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Pesticide Resistance: Strategies and Tactics for Management. 1986. National Academy Press, Washington, D.C. Quantitative Genetic Models and the Evolution of Pesticide Resistance SARA VIA When tolerance to pesticides varies continuously among indi- viduals, a quantitative genetic approach to resistance evolution is more useful than is the usual single-locus view. Relative char- acteristics of polygenic and single-gene resistance are described; then the evolution of polygenic resistance is discussed in terms of basic quantitative genetics principles. Finally, polygenic models that use the quantitative genetic analog of negative cross-resis- tance (genetic correlations are described. These models suggest that the joint application of selected compounds in some spatial array may be a useful means of retarding the evolution of polygenic resistance. Further refinements of the models and ways to validate them with experimental data are considered. Estimates of genetic parameters and selection intensities are essential to assess the validity of the suggestions presented here. These models are dis- cussed primarily as heuristic tools that may provide a new con- ceptual view on the problem of pesticide resistance; they do not as yet provide descriptions of particular cases of resistance evo- lution in real pest populations. INTRODUCTION The increasing frequency of pesticide resistance is an undeniable example of the process of evolution. Basic Darwinian principles assert that when genetic variation is available, populations under selection by some aspect of the environment will increase adaptation through evolutionary change. When pesticides are the agents of selection, the response will be some form of 222
QUANTITATIVE GENETIC MODELS 223 pesticide resistance, such as detoxification, physiological adaptation, or be- havioral avoidance (Georghiou, 1972; Wood and Bishop, 19811. Mathematical models have been instrumental in the identification and study of the genetic and environmental factors that influence the rate and direction of evolution. Because pesticides are agents of selection, pesticide resistance can be studied by using the same theoretical frameworks as have been applied to other types of evolutionary change. Previous population genetic models have considered that resistance is de- termined by a single gene. These models are generally not immediately applicable when resistance is a quantitative (polygenic) trait, in which the underlying genes may not (and indeed need not) be identified individually. This paper describes how resistance can be studied from a polygenic per- spective and suggests how models that were derived to describe the evolution of quantitative characters in different environments may be used to design genetically sound strategies of pesticide application to retard the evolution of pesticide resistance. Cases of polygenic resistance are well known (Crow, 1954; King, 1954; Liu, 1982; Wood and Bishop, 19811. Although polygenic resistance in field situations may be less common than monogenic resistance, the potential for polygenic resistance may be more widespread than is currently recognized, because different populations exhibit different mechanisms of resistance (Thomas, 1966; Wood and Bishop, 1981) and mutations affecting resistance can be mapped to different loci (Wood and Bishop, 1981; Pluthero and Threlkeld, 19831. In fact the high frequency of major gene resistance in field populations may result more from the very strong selection imposed by current regimes of pesticide application (Lance, 1983; Roush, 1984) than from an inherent bias in genetic potential. The intent of new methods of pesticide application is to lower the effective intensity of selection (Taylor and Georghiou, 1982; Tabashnik and Croft, 1982~. Such methods may in- crease the incidence of polygenic resistance. POLYGENIC RESISTANCE When pesticide resistance is polygenic (owing to effects at several gene loci), the resistance phenotype as expressed in the dose-response curve will be continuous (Figure 1B). The polygenic curve spans the range of the separate resistance classes seen in the single-locus case (Figure 1A). The range in dose response of a single genotype in the true one-locus case is due to environmental effects: if there were no environmental variation, all individuals of a given genotype would die at the same dose, and the dose-response curves in Figure 1A would be vertical lines. In this paper the effects of modifier genes on the dose-response curves for the major locus will be ignored. Such modifiers, however, will lower the slopes of
