Food supplementation to optimize inoculative release of the predatory bug Macrolophus pygmaeus in sweet pepper

Biological control is widespread in management of greenhouse sweet pepper crops. Several species of predatory mites, bugs, and parasitoids are used against a wide range of pest species. However, biological control of particular pests like aphids, caterpillars, and the tobacco whitefly, Bemisia tabaci Gennadius, remains problematic. Macrolophus pygmaeus Rambur (Hemiptera: Miridae) is a generalist predatory bug which is used on a large scale in Western European tomato greenhouses. It has already been demonstrated that M. pygmaeus is a valuable biocontrol option in sweet pepper crops, but it has yet to find its way into common practice. Macrolophus pygmaeus should be introduced at the start of the growing season and determining an optimal release strategy is a key step in this process. In tomato crops, M. pygmaeus requires supplemental food releases to reach sufficient population numbers and dispersal levels. In this study, the need for food supplementation in sweet pepper is investigated. Three strategies were tested: (1) no food supplementation, (2) local food supplementation, and (3) full field food supplementation. Both population numbers and dispersal rates of the second generation were higher under the third strategy. Macrolophus pygmaeus oviposits near food sources, therefore dispersal rates are higher when food is more spread out. Pest control was achieved in all treatments, but faster and at lower pest levels under the full field strategy.     

Evaluation of mirid predatory bugs and release strategy for aphid control in sweet pepper

Zoophytophagous predators of the family Miridae (Heteroptera), which feed both on plant and prey, often maintain a close relationship with certain host plants. In this study, we aimed to select a suitable mirid predatory bug for aphid control in sweet pepper. Four species were compared: Macrolophus pygmaeus (Rambur), Dicyphus errans (Wolff), Dicyphus tamaninii Wagner and Deraeocoris pallens (Reuter). They were assessed on their establishment on sweet pepper plants with and without supplemental food (eggs of the flour moth Ephestia kuehniella Zeller and decapsulated cysts of the brine shrimp Artemia franciscana Kellogg) and on their effects on aphids with releases before and after aphid infestations. None of the predator species was able to control an established population of aphids on sweet pepper plants; however, the predators M. pygmaeus and D. tamaninii could successfully reduce aphid populations when released prior to an artificially introduced aphid infestation. The best results were achieved with M. pygmaeus in combination with a weekly application of supplemental food. Hence, our results demonstrate that the order and level of plant colonization by mirid predators and aphids determines how successful biological control is. Further studies are needed to evaluate the performance of mirid predatory bugs in sweet pepper crops in commercial greenhouses with multiple pests and natural enemies, in particular to understand how increased variation in food sources affects their feeding behaviour and preferences.     

Genetically modified plants and plant protection problems: Progress and estimation of potential risks

In this review, the achievements and perspectives for the creation of transgenic plants are analyzed. Until now, virtually all commercially cultivated genetically modified plants have been developed for the purpose of getting a solution to the problem of plant protection: such plants carry transgenes conferring resistance to herbicides, pests, and viruses. Approaches used for the development of commercial genetically modified varieties resistant to herbicides, insects, and viruses were considered; strategic approaches and perspectives for the development of commercial genetically modified plants resistant to fungal and bacterial pathogens and nematodes were also examined. The ecological (including agronomic issues) and social risks connected with commercial cultivation of transgenic crops were discussed.     

Effect of emamectin benzoate under semi-field and field conditions on key predatory biological control agents used in vegetable greenhouses

Predatory arthropods are commonly used as biological control agents (BCAs). They are released in commercial vegetable greenhouses as primary elements of integrated pest management programmes for some of the most devastating pests on pepper and tomato in southeastern Spain. Emamectin benzoate, a macro-cyclic lactone insecticide derived from the avermectin family of natural products, is being developed for the control of Lepidoptera pests on a variety of crops in Europe including vegetables. The compatibility of emamectin benzoate with the predatory BCAs Amblyseius swirskii Athias-Henriot and Orius laevigatus (Fieber) in field trials (direct spray and aged residues) and Macrolophus pygmaeus (Rambur) and Chrysoperla carnea (Stephens) in semi-field studies was studied. Emamectin benzoate at the highest recommended concentration (14.25 mg L^?1) was compatible with A. swirskii and O. laevigatus when applied 3 days before the introduction of the arthropods, but it was toxic when directly sprayed. M. pygmaeus and C. carnea adults survived to direct spray applications.     

