Group Movement in Entomopathogenic Nematodes: Aggregation Levels Vary Based on Context.

Maintenance of an aggregated population structure implies within-species communication. In mixed-species environments, species-specific aggregations may reduce interspecific competition and promote coexistence. We studied whether movement and aggregation behavior of three entomopathogenic nematode species changed when isolated, as compared to mixed-species arenas. Movement and aggregation of Steinernema carpocapsae, S. feltiae and S. glaseri were assessed in sand. Each species demonstrated significant aggregation when alone. Mixed-species trials involved adding two species of nematodes, either combined in the center of the arena or at separate corners. While individual species became less aggregated than in single-species conditions when co-applied in the same location, they became more aggregated when applied in separate corners. This increased aggregation in separate-corner trials occurred even though the nematodes moved just as far when mixed together as they did when alone. These findings suggest that maintenance of multiple species within the same habitat is driven, at least in part, by species-specific signals that promote conspecific aggregation, and when the species are mixed (as occurs in some commercial formulations involving multiple EPN species), these signaling mechanisms are muddled.

Enhancing entomopathogenic nematode efficacy with Pheromones: A field study targeting the pecan weevil.

Consistent efficacy is required for entomopathogenic nematodes to gain wider adoption as biocontrol agents. Recently, we demonstrated that when exposed to nematode pheromone blends, entomopathogenic nematodes showed increased dispersal, infectivity, and efficacy under laboratory and greenhouse conditions. Prior to this study, the impact of entomopathogenic nematode-pheromone combinations on field efficacy had yet to be studied. Steinernema feltiae is a commercially available entomopathogenic nematode that has been shown to increase mortality in insect pests such as the pecan weevil Curculio caryae. In this study, the pecan weevil was used as a model system to evaluate changes in S. feltiae efficacy when treated with a partially purified ascaroside pheromone blend. Following exposure to the pheromone blend, the efficacy of S. feltiae significantly increased as measured with decreased C. caryae survival despite unfavorable environmental conditions. The results of this study highlight a potential new avenue for using entomopathogenic nematodes in field conditions. With increased efficacy, using entomopathogenic nematodes will reduce reliance on conventional management methods in pecan production, translating into more environmentally acceptable practices.

Strategies for eQTL mapping in allopolyploid organisms.

KEY MESSAGE: This study uses simulations to explore statistical power and false-positive rates for eQTL mapping in allopolyploid organisms and provides guidelines to apply eQTL mapping in these organisms. In recent years, RNA-seq has become the dominant technology for eQTL studies. However, most work has been in diploid organisms. Many species of economic and environmental importance are polyploid, and approaches for eQTL mapping in polyploids are not well developed. High similarity between duplicated genes in polyploids will cause misassignment of sequence reads and may cause false-positive results and/or lack of power to detect eQTL. In this paper, we first explore the similarity of homoeologous transcripts in polyploid organisms. We find that 5-20% of genes (varying with organism) in important agricultural plants such as wheat, soybean, and switchgrass are not sufficiently diverged between duplicated genomes to allow unambiguous assignment of reads. Second, we examine the impact of misassigned reads on eQTL mapping and show that both false-positive and false-negative rates can be greatly inflated. Third, we compare four strategies for dealing with ambiguous reads: (1) dividing ambiguous reads evenly between homoeologous transcripts, (2) assigning them proportionally, (3) using all reads for all genes, and (4) discarding ambiguous reads. We find that the strategy of discarding ambiguous reads gives the best balance of false-positive and false-negative rates for most genes. However, for genes that are very similar between genomes, using all reads is the only choice. This leads to reduced power, but false-positive rates will be maintained. We also discuss QTL mapping in polyploids using allele-specific expression (ASE) and show how the proportion of ASE-informative reads varies according to the divergence between homoeologous genes.

SEG - A Software Program for Finding Somatic Copy Number Alterations in Whole Genome Sequencing Data of Cancer.