224 >a 95 - 50 o 5 By a At: Lo POPULATION BIOLOGY OF PESTICIDE RESISTANCE SINGLE GENE A / / POLYGENIC I B , , , 1 LD50Ss LD50Rs LD50RR LD50 _ &~t LD50ss LD505?S LD50RR tOLE RANCE D ~ / ~1 LD50 FIGURE 1 Comparison of dose-response curves (A,B) and tolerance distributions (C,D) for pesticide resistance with single-gene or polygenic genetic basis. A,B: Dose-reponse curves corresponding to the cumulative distribution of mortality with increasing dose on a log scale. C,D: Tolerance curves are probability density functions for the sensitivity to dose. (Redrawn from Via and Lande, 1985.) the dose-response curves in Figure 1A, having the same effect as envi- ronmental variance. In polygenic resistance a continuous dose-response relationship results from the combination of environmental and genetic factors. No distinct genotypic classes can be identified because classes overlap when several loci determine a trait; polygenic characters thus are also called "continuous characters" (Falconer, 19811. Because only the additive genetic variance in tolerance to a given compound (VA) contributes to the evolution of resistance by individual selection, it is necessary to determine the fraction of the total phenotypic variance in tolerance to that pesticide (Vp) that is due to additive genetic causes. This is accomplished by partitioning Vp into its components, VP = VA + VE (1) where VE includes the nonadditive genetic variance plus the microenviron- mental variation in tolerance. Other more complete partitionings are also possible (Falconer, 19811. The various partitionings of the phenotypic variance into its causal com- ponents rely on theory first developed by R. A. Fisher (19181. The theory of quantitative genetics is based on the fact that family members resemble one another because they share genes; variation among families can thus be
QUANTITATIVE GENETIC MODELS 225 used to estimate genetic variation. Experiments designed to determine the genetic components of variance for quantitative traits therefore rely heavily on breeding designs that generate family groupings with certain degrees of relatedness (Falconer, 19811. Variation in the phenotypic characters of in- terest (here, tolerance to certain pesticides) can then be estimated within and among families to derive the desired estimates of the genetic components of variance (Via, 1984a,b). Selection for Tolerance The dose-response curves in Figures 1A and 1B are cumulative distribution functions (Mood et al., 1963j. They express the total fraction of the popu- lation that is dead by the time a pesticide has reached a certain dosage. In contrast Figures 1C and ID are probability distribution functions (Mood et al., 1963) that express the proportion of individuals that die at a particular dosage. These probability distribution functions represent tolerance curves for the population. A normal distribution of tolerance means that a few individuals in the population are very sensitive to pesticide treatment, a few will survive until the dose is extremely high, and most will have an average degree of tolerance. Tolerance curves illustrate the proportion of the popu- lation that dies at a particular dose. Variation in tolerance for each curve in the single-locus case is presumed to be entirely environmental. In the po- lygenic case, variation is the sum of genetic and environmental components. The mean tolerance in a population is the LDso (Figure 11. In the presence of a pesticide, selection will act to increase the LDso individuals with high tolerance are favored. The selection response of a quantitative trait is the product of the proportion of variation in a character that is caused by additive genetic variation and the intensity of selection (Falconer, 19811. Using this result the dynamics of the evolution of tolerance when the population is exposed to a single pesticide can be described mathematically as ALDso= (VA/VP)S (2) where ALDso is the change in the mean tolerance in every generation, and s is the difference in mean tolerance before and after selection (the selection dif- ferential). Equation 2 illustrates that the rate at which pesticide resistance (tol- erance) evolves is proportional to the magnitude of the total variation in tolerance that is additive genetic and to the intensity of selection. Although the genetic parameters may change during selection, equation 2 will hold for several gen- erations, after which the genetic parameters must be reestimated. Genetic Correlations Among Traits The univariate formulation presented in equation 2 applies only when selection acts on a single character, such as tolerance to a particular pesticide.
