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E. A. Thompson
6.1
Introduction
6.1.1 Identity by Descent
Genetic similarities, whether at the population level or between close relatives, result
from coancestry. Copies of DNA that descend to current individuals from a single
copy of DNA in a common ancestor are, with high probability, of the same allelic
type, implying greater phenotypic similarity. Such DNA is said to be identical by
descent or IBD, and this concept is of key importance in analysis of phenotypic
variation, across species of plants and animals (including humans), and across traits
including disease traits, selected traits in agriculture, and normal variation.
Defining IBD is not straightforward. At every point in the genome, among any
group of organisms, the coalescent ancestry will at some point converge in the most
recent common ancestor (MRCA), and relative to this point all the organisms are
IBD. Although models for this time of the MRCA of a pair of haploid genomes
across genetic loci can be used for inference (Li and Durbin, 2011), for genetic
mapping it will be important to have models for the changing patterns of IBD among
individuals across the genome. We therefore define IBD relative to an ancestral
population or time point of interest. In studies of data on defined pedigrees, IBD
has often been measured relative to the pedigree founders, but these founders are
members of a population and may be related or inbred relative to an earlier point in
the population’s history.
The choice of the time-depth of interest for analyses in IBD will depend on
the scientific question. New variants arising in the distant past descend to current
individuals and remain in linkage disequilibrium (LD) with the genetic background
on which they arose. This ancient coancestry (IBD) gives rise to the patterns of LD
we see in populations today and provides information on population structure and
demographic history. At the other end of the scale, IBD among close relatives may
be important in analysis of family data, but generally close pedigree relationships
are known. In this chapter we focus on IBD relative to ancestors at a timedepth of 10 to 40 generations. For human populations, this is beyond the depth
for which pedigree information is available or, even if available, provides useful
information on coancestry of genome. On the other hand, the last 1000 years of
human history encompasses a large part of the huge expansion of the human species
and has established the current patterns of genetic variation within and among local
populations.
DNA is copied from parents to offspring in accordance with the process
of meiosis. Throughout this chapter we restrict attention to nuclear autosomal
chromosomes; that is, we consider neither the sex (X and Y ) chromosomes nor
mitochondrial DNA. At any given locus, the process is as specified by Mendel’s
first law (Mendel, 1866). A randomly chosen one of the two homologous copies of
the parental DNA is copied to an offspring. A fundamental feature of the process is
that this random choice is made independently in distinct meioses. Figure 6.1 shows
a schematic view of DNA descent at a locus in a small family. At this locus, brothers
E. A. Thompson
6.1
Introduction
6.1.1 Identity by Descent
Genetic similarities, whether at the population level or between close relatives, result
from coancestry. Copies of DNA that descend to current individuals from a single
copy of DNA in a common ancestor are, with high probability, of the same allelic
type, implying greater phenotypic similarity. Such DNA is said to be identical by
descent or IBD, and this concept is of key importance in analysis of phenotypic
variation, across species of plants and animals (including humans), and across traits
including disease traits, selected traits in agriculture, and normal variation.
Defining IBD is not straightforward. At every point in the genome, among any
group of organisms, the coalescent ancestry will at some point converge in the most
recent common ancestor (MRCA), and relative to this point all the organisms are
IBD. Although models for this time of the MRCA of a pair of haploid genomes
across genetic loci can be used for inference (Li and Durbin, 2011), for genetic
mapping it will be important to have models for the changing patterns of IBD among
individuals across the genome. We therefore define IBD relative to an ancestral
population or time point of interest. In studies of data on defined pedigrees, IBD
has often been measured relative to the pedigree founders, but these founders are
members of a population and may be related or inbred relative to an earlier point in
the population’s history.
The choice of the time-depth of interest for analyses in IBD will depend on
the scientific question. New variants arising in the distant past descend to current
individuals and remain in linkage disequilibrium (LD) with the genetic background
on which they arose. This ancient coancestry (IBD) gives rise to the patterns of LD
we see in populations today and provides information on population structure and
demographic history. At the other end of the scale, IBD among close relatives may
be important in analysis of family data, but generally close pedigree relationships
are known. In this chapter we focus on IBD relative to ancestors at a timedepth of 10 to 40 generations. For human populations, this is beyond the depth
for which pedigree information is available or, even if available, provides useful
information on coancestry of genome. On the other hand, the last 1000 years of
human history encompasses a large part of the huge expansion of the human species
and has established the current patterns of genetic variation within and among local
populations.
DNA is copied from parents to offspring in accordance with the process
of meiosis. Throughout this chapter we restrict attention to nuclear autosomal
chromosomes; that is, we consider neither the sex (X and Y ) chromosomes nor
mitochondrial DNA. At any given locus, the process is as specified by Mendel’s
first law (Mendel, 1866). A randomly chosen one of the two homologous copies of
the parental DNA is copied to an offspring. A fundamental feature of the process is
that this random choice is made independently in distinct meioses. Figure 6.1 shows
a schematic view of DNA descent at a locus in a small family. At this locus, brothers