Pest Control by Genetic Manipulation of Sex Ratio

Transcription

1 BIOLOGICAL AND MICROBIAL CONTROL Pest Control by Genetic Manipulation of Sex Ratio PAUL SCHLIEKELMAN, 1 STEPHEN ELLNER, 2 AND FRED GOULD 3 J. Econ. Entomol. 98(1): 18Ð34 (2005) ABSTRACT We model the release of insects carrying an allele at multiple loci that shifts sex ratios in favor of males. We model two approaches to sex ratio alteration. In the Þrst (denoted SD), meiotic segregation (or sperm fertility) is distorted in favor of gametes carrying the male-determining genetic element (e.g., Y-chromosome). It is assumed that any male carrying at least one copy of the SD allele produces only genotypically male offspring. In the second approach (denoted PM), the inserted allele alters sex ratio by causing genetically female individuals to become phenotypically male. It is assumed that any insect carrying at least one copy of the PM allele is phenotypically male. Both approaches reduce future population growth by reducing the number of phenotypic females. The models allow variation in the number of loci used in the release, the size of the release, and the negative Þtness effect caused by insertion of each sex ratio altering allele. We show that such releases may be at least 2 orders of magnitude more effective than sterile male releases (SIT) in terms of numbers of surviving insects. For example, a single SD release with two released insects for every wild insect and a 5% Þtness cost per inserted allele could reduce the target population to 1/1000th of the no-release population size, whereas a similar-sized SIT release would only reduce the population to one-þfth of its original size. We also compare these two sex ratio alteration approaches to a female-killing (FK) system and the sterile male technique when there are repeated releases over a number of generations. In these comparisons, the SD approach is the most efþcient with equivalent pest suppression achieved by release of 1 SD, 1.5Ð20 PM, 2Ð70 FK, and 16Ð3,000 SIT insects, depending on conditions. We also calculate the optimal number of SD and PM allele insertions to be used under various conditions, assuming that there is an additional genetic load incurred for each allelic insertion. KEY WORDS sterile male, multilocus, segregation distortion, pest control GENETIC METHODS FOR PEST control have a long, if mixed, history (Gould and Schliekelman 2004). The Þrst use of genetically altered insects for pest control was in the early 1960s when sterile male releases were used with spectacular success in eradicating the screwworm, Cochliomyia macellaria (F.), in the southwestern United States (Bushland 1974). This success sparked great interest and the sterile male technique (SIT) was subsequently used widely (Bushland 1974, Klassen et al. 1994), but the use of SIT with other insect species has been relatively disappointing. Although SIT has proven useful in geographically isolated settings and in preventing establishment of exotic pests, it has not lived up to its initial promise as a more general pest control technique. Experience has shown that a very large ratio of sterile to wild males must be maintained to achieve wild population reduction and must be achieved over an area large enough for migration to be low (Prout 1979) relative to population size. 1 Department of Statistics, University of Georgia, Athens, GA 30602Ð Department of Ecology and Evolutionary Biology, Cornell University, Ithaca, NY 14853Ð Department of Entomology, North Carolina State University, Raleigh, NC 27695Ð7634. Other genetic control techniques were researched in the 1960s and 1970s in an effort to improve on the efþciency of the sterile male technique (Whitten 1985): natural sterility (e.g., hybrid sterility and cytoplasmic incompatibility), translocations, meiotic drive and positive heterosis (to drive deleterious genes into the target population), and conditional lethal traits. Although promising, none of these techniques have been implemented on a large scale, due mainly to the difþculty in producing insects with the required characteristics. At least in part due to these technical problems, interest in genetic control techniques declined in the 1980s and 1990s (Gould and Schliekelman 2004). However, new genetic engineering techniques may be able to overcome these problems (for review, see Handler 2002). It may soon be feasible to mass-produce insects carrying a variety of engineered traits. The ability to do this would allow an array of new methods for pest control, with far more power than envisioned by earlier researchers. In three previous article, we modeled the release of pest insects carrying conditional lethal traits (Schliekelman and Gould 2000a, Schliekelman 2003) and female-killing (FK) traits (Schliekelman and Gould 2000b). We showed that such alleles could be /05/0018Ð0034$04.00/ Entomological Society of America

2 February 2005 SCHLIEKELMAN AND GOULD: PEST CONTROL BY GENETIC MANIPULATION OF SEX RATIO 19 spread widely through target populations in a small number of generations if inserted at multiple loci. Under appropriate circumstances, such releases would be orders of magnitude more effective than sterile male releases. Demonstrating the feasibility of such approaches, Thomas et al. (2000) and Heinrich and Scott (2000) described female-killing systems in Drosophila melanogaster (Meigen) (Diptera). They constructed laboratory strains in which a dominant female-killing trait is only expressed in the absence of tetracycline in the diet (Gossen and Bujard 1992). Although potentially very effective, both of these techniques have shortcomings. For high effectiveness, a conditional lethal trait needs at least four generations between the time of release and the activation of the conditional lethal trait (Schliekelman and Gould 2000a). Because most potential conditional lethal traits are triggered by annual events (e.g., a heat shock promoter or diapause-blocking trait), this would be difþcult to achieve in species with fewer than four generations per year. If there is selection against the conditional lethal alleles before lethality, then the triggering event cannot be delayed too much either, or selection will have removed most alleles before they are activated. Another problem is that there is no population control until the conditional lethal is activated. Finally, the conditional lethal gene is completely removed from the population once it is activated; thus, a new release must be made to get additional target population reduction. Releases with female-killing alleles are less powerful in ideal circumstances, but they have less stringent timing constraints and are less affected by Þtness damage caused by the insertion of the alleles (Schliekelman and Gould 2000b). In this article, we model the release of insects carrying alleles that distort an insect populationõs sex ratio either by interfering with the production and fertility of X-bearing sperm (in XY male systems), or by phenotypically masculinizing XX offspring through alteration of sexual development. We refer to these systems as the segregation distortion (SD) and phenotypically male (PM) systems, respectively. We refer to them collectively as sex ratio alteration (SRA) systems. Our theoretical analysis suggests that SRA alleles are potentially far more effective for pest control than either SIT, conditional lethal, or female-killing alleles. Alleles that interfere with the ability of X sperm to fertilize eggs have been studied for some time, both experimentally and theoretically, as an example of the general phenomenon of meiotic drive (Jaenike 2001). The potential to genetically alter sexual developmental pathways via transgenesis or transient gene expression is a new area of research. However, successful production of fertile XX males has been attained in Mediterranean fruit ßy, Ceratitis capitata (Wiedemann), through use of transient RNA interference (Pane et al. 2002). Because XX males are produced due to a gene product that inhibits the female developmental pathways, transgenes for male production are typically expected to be dominant. In natural systems, genes involved in sexual determination are found both on sex chromosomes and on autosomes. Although the master genes in the sexual determination pathway have differentiated extensively over evolutionary time, the genes that more closely regulate the sexual developmental pathways seem to be evolutionarily conserved (Graham et al. 2003). This later class of genes would therefore be more appropriate as a general tool for genetic control strategies intended for use in multiple species. Transgenes that could act by permitting only Y-bearing sperm to fertilize eggs (or that would not allow fertilization of Z-bearing eggs in species with heterogametic females) have not yet been discovered. However, we show here that such genes would be very effective for genetic control and would be worth pursuing. Both of these approaches have similarities to the female-killing system modeled in Schliekelman and Gould (2000b), but turn potential females into males instead of killing them. This increases the number of SRA-carrying males and keeps the frequency of the no-sra genotype (the only female-producing genotype) low for a longer period than is expected in the female-killing system. Questions Addressed in this Article. How effective are SRA systems at reducing pest populations in the ideal case? How do ideal SRA systems compare with ideal SIT, ideal conditional lethal (CL) releases, and ideal FK releases? By an ideal release, we mean one in which the released males have genetic Þtness equal to the wild males (although there will still be Þtness differences due to selection for equal sex ratio) and in which various ecological complications (e.g., weather or migration) are not acting. This gives a bound on the effectiveness of the method and is useful for comparisons with other pest control methods. How do reductions in fitness due to the insertion of the SRA alleles impact the effectiveness of the SRA technique? How does this compare with releases of insects carrying conditional lethal or female-killing alleles? It is unlikely that a large number of alleles can be inserted into the genome of an insect without doing some damage to Þtness (e.g., insertions within coding regions). Given this, how much genetic load can the released insects sustain and still be useful in spreading the SRA trait? Here, we are only concerned with variation in Þtness due to the genetic manipulations and assume that insects produced with all techniques, including sterile releases, have Þtness reduction due to laboratory rearing (for more detailed discussion, see Schliekelman and Gould (2000)). What is the optimal number of loci to use with the SRA technique? The probability that the descendents of matings between released and wild-type insects pass on no copies of the SRA allele to their offspring is reduced by each additional locus that the SRA allele is inserted on. If the SRA allele carries no Þtness cost, then it will be advantageous to use as many loci as possible. However, if each SRA allele carries a constitutively expressed Þtness cost, there should be an optimal locus number balancing the Þtness reduction in the released insects with the increase in fraction of offspring carrying the SRA allele.