226 POPULATION BIOLOGY OF PESTICIDE RESISTANCE Usually many characters are under selection simultaneously. For example, natural selection on fertility and fecundity operates at the same time as selection for pesticide resistance. The disadvantage of individuals with major genes for insecticide resistance, with respect to natural selection on correlated traits, may account for some of the reversion of resistance seen in the absence of pesticides (Abed) and Brown, 1960; Curtis et al., 1978; McKenzie et al., 1982~. The case considered here concerns simultaneous selection of toler- ances to multiple pesticides and considers the effect of genetic correlations in tolerances on the evolution of resistance. A study of the evolution of suites of characters must consider the degree to which the traits of interest have the same genetic basis. The genetic similarity of two traits can be estimated as the genetic correlation (Falconer, 19811. Genetic correlations result from the pleiotropic (multiple) effects of genes. Because pleiotropy is considered to be universal (Wright, 1968), significant genetic correlations among traits are common. Genetic correlations affect the course of evolution; when selection impinges on any character in a correlated group, all traits that are influenced by the same genes will also show an evolutionary change in their phenotypes, even if they are not directly affected by selection. This is called correlated response to selection. These correlated changes are not necessarily in the direction that is adaptive for all characters. Correlated characters cannot evolve in- dependently: if two traits are negatively correlated, selection for one to increase may result in a correlated decrease in the other even if this is disadvantageous. Therefore, genetic correlations can constrain the evolution of the whole phenotype and can cause maladaptation of some traits within a correlated suite. This process may be a useful way to temporarily retard evolution in insect pest populations. Genetic Correlations in Tolerance to Different Pesticides The present model illustrates what may happen when different pesticides are sprayed in adjacent fields. The key feature of the model is an observation first made by Falconer (19521: a character expressed in two environments can be considered as two genetically correlated traits. Here, tolerance to two pesticides is considered to be two traits that may have a genetic correlation of less than + 1 if different genes produce tolerance to each compound. For example, if different enzymes are required to detoxify two compounds or if different loci are involved in behavioral avoidance (Wood and Bishop, 1981), the genetic correlation in tolerance to the pair of compounds may be low. With this view the basic theory of evolution in correlated characters (Hazel, 1943; Lande, 1979) can be expanded to encompass genetic correlations across environments (Via and Lande, in press). Here, the correlations of interest are across pesticides.
QUANTITATIVE GENETIC MODELS 227 The Model Consider tolerance to a particular pesticide to be a normally distributed character, as illustrated in Figure 1B. The phenotypic variation in tolerance may be decomposed into additive genetic and environmental components, as in equation 1, using the resemblances among relatives (par- ent-offspring regression or some other standard breeding design such as sibling analysis) (Falconer, 1981; Via, 1984a). From such an analysis the additive genetic variation in tolerance to each pesticide can be determined. Environmental effects influencing tolerance to a particular pesticide are as- sumed to follow a Gaussian (normal) distribution. When several loci of small effect influence the tolerance phenotype, the distribution of additive genetic effects on tolerance can also be assumed to be approximately Gaussian. If one simultaneously measures the tolerances of family members to two pesticides by subjecting some siblings to each compound, the additive genetic correlation in tolerance to the two compounds can be estimated (Falconer, 1981; Via, 1984b). As discussed previously the genetic correlation between tolerances to the two pesticides is an estimate of the extent to which they have the same genetic basis. The specific scenario modeled here concerns adjoining fields that are sprayed with different compounds. Individuals are assumed to assort at ran- dom into the fields with some probability (q into the fields with the first pesticide and 1 - q into the fields sprayed with the other compound). The term q represents either some fixed preference for the different field types that is uniform among all individuals or denotes the proportional represen- tation of each pesticide in the overall environment. In this model any given individual experiences only one pesticide. This model is presented here primarily for its heuristic value; it is not ready for immediate application to field problems. The model is limited in its applicability for several reasons: · The characters must be normally distributed (such as "tolerance" in Figure ID), with independent mean and variance (Wright, 1968~. · The characters are