Kinematics of swimming of the manta ray: three-dimensional analysis of open-water maneuverability.

For aquatic animals, turning maneuvers represent a locomotor activity that may not be confined to a single coordinate plane, making analysis difficult, particularly in the field. To measure turning performance in a three-dimensional space for the manta ray (Mobula birostris), a large open-water swimmer, scaled stereo video recordings were collected. Movements of the cephalic lobes, eye and tail base were tracked to obtain three-dimensional coordinates. A mathematical analysis was performed on the coordinate data to calculate the turning rate and curvature (1/turning radius) as a function of time by numerically estimating the derivative of manta trajectories through three-dimensional space. Principal component analysis was used to project the three-dimensional trajectory onto the two-dimensional turn. Smoothing splines were applied to these turns. These are flexible models that minimize a cost function with a parameter controlling the balance between data fidelity and regularity of the derivative. Data for 30 sequences of rays performing slow, steady turns showed the highest 20% of values for the turning rate and smallest 20% of turn radii were 42.65±16.66 deg s-1 and 2.05±1.26 m, respectively. Such turning maneuvers fall within the range of performance exhibited by swimmers with rigid bodies.

REFINING GENETICALLY INFERRED RELATIONSHIPS USING TREELET COVARIANCE SMOOTHING.

Recent technological advances coupled with large sample sets have uncovered many factors underlying the genetic basis of traits and the predisposition to complex disease, but much is left to discover. A common thread to most genetic investigations is familial relationships. Close relatives can be identified from family records, and more distant relatives can be inferred from large panels of genetic markers. Unfortunately these empirical estimates can be noisy, especially regarding distant relatives. We propose a new method for denoising genetically-inferred relationship matrices by exploiting the underlying structure due to hierarchical groupings of correlated individuals. The approach, which we call Treelet Covariance Smoothing, employs a multiscale decomposition of covariance matrices to improve estimates of pairwise relationships. On both simulated and real data, we show that smoothing leads to better estimates of the relatedness amongst distantly related individuals. We illustrate our method with a large genome-wide association study and estimate the "heritability" of body mass index quite accurately. Traditionally heritability, defined as the fraction of the total trait variance attributable to additive genetic effects, is estimated from samples of closely related individuals using random effects models. We show that by using smoothed relationship matrices we can estimate heritability using population-based samples. Finally, while our methods have been developed for refining genetic relationship matrices and improving estimates of heritability, they have much broader potential application in statistics. Most notably, for error-in-variables random effects models and settings that require regularization of matrices with block or hierarchical structure.

Using ancestry matching to combine family-based and unrelated samples for genome-wide association studies.

We propose a method to analyze family-based samples together with unrelated cases and controls. The method builds on the idea of matched case-control analysis using conditional logistic regression (CLR). For each trio within the family, a case (the proband) and matched pseudo-controls are constructed, based upon the transmitted and untransmitted alleles. Unrelated controls, matched by genetic ancestry, supplement the sample of pseudo-controls; likewise unrelated cases are also paired with genetically matched controls. Within each matched stratum, the case genotype is contrasted with control/pseudo-control genotypes via CLR, using a method we call matched-CLR (mCLR). Eigenanalysis of numerous SNP genotypes provides a tool for mapping genetic ancestry. The result of such an analysis can be thought of as a multidimensional map, or eigenmap, in which the relative genetic similarities and differences amongst individuals is encoded in the map. Once constructed, new individuals can be projected onto the ancestry map based on their genotypes. Successful differentiation of individuals of distinct ancestry depends on having a diverse, yet representative sample from which to construct the ancestry map. Once samples are well-matched, mCLR yields comparable power to competing methods while ensuring excellent control over Type I error.

A genome-wide scan for common alleles affecting risk for autism.

