Algorithms for comparing large pedigree graphs

The importance of pedigrees is translated by geneticists as a tool for diagnosing genetic diseases. Errors resulting during collection of data and missing information of individuals are considered obstacles in deducing pedigrees, especially larger ones. Therefore, the reconstructed pedigree graph evaluation needs to be undertaken for relevant diagnosis. This requires a comparison between the derived and the original data. The present study discusses the isomorphism of huge pedigrees with labeled and unlabeled leaves, where a pedigree has hundreds of families, which are monogamous and generational. The algorithms presented in this paper are based on a set of bipartite graphs covering the pedigree and the problem addressed is parameter tractable. The Bipartite graphs Covering the Pedigree (BCP) problem is said to possess a time complexity of $f(k).mod(X)^{O(1)}$ where $f$ is the computing function that grows exponentially. The study presents an algorithm for the BCP problem that can be categorized as a polynomial-time-tractable evaluation of the reconstructed pedigree. The paper considers pedigree graphs that consist of both labeled and unlabeled leaves that make use of parameterized and kernelization algorithms to solve the problem. The kernelization algorithm executes in $O(k^3)$ for the BCP graphs

Conflation of short identity-by-descent segments bias their inferred length distribution

Identity-by-descent (IBD) is a fundamental concept in genetics with many applications. In a common definition, two haplotypes are said to contain an IBD segment if they share a segment that is inherited from a recent shared common ancestor without intervening recombination. Long IBD segments (> 1cM) can be efficiently detected by a number of algorithms using high-density SNP array data from a population sample. However, these approaches detect IBD based on contiguous segments of identity-by-state, and such segments may exist due to the conflation of smaller, nearby IBD segments. We quantified this effect using coalescent simulations, finding that nearly 40% of inferred segments 1-2cM long are results of conflations of two or more shorter segments, under demographic scenarios typical for modern humans. This biases the inferred IBD segment length distribution, and so can affect downstream inferences. We observed this conflation effect universally across different IBD detection programs and human demographic histories, and found inference of segments longer than 2cM to be much more reliable (less than 5% conflation rate). As an example of how this can negatively affect downstream analyses, we present and analyze a novel estimator of the de novo mutation rate using IBD segments, and demonstrate that the biased length distribution of the IBD segments due to conflation can lead to inflated estimates if the conflation is not modeled. Understanding the conflation effect in detail will make its correction in future methods more tractable

Fast Genome-Wide QTL Association Mapping on Pedigree and Population Data

Since most analysis software for genome-wide association studies (GWAS) currently exploit only unrelated individuals, there is a need for efficient applications that can handle general pedigree data or mixtures of both population and pedigree data. Even data sets thought to consist of only unrelated individuals may include cryptic relationships that can lead to false positives if not discovered and controlled for. In addition, family designs possess compelling advantages. They are better equipped to detect rare variants, control for population stratification, and facilitate the study of parent-of-origin effects. Pedigrees selected for extreme trait values often segregate a single gene with strong effect. Finally, many pedigrees are available as an important legacy from the era of linkage analysis. Unfortunately, pedigree likelihoods are notoriously hard to compute. In this paper we re-examine the computational bottlenecks and implement ultra-fast pedigree-based GWAS analysis. Kinship coefficients can either be based on explicitly provided pedigrees or automatically estimated from dense markers. Our strategy (a) works for random sample data, pedigree data, or a mix of both; (b) entails no loss of power; (c) allows for any number of covariate adjustments, including correction for population stratification; (d) allows for testing SNPs under additive, dominant, and recessive models; and (e) accommodates both univariate and multivariate quantitative traits. On a typical personal computer (6 CPU cores at 2.67 GHz), analyzing a univariate HDL (high-density lipoprotein) trait from the San Antonio Family Heart Study (935,392 SNPs on 1357 individuals in 124 pedigrees) takes less than 2 minutes and 1.5 GB of memory. Complete multivariate QTL analysis of the three time-points of the longitudinal HDL multivariate trait takes less than 5 minutes and 1.5 GB of memory