assumed to be under stabilizing selection, that is, the fitness function has an intermediate optimum. The models use Gaussian (normal) fitness functions for selection on characters with intermediate op- tima. This approximation is most accurate when the population is near the optimum value of the character. Because an intermediate optimum is as- sumed, the model does not apply to characters like total fitness or survival, which are assumed to be under continual directional selection to increase. Pesticide tolerance may have an intermediate optimum: individuals with high membrane impermeability or excessive behavioral avoidance of chemicals that they could metabolize may be at a disadvantage relative to individuals with more intermediate values of the features that confer tolerance. The shape of the fitness function for individuals exposed to pesticides is an empirical
228 POPULATION BIOLOGY OF PESTICIDE RESISTANCE question. Estimates could be made by using a regression technique like that described in Lande and Arnold (1983), but to date no such estimates exist. · The population is assumed to be panmictic: individuals subjected to each pesticide are assumed to mix in a mating pool and then to reassert into locations where the various pesticides are sprayed. This assumption makes the models more accurate for species that mate in a common place away from the site of exposure than for species that have several generations per season and mate at the site where selection occurs. Subdivided population models (Via and Lande, 1985) suggest that the retardation of evolution will not be as effective when migration is low among fields sprayed with different compounds as it is when there is complete panmixis. · The models were originally formulated for weals selection. This main- tains normality in the phenotypic distributions and allows genetic variation, which is depleted by selection, to be replenished by mutation (Lance, 1976; 1980~. With strong selection, as is probable when pesticides are applied intensively, the approximate course and rate of evolution described by these models will be less accurate. The extent to which the models discussed here will actually describe the course of evolution in laboratory or field populations remains to be deter- mined: it is an empirical problem. The applicability of these and other genetic models must be tested by estimating genetic parameters and selection in- tensities. Until they are tested or proved, the models function primarily to introduce hypotheses about what can happen in the course of evolution of pesticide resistance. The mode of selection that seems most realistic here is so-called hard selection, in which the contribution of each patch to the mating pool after selection is proportional to both q and to the relative mean fitness of indi- viduals selected in that patch (WilW, where W = qW~ + (1 - qjW2~. The relative mean fitness of a subpopulation (Wi) can qualitatively be considered to be proportional to its contribution to the total population; mean fitness is an indicator of population growth rate (Lance, 19831. In this case the expected changes in LDsoS (the tolerances to the two compounds) are Direct Responses Correlated Responses ~LDso(~) = [qW~lWlG~P~ - ash + [~1 -q jW2/W]G~2p22 asp <3' ALDso(2)= t(1 -qjw2lw]G22p22 Is2 + [qW~lW]G2~P~-~s~ where Gil is the additive genetic variance in tolerance to the ith compound, Gij is the additive genetic covariance in tolerances (i 7` j), and Pii~~si is the selection intensity on tolerance to the ith compound (Lance and Arnold, 1983~. The evolutionary effects of genetic correlation between tolerances to dif- ferent compounds on the rate and direction of the evolution of pesticide
QUANTITATIVE GENETIC MODELS 229 resistance can be seen in equation 3: the responses to selection of correlated characters have two components. For example, in LDso`~' the direct response is the product of (1) the increase in tolerance to pesticide 1 resulting from direct selection on resistance to that compound (P~~~s~), (2) the genetic variance of tolerance to that pesticide (Gil), and (3) a weighting factor (quasi W) that is required because only part of the population experiences compound 1 . The correlated response is the product of ( 1 ) selection on the other pesticide (P22-IS2), (2) the genetic covariance between tolerances to the two com- pounds (Go), and (3) the weighting factor [~1 - qjW2lW]. Equation 3 illustrates that the magnitude and sign of the genetic covariance between tolerances to different pesticides can affect the rate of response of either of the tolerances viewed singly. If the genetic covariance for tolerance to different pesticides (Go) is negative, and both characters are selected to increase Use > 0 and s2 > 0), the change in tolerance to pesticide 1 will be less than if GO is positive. This is the obvious way that unfavorable genetic correlations in tolerance to different compounds can be used to retard evo- lution in pest populations. The same principle has been invoked in discussions of negative cross-resistance for the single-locus case (Dittrich, 1969; Curtis et al., 1978; Chapman and Penman, 1979~. As