3 20 JOURNAL OF ECONOMIC ENTOMOLOGY Vol. 98, no. 1 Materials and Methods Model Derivation. This model assumes that the released insects carry a dominant SRA allele that either 1) prevents X-bearing sperm from fertilizing eggs (SD system) or 2) causes all SRA-carrying individuals to be phenotypically male (PM system). We assume that the male determining element lies on the Y-chromosome, although the model is valid for any heterogametic species that has sex determined by a single chromosome or gene in males. The SRA alleles are carried in homozygous form on L loci in all released insects. The loci are all on somatic chromosome and far enough apart that the recombination fraction is one-half. We assume nonoverlapping generations. Derivation of Iteration Equations. Under our assumptions, all females carry 0 copies of the SRA allele, and a maleõs Þtness is determined by the number of copies of the SRA allele that he carries. Therefore, the state of the population in generation t is described by the probability distribution {F t (x), x 0, 1, 2,... } the proportion of males in generation t that carry x copies of the SRA allele. We need to derive an equation for F(x, t 1) in terms of F(x, t). We initially consider the SD system in which the SRA allele prevents production of X-chromosomebearing sperm or prevents X-bearing sperm from fertilizing eggs and therefore causes all offspring of SRAbearing males to be male. We assume that fertility of the SD-bearing males is not affected (see Discussion). A son (male offspring) in generation t 1 necessarily receives from its mother a gamete [X ], with X indicating an X-chromosome and 0 indicating the absence of the SRA allele on the autosomal locus where it has been inserted. From its father, the son receives a gamete [Y a 1 a 2...a L ], where Y indicates a Y-chromosome and each a i is a random draw from the fatherõs two alleles at that locus. For insects that are not newly released, one of the two alleles is necessarily a 0 (inherited from the fatherõs mother). The number of SRA alleles in the son is thus a binomial random variable, with parameters n equaling the number of copies of the SRA allele carried by the father, and p one-half (50% chance of inheriting each of the fatherõs SRA alleles). So given that the father carries z copies of the SRA allele, the probability that a son carries x copies is the binomial probability z x 2 1 x 1 2 z x z x [1] where ( x z ) is the standard binomial coefþcient, with the convention that ( x z ) 0ifx z. Fathers with 0 copies of the SRA allele contribute half as many Y-chromosome bearing gametes to the next generation as fathers with one or more copies of the SRA allele. The distribution of the number of SRA alleles in Y-chromosome bearing gametes is therefore proportional to{ 1 2 F t (0), F t (1), F t (2),... }. Normalizing these to sum to one gives the probability distribution for the number of SRA alleles in males contributing to the male gamete pool: F t z 1 2 F t F t 0 z 0 F t z F t 0 z 0 [2] Combining equations 1 and 2, we obtain the probability distribution for the number of SRA alleles in males of the next generation, L F t 1 x z x z x 2 1 z F t z. [3] If selection acts on paternal male genotypes, such that a male with z copies of the SRA allele has relative mating success W(z), then equation 2 is modiþed to 1 2 F t 0 w t F t 0 w t 0 z 0 F t z F t z w t z 1 1 [4] 2 F t 0 w t 0 z 0 L where w t (x) W(x)/ y 0 W(y)F t (y). Equation 3 remains the same, because gamete-phase selection is assumed not to occur. In the second system we consider, PM, all individuals carrying at least one SRA allele are phenotypically male. The ßow of gametes in the PM system is identical to the SD system except for gametes with 0 SRA alleles produced by SRA-bearing males. That is, sex is determined by the presence of SD alleles in the father, but the presence of PM alleles in the offspring. All offspring of SD-bearing males are male, whereas offspring of PM-bearing males who themselves have no PM alleles are one-half male and one-half female. Thus, the probability of being male in generation t is P t male 1 1 L 2 z z G t 1 z [5] where {G t (x), x 0, 1, 2,... } is the frequency of males in generation t that carry x copies of the PM allele. (1/2) z G t 1 (z) is the probability of a male with z PM alleles producing an offspring with 0 such alleles. Onehalf of these offspring will be female. Figure 4 shows the ßow of gametes from SRA-bearing males for the three systems (SD, PM, and FK) that we study. See Results for further discussion. The frequency among males of the genotype with x PM alleles is the joint frequency of a male-derived gamete having x PM alleles and being male divided by the probability of being male: G t x 2 1 i 0 L z x 1 1 L 2 z x 2 1 z G t 1 z z z G t 1 z, [6]