As next-generation sequencing technology advances and the cost decreases, whole genome sequencing (WGS) has become the preferred platform for the identification of somatic copy number alteration (CNA) events in cancer genomes. To more effectively decipher these massive sequencing data, we developed a software program named SEG, shortened from the word "segment". SEG utilizes mapped read or fragment density for CNA discovery. To reduce CNA artifacts arisen from sequencing and mapping biases, SEG first normalizes the data by taking the log2-ratio of each tumor density against its matching normal density. SEG then uses dynamic programming to find change-points among a contiguous log2-ratio data series along a chromosome, dividing the chromosome into different segments. SEG finally identifies those segments having CNA. Our analyses with both simulated and real sequencing data indicate that SEG finds more small CNAs than other published software tools.

Movement patterns in Entomopathogenic nematodes: Continuous vs. temporal.

To exploit resources, animals implement various foraging behaviors to increase their fitness. Entomopathogenic nematodes are obligate parasites of insects in nature. In previous studies, entomopathogenic nematodes were reported to exhibit group movement behavior in the presence and absence of insect hosts. However, it was not determined if group movement is continuous or temporal. For example, nematode movement behavior upon emergence from the host might start out in an independent fashion prior to aggregation, or group movement may be exhibited continuously. In the present study, we explored the propensity for innate group movement behavior of two insect parasitic nematodes in two families and genera: Heterorhabditis indica and Steinernema carpocapsae. We hypothesized the nematode populations would initially move independently from their origin and then come together for group movement. Movement patterns were investigated in sand when nematodes were applied in aqueous suspension (via filter paper) to a specific locus or when the nematodes emerged naturally from infected insect hosts. To compare nematode movement behavior over time and space, nematode dispersal was monitored at three distances (2.5, 4.5 and 8.0 cm) from the center (origin) and at two different time periods, 2 days and 3 days after nematode addition. We discovered that nematode dispersal continuously exhibited an aggregative pattern (independent movement was not observed). Results from both nematode species as well as the host-cadaver and filter paper (aqueous nematode suspension) application methods indicated a continuous aggregative pattern. The discovery of continuous aggregative movement patterns in steinernematid and heterorhabditid nematodes elucidates further the complexity of their foraging behavior and may serve as basis for exploring foraging behavior in other host-parasite systems.

RElative QUantitation Inferred by Evaluating Mixtures (REQUIEM).

Motivated by the lack of easily implementable and generally applicable strategies to increase and assess data accuracy, we devised a novel label-free approach, termed REQUIEM, to address challenges in relative quantitation. For comparing the relative amounts of analytes in two samples, a mixture is prepared from aliquots of the samples, and the samples and the mixture are analyzed in parallel according to the intended workflow. Processing of the resulting data using the REQUIEM algorithm yields unbiased analyte fold-changes and associated statistics, allowing several types of errors to be diagnosed or eliminated. Extensive simulations and analysis of carefully prepared standard samples demonstrated the rigorous foundations of REQUIEM. We applied REQUIEM to several real-world analytical techniques and workflows, notably to tandem mass spectrometry analysis by using isomeric oligosaccharides as test analytes. We conclude that REQUIEM can reveal inaccuracies in the data that are difficult to identify by using traditional approaches.

Unsupervised statistical discovery of spaced motifs in prokaryotic genomes.

BACKGROUND: DNA sequences contain repetitive motifs which have various functions in the physiology of the organism. A number of methods have been developed for discovery of such sequence motifs with a primary focus on detection of regulatory motifs and particularly transcription factor binding sites. Most motif-finding methods apply probabilistic models to detect motifs characterized by unusually high number of copies of the motif in the analyzed sequences. RESULTS: We present a novel method for detection of pairs of motifs separated by spacers of variable nucleotide sequence but conserved length. Unlike existing methods for motif discovery, the motifs themselves are not required to occur at unusually high frequency but only to exhibit a significant preference to occur at a specific distance from each other. In the present implementation of the method, motifs are represented by pentamers and all pairs of pentamers are evaluated for statistically significant preference for a specific distance. An important step of the algorithm eliminates motif pairs where the spacers separating the two motifs exhibit a high degree of sequence similarity; such motif pairs likely arise from duplications of the whole segment including the motifs and the spacer rather than due to selective constraints indicative of a functional importance of the motif pair. The method was used to scan 569 complete prokaryotic genomes for novel sequence motifs. Some motifs detected were previously known but other motifs found in the search appear to be novel. Selected motif pairs were subjected to further investigation and in some cases their possible biological functions were proposed. CONCLUSIONS: We present a new motif-finding technique that is applicable to scanning complete genomes for sequence motifs. The results from analysis of 569 genomes suggest that the method detects previously known motifs that are expected to be found as well as new motifs that are unlikely to be discovered by traditional motif-finding methods. We conclude that our approach to detection of significant motif pairs can complement existing motif-finding techniques in discovery of novel functional sequence motifs in complete genomes.