will be shown later, however, a negative genetic correlation in tolerance to different compounds is not absolutely required for maladaptation to one of the compounds to occur. Two scenarios follow that illustrate the models. For these examples, several simplifying assumptions were made: · Genetic and phenotypic variances in tolerance to each compound are assumed to be equal. · The width of the fitness function is the same for tolerance to each pesticide (resistance to each compound is assumed to be under equal strengths of stabilizing selection). · Genetic variances are assumed to remain constant. This assumption is violated if selection is very strong, but it is otherwise correct (Via and Lande, 1985). In example 1 the population has low tolerance to each of two compounds. One compound is used over a larger acreage than the other (70 percent of the total). When the correlation in tolerance to the two pesticides is positive, evolution of resistance to both will occur readily (Figure 21. If, however, the genetic correlation is low, evolution of resistance to the rarer compound will be slow to occur; most of the population experiences the other pesticide. For strongly negative genetic correlations, Figure 2 illustrates that tolerance to the rare compound can actually decrease as the evolution of resistance to the common pesticide occurs. In example 2 a new compound is used in conjunction with a compound to which the pests have already become highly resistant. Here the pesticides
230 POPULATION BIOLOGY OF PESTICIDE RESISTANCE are deployed in equal proportions in some spatial array in a local area. As evolution increases tolerance to the new compound, either a high positive or a large negative genetic correlation in tolerances will lead to maladaptation (decrease in tolerance) to the old pesticide (Figure 3~. This example requires that an intermediate optimum tolerance actually exists, so that a positive genetic correlation in tolerances will cause an overshoot of the optimum tolerance to pesticide 1 and a corresponding decrease in mean fitness. When maladaptation is occurring, mean fitness in the population will decrease. Thus, not only will resistance be less and less among the survivors, the population size and growth rate will be expected to decrease. Using pesticides in combinations that wouicl create maladaptation to one of the pair could be an effective way to combat the nearly ubiquitous increases in pes- ticide resistance. 50 60 _ 40 - o uo on J 20 10 \: 1 \ O __ I , N7 1 1 0 10 20 30 40 50 60 LD50(1 ) FIGURE 2 Expected evolutionary trajectories for populations with different additive ge- netic correlations in tolerance to two pesticides. Seventy percent of the total area is sprayed with compound 1. The joint optimum tolerance is the point at which most of the trajectories eventually converge (40,501. Values of the genetic correlations are + 1 (O), + 0.75 (O), + 0.375 (l!), 0 ~ ~ ), - 0.375 ~ x ), - 0.75 ~ O ), - 1 (V). Selected values are indicated on the graph near the corresponding trajectories. Evolution occurs in the direction of the arrows. Parameters are q = 0.7, Gll = G22 = 10, Pll - P22 - 20; width of both hltness functions = 200, LDso~l' = 27, LD50~2~ - 25. (Redrawn from Via and Lande, 1985.)
QUANTITATIVE GENETIC MODELS 60 50 40 N - o Cal 30 20 10 ~5 o 231 10 20 30 40 50 60 LD50(1 ) FIGURE 3 Expected evolutionary trajectories when resistance is high for compound 1 at the time a second compound is introduced. The two pesticides are then applied in a joint spraying regime. The joint optimum tolerance is the point where most of the trajectories converge (40,50~. Values of the correlations and parameter values are the same as in Figure2,exceptq = 0.5,andLD,O`~' = 45. (Redrawn from Via and Lande, 1985.) Other Approaches As seen in Figures 2 and 3, the effect of the genetic correlation in tolerance on resistance evolution depends on the initial mean tolerance to each com- pound relative to the optimum level of tolerance. Within the context of the basic model described here and its attendant assumptions, several alternative strategies of pesticide application could be investigated. Simultaneous Application of Pesticides The suggestion has been made that mixtures of pesticides with different modes of action might prevent adaptation in pest populations with single-locus negative pleiotropic effects (negative cross-resistance) (Ogita, 1961a,b; Chapman and Penman, 1979; Gressel, in press). The simultaneous application of compounds means that all individuals experience both pesticides. In this case tolerance to compound 1 and tolerance to compound 2 are two genetically correlated characters that can be measured on the same individual (in the previous example each