Development of a PCR‐based method to monitor arthropod dispersal in agroecosystems: Macrolophus pygmaeus (Hemiptera: Miridae) from banker plants to tomato crops

Development of conservation biological control programs requires the identification of sources that contribute to predator colonization of crops. Macrolophus pygmaeus (Rambur) (Hemiptera: Miridae) is an efficient polyphagous predator used in biological control programs in vegetable crops in Europe. We have developed a marking method based on spraying with a solution of the brine shrimp Artemia spp. (Anostraca: Artemiidae) cysts, followed by a PCR detection of Artemia DNA to monitor M. pygmaeus dispersal from banker plants to tomato crops. Experiments conducted in climatic chambers show that the topical application of this marking solution on M. pygmaeus does not significantly reduce adult longevity and that it is detected up to 6 d after the application. When this Artemia solution was applied on Calendula officinalis L. banker plants harboring M. pygmaeus and maintained outdoors, Artemia DNA was still detected on 62% of the insects after 6 d. The conducted field applications in commercial greenhouses have confirmed the usefulness of this method to monitor M. pygmaeus dispersal from banker plants to a newly planted tomato crop. This method can be used to assess arthropod movement, being an interesting molecular approach for further improving future pest management strategies.     

Microbial community of predatory bugs of the genus Macrolophus(Hemiptera: Miridae)

Background

The predatory mirids of the genus Macrolophus are key natural enemies of various economically important agricultural pests. Both M. caliginosus and M. pygmaeus are commercially available for the augmentative biological control of arthropod pests in European greenhouses. The latter species is known to be infected with Wolbachia -inducing cytoplasmic incompatibility in its host- but the presence of other endosymbionts has not been demonstrated. In the present study, the microbial diversity was examined in various populations of M. caliginosus and M. pygmaeus by 16S rRNA sequencing and denaturing gradient gel electrophoresis.

Results

Besides Wolbachia, a co-infection of 2 Rickettsia species was detected in all M. pygmaeus populations. Based on a concatenated alignment of the 16S rRNA gene, the gltA gene and the coxA gene, the first is phylogenetically related to Rickettsia bellii, whereas the other is closely related to Rickettsia limoniae. All M. caliginosus populations were infected with the same Wolbachia and limoniae-like Rickettsia strain as M. pygmaeus, but did not harbour the bellii-like Rickettsia strain. Interestingly, individuals with a single infection were not found. A PCR assay on the ovaries of M. pygmaeus and M. caliginosus indicated that all endosymbionts are vertically transmitted. The presence of Wolbachia and Rickettsia in oocytes was confirmed by a fluorescence in situ hybridisation. A bio-assay comparing an infected and an uninfected M. pygmaeus population suggested that the endosymbionts had minor effects on nymphal development of their insect host and did not influence its fecundity.

Conclusion

Two species of the palaearctic mirid genus Macrolophus are infected with multiple endosymbionts, including Wolbachia and Rickettsia. Independent of the origin, all tested populations of both M. pygmaeus and M. caliginosus were infected with three and two endosymbionts, respectively. There was no indication that infection with endosymbiotic bacteria had a fitness cost in terms of development and fecundity of the predators.

     

Sticky trap monitoring of a pest–predator system in glasshouse tomato crops: are available trap colours sufficient?

Monitoring of pest presence and population development in the crop during the season is essential for integrated pest management. Although many tools, for instance coloured sticky traps, have been developed, the full advantage of available information is rarely taken into account in decision‐making. The reasons behind include high workload in practice but also the poorly studied relationships between trap catches and populations in the crop. Here, we investigate whether commercially available coloured sticky traps can be used as tool to monitor population densities of a pest–predator system in glasshouse tomato. The response of Macrolophus pygmaeus (Rambur) (Hemiptera, Miridae) to blue and yellow sticky traps was tested in laboratory and glasshouse experiments. The results indicate that M. pygmaeus can be monitored equally well with both trap colours. The number of trapped insects showed good correlation with the population densities on the crop. Under growing conditions, more M. pygmaeus were trapped on blue compared with yellow sticky traps. However, due to the known preference of Trialeurodes vaporariorum (Westwood) (Hemiptera, Aleyrodidae), yellow traps should be used for a combined pest–predator monitoring.     

