Variation in Genetic Relatedness Is Determined by the Aggregate Recombination Process

The genomic proportion that two relatives share identically by descent—their genetic relatedness—can vary depending on the history of recombination and segregation in their pedigree. Previous calculations of the variance of genetic relatedness have defined genetic relatedness as the proportion of total genetic map length (cM) shared by relatives, and have neglected crossover interference and sex differences in recombination. Here, we consider genetic relatedness as the proportion of the total physical genome (bp) shared by relatives, and calculate its variance for general pedigree relationships, making no assumptions about the recombination process. For the relationships of grandparent-grandoffspring and siblings, the variance of genetic relatedness is a simple decreasing function of r¯, the average proportion of locus pairs that recombine in meiosis. For general pedigree relationships, the variance of genetic relatedness is a function of metrics analogous to r¯. Therefore, features of the aggregate recombination process that affect r¯ and analogs also affect variance in genetic relatedness. Such features include the number of chromosomes and heterogeneity in their size, the number of crossovers and their spatial organization along chromosomes, and sex differences in recombination. Our calculations help to explain several recent observations about variance in genetic relatedness, including that it is reduced by crossover interference (which is known to increase r¯). Our methods further allow us to calculate the neutral variance of ancestry among F2s in a hybrid cross, enabling precise statistical inference in F2-based tests for various kinds of selection.

Variation in genetic relatedness is determined by the aggregate recombination process

The genomic proportion that two relatives share identically by descent—their genetic relatedness— can vary depending on the history of recombination and segregation in their pedigree. This variation is important in many applications of genetics, including pedigree-based estimation of the genetic variance and heritability of traits, and estimation of pedigree relationships from sequence data. Here, we calculate the variance of genetic relatedness for general pedigree relationships, making no assumptions about the recombination process. For the specific relationships of grandparent-grandoffspring and siblings, the variance of genetic relatedness is a simple decreasing function of , the average proportion of locus pairs that recombine in meiosis. For general pedigree relationships, the variance of genetic relatedness is likewise the average of some function of pairwise recombination rates. Therefore, features of the aggregate recombination process that affect and analogs also affect variance in genetic relatedness. Such features include the number of chromosomes and heterogeneity in their size, and the number of crossovers and their location along chromosomes. Our calculations help to explain several recent observations about variance in genetic relatedness, including that it is reduced by crossover interference (which is known to increase ). Our methods further allow us to calculate the neutral variance of ancestry among F2s in a hybrid cross, enabling precise statistical inference in F2-based tests for various kinds of selection.

Comparison of granddaughter design and general pedigree design analysis of QTL in dairy cattle: a simulation study

Traditional methods for detection and mapping of quantitative trait loci (QTL) in dairy cattle populations are usually based on daughter design (DD) or granddaughter design (GDD). Although these designs are well established and usually successful in detecting QTL, they consider sire families independently of each other, thereby ignoring relationships among other animals in the population and consequently, reducing the power of QTL detection. In this study we compared a traditional GDD with a general pedigree design (GPD) and assessed the precision and power of both methods for detecting and locating QTL in a simulated complex pedigree. QTL analyses were performed under the variance component model containing a random QTL and a random polygenic effect. The covariance matrix of the polygenic effect was a standard additive relationship matrix. The (co)variance matrix of the random QTL effect contained probabilities that QTL alleles shared by two individuals were identical by descent (IBD). In the GDD analysis, IBD probabilities were calculated using sires’ and daughters’ marker genotypes. In the GPD analysis, IBD probabilities were obtained using a deterministic approach. The estimation of QTL position and variance components was conducted using REML algorithm. Although both methods were able to locate the region of the QTL properly, the GPD method showed better precision of QTL position estimates in most cases and significantly higher power than the GDD method.