4 February 2005 SCHLIEKELMAN AND GOULD: PEST CONTROL BY GENETIC MANIPULATION OF SEX RATIO 21 Fig. 1. Diagram of matings in the release generation. I is the fraction that the released males make up of the total male population. W all-sra is the Þtness of the all-sra (released) genotype, W no-sra is the Þtness of the no-sra (wild) genotype, and W avg is the average Þtness of the population. The uppercase letters (A, B,... ) represent the SRA alleles on the loci (1, 2,... ) and lowercase letters indicate the absence of the SRA allele on the corresponding locus. where i 0 1 for x 0 and 0 otherwise. These equations are modiþed for selection on male genotypes in a manner identical to the previous system. Mackay et al. (1992) studied the effects of P-element insertions on viability of D. melanogaster. They found that each insertion decreased viability of insects by an average of 5.5% for heterozygotes and 12.2% for homozygotes. Regression of viability on number of insertions yielded an expression with signiþcant linear and quadratic terms. The resulting quadratic expression is reasonably approximated by a multiplicative expression of the form W X 1 s X [7] We use a Þtness function of this form, where W(X)is the Þtness of the male genotype with X introducedtype alleles. Note that this Þtness is relative to males only, and is in addition to selection resulting from the skewed sex ratio (see Results). Decreases in viability likely underestimate the total decrease in Þtness. However, Mackay et al. (1992) were working with random insertions events; these insertions can be screened to Þnd the ones that cause the least Þtness damage. More recently, Moreira et al. (2004) looked at the Þtness of transgenic mosquitoes and found no Þtness loss for one transgenic strain relative to a nontransgenic control and a large Þtness cost in another independent transgenic strain, indicating that low Þtness costs are possible for at least some transgenes. Catteruccia et al. (2003) found large Þtness reductions in four independent transgenic strains. However, unlike Moreira et al. (2004), there experimental design did not separate Þtness reductions due to inbreeding from reductions due to the transgenes themselves, and it seems that most of the Þtness was due to inbreeding (Moreira et al. 2004). Whereas inbreeding will be a major issue with transgenic strains, it is (at least in principle) preventable. For SRA releases, the impact of inbreed is very limited in generations subsequent to the release generation itself because all SRA-carrying individuals have a wild-type mother and therefore will not express deleterious recessive traits. We assume that all loci contribute equally to Þtness. Because the Þtness reduction is due to random damage to the genome caused by the insertion of the SRA alleles (e.g., insertions in coding regions), this assumption is unlikely to hold in reality. However, no major qualitative features seem to be lost by this assumption (Schliekelman and Gould 2000a, b). We make comparisons between SRA and sterile male releases. To make a fair comparison, we must include the Þtness reductions caused by the process of sterilization. Laboratory studies have shown that sterilized males have their mating competitiveness reduced to 20Ð50% of that of unsterilized males (Holbrook and Fujimoto 1970, Hooper and Katiyar 1971, Ohinata et al. 1971). The Release. We assume that the released population consists entirely of males carrying the introduced allele in homozygous form on L loci. This requires that the use of a mechanism for suppression of the SRA trait until release. A system similar to the female-killing traits engineered by Thomas et al. (2000) or Heinrich and Scott (2000) would sufþce. The matings in the Þrst release generation will be as shown in Fig. 1. All newly released insects are males homozygous for the SRA allele. In subsequent generations, we assume that wild females mate with newly released males in a proportion equal to the proportion that the newly released males make of the total male population. All offspring of such matings are heterozygotes at all L loci and the frequency F t (L) is modiþed accordingly. A single release in the model means a release during a single generation of the wild population and does not necessarily mean that all insects are released on one day. We assume that releases are conducted in such a way that all native female insects have an equal probability of mating with a released male (even if adult emergence is spread over time). We assume that the wild population has an equal sex ratio initially.

5 22 JOURNAL OF ECONOMIC ENTOMOLOGY Vol. 98, no. 1 Size of Population: SD System. Only males with no SD alleles produce female offspring. Therefore, the fraction of females in the population in generation t is F t 1 (0)/2. The size N t of the population relative to what it would have been with no release, assuming density independent mortality and fecundity, is t 1 N t F s 0. [8] s 0 Size of Population: PM System. All individuals with any PM alleles are phenotypically male. Therefore, the only phenotypically female individuals are those with no PM alleles. The number of females with no PM alleles is proportional to the frequency of the no-pm gametes produced last generation. The female reproduction in generation t is therefore R t z 0 (1/2) z L G t 1 (z). That is the normal production of females per female, R t, multiplied by the probability that the male mate produces a gamete with no PM alleles. Then the size M t of the population relative to what it would have been with no release, assuming density independent mortality, is L t 1 t 1 G s 0 G s 0 J t, M t s o where z G s z L J t z 1 s 0 [9] 2 1 z G s z [10] is the proportion of gametes that are no-pm but produced by PM-bearing males in generation t. Except where explicitly stated otherwise, population growth is assumed density independent. Repeated Releases and Density Dependence. If density dependence is important, then there will be compensation in the growth rate for any population reduction due to a release. In such cases, the effect of a single release will diminish with time. Most mass release strategies aim to eradicate target populations and repeated releases are necessary to achieve this goal. To explore the effectiveness of the SRA method at achieving eradication of a pest population, we must assume a model for density dependence. We use a simple threshold model to simulate pesticide spraying triggered by insect density. Each time the threshold is exceeded, the population is subjected to one-time pesticide mortality. Between such episodes, the population size grows according to equations 8 or 9 multiplied by the normal (in absence of release) population growth rate R t across generations. This model is fairly reasonable for a pest population subject to spraying. For all results using the density-dependent model in this article, the population is reduced to 20% of the spraying threshold each time the threshold is exceeded. Wild populations always start at 1/10 the threshold level. We also use a density-independent repeated release model in which the number of insects released is a constant fraction of the current wild population. If the population size is changing then this implies that the absolute size of the release also is changing. Although this model is not completely realistic, it does allow the exploration of repeated release dynamics without specifying a model for population growth and regulation. This has some advantages (discussed in Results). Model Simulation. We used a C program to iterate the difference equations and calculate output quantities. These iterations were exact and used no numerical approximations. Individual components of the model were tested against manual calculations. The full program was tested against manual calculations for one- and two-locus examples. This program is available upon request. Results No Fitness Cost of SRA Allele Insertion. Figs. 2 and 3 show outcomes for a single release where the number of released insects results in 80% of males being SRA carriers immediately after the release. The Þgures show 1) the frequency of the no-sra genotype in males and 2) the population size plotted against generations for L values ranging from 1 to 15 for the SD system (Fig. 2) and the PM system (Fig. 3). The initial no-sra frequency in males is 0.2 and it is for both systems and all values of L in the F1 generation. The two systems diverge after F1. SD System. The no-sd frequency in the F2 generation and beyond depends on L. The average SDcarrying male gives twice the contribution over no-sd males to the Y-bearing gamete pool going into the next generation. Thus, many more females mate with SDbearing males than with no-sd males in that generation. Because females carry no SD alleles, male offspring can carry only one SD allele at each locus. Therefore, each male offspring only has a one-half chance of inheriting an SD allele on each locus where its father carries one and SD alleles are quickly lost. All offspring of no-sd males are themselves no-sd and additional no-sd offspring are born to SD-bearing males. However, the no-sd frequency drops initially because SD-bearing males are making twice the contribution to the next generationõs gamete pool. If the number of SD loci is high, then SD-bearing males will typically be carrying many SD alleles in the early generations after the release. Thus, for several generations most of their offspring are carrying at least one SD allele and the no-sd individuals are at a heavy disadvantage in producing male gametes. Thus, we see the no-sd frequency drops for several generations when L is higher. However, SD alleles rapidly disappear and the distribution of male genotypes shifts from higher SD-allele numbers to lower SD-allele numbers. As this happens, more and more offspring of SDbearing males are no-sd and the disadvantage of no-sd individuals decreases. After a few generations, the no-sd frequency begins to increase. The lower L