Effect of mass rearing on the genetic diversity of the predatory mite Amblyseius swirskii

Amblyseius swirskii Athias‐Henriot (Acari: Phytoseiidae) is a predatory mite used to control whiteflies and thrips in protected crops. This biocontrol agent, originating from the Eastern Mediterranean region, has been mass‐reared for commercial use since 2005 and is widely used in augmentative biocontrol programs. As a polyphagous predator, it has to cope with different biotic and abiotic factors. However, possible adaptation to mass rearing for production might be hindering its resilience and capacity for optimum performance in the field. In this study, we investigated the effect of long‐term mass rearing on the genetic diversity of A. swirskii. We identified six microsatellite loci from whole‐genome nanopore sequencing of A. swirskii and used these in a comparative analysis of the genetic diversity and differentiation in eight wild populations collected from Israel in 2017 and a commercially available population. Our results indicate that the commercial population is 2.5× less heterozygous than the wild A. swirskii. Furthermore, the commercial population has the highest genetic differentiation from all the natural populations, as indicated by higher pairwise F_st values. Overall, we show that commercially reared A. swirskii have reduced genetic variation compared to their wild counterparts, which may reduce their performance when released to control pests in an integrated pest management (IPM) context.     

Modelling the effects of inherited sterility for the application of the sterile insect technique

1 The sterile insect technique (SIT) involves the release of large numbers of sterile or partially‐sterile insects into a wild pest population to dilute the number of successful wild matings, with the eventual aim of eradication or area‐wide suppression. General population models, encompassing a wide range of SIT types, were used to derive principles for optimizing the success of SIT, with particular emphasis on the application of partial sterility leading to inherited sterility in the F₁ population. 2 The models show that inherited sterility can only be guaranteed to be more effective than complete sterility if matings between irradiated‐lineage partners are unsuccessful. This is widely assumed but rarely examined experimentally. 3 The models allow the critical overflooding ratio, φ_c, to be calculated for a particular target species, suggesting the release rate required to prevent population increase. Successful eradication using SIT alone should aim for a substantially higher release rate than suggested by φ_c. 4 The models show that pest populations may continue to increase in the first few generations of SIT releases, regardless of release rate, as irradiated‐lineage individuals infiltrate the population. This does not necessarily imply that the SIT programme will be unsuccessful in the longer term. 5For pests with overlapping generations, the models suggest that frequent small releases may be more effective than less frequent large releases, particularly when the average release rate is close to the critical threshold for success.     

Nesidiocoris tenuis as a pest in Northwest Europe: Intervention threshold and influence of Pepino mosaic virus

The use of Nesidiocoris tenuis (Hemiptera: Miridae) as a biocontrol agent is controversial as it is considered a pest in Northwest European tomato greenhouses, due to its tendency to damage the plant and fruit. Necessary chemical plant protection products to control N. tenuis have toxic side effects on important beneficials like Macrolophus pygmaeus (Hemiptera: Miridae), which jeopardizes the whole IPM programme. In this study, several commercial tomato greenhouses were monitored for mirid populations. The relationship between the number of N. tenuis individuals and plant damage was assessed in function of availability of prey and interaction with M. pygmaeus. These greenhouse data were used to determine a practical density intervention threshold. Next, the hypothesis that a Pepino mosaic virus (PepMV) infection increases plant and fruit damage by N. tenuis (as has been shown for M. pygmaeus) was tested. Plant damage occurred when the average number of predatory bugs in the head of the plant exceeded 16 per ten plants. Plant damage increased in severity at increasing predatory bug densities, independent of the availability of prey and M. pygmaeus presence. Plant and fruit damage were not affected by the presence of PepMV, as was shown for fruit damage in previous studies for M. pygmaeus. Our study provides a practical density intervention threshold for growers in greenhouse crops. Simple monitoring of the number of predatory bugs in the head of the plant can be used to take specific biocontrol actions. It was also shown that only the predatory bug N. tenuis itself causes damage, and there is no interaction with PepMV.     

Experimentally comparing the attractiveness of domestic lights to insects: Do LEDs attract fewer insects than conventional light types?