A Multivariate Mixture Model to Estimate the Accuracy of Glycosaminoglycan Identifications Made by Tandem Mass Spectrometry (MS/MS) and Database Search.

We present a statistical model to estimate the accuracy of derivatized heparin and heparan sulfate (HS) glycosaminoglycan (GAG) assignments to tandem mass (MS/MS) spectra made by the first published database search application, GAG-ID. Employing a multivariate expectation-maximization algorithm, this statistical model distinguishes correct from ambiguous and incorrect database search results when computing the probability that heparin/HS GAG assignments to spectra are correct based upon database search scores. Using GAG-ID search results for spectra generated from a defined mixture of 21 synthesized tetrasaccharide sequences as well as seven spectra of longer defined oligosaccharides, we demonstrate that the computed probabilities are accurate and have high power to discriminate between correctly, ambiguously, and incorrectly assigned heparin/HS GAGs. This analysis makes it possible to filter large MS/MS database search results with predictable false identification error rates.

Prioritizing hypothesis tests for high throughput data.

MOTIVATION: The advent of high throughput data has led to a massive increase in the number of hypothesis tests conducted in many types of biological studies and a concomitant increase in stringency of significance thresholds. Filtering methods, which use independent information to eliminate less promising tests and thus reduce multiple testing, have been widely and successfully applied. However, key questions remain about how to best apply them: When is filtering beneficial and when is it detrimental? How good does the independent information need to be in order for filtering to be effective? How should one choose the filter cutoff that separates tests that pass the filter from those that don't? RESULT: We quantify the effect of the quality of the filter information, the filter cutoff and other factors on the effectiveness of the filter and show a number of results: If the filter has a high probability (e.g. 70%) of ranking true positive features highly (e.g. top 10%), then filtering can lead to dramatic increase (e.g. 10-fold) in discovery probability when there is high redundancy in information between hypothesis tests. Filtering is less effective when there is low redundancy between hypothesis tests and its benefit decreases rapidly as the quality of the filter information decreases. Furthermore, the outcome is highly dependent on the choice of filter cutoff. Choosing the cutoff without reference to the data will often lead to a large loss in discovery probability. However, naïve optimization of the cutoff using the data will lead to inflated type I error. We introduce a data-based method for choosing the cutoff that maintains control of the family-wise error rate via a correction factor to the significance threshold. Application of this approach offers as much as a several-fold advantage in discovery probability relative to no filtering, while maintaining type I error control. We also introduce a closely related method of P-value weighting that further improves performance. AVAILABILITY AND IMPLEMENTATION: R code for calculating the correction factor is available at http://www.stat.uga.edu/people/faculty/paul-schliekelman CONTACT: pdschlie@stat.uga.edu SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Quantifying the effect of competition for detection between coeluting peptides on detection probabilities in mass-spectrometry-based proteomics.

There are many factors that contribute to the variation in detection probabilities of proteins in LC-MS/MS experiments, and currently little is known about their relative importance. In this study, we analyze the effect of competition for detection between coeluting peptides on peptide detection probability. Using a novel method for estimating peptide detection probabilities, we show that these probabilities can vary by an order of magnitude between peptides that elute from the liquid chromatograph at the same time as many other peptides and those that elute with fewer other peptides. To explore these results, we use a mathematical model to show that competition for detection between peptides is expected to be a major source of missed detections in complex mixtures because there will be many MS/MS scanning intervals that contain more coeluting peptides than can be subjected to MS/MS analysis. Our data and simulation results show that the number of coeluting peptides is a primary determinant of whether a peptide will be detected. In our data, this had a several-fold larger effect on peptide detection probability than did peptide abundance. Furthermore, the distribution of elution times for the most frequently detected peptides was strongly shifted toward values where there were few coeluting peptides, indicating that the number of coeluting peptides is a major determinant of whether a peptide is proteotypic.