6 February 2005 SCHLIEKELMAN AND GOULD: PEST CONTROL BY GENETIC MANIPULATION OF SEX RATIO 23 Fig. 2. Simulation output for a release of size 2:1 (released:wild insects) (I 0.8) SD release with no Þtness cost to the SD alleles in males. The left-hand panel shows the frequency of wild-type males (i.e., those with no SD alleles). The right-hand panel shows the population size relative to that with no release, assuming no density dependence. The numbers on the curves indicate the number of loci in the released insects that carry the SD allele. The population size for a 2:1 sterile male release also is shown. Note that the population sizes are on a log scale. is, the more quickly the genotype distribution shifts to lower numbers of SD alleles and the more quickly the no-sd frequency begins to increase. Note that this rapid loss of SD alleles can be understood in terms of selection due to the skewed sex ratio. All surviving females mate every generation, whereas many males do not mate. For every mating and every locus, one of the gametes contains no SD allele (because all females are no-sd genotype). The presence of an SD allele at a locus causes offspring to be male and thus lowers their chance of mating. Selection favors no SD allele at a locus because it increases the probability of being female from 0 to 0.5. In the absence of density effects, the size of the population (relative to what it would have been with no release) is the product of fraction of females across generations (equation 8). Thus, the relative population size drops rapidly. By 10 generations after the 2:1 release, the population size in the SD releases ranges from 10 2 for L 1Ð10 7 for L 15. This compares with a relative population size of 0.33 for the sterile male release of the same size (Fig. 2b). PM System. The dynamics of the PM system is similar. As noted in Materials and Methods, the dynamics of the SD and PM systems are identical except for the no-sra gametes produced by SRA-bearing males. In the PM system, these produce one-half male and onehalf females, whereas in the SD system all gametes produced by SD-bearing males are male-producing (because it is the genotype of the father, not the gametes, that determines sex of offspring in the SD system). There are two opposing effects due to this difference. First, it increases the frequency of females produced, which increases the population growth in the PM system relative to the SD system. Second, however, it also decreases the frequency of no-sra individuals among males, which decreases future numbers of females. The relative efþcacy of the systems is determined by which of these effects is more important. We can see from equations 8 and 9 that the following must hold for the population growth in generation t to be higher in the SD system than in the PM system: F t 0 G t 0 J t [11] Because F 1 (0) G 1 (0)), we see that the F2 population is always higher in the PM system than the SD system. Comparing Figs. 2a and 3a, we see that the

7 24 JOURNAL OF ECONOMIC ENTOMOLOGY Vol. 98, no. 1 Fig. 3. Simulation output for a release of size 2:1 (released : wild insects) (I 0.8) PM release with no Þtness cost to the PM alleles in males. Otherwise similar to Fig. 2. no-sd frequency is higher than the no-pm frequency in the F2 and beyond. For example for L 5, the no-sd frequency is 0.08 in the F2, 0.25 in the F3, and 0.45 in the F4. By comparison, the no-pm frequency is 0.07 in the F2, 0.16 in the F3, and 0.30 in the F4. However, the values of J t in the same generations are 0.20, 0.31, and 0.30, respectively. Thus, the difference in no-sd and no-pm frequency never becomes large enough to satisfy equation 11. The population size in the F10 and beyond with the SD system is an order of magnitude lower than with the PM system. This same pattern holds for other parameter values and the SD system always achieves greater population reduction than the PM. Examination of equations 4 and 6 shows that the difference in the no-pm and no-sd frequency in generation t can be written as 1 2 F t K t 1 F t 0 G t F t G t J 1 t 1 2 K t G t J t F t 1 0 [12] L where K t z 1 (1/2) z F s (z) is the proportion of gametes that are no-sd but produced by an SD-bearing father. The Þrst two terms are nearly equal in magnitude and thus cancel each out. They are equal in the F1 and the difference increases slowly from there, never being for Figs. 2 and 3. F t-1 (0) is bigger than G t-1 (0), but this is mostly canceled out by the smaller denominator in the second term. Most of the difference between F t (0) and G t (0) is from the third term, which is due to all of the no-sd gametes being male and only one-half of the no-pm gametes being male. The denominator (the probability of being male in the SD system) starts near one (0.9 for Fig. 2) and gradually drops to 0.5. Thus, the third term varies from 0.5K t 1 to K t. After the F1 generation K t is always smaller than J t, because the PM-bearing gamete frequencies are overall higher than the SDbearing ones. Therefore, the third term never exceeds J t and condition (equation 11) is never satisþed. Comparison to FK System. The dynamics of the FK system explored in Schliekelman and Gould (2000b) are identical to the PM system, except that FK-bearing females die before reproduction, whereas PM-bearing females are phenotypically male. See Fig. 4. In both systems, the current reproducing female population size is proportional to the frequency of wild-type (no-fk or no-pm) females. Thus, if the frequencies were equal, then the population reduction would be

8 February 2005 SCHLIEKELMAN AND GOULD: PEST CONTROL BY GENETIC MANIPULATION OF SEX RATIO 25 Fig. 4. Flow of gametes from males for the three systems. This Þgure shows the ßow of gametes created by SRA-bearing males in the three systems we study (FK, PM, and SD). In each case, X is the number of SRA alleles carried by the individual. In all three systems, a fraction 1 2 X of gametes carry no SRA alleles and the remainder carry at least one SRA allele. The way in which these gametes divide between male and female differs for the three systems and is shown here. the same. However, it is clear that, all else being equal, the no-fk frequency will be higher than the no-pm frequency. The contribution of FK allele-bearing males to the male gamete pool is weighted the same as the non-fk bearing males. Thus, the frequency of no-fk males immediately begins increasing from its level in the F1 generation. However, the no-sra frequency in both the PM and the SD system typically drops for a few generations because the contribution of no-sra males is weighted less than SRA-bearing males in determining the male genotype distribution. Therefore, the PM system is superior to the FK system. Comparisons between Fig. 3 and the parallel Þgure in Schliekelman and Gould (2000b) show that the population size in the PM system is 1Ð2 orders of magnitude lower than in the FK system. For example, the FK population in the F10 generation is 10 times higher for L 5 and 20 times higher for L 11. Effect of Fitness Cost to SRA Alleles in Males. The dynamics are more complicated when we include a Þtness cost to the SRA allele in males. Figures 5 and 6 show simulations of 2:1 releases with a 2.5 and 5% Þtness cost to the introduced SRA alleles in males for the SD and PM systems. The released insects carry 2L SRA alleles. As L is increased, the Þtness of the released individuals decreases and the relative Þtness of the no-sra individuals increases. The pattern is the same in the F1 generation (when the descendents of the released insects have L SRA-alleles). Thus, we see in Fig. 5a that the no-sra frequency in the F1 increases with L. For larger L values, the F1 no-sra frequency is higher than in the release generation. For s 0.025, the dynamics in the F2 generation and beyond are similar to the s 0 case: the no-sra frequency continues to decrease for one to several generations (depending on L) before beginning to increase. For s 0.05, the L 15 no-sra frequency increases again in the F2 generation before decreasing for another generation or two. This happens because the SRA alleles are still in high enough association in the F2 (and thus dragging each other down ) to make the no-sra Þtness sufþciently high to increase the no-sra frequency (even in the face of an increasing pool of SRA-bearing males). The decrease in population size is much less than with s 0. Selection keeps the no-sra frequencies higher, which keeps the frequencies of females higher. The difference is small for low L, but increases with L. The optimal L for s is around 13. At this L, the relative population size in generation 10 is For s 0.05, the optimal L in generation 10 is around 7. The relative population size is Whereas these population sizes are orders of magnitude larger than with the s 0 case, they are still very low even though this is the result of just a single release. The dynamics for the PM system with selection are very similar to the SD system, again with a difference in population size of about an order of magnitude. Optimal Locus Number. Figs. 7 and 8 show contour plots of the optimal value of L (Figs. 7a and 8a) and the population size at that L in the F10 generation (Figs. 7b and 8b) plotted against I (the fraction of the population that is released type immediately after the release) and s. This is for a single release in generation