232 POPULATION BIOLOGY OF PESTICIDE RESISTANCE individual expressed tolerance to only one pesticide, owing to spatial sepa- ration of application). General models for evolution in correlated characters similar to equation 2, but including no weighting terms (Lance, 1979), could be used to investigate the implications of simultaneous application. Because all individuals experience both pesticides, the overall rate of evolution will probably be more rapid than in example 1, implying more rapid resistance evolution to one of the compounds, but perhaps also a more rapid correlated decrease in tolerance to the other. One drawback of simultaneous application is that it may radically increase the overall intensity of selection (Gressel, in press). Alternating the Proportion of Acreage Sprayed with Different Com- pounds Maladaptation may occur to a pesticide that is even slightly rare (Figure 2, where 30 percent of the total population experienced compound 21. If one compound is "rare" for several years and then the other compound is made the rare one, the overall progress toward total resistance may be seriously retarded. If no alternation is made, resistance will evolve relatively quickly to the more common compound. Temporal Alternation Resistance evolution may be retarded if individuals are selected for resistance to one compound and then a few years later are selected for resistance to another compound. This technique will be effective only if tolerance to the two compounds is negatively genetically correlated. The expected results in this case are the same as in the extreme case of the alternating frequency of compounds described above. Use of More than Two Pesticides in a Given Area With a larger matrix of potentially antagonistic genetic correlations in tolerance, evolution may be retarded for even longer than in the two examples previously described. This approach, however, has two drawbacks: (1) resistance will evolve to many of the available compounds at once, decreasing reserves; and (2) with spatially patchy deployment a larger area would have to be involved, less- ening the degree of panmixia and reducing the retarding effect of antagonistic correlations in tolerance, which work only with mixing of individuals with different selection (pesticide exposure) histories. Simultaneous application of multiple pesticides is not the answer, since it could cause an increase in selection intensity and thus would probably speed rather than retard evolution of resistance. To improve the descriptive power of a quantitative genetic model of pes- ticide resistance, a model of directional selection that is not tied to the weak selection requirement is necessary. In such a model genetic variance for tolerance would be expected to be exhausted, and the response to selection would be a function of mutation. Such a model does not presently exist, although it is possible that a modification of Lande's (1983) treatment of the
QUANTITATIVE GENETIC MODELS 233 relative rates of spread of a single locus and polygenic characters under directional selection could provide a useful beginning. CONCLUSION These simple quantitative genetic models are only a first step toward a population-genetic and evolutionary approach to the problem of polygenic pesticide resistance. Problems in pest management must be addressed as evolutionary problems. The pests are evolving to become better adapted, not only to the use of toxic compounds but also to resistant plant varieties (Pathak and Heinrichs, 1982) and a host of other management practices. Pests, like every other class of organisms on earth, evolve by virtue of heritable genetic variation and selection by some environmental agent. Agroevolution differs from evolution in natural populations only in that humans impose selection in the form of various management strategies. Understanding the processes that lead to certain evolutionary outcomes is the function of population genetic modeling. The applicability of particular models is an empirical issue that cannot be resolved without experimental estimates of critical parameters in the models. Genetic variances and covariances (or correlations) in tolerance to different pesticides are virtually unknown. The quantitative genetic variance in tol- erance can be estimated by breeding individuals to generate families and then exposing some siblings from each family to the different compounds in replicate groups. If one notes the dose at which each individual dies, then variation in tolerance within and among families can be estimated. The among-family variations can be used to derive an estimate of the genetic variance for tolerance. Other parameters that require estimation are · The intensity of selection attributable to different compounds (Lance and Arnold, 1983) · The extent of migration among groups of individuals subjected to dif- ferent pesticides · The shape of the fitness functions for tolerance to different pesticides (Lance and Arnold, 19831: are they directional or stabilizing, and how well are they approximated by the usual exponential or Gaussian functions? Empiricists have another role: to determine the validity of the models as descriptions of evolution. Experiments must be designed to produce obser- vations of evolution in conjunction with models that can produce predictions based on parameters estimated before selection. Empiricists and theoreticians must work together. With a better under- standing of how pests evolve, improved strategies to retard that evolution can be developed.
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