LED lighting is predicted to constitute 70% of the outdoor and residential lighting markets by 2020. While the use of LEDs promotes energy and cost savings relative to traditional lighting technologies, little is known about the effects these broad‐spectrum “white” lights will have on wildlife, human health, animal welfare, and disease transmission. We conducted field experiments to compare the relative attractiveness of four commercially available “domestic” lights, one traditional (tungsten filament) and three modern (compact fluorescent, “cool‐white” LED and “warm‐white” LED), to aerial insects, particularly Diptera. We found that LEDs attracted significantly fewer insects than other light sources, but found no significant difference in attraction between the “cool‐” and “warm‐white” LEDs. Fewer flies were attracted to LEDs than alternate light sources, including fewer Culicoides midges (Diptera: Ceratopogonidae). Use of LEDs has the potential to mitigate disturbances to wildlife and occurrences of insect‐borne diseases relative to competing lighting technologies. However, we discuss the risks associated with broad‐spectrum lighting and net increases in lighting resulting from reduced costs of LED technology.     

Comparing the effects of GM and non‐GM soybean varieties on non‐target arthropods

In order to guarantee the safety of genetically modified (GM) soybean crops, it is important to assess the potential toxicity of their expressed insecticidal proteins to non‐target organisms. In the present study, the effects of the GM soybean Insulin‐like Growth Factor (IGF), which is tolerant to the herbicide glufosinate, on plant‐dwelling non‐target insects and arachnids were evaluated in soybean agroecosystems. For comparison, the non‐GM parental cultivar of soybean Gwangan‐kong was used as a control. Data were collected in 2016 and 2017 via surveying at Ochang and Jeonju, Korea. In total, 13,031 individual insects and arachnids, representing 64 families in 11 orders, were captured during the study. Firstly, the results indicate that the GM soybean IGF did not negatively affect plant‐dwelling non‐target insects and arachnids. However, the numbers of captured individuals on both IGF and Gwangan‐kong were higher at Ochang in 2017. The occurrence of insect pests, natural enemies, and other insects differed significantly according to region, region and survey year, and survey year, respectively. In addition, the dominance, diversity, evenness, and richness indices for the collected insects varied significantly among the regions and survey years regardless of soybean variety. The score from PROXSCAL multidimensional scaling using combined data showed that insects and arachnids in different natural environments were separated by their cultivation regions and years irrespective of soybean cultivars.     

Genetic improvement of the biological control nematode Heterorhabditis bacteriophora (Rhabditidomorpha: Heterorhabditidae): heterosis effect enhances desiccation but not heat tolerance

The entomopathogenic nematode Heterorhabditis bacteriophora is commercially used in biological control of soil dwelling insect pests. It reproduces by autogamy (hermaphrodites) enabling the production of inbred lines, but also by amphimixis (through mating of male and female) which allows cross-breeding. When H. bacteriophora is produced in liquid culture, copulation of male and female is prevented and reproduction is solely by self-fertilisation of hermaphrodites. When reared in insects, crosses are possible resulting in heterozygous offspring. Heat and desiccation tolerance of these nematodes have been successfully improved by selective breeding. Trait deterioration was prevented by producing homozygous inbreds through consecutive reproduction in liquid culture, the method also used for commercial mass production. In this study, we investigated possible heterosis effects in desiccation and heat tolerance after cross-breeding of homozygous inbred lines of H. bacteriophora. Increased desiccation tolerance of the heterozygous progeny in comparison to homozygous inbred lines was recorded indicating that heterosis is a possible means for further improvement of this trait. In contrast, the heat tolerance of the heterozygous offspring was lower than that of the homozygous population. The results provide evidence for the tremendous potential of classical genetics to improve beneficial traits of a biological control agent and carry domestication of H. bacteriophora a significant step forward.     

Plant preference in the zoophytophagous generalist predator Macrolophus pygmaeus (Heteroptera: Miridae)

Macrolophus pygmaeus (Heteroptera: Miridae) is an omnivourus predator used to control several pests of horticultural greenhouses. With the aim to explore the relationship between M. pygmaeus and different host plants compared with tomato, plant preferences and bio-cycle traits were studied using: Capsicum annuum, Calendula officinalis, Salvia officinalis, Parietaria officinalis and Solanum nigrum. Species were selected among natural host crop and wild plants. Plant preference was measured by multi-choice host plant selection and olfactometric bioassays. Bio-cycle traits were assessed on reproduction and on nymphal development with and without animal diet support. Among tested plants, P. officinalis was the least attractive under laboratory conditions. Furthermore the availability of prey was crucial for the successful establishment of M. pygmaeus on tested plants, suggesting the inability of nymphs to complete development to adulthood on a strictly phytophagous diet. Nevertheless, M. pygmaeus seemed to prefer plants where phytophagy provides a fitness benefit.     

