Fifty-One Biallelic Two-locus Models Incorporating Varying Degrees of Epistasis

<p>Each row indexes the genotype at the first locus and each column refers to the genotype at the second locus. The number in each cell is the trait mean for that genotype. Models range from the very simple (e.g., M1) to the more exotic (e.g., M170).</p

Power Associated with the Two-Stage Strategies in the Case of Two Loci Responsible for 5% of the Trait Variance Generated under Model M27 in which an Individual Requires at Least One Copy of the Increaser Allele at Both Loci in Order to Increase the Quantitative Phenotype above Baseline Levels as Applied to 1,000 Individuals

<p>Five different first-stage thresholds are shown. In the case of the Both Significant Two-Stage Strategy, there is a rapid decrease in power with increasingly stringent first-stage thresholds, except for a small proportion of the space of possible allele frequencies where there is a small gain in power. In the case of the Either Significant Strategy, power declines more slowly as the first-stage threshold becomes increasingly stringent.</p

Power to Detect Association for 1,500 Individuals where Both Loci Are Responsible for 5% of the Trait Variance

<p>Power is displayed on the vertical axis, allele frequencies at both loci on the horizontal axes. Results are shown for an (A) additive model where there is no epistasis (MA), (B) a simple looking epistatic model (M27) in which an individual requires at least one copy of the increaser allele at both loci in order to increase the quantitative phenotype above baseline levels, and (C) a more exotic model where an individual has to be heterozygous at both loci in order to have a trait mean above baseline (M16).</p

Switch error (SE) rates for different methods applied to extended pedigrees.

<p>We evaluate SE for individuals who are members of a complex pedigree (pedigrees that are larger than a parent-child duo and father-mother-child trio). The first row is the number of individuals from each cohort in such pedigrees. The second row shows the yield of SLRP when applied to each cohort. Rows 3–6 show the SE for SHAPEIT2, SLRP, Beagle and HAPI-UR within SLRP detected IBD regions. Rows 7–9 show the SE for SHAPEIT2, Beagle and HAPI-UR outside SLRP detected IBD regions. Rows 10–12 show the overall SE for SHAPEIT2, Beagle and HAPI-UR. Rows 13–15 show the overall SE for SHAPEIT2, Beagle and HAPI-UR haplotypes after correction with the duoHMM method. Row 16 show the overall SE for Beagle applied to pedigrees partitioned into duos and trios where possible. Rows 17–18 show the switch error rate for the SHAPEIT2+duoHMM and Beagle Duo/Trio phasing <i>after</i> masking genotypes flagged as erroneous by the duoHMM.</p

Summary of DuoHMM state transitions for each cohort.

<p>The mean number of switches occurring (excluding ) found by the Viterbi path through our four state HMM for SHAPEIT2 and Beagle maximum likelihood haplotypes for chromosome 10 for paternal (P) and maternal (M) duos. SHAPEIT2 has very few impossible transitions ( and ) and the number possible recombinations () are much closer to the genetic length of chromosome 10 than Beagle. The 2002 deCODE map gives the chromosome 10 genetic length as 1.34 and 2.18 Morgans for males and females respectively.</p

Summary of IBD sharing in cohorts.

<p>Left: The proportion of heterozygote sites phased by SLRP for all individuals (pink) and when individuals with close relatives () are removed (blue). Right: The distributions of the average number of “surrogate” parents for each cohort when closely related pairs () are removed.</p

Recombination detection accuracy in uninformative duos simulated from chromosome X data in the Val Borbera cohort.

<p>The green values are for a cohort with nominally unrelated individuals and the orange values are for a cohort that has been filtered such that no individuals are closely related (). Left: The ROC curves for recombination detection in uninformative duos for our duo HMM using the SHAPEIT2 haplotypes. Right: The average number of correct detections against the average posterior probability. Setting a high probability threshold ensures a very low false discovery rate.</p

Distributions of the number of detected crossovers for all cohorts.

<p>Only duos that were part of an informative pedigree were used. Top: The mean number of recombinations per meiosis (for all informative duos from all cohorts) found for each chromosome against the expected number (from the 2002 deCODE map) for paternal meioses (left) and maternal meioses (right). Merlin's values are substantially inflated whilst SHAPEIT2's are more consistent with the well known deCODE map genetic lengths. Bottom: Q-Q plots for the observed against expected number of recombinations estimated by each method for paternal meioses (left) and maternal meioses (right). For the expected distribution of recombination rates, a Poisson distribution using the genetic lengths from the 2002 deCODE Map was used (with rate parameter 42.81 and 25.9 for maternal and paternal recombinations respectively). SHAPEIT2's rates are less inflated than those of the Merlin.</p

Inferred gene flow by Merlin (purple) and our method (grey) for ten informative meioses on chromosome 10 taken from Val Borbera cohort pedigrees.

<p>The light and dark purple represent genetic material from the grand-paternal and grand-maternal chromosomes (as inferred by Merlin's Viterbi algorithm), hence changing from light to dark implies a a recombination event. The grey rectangles contain the posterior probability (in black) of recombination from our method. The two methods broadly agree, although Merlin has inferred a number of implausibly small cross over events.</p

Comparison of recombination detection using our method and Merlin for all informative paternal (P) and maternal (M) meioses events in each cohort.

<p>SHAPEIT2 concordance is the percentage of SHAPEIT2 crossover events that intersected a Merlin crossover event, the proceeding column is vice versa. We also provide the mean number of paternal/maternal recombination events detected for informative meioses by Merlin and SHAPEIT2. For comparison, the frequently cited deCODE 2002 genetic map estimated an average of 42.81 and 25.9 autosomal recombinations per paternal and maternal meioses respectively. SHAPEIT2's estimates are consistently closer to the deCODE values which are considered to be of high quality.</p