Quantitative Analysis of Single Nucleotide Polymorphisms within Copy Number Variation

Background Single nucleotide polymorphisms (SNPs) have been used extensively in genetics and epidemiology studies. Traditionally, SNPs that did not pass the Hardy-Weinberg equilibrium (HWE) test were excluded from these analyses. Many investigators have addressed possible causes for departure from HWE, including genotyping errors, population admixture and segmental duplication. Recent large-scale surveys have revealed abundant structural variations in the human genome, including copy number variations (CNVs). This suggests that a significant number of SNPs must be within these regions, which may cause deviation from HWE. Results We performed a Bayesian analysis on the potential effect of copy number variation, segmental duplication and genotyping errors on the behavior of SNPs. Our results suggest that copy number variation is a major factor of HWE violation for SNPs with a small minor allele frequency, when the sample size is large and the genotyping error rate is 0~1%. Conclusions Our study provides the posterior probability that a SNP falls in a CNV or a segmental duplication, given the observed allele frequency of the SNP, sample size and the significance level of HWE testing.

The Retail Market for Bednets in Kenya: How Well Is It Working?

Background Achieving the goals set by Roll Back Malaria and the Government of Kenya for use of insecticide treated bednets (ITNs) will require that the private retail market for nets and insecticide treatments grow substantially. This paper applies some basic concepts of market structure and pricing to a set of recently-collected retail price data from Kenya in order to answer the question, “How well are Kenyan retail markets for ITNs working?” Methods Data on the availability and prices of ITNs at a wide range of retail outlets throughout Kenya were collected in January 2002, and vendors and manufacturers were interviewed regarding market structure. Findings Untreated nets are manufactured in Kenya by a number of companies and are widely available in large and medium-sized towns. Availability in smaller villages is limited. There is relatively little geographic price variation, and nets can be found at competitive prices in towns and cities. Marketing margins on prices appear to be within normal ranges. No finished nets are imported. Few pre-treated nets or net+treatment combinations are available, with the exception of the subsidized Supanet/Power Tab combination marketed by a donor-funded social marketing project. Conclusions Retail markets for untreated nets in Kenya are well established and appear to be competitive. Markets for treated nets and insecticide treatment kits are not well established. The role of subsidized ITN marketing projects should be monitored to ensure that these projects support, rather than hinder, the development of retail markets.

On the Geographic Location of Internet Resources

One relatively unexplored question about the Internet's physical structure concerns the geographical location of its components: routers, links and autonomous systems (ASes). We study this question using two large inventories of Internet routers and links, collected by different methods and about two years apart. We first map each router to its geographical location using two different state-of-the-art tools. We then study the relationship between router location and population density; between geographic distance and link density; and between the size and geographic extent of ASes. Our findings are consistent across the two datasets and both mapping methods. First, as expected, router density per person varies widely over different economic regions; however, in economically homogeneous regions, router density shows a strong superlinear relationship to population density. Second, the probability that two routers are directly connected is strongly dependent on distance; our data is consistent with a model in which a majority (up to 75-95%) of link formation is based on geographical distance (as in the Waxman topology generation method). Finally, we find that ASes show high variability in geographic size, which is correlated with other measures of AS size (degree and number of interfaces). Among small to medium ASes, ASes show wide variability in their geographic dispersal; however, all ASes exceeding a certain threshold in size are maximally dispersed geographically. These findings have many implications for the next generation of topology generators, which we envisage as producing router-level graphs annotated with attributes such as link latencies, AS identifiers and geographical locations.