Aggregative group behavior in insect parasitic nematode dispersal.

Movement behavior of foraging animals is critical to the determination of their spatial ecology and success in exploiting resources. Individuals sometimes gain advantages by foraging in groups to increase their efficiency in garnering these resources. Group movement behavior has been studied in various vertebrates. In this study we explored the propensity for innate group movement behavior among insect parasitic nematodes. Given that entomopathogenic nematodes benefit from group attack and infection, we hypothesised that the populations would tend to move in aggregate in the absence of extrinsic cues. Movement patterns of entomopathogenic nematodes in sand were investigated when nematodes were applied to a specific locus or when the nematodes emerged naturally from infected insect hosts; six nematode species in two genera were tested (Heterorhabditis bacteriophora, Heterorhabditis indica, Steinernema carpocapsae, Steinernema feltiae, Steinernema glaseri and Steinernema riobrave). Nematodes were applied in aqueous suspension via filter paper discs or in infected insect host cadavers (to mimic emergence in nature). We discovered that nematode dispersal resulted in an aggregated pattern rather than a random or uniform distribution; the only exception was S. glaseri when emerging directly from infected hosts. The group movement may have been continuous from the point of origin, or it may have been triggered by a propensity to aggregate after a short period of random movement. To our knowledge, this is the first report of group movement behavior in parasitic nematodes in the absence of external stimuli (e.g., without an insect or other apparent biotic or abiotic cue). These findings have implications for nematode spatial distribution and suggest that group behavior is involved in nematode foraging.

Identification of altered MicroRNA expression in canine lymphoid cell lines and cases of B- and T-Cell lymphomas.

Canine lymphoma is a common spontaneous tumor with many similarities to human lymphoma, and thus has potential to be an important animal model of lymphomagenesis. This study determined that microRNA (miRNA) expression in canine tumors can be assessed using a commercially available human cancer miRNA qPCR array. miRNA expression in six different canine lymphoid cell lines and in naturally occurring canine B- and T-cell lymphomas was compared using RNA harvested from normal canine peripheral blood mononuclear cells (PBMC) and normal lymph nodes (LN) as controls. We found that false discovery rate (FDR) correction for multiple testing after quantile normalization controlled for variation across arrays and that they were the best methods for normalization and statistical analysis. Increases in miRNAs known to upregulate oncogenes (miR19a+b, miR17-5p) and decreased expression of miRNAs with tumor suppressor functions (miR-203, miR-218, and miR-181a) also seen in human lymphoid malignancies were observed. However, there were few similarities between canine groups. The results of this study indicate that the use of both PBMC and LN cells as controls provides different, but potentially equally important targets for further analysis. Our findings of miRNA dysregulation in canine lymphoid cell lines and clinical cases of lymphoma emphasize the potential of canine lymphoma as an important spontaneous, large animal model of human B- and T-cell lymphomas.

A genetical genomics approach to genome scans increases power for QTL mapping.

We describe a method for integrating gene expression information into genome scans and show that this can substantially increase the statistical power of QTL mapping. The method has three stages. First, standard clustering methods identify small (size 5-20) groups of genes with similar expression patterns. Second, each gene group is tested for a causative genetic locus shared with the clinical trait of interest. This is done using an EM algorithm approach that treats genotype at the putative causative locus as an unobserved variable and combines expression information from all of the genes in the group to infer genotype information at the locus. Finally, expression QTL (eQTL) are mapped for each gene group that shares a causative locus with the clinical trait. Such eQTL are candidates for the causative locus. Simulation results show that this method has far superior power to standard QTL mapping techniques in many circumstances. We applied this method to existing data on mouse obesity. Our method identified 27 putative body weight QTL, whereas standard QTL mapping produced only one. Furthermore, most gene groups with body weight QTL included cis genes, so candidate genes could be immediately identified. Eleven body weight QTL produced 16 candidate genes that have been previously associated with body weight or body weight-related traits, thus validating our method. In addition, 15 of the 16 other loci produced 32 candidate genes that have not been associated with body weight. Thus, this method shows great promise for finding new causative loci for complex traits.