9 26 JOURNAL OF ECONOMIC ENTOMOLOGY Vol. 98, no. 1 Fig. 5. Effect of a Þtness cost in males of the SD allele. a and b show simulation results for a 2:1 release with each SD allele carrying a 2.5% Þtness cost. c and d show a 2:1 release with the SD alleles carrying a 5% Þtness cost. The numbers on the curves indicate the number of loci in the released insects that carry the SD allele. For d in generation 10, the order of the curves from top to bottom is L 1, 15, 3, 13, 11, 5, 9, and 7. Note that the population size graphs are on a log scale. The Þtness cost refers to probability of achieving mating. 0. The optimal L is the value that gives the lowest population size in the F10 generation. The contours show optimal L for a given combination of I and s. For example, for the SD system the optimal L is between 4 and 6 for s 0.05 and I 0.6 (point A in the Þgure) If I is increased to 0.9, then the optimal L is between 6 and 8 (point B in the Þgure). We see that the optimal value of L decreases with increasing sñincreasing s raises the costs of the SRA alleles. Optimal L also increases with I (except for small I). Increasing the release size decreases the amount of favorable genetic variation and thus decreases the effectiveness of selection against the SRA allele. The gradient in optimal L is very steep (inþnite, in fact) with respect to I as I goes to one and with s as s goes to zero. At these limits, selection against the SRA alleles in males goes to zero and the optimal L goes to inþnity. However, optimal L decreases toward one when selection is at its maximum for high s and small to intermediate release sizes. There are only small differences in the optimal L between the SD and PM systems. Summary of Effect of Release Size and Strength of Selection against SRA Alleles. Figs. 7b and 8b show contours of the surviving population in generation 10 after a single release at optimal L plotted versus I and s. As expected, the surviving population increases as s increases and I decreases. The surviving population tracks closely with the optimal L. The gradient in s is steepest for intermediate release size, when selection is strongest. For large releases and small s, the surviving population is 2 orders of magnitude larger in the SD system than the PM. The difference shrinks as the release size becomes smaller and s becomes bigger. For example, at I 0.8 and s 0.025, the surviving PM population is 9 times larger than the surviving SD population. At I 0.1 and s 0.06, the PM population size is only about 2 times larger than the SD population. Repeated Releases and Density-Dependent Dynamics. If the goal of the pest control project is eradication of the local pest population, then repeated releases will usually be necessary. Sterile male releases have generally relied on repeated overßooding of the target population. With the threshold model for density regulation used in this study, the dynamics of the sterile male release are simple. If I is the release proportion (fraction of males which are sterile immediately after the release), R is the per capita growth rate, and W s is the mating Þtness of the sterile males relative to a Þtness of one for wild males, then the condition to achieve a decrease in population size with one release is

10 February 2005 SCHLIEKELMAN AND GOULD: PEST CONTROL BY GENETIC MANIPULATION OF SEX RATIO 27 Fig. 6. Effect of Þtness cost in males of the PM allele. Otherwise similar to Fig. 5. For d in generation 10, the order of the curves from top to bottom is L 1, 15, 3, 13, 11, 5, 9, and 7. 1 I / IW s 1 I 1 R. [13] Because the population growth rate is constant, except when the spraying threshold is exceeded, then releases once per generation of this size will continually decrease the population and eventually eradicate it. If the release proportion does not meet this criterion in the Þrst generation, then it never will (assuming that R 1). See Schliekelman and Gould (2000b) for more details. In an SRA release, the SRA alleles remain in males in the population for several generations and continue to cause a loss in reproduction until they are all removed from the population. If there are new releases in subsequent generations, then the frequency of SRA alleles can build and cause increasing levels of population reduction. Figure 9 shows the frequency of wild-type males (Fig. 9a) and the population size (Fig. 9b) when SD releases are conducted every generation. The threshold-spraying model for density regulation discussed in Materials and Methods was used. The release size is one released insect for every two wild insects at the time of initial release. The absolute size of the release remains constant, so that the relative size increases in subsequent generations as the population is reduced. For L 4, except L 16, the population size drops to eradication levels within 10Ð15 generations. With repeated releases, the frequency of SD alleles builds up very quickly and very few females mate with no-sd females and the population size decreases rapidly. The population size for a 1:2 sterile male release also is shown, and we see that no signiþcant population control occurs. For L 16, selection against the SD alleles is very high and the release is not effective. Figure 9, c and d, show similar plots for repeated PM releases with a release size of 1:1. The dynamics is similar. Both the relative and absolute effectiveness of the various pest control methods are strongly dependent on the speciþcs of the population model. Although the rank in effectiveness of the optimal use of each of the four methods is always the same (SD, PM, FK, and SIT), the magnitude of the differences changes substantially with different population models. The relationship between the methods is obscured (sometimes magniþed and sometimes diminished) by the effects of the population dynamics. A detailed examination of the effect of population dynamics is beyond the scope of this study. Rather than arbitrarily choosing a population model, we return to a focus on density-independent results for the comparison between methods under repeated releases.

