Am = Aphelinus mali, At = Aphelopus typhlocyba, Cc = Chrysopa carnea, Cm = Coleomegilla maculata lingi, Hh = Hyaliodes hart), 0i = 0rius insidiosus, Sp = Stethorus punctum, Sr = Syrphus ribesii, To = Typhlodromus occidentalis. Source: Tabashnik and Croft, 19851. enemies were modified to incorporate the preadaptation and food-limitation hypotheses. Incorporating the preadaptation hypothesis (pests are preadapted to detoxify pesticides because they detoxify plant poisons, but natural enemies are less preadapted) (Croft and Morse, 1979; Mullin et al., 1982) did not substantially improve the correspondence between predicted and observed times. Adding the food-limitation hypothesis (a natural enemy evolves re- sistance only after its prey/host is resistant, because pesticides drastically reduce food for natural enemies by eliminating susceptible prey/hosts) (Huf

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202 POPULATION BIOLOGY OF PESTICIDE RESISTANCE >25 25 _% a) c' O 10 - u' c. c, 5 >' a) ._ ~ 2 a) ._ ~ 0.5 0.25 ! ,' ~ L '' I' 1 2 5 10 ,' Aa ~ Cc) Tol' jAf Asp l ~1 I ~ I 25 >25 Observed Time (years-log scale) F~GuRE 4 Effects of the food-limitation hypothesis on predicted times for natural enemies to evolve resistance. n = 12. rS = 0.806, p < 0.005 (see Figure 3 for key to species names). Open circles indicate predictions with the food-lim~tation hypothesis incorporated; dark circles indicate predictions under initial assumptions. Arrows show change in pre- dictions due to food-limitation hypothesis. faker, 1971), however, substantially improved the correspondence between predicted and observed times for all six natural enemies that were initially predicted to evolve resistance too fast (Figure 4~. These results suggest that food limitation following pesticide applications may be an important factor in retarding evolution of resistance in natural enemies. If this is so it may be possible to promote resistance development in natural enemies by ensuring them an adequate food supply following sprays either by reducing mortality to their prey/hosts or by providing an alternate food source when prey/hosts are scarce. The validation study of Tabashnik and Croft (1985) provides encourage- ment that model results can be applied to field situations. That study, how- ever, relies on estimated values for many important parameters. Tabashnik and Croft (1985) address this problem in part by a sensitivity analysis dem- onstrating that many of the model's predictions were minimally affected by substantial variation in some key parameters that are difficult to estimate, but that are potentially influential (immigration, initial population size, and fecundity; see sensitivity bars in Figure 31.

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COMPUTER SIMULATION TABLE 3 Predicted Time (years) for the European Red Mite (Panonychus ulmi) to Evolve Pesticide Resistance under Different Pesticide Doses and Application Frequencies 203 Application Frequency Pesticide Initial (Sprays/Year) Dosea Mortality 6 3 1 112b 0.01 93% 1.5 1.7 2.6 5.7 0.002 73% 1.6 1.9 6.5 19.6 0.001 50% 1.5 2.2 13.6 >25 aArbitrary units bOne spray every 2 years SOURCE: Tabashnik and Croft (1985). It seems that a powerful approach to testing resistance models can be developed by combining elements from both of the studies described above. Guidelines are as follows: Establish baseline data on susceptibility before populations are selected for pesticide resistance. Rates of resistance development can be measured only if initial susceptibility is known. Conduct tests under field conditions or conditions similar to the field. It may be especially important to use large initial population sizes if genes conferring resistance are rare. Obtain experimental estimates of basic biological parameters (e.g., fe- cundity) required for modeling. Replicate treatments. Field experiments that might promote rapid evolution of new resistances in pests should not be performed. Although experimental selection for re- sistance is costly and time-consuming (Taylor, 1983), unintentional selection for resistance is widespread. Extremely valuable data bases on resistance could be developed by concomitant monitoring of field treatment regimes and susceptibility levels in field populations. Such data would provide a sound basis for evaluating management tactics as well as models of pesticide resistance. MANAGEMENT APPLICATIONS Computer simulations can be used to project the consequences of alter- native control strategies. For example, Tabashnik and Croft (1985) simulated resistance development by the European red mite (Panonychus ulmi) under 12 management schemes based on three pesticide doses and four application schedules (Table 31. Resistance was predicted to occur within three years when intermediate to high acaricide doses (causing 50 to 93 percent initial

