6 Identity by Descent in the Mapping of Genetic Traits
127
relationships). We present many of the ideas through numerical examples, but
the reader should not (unless they wish to) be concerned with the details of
computations and derivations. Focus instead on the qualitative message in the
numbers provided: do the results make sense? and why does a given table or result
provide insight into the approach to and goals of genetic mapping?
In Sect. 6.2 we consider probabilities of the underlying IBD in related individuals. At any locus, even a small number of gametes can share IBD in many
different ways. The changes in the IBD pattern across a chromosome that result from
recombination events in ancestral meioses add additional complexity. Additionally,
these ancestral processes have high variance. Against these complexities are the
facts that, on a bp scale, IBD changes slowly across the chromosome and that, in
populations, relatively simple prior models for IBD can provide a basis for inference. Sections 6.2.3 and 6.2.4 show the importance of IBD. Given a specification of
the IBD and a penetrance model, probabilities of genotypes and phenotypes, jointly
across sets of observed individuals can be computed, without further reference to
the descent structure that gave rise to the IBD.
While Sect. 6.2.3 provides probabilities of marker genotype data given a pattern
of IBD, in Sect. 6.3 we consider the reverse problem—the inference of IBD from
genetic marker data. As dense genetic marker data become increasingly available,
and traits of interest become increasingly complex, there has been a shift in the
paradigm of joint analysis of trait and marker data for purposes of gene mapping.
Whereas models for complex traits may involve several genetic loci, each genetic
marker corresponds to a single locus and simple models apply. By first analyzing
the marker data to obtain patterns of IBD across a chromosome among observed
individuals, direct joint consideration of marker and trait data may be avoided.
Instead the patterns of IBD inferred from marker data may be used to investigate
multiple trait models and hypotheses or even multiple traits observed on subsets of
the same individuals (see, e.g., Chapman et al. 2015, Peter et al. 2016 and Saad
et al. 2016). Efficient methods for realizing, estimating, and storing complex IBD
summaries based on genetic marker data are key to success of this approach. This
applies both in the presence of defined pedigree structures and also in populations:
Sect. 6.3 considers both cases.
Finally, in Sect. 6.4 we consider approaches to genetic mapping of loci underlying phenotypes of interest, using the IBD inferred from genetic marker data. Both
classical and modern approaches can be phrased in terms of IBD, and placing
analyses in this framework shows there is no fundamental difference between
pedigree-based and population-based approaches. Indeed, framing the problem in
terms of IBD allows the combination of pedigree and population data. For close
relatives, where relationships can be well-validated, the assumed pedigree is useful,
not least in providing phase information on individual haplotypes. However, the
location-specific IBD resulting from more remote relationships is often better
inferred without reference to an assumed pedigree, and this IBD may be used in
exactly the same way as pedigree-based IBD in genetic mapping algorithms. A final
conclusion is thus that, with modern genetic marker data, it is not a choice between
127
relationships). We present many of the ideas through numerical examples, but
the reader should not (unless they wish to) be concerned with the details of
computations and derivations. Focus instead on the qualitative message in the
numbers provided: do the results make sense? and why does a given table or result
provide insight into the approach to and goals of genetic mapping?
In Sect. 6.2 we consider probabilities of the underlying IBD in related individuals. At any locus, even a small number of gametes can share IBD in many
different ways. The changes in the IBD pattern across a chromosome that result from
recombination events in ancestral meioses add additional complexity. Additionally,
these ancestral processes have high variance. Against these complexities are the
facts that, on a bp scale, IBD changes slowly across the chromosome and that, in
populations, relatively simple prior models for IBD can provide a basis for inference. Sections 6.2.3 and 6.2.4 show the importance of IBD. Given a specification of
the IBD and a penetrance model, probabilities of genotypes and phenotypes, jointly
across sets of observed individuals can be computed, without further reference to
the descent structure that gave rise to the IBD.
While Sect. 6.2.3 provides probabilities of marker genotype data given a pattern
of IBD, in Sect. 6.3 we consider the reverse problem—the inference of IBD from
genetic marker data. As dense genetic marker data become increasingly available,
and traits of interest become increasingly complex, there has been a shift in the
paradigm of joint analysis of trait and marker data for purposes of gene mapping.
Whereas models for complex traits may involve several genetic loci, each genetic
marker corresponds to a single locus and simple models apply. By first analyzing
the marker data to obtain patterns of IBD across a chromosome among observed
individuals, direct joint consideration of marker and trait data may be avoided.
Instead the patterns of IBD inferred from marker data may be used to investigate
multiple trait models and hypotheses or even multiple traits observed on subsets of
the same individuals (see, e.g., Chapman et al. 2015, Peter et al. 2016 and Saad
et al. 2016). Efficient methods for realizing, estimating, and storing complex IBD
summaries based on genetic marker data are key to success of this approach. This
applies both in the presence of defined pedigree structures and also in populations:
Sect. 6.3 considers both cases.
Finally, in Sect. 6.4 we consider approaches to genetic mapping of loci underlying phenotypes of interest, using the IBD inferred from genetic marker data. Both
classical and modern approaches can be phrased in terms of IBD, and placing
analyses in this framework shows there is no fundamental difference between
pedigree-based and population-based approaches. Indeed, framing the problem in
terms of IBD allows the combination of pedigree and population data. For close
relatives, where relationships can be well-validated, the assumed pedigree is useful,
not least in providing phase information on individual haplotypes. However, the
location-specific IBD resulting from more remote relationships is often better
inferred without reference to an assumed pedigree, and this IBD may be used in
exactly the same way as pedigree-based IBD in genetic mapping algorithms. A final
conclusion is thus that, with modern genetic marker data, it is not a choice between