11 28 JOURNAL OF ECONOMIC ENTOMOLOGY Vol. 98, no. 1 Fig. 7. Summary of the effect of release size and cost to SD alleles in males. Contour plots of the optimal L and the generation 10 population size at that L as functions of release size I and cost s of the SD alleles in males. In a, the contours show the optimal L for the given I and s. For example, the optimal L at s 0.05 and I 0.6 (point A in the Þgure) is 5 or 6. If I is increased to 0.9 (point B), then optimal L is 6Ð8. In b, the contours show the population size in generation 10 for the optimal L for the given I and s. Note that I is the fraction of males that are released type immediately after the release. This is related to the ratio of released to wild insects by N I/(2(1 I)), where N is the number of released insects to each wild insect. The waviness in the contours occurs because of interpolation between grid points by the graphing program. The steep gradient with respect to I as it goes to one is partly because the ratio of released to wild insects (which equals I/2/(1 I)) changes very rapidly as I approaches one. Thus, it is an artifact of the way in which the results are presented and is not a property of the dynamics of the system. The down side of this is that is not possible to model releases of constant size. To calculate the fraction of the population that newly released insects will compose, it is necessary to know the current population size relative to the release size. Because we are not specifying a population model, we cannot track the absolute population size. Instead, we assume that all releases make up a constant fraction of the population. Assuming that the wild population is being reduced in size by the releases, this implies that the releases are of smaller absolute size each generation. Although this is not realistic, it allows a clearer comparison of the different methods than in a density-dependent setting and is preferable because it is the relative and not the absolute effectiveness of the methods that is the focus of this study. Figures 10 and 11 show the surviving population size after 10 generations of releases for SD (Fig. 10a), PM (Fig. 10b), FK (Fig. 11a), and SIT (Fig. 11b) releases versus release fraction (I) and selection coefþcient (s). For the SIT release, the selection coefþcient is the total Þtness reduction of the sterile males, whereas for the other three plots it is the Þtness reduction per introduced type allele. The value of L was six (as opposed to Figs. 7 and 8 where the optimal L was calculated). We see that the effect of selection is less with repeated releases (as evidenced by the steeper contour lines in Figs. 10 and 11 than in Figs. 7 and 8). This is because with repeated releases, the population quickly becomes dominated by SRA alleles and there is little variation for selection to act on. We see very small population sizes by generation 10. For example, the population size for a 2:1 sized release with s 0.05 is for an SD release and for a PM release. However, the absolute magnitudes of the population sizes are not especially meaningful. More important is the relative sizes with the different methods. For the

12 February 2005 SCHLIEKELMAN AND GOULD: PEST CONTROL BY GENETIC MANIPULATION OF SEX RATIO 29 Fig. 8. Summary of the effect of release size and cost to PM alleles in males. Otherwise similar to Fig. 7. same parameter values, the FK population size is The SIT population size is in the range 10 4 to 10 5 for total Þtness reductions in the range 0.4Ð0.6. Perhaps the most relevant comparison is to determine the increase in release size needed for a less effective method to achieve the same population reduction as a more effective method. The ratio of released to wild insects is I/2/(1 I), relative to the initial wild population. The factor of two accounts for the wild females. The ratio of release sizes for release fractions I 1 and I 2 is I 1 (1 I 2 )/(1 I 1 )/I 2. For example, an SD release with I 0.85 and s 0.04 reduces the population to In order for an FK release with s 0.04 to reduce the population to 10 26, I must be equal to Using the above-mentioned formula, this means that the difference in numbers of released insects is about a factor of 4. To achieve the same population reduction with an SIT release with even full Þtness insects would require an I value of roughly 0.999, a release roughly 175 times bigger. The difference is more dramatic when we use realistic Þtness values for the sterilized males. Table 1 shows the number of insects required per SD insect for each method to achieve the same population reduction in the F10 generation as SD. Overall, we see that the PM releases require on the order of 1.5Ð2.5 as many insects as SD for smaller (1:2 and 2:1) releases and 10Ð20 times more for the larger release (25:1). FK releases require roughly 2Ð4 times as many insects as a comparable SD release for the smaller releases and up to 68 times more for the large release size. SIT releases require from 16 to 3,000 time more insects than SD. In all cases, the difference becomes larger for larger release sizes. This is because as I approaches 1, larger increments in number of released insects are needed to achieve the same increment in I. Tables showing the numerical values in these Þgures are available for detailed comparison at the Web site of P.S. ( uga.edu/faculty/schliekelman/paul.html). A similar approach can be used to explore the tradeoff between release size and selection coefþcient. For example at s 0, a release fraction I 0.5 results in a population size of for an SD release. At s 0.05, a release fraction of 0.65 achieves the same population reduction, a 1.9-fold increase in number of insects. Discussion Pane et al. (2002) recently succeeded in producing fertile XX male Mediterranean fruit ßies by injecting embryos with an RNA interference construct that interfered with production of Cctra, which is the structural and functional homolog of the Drosophila sexdetermination gene, transformer (tra). Although the XX males seemed to be Þt under laboratory condi-

13 30 JOURNAL OF ECONOMIC ENTOMOLOGY Vol. 98, no. 1 Fig. 9. Dynamics of SD (a and b) and PM (c and d) systems with repeated releases. The plot shows frequency of wild-type males (a and c) and the population size (b and d) when releases are conducted every generation. The SD release size is one released insect for every two wild insects, and the PM release size is one released insect for every one wild insect at the time of initial release and s for both. The absolute size of the release remains constant, so that the relative size increases in subsequent generations as the population is reduced. The threshold spraying model for density regulation discussed in the Methods section was used. The initial population was 1/10 of the spraying threshold and after spraying the population was reduced to one-þfth of the spraying threshold. Output is just after the release in the initial release generation, but just before the release in subsequent generations. The population curves disappear when the population drops below the ßoating point underßow threshold. tions, their potential to compete with wild males in a natural habitat is yet to be determined. The potential to produce fertile XX males based on expression of a single gene indicates that the theoretical results described in this article could have applicability in the near future. It should be noted that unlike the results with Mediterranean fruit ßy, older work with Drosophila has shown that there are speciþc genes on the Y-chromosome that are required for male fertility (Hackstein and Hochstenbach 1995). Therefore, although the expression of tra dsrna might result in male phenotypes, these males would expected to be sterile. To be effective, a transgenic insertion would at least need to include the tra double strand RNA and active fertility genes. In all of the constructs, expression of the transgenes would need to be regulated by a repressible promoter so that stocks with a 1:1 sex ratio could be produced in a rearing facility. However, the release of some sterile males is useful if they prevent fertile females from Þnding fertile mates. In the case of genes that alter sexual phenotype, Þtness of the altered individuals is a major concern. In contrast, a transgene that solely prevented X-bearing sperm from fertilizing eggs would not be expected to have impacts on other life stages unless the promoter was not tissue speciþc and the gene product had negative pleiotropic effects. A more likely problem for such a gene would be that the males carrying the gene would only produce one-half as many fertile sperm as other males. At high densities where females mated with multiple males, sperm competition could result in a disadvantage to the transformed insects. Under low densities, where most females only mated once, there also could be a disadvantage to these males if female reproduction was sperm limited (for a detailed discussion, see Jaenike 2001). How Effective Are SD and PM Systems at Reducing Pest Populations in the Ideal Case? How Does This Compare with FK and SIT Releases? Mass release strategies suffer from many complications, including migration of insects, poor timing of release, weather