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204 POPULATION BIOLOGY OF PESTICIDE RESISTANCE mortality) and frequent applications (three to six per season) were simulated. If both dose and application frequency are reduced, resistance in the European red mite is predicted to be delayed from 7 to more than 25 years. The projected times for resistance development in the European red mite are consistent with observed patterns of resistance to the acaricide cyhexatin in the United States. Since cyhexatin was introduced in 1970, resistance has not occurred in apple orchards, where it has been used judiciously in con- junction with biological control by predators. Cyhexatin resistance has oc- curred rapidly, however, in pear-apple interplants, where biological control is difficult and acaricide use is more intensive (Croft and Bode, 19831. CONCLUSION Modelers of pesticide resistance face three major challenges in the im- mediate future. First, and most important, models of pesticide resistance must be tested. Second, the implications of polygenically based pesticide resistance need to be explored. With few exceptions models of pesticide resistance assume one locus-two allele genetics, but many resistances may be polygenic (Plapp et al., 1979~. Two of the papers in this volume take important steps toward addressing this challenge (Uyenoyama, Via). Third, alternative control methods such as biological control should be incorporated into models of pesticide resistance. The most promising way to retard resis- tance is to reduce pesticide use by integrating pesticides with other controls, yet current models generally assume that pesticides are the sole control method. If these challenges are addressed, modeling will play an increasingly important role in managing pesticide resistance. ACKNOWLEDGMENTS Special thanks to B. A. Croft for his assistance and encouragement. R. T. Roush and R. M. May provided valuable comments. Support was provided by the Research and Training Fund, University of Hawaii and USDA- HAW00947H. Paper Number 2919 of the Hawaii Institute of Tropical Ag- nculture and Human Resources journal series. REFERENCES Comins, H. N. 1977a. The development of insecticide resistance in the presence of migration. J. Theor. Biol. 64:177-197. Comins, H. N. 1977b. The management of pesticide resistance. J. Theor. Biol. 65:399-420. Comins, H. N. 1979. The control of adaptable pests. Pp. 217-266 in Pest Management, Proceedings of an International Conference, G. A. Norton and C. S. Holling, eds. Oxford: Pergamon. Cook, L. M. 1981. The ecological factor in assessment of resistance in pest populations. Pestic. Sci. 12:582-586.

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COMPUTER SIMULATION 205 Croft, B. A. 1982. Arthropod resistance to insecticides: A key to pest control failures and successes in North American apple orchards. Entomol. Exp. Appl. 3:88-110. Croft, B. A., and W. M. Bode. 1983. Tactics for deciduous fruit IPM. Pp. 270-291 in Integrated Management of Insect Pests of Pome and Stone Fruits, B. A. Croft and S. C. Hoyt, eds. New York: Interscience. Croft, B. A., and J. G. Morse. 1979. Recent advances on pesticide resistance in natural enemies. Entomophaga 24:3- 11. Croft, B. A., and K. Strickler. 1983. Natural enemy resistance to pesticides: Documentation, characterization, theory and application. Pp. 669-702 in Pest Resistance to Pesticides, G. P. Georghiou and T. Saito, eds. New York: Plenum. Curtis, C. F. 1981. Possible methods of inhibiting or reversing the evolution of insecticide resistance in mosquitoes. Pestic. Sci. 12:557-564. Curtis, C. F., L. M. Cook, and R. J. Wood. 1978. Selection for and against insecticide resistance and possible methods of inhibiting the evolution of resistance in mosquitoes. Ecol. Entomol. 3:273-287. Dowd, P. F., T. C. Sparks, and F. L. Mitchell. 1984. A microcomputer simulation program for demonstrating the development of insecticide resistance. Bull. Entomol. Soc. Am. 30:37-41. Georghiou, G. P. 1980. Insecticide resistance and prospects for its management. Residue Rev. 76:131-145. Georghiou, G. P., R. B. March, and G. E. Printy. 1963. A study on genetics of dieldrin resistance in the house fly (Musca domestica L.). Bull. W. H. O. 29:155-165. Georghiou, G. P., and R. B. Mellon. 1983. Pesticide resistance in time and space. Pp. 1-46 in Pest Resistance to Pesticides, G. P. Georghiou and T. Saito, eds. New York: Plenum. Georghiou, G. P., and C. E. Taylor. 1977a. Genetic and biological influences in the evolution of insecticide resistance. J. Econ. Entomol. 70:319-323. Georghiou, G. P., and C. E. Taylor. 1977b. Operational influences in the evolution of insecticide resistance. J. Econ. Entomol. 70:653-658. Greever, J., and G. P. Georghiou. 1979. Computer simulations of control strategies for Culex tarsalis (Diptera: Culicidae). J. Med. Entomol. 16:18~188. Gressel, J., and L. A. Segel. 1978. The paucity of plants evolving genetic resistance to herbicides: Possible reasons and implications. J. Theor. Biol. 75:349-371. Guttierez, A. P., U. Regev, and C. G. Summers. 1976. Computer model aids in weevil control. Calif. Agric. April:8-9. Guttierez, A. P., U. Regev, and H. Shalet. 1979. An economic optimization model of pesticide resistance: Alfalfa and Egyptian alfalfa weevil an example. Environ. Entomol. 8:101-109. Hueth, D., and U. Regev. 1974. Optimal agricultural pest management with increasing pest resis- tance. Am. J. Agric. Econ. 56:543-552. Huffaker, C. B. 1971. The ecology of pesticide interference with insect populations. Pp. 92-107 in Agricultural Chemicals- Harmony or Discord for Food, People, and the Environment, J. E. Swift, ed. Berkeley: University of California, Division of Agricultural Science. Kable, P. F., and H. Jeffery. 1980. Selection for tolerance in organisms exposed to sprays of biocide mixtures: A theoretical model. Phytopathology 70:8-12. Knipling, E. F., and W. Klassen. 1984. Influence of insecticide use patterns on the development of resistance to insecticides: A theoretical study. Southwest. Entomol. 9:351-368. Levy, Y., R. Levi, and Y. Cohen. 1983. Buildup of a pathogen subpopulation resistant to a systemic fungicide under various control strategies: A flexible simulation model. Phytopathology 73: 1475- 1480. Logan, J. A. 1982. Recent advances and new directions in phytoseiid population models. Pp. 49- 71 in Recent Advances in Knowledge of the Phytoseiidae, M. A. Hoy, ed. Publ. 3284. Berkeley, Calif.: Agricultural Sciences Publications (Publ. No. 3284.) MacDonald, G. 1959. The dynamics of resistance to insecticides by anophelines. Riv. di Parassitol. 20:305-315.