The omnivorous predator Macrolophus pygmaeus,a good candidate for the control of both greenhouse whitefly and poinsettia thrips on gerbera plants

The poinsettia thrips Echinothrips americanus Morgan is a relatively new pest that has spread rapidly worldwide and causes serious damage in both vegetable and ornamental plants. In this study, we investigated if and how effective this pest can be controlled in gerbera by the omnivorous predator Macrolophus pygmaeus (Rambur). Because herbivores on plants can interact through a shared predator, we also investigated how poinsettia thrips control is affected by the presence of the greenhouse whitefly Trialeurodes vaporariorum (Westwood), a pest that commonly coexists with E. americanus in gerbera. In laboratory studies, we found that the predator M. pygmaeus fed on both pests when offered together. Olfactometer tests showed a clear preference of the predators for plants infested by whiteflies but not by thrips. In a greenhouse experiment, densities of both pests on single gerbera plants were reduced to very low levels by the predator, either with both pests present together or alone. Hence, predator‐mediated effects between whiteflies and thrips played only a minor role. The plant feeding of the shared predator probably reduced the dependence of predator survival and reproduction on the densities of the two pests, thereby weakening potential predator‐mediated effects. Thus, M. pygmaeus is a good candidate for biological control of both pests in gerbera. However, further research is needed to investigate pest control at larger scales, when the pests can occur on different plants.     

Genetic Structure of Threatened Native Populations and Propagules Used for Restoration in a Clonal Species,American Beachgrass (Ammophila breviligulata Fern.)

An important goal of native plant restorations was to reconstitute populations that are genetically similar to native ones, thereby increasing the probably of successful establishment and persistence. We examined the extent to which this goal has been accomplished in Great Lakes restorations of Ammophila breviligulata Fern., a beachgrass species that is widely used for habitat restoration and is considered threatened in the study areas. In parallel studies on Lake Michigan and Lake Superior, we used polymorphic Intersimple Sequence Repeat markers to assess genetic similarity between well‐established and new native populations, restored populations, and restoration propagules obtained from two commercial suppliers. Native populations were generally more diverse than expected for a clonal species, whereas the commercially cultivated releases were monotypic. One of the commercial releases used in Minnesota was exclusively found in restored populations and did not occur in any other native population at this site. The propagules used in the newly planted restoration in Illinois were derived from a release that commercial suppliers maintain was derived from a native Michigan population, as opposed to a selected release. Diversity in this restoration was equivalent to that native Illinois’ populations; however, many of the genotypes were not of local origin. Overall, study underscores the importance of obtaining baseline genetic surveys of remnant native populations and restoration propagules before restoration efforts are initiated, especially when the populations are threatened or endangered.     

Agroforestry coffee soils increase the insect‐suppressive potential offered by entomopathogenic fungi over full‐sun soils: A case proposing a “bait survival technique”

Entomopathogenic fungi are important natural enemies of insects. However, there is little information on the insect‐suppressive potential of these fungi and possible effects of farming management on this. Meanwhile, changes in natural landscapes due to agricultural intensification have caused considerable biodiversity loss and consequent decay of ecosystem services. However, the adoption of practices such as agroforestry in agroecosystems can foster abiotic and biotic conditions that conserve biodiversity, consequently restoring the provision of ecosystems services. Here, we assessed the effect of management systems (agroforestry or full‐sun) on the pest‐suppressive potential of entomopathogenic fungi in Brazilian coffee plantations. We used the insect bait method coupled with survival analyses to assess the speed of kill by entomopathogenic fungi and their presence in soil samples from both farming systems. We found that insects exposed to agroforestry soils died more quickly than insects exposed to full‐sun soils. Of the fungi isolated from the bait insects, Metarhizium was found most frequently, followed by Beauveria. Meanwhile, Fusarium was frequently isolated as primary or secondary infections. We propose that the differential survival of insects is indicative of a greater suppressive potential by entomopathogenic fungi in agroforestry, and that this could be promoted by the diversified landscape, microclimatic stability, and reduced soil disturbance in agroforestry systems. Furthermore, our results provide a useful demonstration of the potential use of the insect bait method to investigate pest‐suppressive potential through bait insect mortality, and we term this the “bait survival technique.”     

