Exponential smoothing: Behavior of the ex-post sum of squares near 0 and 1

When using simple exponential smoothing on a given time series the nature of the relationship between the optimal smoothing constant and the autocorrelation structure of the series remains an unresolved question. Although numerical search routines can easily be used to find optimal values of the smoothing constant, they offer little insight into the nature of the relationship between the estimated smoothing constant and the structure of the underlying time series. We suggest that renewed investigations of the ex-post sum of squares function may prove helpful in this pursuit. Results are presented that illustrate how the optimal smoothing constant depends upon the value used to initialize the smoothing and upon the sample autocorrelation coefficients of the observed series. These results are based on a new formula for the derivative of the ex-post sum of squares function. In particular, the derivative is examined near 0 and 1, where great simplifications occur in its form, thereby facilitating investigations near these points. A necessary and sufficient condition is stated for when the ex-post sum of squares must have a positive derivative at 0 and the autocorrelation coefficients of the differenced series are shown to affect the sign of the derivative near 1. Based on these results, a general algorithm is presented as an alternative to grid search routines for minimizing the ex-post sum of squares.     

A single positively selected West Nile viral mutation confers increased virogenesis in American crows

West Nile virus (WNV), first recognized in North America in 1999, has been responsible for the largest arboviral epiornitic and epidemic of human encephalitis in recorded history. Despite the well-described epidemiological patterns of WNV in North America, the basis for the emergence of WNV-associated avian pathology, particularly in the American crow (AMCR) sentinel species, and the large scale of the North American epidemic and epiornitic is uncertain. We report here that the introduction of a T249P amino acid substitution in the NS3 helicase (found in North American WNV) in a low-virulence strain was sufficient to generate a phenotype highly virulent to AMCRs. Furthermore, comparative sequence analyses of full-length WNV genomes demonstrated that the same site (NS3-249) was subject to adaptive evolution. These phenotypic and evolutionary results provide compelling evidence for the positive selection of a mutation encoding increased viremia potential and virulence in the AMCR sentinel bird species.     

Mutations in the gene encoding the basal body protein RPGRIP1L, a nephrocystin-4 interactor, cause Joubert syndrome

Protein-protein interaction analyses have uncovered a ciliary and basal body protein network that, when disrupted, can result in nephronophthisis (NPHP), Leber congenital amaurosis, Senior-L?ken syndrome (SLSN) or Joubert syndrome (JBTS). However, details of the molecular mechanisms underlying these disorders remain poorly understood. RPGRIP1-like protein (RPGRIP1L) is a homolog of RPGRIP1 (RPGR-interacting protein 1), a ciliary protein defective in Leber congenital amaurosis. We show that RPGRIP1L interacts with nephrocystin-4 and that mutations in the gene encoding nephrocystin-4 (NPHP4) that are known to cause SLSN disrupt this interaction. RPGRIP1L is ubiquitously expressed, and its protein product localizes to basal bodies. Therefore, we analyzed RPGRIP1L as a candidate gene for JBTS and identified loss-of-function mutations in three families with typical JBTS, including the characteristic mid-hindbrain malformation. This work identifies RPGRIP1L as a gene responsible for JBTS and establishes a central role for cilia and basal bodies in the pathophysiology of this disorder.     

Mutations in TTBK2, encoding a kinase implicated in tau phosphorylation, segregate with spinocerebellar ataxia type 11

The microtubule-associated protein tau (encoded by MAPT) and several tau kinases have been implicated in neurodegeneration, but only MAPT has a proven role in disease. We identified mutations in the gene encoding tau tubulin kinase 2 (TTBK2) as the cause of spinocerebellar ataxia type 11. Affected brain tissue showed substantial cerebellar degeneration and tau deposition. These data suggest that TTBK2 is important in the tau cascade and in spinocerebellar degeneration.     

Genome-wide genetic association of complex traits in heterogeneous stock mice

Difficulties in fine-mapping quantitative trait loci (QTLs) are a major impediment to progress in the molecular dissection of complex traits in mice. Here we show that genome-wide high-resolution mapping of multiple phenotypes can be achieved using a stock of genetically heterogeneous mice. We developed a conservative and robust bootstrap analysis to map 843 QTLs with an average 95% confidence interval of 2.8 Mb. The QTLs contribute to variation in 97 traits, including models of human disease (asthma, type 2 diabetes mellitus, obesity and anxiety) as well as immunological, biochemical and hematological phenotypes. The genetic architecture of almost all phenotypes was complex, with many loci each contributing a small proportion to the total variance. Our data set, freely available at http://gscan.well.ox.ac.uk, provides an entry point to the functional characterization of genes involved in many complex traits.     

MYH9 is associated with nondiabetic end-stage renal disease in African Americans

As end-stage renal disease (ESRD) has a four times higher incidence in African Americans compared to European Americans, we hypothesized that susceptibility alleles for ESRD have a higher frequency in the West African than the European gene pool. We carried out a genome-wide admixture scan in 1,372 ESRD cases and 806 controls and found a highly significant association between excess African ancestry and nondiabetic ESRD (lod score = 5.70) but not diabetic ESRD (lod = 0.47) on chromosome 22q12. Each copy of the European ancestral allele conferred a relative risk of 0.50 (95% CI = 0.39-0.63) compared to African ancestry. Multiple common SNPs (allele frequencies ranging from 0.2 to 0.6) in the gene encoding nonmuscle myosin heavy chain type II isoform A (MYH9) were associated with two to four times greater risk of nondiabetic ESRD and accounted for a large proportion of the excess risk of ESRD observed in African compared to European Americans.     

Yersinia pestis genome sequencing identifies patterns of global phylogenetic diversity

Plague is a pandemic human invasive disease caused by the bacterial agent Yersinia pestis. We here report a comparison of 17 whole genomes of Y. pestis isolates from global sources. We also screened a global collection of 286 Y. pestis isolates for 933 SNPs using Sequenom MassArray SNP typing. We conducted phylogenetic analyses on this sequence variation dataset, assigned isolates to populations based on maximum parsimony and, from these results, made inferences regarding historical transmission routes. Our phylogenetic analysis suggests that Y. pestis evolved in or near China and spread through multiple radiations to Europe, South America, Africa and Southeast Asia, leading to country-specific lineages that can be traced by lineage-specific SNPs. All 626 current isolates from the United States reflect one radiation, and 82 isolates from Madagascar represent a second radiation. Subsequent local microevolution of Y. pestis is marked by sequential, geographically specific SNPs.     

Conditional and joint multiple-SNP analysis of GWAS summary statistics identifies additional variants influencing complex traits

We present an approximate conditional and joint association analysis that can use summary-level statistics from a meta-analysis of genome-wide association studies (GWAS) and estimated linkage disequilibrium (LD) from a reference sample with individual-level genotype data. Using this method, we analyzed meta-analysis summary data from the GIANT Consortium for height and body mass index (BMI), with the LD structure estimated from genotype data in two independent cohorts. We identified 36 loci with multiple associated variants for height (38 leading and 49 additional SNPs, 87 in total) via a genome-wide SNP selection procedure. The 49 new SNPs explain approximately 1.3% of variance, nearly doubling the heritability explained at the 36 loci. We did not find any locus showing multiple associated SNPs for BMI. The method we present is computationally fast and is also applicable to case-control data, which we demonstrate in an example from meta-analysis of type 2 diabetes by the DIAGRAM Consortium.