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206 POPULATION BIOLOGY OF PESTICIDE RESISTANCE Muggleton, J. 1982. A model for the elimination of insecticide resistance using heterozygous disadvantage. Heredity 49:247-251. Mullin, C. A., B. A. Croft, K. Strickler, F. Matsumura, and J. R. Miller. 1982. Detoxification enzyme differences between an herbivorous and predatory mite. Science 217:1270-1272. Plapp, F. W., Jr., C. R. Browning, and P. J. H. Sharpe. 1979. Analysis of rate of development of insecticide resistance based on simulation of a genetic model. Environ. Entomol. 8:494-500. Shoemaker, C. A. 1982. Optimal integrated control of univoltine pest populations with age structure. Oper. Res. 30:40-61. Skylakakis, G. 1981. Effects of alternating and mixing pesticides on the buildup of fungal resistance. Phytopathology 71:1119-1121. Tabashnik, B. E., and B. A. Croft. 1982. Managing pesticide resistance in crop-arthropod complexes: Interactions between biological and operational factors. Environ. Entomol. 11:1137-1144. Tabashnik, B. E., and B. A. Croft. 1985. Evolution of pesticide resistance in apple pests and their natural enemies. Entomophaga 30:37-49. Taylor, C. E. 1983. Evolution of resistance to insecticides: The role of mathematical models and computer simulations. Pp. 163-173 in Pest Resistance to Pesticides, G. P. Georghiou and T. Saito, eds. New York: Plenum. Taylor, C. E., and G. P. Georghiou. 1979. Suppression of insecticide resistance by alteration of gene dominance and migration. J. Econ. Entomol. 72:105-109. Taylor, C. E., and G. P. Georghiou. 1982. Influence of pesticide persistence in evolution of resistance. Environ. Entomol. 11:746-750. Taylor, C. E., F. Quaglia, and G. P. Georghiou. 1983. Evolution of resistance to insecticides: A cage study on the influence of migration and insecticide decay rates. J. Econ. Entomol. 76:704- 707. Taylor, C. R., and J. C. Headley. 1975. Insecticide resistance and the evolution of control strategies for an insect population. Can. Entomol. 107:237-242. Wood, R. J., and G. S. Mani. 1981. The effective dominance of resistance genes in relation to the evolution of resistance. Pestic. Sci. 12:573-581.