Linking plant genes to insect communities: Identifying the genetic bases of plant traits and community composition

Community genetics aims to understand the effects of intraspecific genetic variation on community composition and diversity, thereby connecting community ecology with evolutionary biology. Thus far, research has shown that plant genetics can underlie variation in the composition of associated communities (e.g., insects, lichen and endophytes), and those communities can therefore be considered as extended phenotypes. This work, however, has been conducted primarily at the plant genotype level and has not identified the key underlying genes. To address this gap, we used genome‐wide association mapping with a population of 445 aspen (Populus tremuloides) genets to identify the genes governing variation in plant traits (defence chemistry, bud phenology, leaf morphology, growth) and insect community composition. We found 49 significant SNP associations in 13 Populus genes that are correlated with chemical defence compounds and insect community traits. Most notably, we identified an early nodulin‐like protein that was associated with insect community diversity and the abundance of interacting foundation species (ants and aphids). These findings support the concept that particular plant traits are the mechanistic link between plant genes and the composition of associated insect communities. In putting the “genes” into “genes to ecosystems ecology”, this work enhances understanding of the molecular genetic mechanisms that underlie plant–insect associations and the consequences thereof for the structure of ecological communities.     

Increased control of thrips and aphids in greenhouses with two species of generalist predatory bugs involved in intraguild predation

The combined release of species of generalist predators can enhance multiple pest control when the predators feed on different prey, but, in theory, predators may be excluded through predation on each other. This study evaluated the co-occurrence of the generalist predators Macrolophus pygmaeus Rambur and Orius laevigatus (Fieber) and their control of two pests in a sweet pepper crop. Both predators consume pollen and nectar in sweet pepper flowers, prey on thrips and aphids, and O. laevigatus is an intraguild predator of M. pygmaeus. Observations in a commercial sweet pepper crop in a greenhouse with low densities of pests showed that the two predator species coexisted for 8 months. Moreover, their distributions in flowers suggested that they were neither attracted to each other, nor avoided or excluded each other. A greenhouse experiment showed that the predators together clearly controlled thrips and aphids better than each of them separately. Thrips control was significantly better in the presence of O. laevigatus and aphid control was significantly better in the presence of M. pygmaeus. Hence, combined inoculative releases of M. pygmaeus and O. laevigatus seem to be a good solution for controlling both thrips and aphids in greenhouse-grown sweet pepper. The predators are able to persist in one crop for a sufficiently long period and they complement each other in the control of both pests. This study also provides further evidence that intraguild predation does not necessarily have negative effects on biological control.     

Pest control by the release of insects carrying a female-killing allele on multiple loci

With recent advances in genetics, many new strategies for pest control have become feasible. This is the second article in which we model new techniques for pest control based on the mass release of genetically modified insects. In this article we model the release of insects carrying a dominant and redundant female killing or sterilizing (FK) allele on multiple genetic loci. If such insects are released into a target population, the FK allele can become widely spread in the population through the males while reducing the population each generation by killing females. We allow the number of loci used to vary from 1 to 20. We also allow the FK allele to carry a fitness cost in males due to the gene insertions. Using a model, we explore the effectiveness and optimal strategies for such releases. In the most ideal circumstances (no density-dependence and released insects equal in fitness to wild ones), FK releases are several orders of magnitude more effective than equal sized sterile male releases. For example, a single release of 19 FK-bearing males for every two wild males, with the released males carrying the FK allele on 10 loci, reduces the target population to 0.002% of no-release size. An equal sized sterile release reduces the target population to 5% of no-release size. We also show how the effectiveness of the technique decreases as the fitness cost of the FK alleles in males increases. For example, the above mentioned release reduces the target population to 0.7% of no-release size if each FK allele carries a fitness cost in males of 5%. Adding a simple model for density-dependence and assuming that each of the released males carries the FK allele on six loci, we show that the release size necessary to reduce the target population to 1/100 of no-release size in 10 generations of releases varies from 0.44:1 to 4:1 (depending on parameter values). We also calculate the optimal number of loci on which to put the FK allele under various circumstances.