Statistical power of expression quantitative trait loci for mapping of complex trait loci in natural populations.

A number of recent genomewide surveys have found numerous QTL for gene expression, often with intermediate to high heritability values. As a result, there is currently a great deal of interest in genetical genomics--that is, the combination of genomewide expression data and molecular marker data to elucidate the genetics of complex traits. To date, most genetical genomics studies have focused on generating candidate genes for previously known trait loci or have otherwise leveraged existing knowledge about trait-related genes. The purpose of this study is to explore the potential for genetical genomics approaches in the context of genomewide scans for complex trait loci. I explore the expected strength of association between expression-level traits and a clinical trait, as a function of the underlying genetic model in natural populations. I give calculations of statistical power for detecting differential expression between affected and unaffected individuals. I model both reactive and causative expression-level traits with both additive and multiplicative multilocus models for the relationship between phenotype and genotype and explore a variety of assumptions about dominance, number of segregating loci, and other parameters. There are two key results. If a transcript is causative for the disease (in the sense that disease risk depends directly on transcript level), then the power to detect association between transcript and disease is quite good. Sample sizes on the order of 100 are sufficient for 80% power. On the other hand, if the transcript is reactive to a disease locus, then the correlation between expression-level traits and disease is low unless the expression-level trait shares several causative loci with the disease--that is, the expression-level trait itself is a complex trait. Thus, there is a trade-off between the power to show association between a reactive expression-level trait and the clinical trait of interest and the power to map expression-level QTL (eQTL) for that expression-level trait. Gene expression-level traits that are most strongly correlated with the clinical trait will themselves be complex traits and therefore often hard to map. Likewise, the expression-level traits that are easiest to map will tend to have a low correlation with the clinical trait. These results show some fundamental principles for understanding power in eQTL-based mapping studies.

Kin selection and evolution of infectious disease resistance.

Discoveries of mutations conferring resistance to infectious diseases have led to increased interest in the evolutionary dynamics of disease resistance. Several recent papers have estimated the historical strength of selection for mutations conferring disease resistance. These studies are based on simple population genetic models that do not take account of factors such as spatial and family structure. Such factors may have a substantial impact on the strength of natural selection through inclusive fitness effects. That is, people have a strong tendency to live with relatives and therefore have a high probability of transmitting infectious diseases to them. Thus, an allele that protects an individual against disease infection also protects that individual's family members. Because some of these family members are likely to also be carrying the allele, selection for that allele is magnified by family structure. In this paper, I use mathematical modeling techniques to explore the impact of such kin selection on the strength of selection for infectious disease resistance alleles. I show that if the resistance allele has the same proportional effect on both within- and between-family transmission, then the impact of kin selection is relatively minor. Selection coefficients are increased by 5-35%, with a greater benefit for weaker alleles. The reason is that an individual with a strong resistance allele does not need much protection from infection by family members and thus does not benefit much from their alleles. The effect of kin selection can be dramatic, however, if the resistance allele has a larger effect on between-family transmission than within-family transmission (which can occur if between-family infection rates are much smaller than within-family rates), increasing selection coefficients by as much as two- to threefold. These results show conditions when it is important to consider family structure in estimates of the strength of selection for infectious disease resistance alleles.

Pest control by genetic manipulation of sex ratio.

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 first (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 fitness 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% fitness 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-fifth 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 efficient with equivalent pest suppression achieved by release of approximately 1 SD, 1.5-20 PM, 2-70 FK, and 16-3,000 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.

Inheritance analysis of congenital left ventricular outflow tract obstruction malformations: Segregation, multiplex relative risk, and heritability.