14 February 2005 SCHLIEKELMAN AND GOULD: PEST CONTROL BY GENETIC MANIPULATION OF SEX RATIO 31 Fig. 10. Summary of the effect of release size (I) and per-allele Þtness cost (s) with a release in each generation for SD and PM releases. The releases are of constant release fraction and therefore of variable absolute size (see text). The value of L is 6. The Þgure is otherwise similar to Fig. 7. conditions, and a multitude of other factors. It is not possible to include all of these factors in modeling new genetic control strategies. We do, however, have decades of data on sterile male releases in a variety of Þeld conditions. We make comparisons between models of idealized sterile male releases and other genetic control strategies to get a sense of how these strategies will perform in the Þeld. As long as all other external factors such as timing and weather are equally problematic for all types of modiþed insect release, the results from our comparisons are informative. Figures 2 and 3 show that if released and wild insects are equally competitive (thus ignoring inbreeding, effects of laboratory rearing, and impacts of genetic manipulation), then SD and PM releases are orders of magnitude more effective than SIT at reducing pest populations. In a sterile male release, the population is reduced by the fraction that the sterile males make of the whole male population. Thus, a sterile male release of size 2:1 reduces the population to 20% of the size that it would have been (because the ratio among males only is 4:1). The SD and PM release reduce the population every generation by the fraction of SRAcarrying males in the previous generation. We see from Figs. 2a and 3a that the fraction of SRA-carrying males starts at 80% and increases for several generations before beginning to decrease. Thus, one SRA release is equivalent to multiple sterile releases. In insects where a high L is possible (e.g., insects with many chromosomes or high recombination rates within chromosomes), we can conceive of near-eradication of the target population with a single release. The rank of effectiveness of the four approaches that we have studied is SD PM FK SIT. For the repeated release scenario that we considered, one SD insect has the same effect as 1.5Ð20 PM insects, 2Ð70 FK insects, and 16Ð3,000 SIT insects. It is unclear how these differences would change under more realistic population conditions. Because it is possible to produce large numbers of insects, it may be most relevant to assume that releases will be large and to focus on the population reduction achievable. The relative advantage of SRA methods increases as the release size increases. After 10 generations of a 2:1 release, the difference between a surviving populations of, say, for SD, for PM, for FK, and 10 7 for SIT release might be the crucial difference between eradicating all insects and eradicating most (keeping in mind that the true population reduction will be much less than in our idealized models). Although SIT is clearly the least effective by far, it is difþcult to say whether the differences between SD, PM, and FK will

15 32 JOURNAL OF ECONOMIC ENTOMOLOGY Vol. 98, no. 1 Fig. 11. Summary of the effect of release size and Þtness cost for FK and SIT releases. For the FK release, s is the Þtness cost per allele. For SIT, s is the total Þtness cost. The Þgure is otherwise similar to Fig. 10. be signiþcant in the face of all of the other biological sources of variation in effectiveness (e.g., lower mating Þtness of XX males). To sort out the differences between these methods, it is critical to understand the Þtness effects of the speciþc insertions, and the population dynamics of the target insect, especially at low densities. How Do Reductions in Fitness Due to the Insertion of the SRA Alleles Impact the Effectiveness of the SRA Technique? How Does This Compare with Releases of Insects Carrying CL or FK Alleles?. In comparing SIT to control strategies using genetically engineered insects, it is useful to separate Þtness reductions due to Table 1. Number of insects required per SD insect for each method to achieve the same population reduction in the F10 generation as SD SD release size s PM FK SIT 1: :2 0.05/ : :1 0.05/ : ,864 25:1 0.05/ Release conditions are the same as for Figs. 10 and 11. The second column is the value of the selection coefþcient (0 or 0.05) for SD, PM, and FK and the total Þtness reduction (0 or 0.5) for SIT. genetic manipulation from Þtness reductions due to laboratory rearing. Undesired selection by laboratory conditions is likely to be an inescapable feature of mass-release strategies. However, damage to the insectõs genome caused by the insertion of new alleles is, at least in principle, under the control of the geneticist. It may be possible to minimize such damage by improving techniques or by screening many insertion events for those with the least Þtness cost. The Þtness reduction in SIT caused by irradiation (the genetic manipulation component) alone reduces Þtness to 20Ð50% of nonirradiated insects (see Introduction for citations). This percentage translates directly to the reduction in effectiveness of SIT. The picture for other genetic control techniques is more complicated, because the Þtness reduction depends on the number of insertions made into the insectõs genome and because the selection occurs over multiple generations instead of just one. Examining Figs. 7b and 8b, we see that for a single release the effectiveness of the SRA releases drops by roughly an order of magnitude for each increment of 0.01 in s. However, the methods are still highly effective even with this reduction. The results of Mackay et al. (1992) (discussed in Materials and Methods) indicate that s 0.05 is attainable. Figure 7b indicates that a single 2:1 SD release with s 0.07, for example, could reduce the

16 February 2005 SCHLIEKELMAN AND GOULD: PEST CONTROL BY GENETIC MANIPULATION OF SEX RATIO 33 target population to 1/1000 of its size with no release. By comparison, an equal size sterile release with no Þtness reduction in the sterile males reduces the population to one-þfth of its no-release size. The Þtness reduction caused by insertions is much less important under repeated release (which is the case of real interest), because the SRA allele becomes so common that there is little variation for selection to act on. In Fig. 10, we see that there is about an order of magnitude increase in surviving population per 0.01 increment of s for smaller release sizes, but little change with s for larger release sizes. Conditional lethal and SD releases perform similarly with s 0, but the SD release is far superior with s 0. SD is superior because the SD alleles cause much of their population reduction before there is time for selection to increase the no-sd genotype frequency substantially. The conditional lethal method is only effective when the conditional lethal alleles have at least three to four generations to spread before activation and during this time selection against the conditional lethal allele acts strongly. The FK method has a similar advantage over the conditional lethal method, but the selection that results from killing all FK-bearing females nulliþes this advantage. Because the SD alleles overcome this selection for a few generations by genetically replacing females with males instead of killing them, it is superior. Selection against the introduced alleles would be especially severe on newly released insects, which carry 2L allele copies. Any measures that could reduce this selection would be of great beneþt. For example, we have assumed that the insects experience a full generation of selection in the release generation. If the insects were released just before mating to reduce their exposure to selective forces, many more insects might survive to the Þrst mating. See Schliekelman (2003) for further discussion. It also might be bene- Þcial in some situations to release males that are hemizygotic for the SRD allele instead of homozygotic to reduce this selection. Because all non-newly released insects in the F1 and later generations have a wild-type mother, any deleterious recessive alleles or maternal effects that have become widespread in the released population under laboratory-rearing conditions will not be expressed. Thus, the impact of such traits will be similar between SIT, FK, and SRA releases. The apparent prevalence of such traits in laboratory-reared populations makes this a crucial advantage of these releases over conditional lethal releases and other genetic control strategies for which it is possible for both parents to be descendents of released insects. Production of insects for SIT releases has generally favored quantity over quality, attempting to overßood the target population. Figures 10 and 11 show that, in many cases, hundreds of times fewer insects are needed for SRA releases than sterile releases. It might then be advantageous to develop production systems that emphasize quality over quantity, to overcome what has been the biggest obstacle to success: the low Þtness of released insects. Figures 7 and 8 and 10 and 11 give information about the tradeoff between the quality and quantity of released insects. For example, Fig. 10 shows that 2:1 (I 0.8) SD release with s 0 achieves the same effect as a 3:1 (I 0.86) release with s Thus, if the cost of producing s 0 insects is 50% higher than producing s 0.04 insects, then it is best to use the s 0 insects. What Is the Optimal Number of Loci to Use in the SRA Technique? The optimal number of loci is highly variable, depending on the release size I and the strength of selection s against the SRA alleles. However, it is very similar between the SD and PM methods. It is 4Ð6 for intermediate s (0.03Ð0.05) and a large range of I (0.1Ð0.8). Optimal L increases quickly as I increases beyond 0.8 and the amount of favorable genetic variation begins decreasing rapidly (although the steepness of the gradient is partially an artifact; see Fig. 7 description). For the overßooding release sizes often used for SIT releases (e.g., 100:1 or higher), the optimal L is effectively inþnite. The optimal L also increases rapidly as s decreases. For a 2:1 release, it is around eight for s and 20 for s With the once-per-generation releases depicted in Figs. 9Ð11, the optimal L is less crucial. The frequency of SRA alleles increases rapidly and selection against the SRA alleles becomes ineffective as the available favorable genetic variation decreases. Thus, the optimal L becomes large. This method is most suitable for species such as Lepidoptera, which have a large number of chromosomes. For species such as Drosophila with only four chromosomes, the method will be less effective. We have assumed that the recombination fraction is one-half between all loci. This is reasonable for species with a large number of chromosomes, where each SRD allele can be inserted on a different chromosome. However, if L is substantially greater than the number of chromosomes such that some loci must lie close to each other on the same chromosome, then this will be not be reasonable. Other Issues. An important issue that we have not addressed is that of gene silencing. Gene silencing occurs when individuals carrying multiple copies of a gene do not express the trait because of interference in the transcriptional or posttranscriptional process. In this case, the SRA allele might be activated only when an individual has a small number of copies of the SRA alleles. The gene silencing would not have a major effect for releases with low L, but releases with high L would have very different dynamics. Males with high copy number would give rise to fertile females. However, as the linkage disequilibrium decreased, the males produced by these females would have only one or a few SRA alleles and would only produce male offspring. It is not clear from the literature whether this would be expected to be an issue for releases with SRA alleles. See Schliekelman and Gould (2000a) for further details. We have used a simple population model without age or spatial structure. In most cases, released and native insects would not be distributed uniformly. The movement characteristics of the species will be vital in determining how the SRA alleles spread after release.

