Efficient maximum likelihood pedigree reconstruction

There has been recent interest in the exploitation of readily available dense genome scan marker data for the identification of relatives. However, there are conflicting findings on how informative these data are in practical situations and, in particular, sets of thinned markers are often used with no concrete justification for the chosen spacing. We explore the potential usefulness of dense single nucleotide polymorphism (SNP) arrays for this application with a focus on inferring distant relative pairs. We distinguish between relationship estimation, as defined by a pedigree connecting the two individuals of interest, and estimation of general relatedness as would be provided by a kinship coefficient or a coefficient of relatedness. Since our primary interest is in the former case, we adopt a pedigree likelihood approach. We consider the effect of additional SNPs and data on an additional typed relative, together with choice of that relative, on relationship inference. We also consider the effect of linkage disequilibrium. When overall relatedness, rather than the specific relationship, would suffice, * Theoretical Population Biology. In Press. http://dx.doi.org/10.1016/j.tpb.2015.10 † Corresponding author. E-mail address: Nuala.Sheehan@leicester.ac.uk 1 we propose an approximate approach that is easy to implement and appears to compete well with a popular moment-based estimator and a recent maximum likelihood approach based on chromosomal sharing. We conclude that denser marker data are more informative for distant relatives. However, linkage disequilibrium cannot be ignored and will be the main limiting factor for applications to real data.

Section: Introductionmentioning

confidence: 99%

On the use of dense SNP marker data for the identification of distant relative pairs

Sun

Jobling

Taliun

et al. 2016

“…The above factorisation of the likelihood is the directed local Markov property that defines a Bayesian network (BN) (Lauritzen, 1996) and is the core of the ILP formulation. Maximising the pedigree likelihood is thus a BN optimisation problem using the fitted pedigree likelihood as the score (Cowell, 2009). The trick is to impose appropriate constraints that restrict the search to valid pedigrees.…”

Section: Methodsmentioning

confidence: 99%

“…It also permits calculation of many high likelihood pedigrees and can hence address uncertainty about the accuracy of a reconstruction. While the alternative guaranteed maximal likelihood approach of Cowell (2009) is only capable of handling pedigrees of up to 30 individuals, simulation studies showed that pedigrees of up to 100 individuals are manageable by our approach and the true pedigree was generally found very quickly unless the pedigree structure was highly complex, as would be the case in animal or plant applications with high levels of inbreeding. Although these would be considered 'large' pedigrees in the reconstruction literature, the new software introduced in this paper is much more efficient and can reconstruct much bigger networks.…”

Section: Introductionmentioning

confidence: 95%

Improved maximum likelihood reconstruction of complex multi-generational pedigrees

Sheehan¹,

Bartlett²,

Cussens³

2014

The reconstruction of pedigrees from genetic marker data is relevant to a wide range of applications. Likelihood-based approaches aim to find the pedigree structure that gives the highest probability to the observed data. Existing methods either entail an exhaustive search, and are hence restricted to small numbers of individuals, or they take a more heuristic approach and deliver a solution that will probably have high likelihood but is not guaranteed to be optimal. By encoding the pedigree learning problem as an integer linear program we can exploit efficient optimisation algorithms to construct pedigrees guaranteed to have maximal likelihood for the standard situation where we have complete marker data at unlinked loci and segregation of genes from parents to offspring is Mendelian. Previous work demonstrated efficient reconstruction of pedigrees of up to about 100 individuals. The modified method that we present here is not so restricted: we demonstrate its applicability with simulated data on a real human pedigree structure of over 1600 individuals. It also compares well with a very competitive approximate approach in terms of solving time and accuracy. In addition to identifying a maximum likelihood pedigree, we can obtain any number of pedigrees in decreasing order of likelihood. This is useful for assessing the uncertainty of a maximum likelihood solution and permits model averaging over high likelihood pedigrees when this would be appropriate. More importantly, when the solution is not unique, as will often be the case for large pedigrees, it enables investigation into the properties of maximum likelihood pedigree estimates * Corresponding author: Department of Health Sciences, University of Leicester, 2nd Floor Adrian Building, University Road, Leicester LE1 7RH, UK Email address: nas11@le.ac.uk (Nuala A Sheehan)Preprint submitted to Theoretical Population Biology July 21, 2014 which has not been possible up to now. Crucially, we also have a means of assessing the behaviour of other approximate approaches which all aim to find a maximum likelihood solution. Our approach hence allows us to properly address the question of whether a reasonably high likelihood solution that is easy to obtain is practically as useful as a guaranteed maximum likelihood solution. The efficiency of our method on such large problems bodes well for extensions beyond the standard setting where some pedigree members may be latent, genotypes may be measured with error and markers may be linked.

“…Almudevar (2003) proposed a simulated annealing approach that avoids the need for age and sex information. Cowell (2009) adapted the Bayesian network learning algorithm of Silander and Myllymäkki (2006) to develop an exhaustive search algorithm that is guaranteed to find a pedigree of highest likelihood; the algorithm has complexity O(n 3 2 n ) in the number n of individuals, but is computationally feasible for up to around 30 individuals. A constraint-based integer programming approach is presented in (Cussens, 2010;Cussens et al, 2012) that can find maximum likelihood pedigrees involving more than 30 individuals, giving examples of pedigrees of up to 64 individuals.…”

Section: Introductionmentioning

confidence: 99%

“…, k th highest likelihood pedigrees may be found by imposing additional constraints as each high-likelihood pedigree is found (Cussens et al, 2012). It is also possible to extend the algorithm of Cowell (2009), along the lines that Tian et al (2010) use for general Bayesian networks, to find the k highest likelihood pedigrees; however the complexity grows as O(kn 3 2 n ), thus limiting k to a relatively small number.…”

Section: Introductionmentioning

confidence: 99%

A simple greedy algorithm for reconstructing pedigrees

Cowell¹

2013

Self Cite

Citation: Cowell, R. (2013). A simple greedy algorithm for reconstructing pedigrees.Theoretical Population Biology, 83, pp. 55-63. doi: 10.1016Biology, 83, pp. 55-63. doi: 10. /j.tpb.2012 This is the accepted version of the paper.This version of the publication may differ from the final published version. Permanent AbstractThis paper introduces a simple greedy-search algorithm for finding high-likelihood pedigrees using micro-satellite (STR) genotype information on a complete sample of related individuals. The core idea behind the algorithm is not new, but it is believed that putting it into a greedy search setting, and specifically the application to pedigree learning, is novel. The algorithm does not exploit age or sex information, but this information can be incorporated if desired. Prior information concerning pedigree structure is readily incorporated after the greedysearch is completed, on the high-likelihood pedigrees found. The algorithm is applied to human and non-human genetic data and in a simulation study.