Although autism spectrum disorders (ASDs) have a substantial genetic basis, most of the known genetic risk has been traced to rare variants, principally copy number variants (CNVs). To identify common risk variation, the Autism Genome Project (AGP) Consortium genotyped 1558 rigorously defined ASD families for 1 million single-nucleotide polymorphisms (SNPs) and analyzed these SNP genotypes for association with ASD. In one of four primary association analyses, the association signal for marker rs4141463, located within MACROD2, crossed the genome-wide association significance threshold of P < 5 × 10(-8). When a smaller replication sample was analyzed, the risk allele at rs4141463 was again over-transmitted; yet, consistent with the winner's curse, its effect size in the replication sample was much smaller; and, for the combined samples, the association signal barely fell below the P < 5 × 10(-8) threshold. Exploratory analyses of phenotypic subtypes yielded no significant associations after correction for multiple testing. They did, however, yield strong signals within several genes, KIAA0564, PLD5, POU6F2, ST8SIA2 and TAF1C.

Functional impact of global rare copy number variation in autism spectrum disorders.

The autism spectrum disorders (ASDs) are a group of conditions characterized by impairments in reciprocal social interaction and communication, and the presence of restricted and repetitive behaviours. Individuals with an ASD vary greatly in cognitive development, which can range from above average to intellectual disability. Although ASDs are known to be highly heritable ( approximately 90%), the underlying genetic determinants are still largely unknown. Here we analysed the genome-wide characteristics of rare (<1% frequency) copy number variation in ASD using dense genotyping arrays. When comparing 996 ASD individuals of European ancestry to 1,287 matched controls, cases were found to carry a higher global burden of rare, genic copy number variants (CNVs) (1.19 fold, P = 0.012), especially so for loci previously implicated in either ASD and/or intellectual disability (1.69 fold, P = 3.4 x 10(-4)). Among the CNVs there were numerous de novo and inherited events, sometimes in combination in a given family, implicating many novel ASD genes such as SHANK2, SYNGAP1, DLGAP2 and the X-linked DDX53-PTCHD1 locus. We also discovered an enrichment of CNVs disrupting functional gene sets involved in cellular proliferation, projection and motility, and GTPase/Ras signalling. Our results reveal many new genetic and functional targets in ASD that may lead to final connected pathways.

An empirical method for establishing positional confidence intervals tailored for composite interval mapping of QTL.

BACKGROUND: Improved genetic resolution and availability of sequenced genomes have made positional cloning of moderate-effect QTL realistic in several systems, emphasizing the need for precise and accurate derivation of positional confidence intervals (CIs) for QTL. Support interval (SI) methods based on the shape of the QTL likelihood curve have proven adequate for standard interval mapping, but have not been shown to be appropriate for use with composite interval mapping (CIM), which is one of the most commonly used QTL mapping methods. RESULTS: Based on a non-parametric confidence interval (NPCI) method designed for use with the Haley-Knott regression method for mapping QTL, a CIM-specific method (CIM-NPCI) was developed to appropriately account for the selection of background markers during analysis of bootstrap-resampled data sets. Coverage probabilities and interval widths resulting from use of the NPCI, SI, and CIM-NPCI methods were compared in a series of simulations analyzed via CIM, wherein four genetic effects were simulated in chromosomal regions with distinct marker densities while heritability was fixed at 0.6 for a population of 200 isolines. CIM-NPCIs consistently capture the simulated QTL across these conditions while slightly narrower SIs and NPCIs fail at unacceptably high rates, especially in genomic regions where marker density is high, which is increasingly common for real studies. The effects of a known CIM bias toward locating QTL peaks at markers were also investigated for each marker density case. Evaluation of sub-simulations that varied according to the positions of simulated effects relative to the nearest markers showed that the CIM-NPCI method overcomes this bias, offering an explanation for the improved coverage probabilities when marker densities are high. CONCLUSIONS: Extensive simulation studies herein demonstrate that the QTL confidence interval methods typically used to positionally evaluate CIM results can be dramatically improved by accounting for the procedural complexity of CIM via an empirical approach, CIM-NPCI. Confidence intervals are a critical measure of QTL utility, but have received inadequate treatment due to a perception that QTL mapping is not sufficiently precise for procedural improvements to matter. Technological advances will continue to challenge this assumption, creating even more need for the current improvement to be refined.