17 34 JOURNAL OF ECONOMIC ENTOMOLOGY Vol. 98, no. 1 Furthermore, Prout (1979) showed that very small amounts of migration could destroy the effectiveness of sterile releases. This will be an issue with all massrelease schemes. Density dependence will have a major impact on mass release schemes and future work should include a detailed examination of the effect of density dependence on these methods. We also have ignored issues of timing in the release. The wild insects do not emerge all at one time, and it may not be easy to time the releases so that all emerging insects have the same probability of mating with a released insect. Another important omission from our work is assortative mating. If released insects inadvertently have characteristics recognizable to other insects, there may be a tendency to nonrandom mating that could reduce the effectiveness of the releases. All of these issues (besides gene silencing) are also issues with sterile male releases. Still, sterile male releases have had successes. Given that SRA releases would likely be far more powerful than sterile male releases, there is good reason to hope that they also would be far more successful. Acknowledgments We thank two anonymous reviewers for suggestions that helped to improve the manuscript. This work was in part supported by National Institutes of Health grant 1 R01 AI A2. References Cited Bushland, R. C Screwworm eradication program. Science (Wash. DC) 184: 1010Ð1011. Catteruccia, F., H.C.J. Godfray, and A. Crisanti Impact of genetic manipulation on the Þtness of Anopheles stephensi mosquitoes. Science 299: 1225Ð1227. Gossen, M., and H. Bujard Tight control of geneexpression in mammalian cells by tetracycline-responsive promoters. Proc. Natl. Acad. Sci. U.S.A. 89: 5547Ð5551. Gould, F., and P. Schliekelman Population genetics of autocidal control and strain replacement. Annu. Rev. Entomol. 49: 193Ð217. Graham, P., J. K. Penn, and P. Schedl Masters change, slaves remain. Bioessays 25: 1Ð4. Hackstein J.H.P., and R. Hochstenbach The elusive fertility genes of Drosophila Ðthe ultimate Haven for selfish genetic elements. Trends Genet. 11: 195Ð200. Handler, A. M Prospects for using genetic transformation for improved SIT and new biocontrol methods. Genetica 116: 137Ð149. Heinrich, J. C., and M. J. Scott A repressible femalespeciþc lethal genetic system for making transgenic insect strains suitable for a sterile-release program. Proc. Natl. Acad. Sci. U.S.A. 97: 8229Ð8232. Holbrook, F. R., and M. S. Fujimoto Mating competitiveness of unirradiated and irradiated Mediterranean fruit ßies. J. Econ. Entomol. 63: 1175Ð1176. Hooper, G.H.S., and K. P. Katiyar Competitiveness of gamma-sterilized males of the Mediterranean fruit ßy. J. Econ. Entomol. 64: 1068Ð1071. Jaenike, J Sex chromosome meiotic drive. Annu. Rev. Ecol. Syst. 32: 25Ð49. Klassen W., D. A. Lindquist, and E. J. Buyckx Overview of the joint FAO/IEA divisionõs involvement in fruit ßy sterile insects technique programs, pp. 3Ð26. In C. O. Calkins, W. Klassen, and P. Liedo [eds.], Fruit ßies and the sterile insect technique. CRC, Boca Raton, FL. Mackay, T.F.C., R. F. Lyman, and M. S. Jackson Effects of P element insertions on quantitative traits in Drosophila melanogaster. Genetics 130: 315Ð332. Moreira, L. A., J. Wang, F. H. Collins, and M. Jacobs-Lorena Fitness of mosquitoes expressing transgenes that inhibit Plasmodium development. Genetics 166: 1337Ð1341. Ohinata, K., D. L. Chambers, M. Fujimoto, S. Kashiwai, and R. Miyabara Sterilization of the Mediterranean fruit ßy by irradiation: comparative mating effectiveness of treated pupae and adults. J. Econ. Entomol. 64: 781Ð784. Pane, A., M. Salvemini, P. Delli Bovi, C. Polito, and G. Saccone The transformer gene in Ceratitis capitata provides a genetic basis for selecting and remembering the sexual fate. Development 129: 3715Ð3725. Prout, T Joint effects of release of sterile males and immigration of fertilized females on a density regulated population. Theor. Popul. Biol. 13: 40Ð71. Schliekelman, P Transient dynamics in multilocus invasions by transgenic organisms. J Math Biol. 46: 171Ð88. Schliekelman, P., and F. Gould. 2000a. Pest control by the introduction of a conditional lethal trait on multiple loci: potential, limitations, and optimal strategies. J. Econ. Entomol. 93: 1543Ð1565. Schliekelman, P., and F. Gould. 2000b. Pest Control by the release of insects carrying a female-killing allele on multiple loci. J. Econ. Entomol. 93: 1566Ð1579. Thomas, D. D., C. A. Donnelly, R. J. Wood, and L. S. Alphey Insect population control using a dominant, repressible, lethal genetic system. Science (Wash. DC) 287: 2474Ð2476. Whitten, M. J The conceptual basis for genetic control, pp. 465Ð528. In G. A. Kerkut and L. I. Gilbert [eds.], Comprehensive insect physiology, biochemistry, and pharmacology, vol. 12. Insect control. Pergamon, Oxford, England. Received 28 May 2004; accepted 8 October 2004.