The left ventricular outflow tract (LVOTO) malformations, aortic valve stenosis (AVS), coarctation of the aorta (COA), and hypoplastic left heart (HLH) constitute a mechanistically defined subgroup of congenital heart defects that have substantial evidence for a genetic component. Evidence from echocardiography studies has shown that bicuspid aortic valve (BAV) is found frequently in relatives of children with LVOTO defects. However, formal inheritance analysis has not been performed. We ascertained 124 families by an index case with AVS, COA, or HLH. A total of 413 relatives were enrolled in the study, of which 351 had detailed echocardiography exams for structural heart defects and measurements of a variety of aortic arch, left ventricle, and valve structures. LVOTO malformations were noted in 30 relatives (18 BAV, 5 HLH, 3 COA, and 3 AVS), along with significant congenital heart defects (CHD) in 2 others (32/413; 7.7%). Relative risk for first-degree relatives in this group was 36.9, with a heritability of 0.71-0.90. Formal segregation analysis suggests that one or more minor loci with rare dominant alleles may be operative in a subset of families. Multiplex relative risk analysis, which estimates number of loci, had the highest maximum likelihood score in a model with 2 loci (range of 1-6 in the lod-1 support interval). Heritability of several aortic arch measurements and aortic valve was significant. These data support a complex but most likely oligogenic pattern of inheritance. A combination of linkage and association study designs is likely to enable LVOTO risk gene identification. This data can also provide families with important information for screening asymptomatic relatives for potentially harmful cardiac defects.

Population genetics of autocidal control and strain replacement.

The concept that an insect species' genome could be altered in a manner that would result in the control of that species (i.e., autocidal control) or in the replacement of a pestiferous strain of the species with a more benign genotype was first proposed in the mid-twentieth century. A major research effort in population genetics and ecology followed and led to the development of a set of classical genetic control approaches that included use of sterile males, conditional lethal genes, translocations, compound chromosomes, and microbe-mediated infertility. Although there have been a number of major successes in application of classical genetic control, research in this area has declined in the past 20 years for technical and societal reasons. Recent advances in molecular biology and transgenesis research have renewed interest in genetically based control methods because these advances may remove some major technical problems that have constrained effective genetic manipulation of pest species. Population genetic analyses suggest that transgenic manipulations may enable development of strains that would be 10 to over 100 times more efficient than strains developed by classical methods. Some of the proposed molecular approaches to genetic control involve modifications of classical approaches such as conditional lethality, whereas others are novel. Experience from the classical era of genetic control research indicates that the population structure and population dynamics of the target population will determine which, if any, genetic control approaches would be appropriate for addressing a specific problem. As such, there continues to be a need for ongoing communication between scientists who are developing strains and those who study the native pest populations.

Evidence for the contribution of LTR retrotransposons to C. elegans gene evolution.

LTR retrotransposons may be important contributors to host gene evolution because they contain regulatory and coding signals. In an effort to assess the possible contribution of LTR retrotransposons to C. elegans gene evolution, we searched upstream and downstream of LTR retrotransposon sequences for the presence of predicted genes. Sixty-three percent of LTR retrotransposon sequences (79/124) are located within 1 kb of a gene or within gene boundaries. Most gene-retrotransposon associations were located along the chromosome arms. Our results are consistent with the hypothesis that LTR retrotransposons have contributed to the structural and/or regulatory evolution of genes in C. elegans.

Transient dynamics in multilocus invasions by transgenic organisms.

With recent advances in molecular genetics, it is likely that releases of genetically modified organisms will be used for a variety of purposes. In many cases, such systems would utilize organisms that have been modified on multiple genetic loci. Predicting the effect of such releases will require an understanding of the transient dynamics in the system. However, theoretical understanding of transient dynamics in multilocus systems is limited, particularly for early generations when gametic disequilibrium is still high. I derive approximate expressions for marginal allele frequency and marginal two-locus disequilibrium that are applicable in this initial period, assuming infinite population size, two alleles per locus, and weak viability selection. I then apply these results to exploring the effect of parameters on the frequency of the resident gamete type in a release of organisms carrying an autocidal allele on multiple loci. This leads to simple approximate expressions for the optimal number of loci carrying the autocidal allele (as a function of release size and the degree of natural selection against the alleles) and the size of release needed to overcome a given level of selection against the released alleles.