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Title: Introduction%20linkage%20analysis,%20Genetic%20markers,%20mapping%20functions%20Lecture%203

Introduction linkage analysis, Genetic markers,
mapping functionsLecture 3
Background Readings Chapter 5 6 (190-193) of
An introduction to Genetics, Griffiths et al.
2000, Seventh Edition.
This class has been edited from several sources.
Primarily from Terry Speeds homepage at Stanford
and the Technion course Introduction to
Genetics and several other courses as specified
on some slides. Changes made by Dan Geiger.
Purpose of human linkage analysisTo obtain a
crude chromosomal location of the gene or genes
associated with a phenotype of interest, e.g. a
genetic disease or an important quantitative
trait.Examples Cystic fibrosis (found),
Diabetes, Alzheimer, and Blood pressure.
Linkage Strategies I
  • Traditional (from the 1980s or earlier)
  • Linkage analysis on pedigrees
  • Association studies candidate genes
  • Allele-sharing methods Affected siblings
  • Animal models identifying candidate genes
  • Cell hybrids
  • Newer (from the 1990s)
  • Focus on special populations (Finland,
  • Haplotype-sharing (many variants)

Linkage Strategies II
  • On the horizon (here)
  • Single-nucleotide polymorphism (SNPs)
  • Functional analyses finding candidate genes
  • Needed (starting to happen)
  • New multilocus analysis techniques, especially
  • Ways of dealing with large pedigrees
  • Better phenotypes ones closer to gene products
  • Large collaborations

Horses for courses
  • Each of these strategies has its domain of
  • Each of them has a different theoretical basis
    and method of analysis
  • Which is appropriate for mapping genes for a
    disease of interest depends on a number of
    matters, most importantly the disease, and the
    population from which the sample comes.

The disease matters
  • Definition (phenotype), prevalence, features such
    as age at onset
  • Genetics nature of genes (Penetrance), number of
    genes, nature of their contributions (additive,
    interacting), size of effect
  • Other relevant variables Sex, obesity, etc.
  • Genotype-by-environment interactions Exposure to

Example Age at onset
Example Y-linked disease
The population matters
  • History pattern of growth, immigration
  • Composition homogeneous or melting pot, or in
  • Mating patterns family sizes, mate choice
  • Frequencies of disease-related alleles, and of
    marker alleles
  • Ages of disease-related alleles

Complex traits
  • Definition vague, but usually thought of as
    having multiple, possibly interacting loci, with
    unknown penetrances and phenocopies.
  • Affected only methods are widely used. The jury
    is still out on which, if any will succeed.
  • Few success stories so far.
  • Important heart disease, cancer susceptibility,
    diabetes, are all complex traits.
  • We focus more on simple traits where success has
    been demonstrated very often. About 6-8 percent
    of human diseases are thought o be simple
    Mendelian diseases.

Design of gene mapping studies
How good are your data implying a genetic
component to your trait? Can you estimate the
size of the genetic component? Have you got, or
will you eventually have enough of the right
sort of data to have a good chance of getting a
definitive result? Power studies. Simulations.
A person is said to be typed if its markers have
been genotyped.
Choice of markers highly polymorphic
preferred. Heterozygosity and polymorphism
information content (PIC) value are measures
commonly used. Reliability of markers important
too Good quality data critical errors can play a
surprisingly large role.
Preparing genotype data for analysis
Data cleaning is the big issue here. Need much
ancillary datahow good is it?
A very large range of methods/programs are
available. Effort to understand their theory
will pay off in leading to the right choice of
analysis tools. Trying everything is not
recommended, but not uncommon. Many
opportunities for innovation.
Interpretation of results of analysis
An important issue here is whether you have
established linkage. The standards seem to be
getting increasingly stringent. What p-value or
LOD should you use? Dealing with multiple
testing, especially in the context of genome
scans and the use of multiple models and multiple
phenotypes, is one of the big issues. E.g.,
Bonferroni correction.
  • Related topics (not covered in this course)
    Exclusion mapping, homozygosity mapping, variance
    component methods, twin studies, and much more.
  • Some of these topics plus others are covered
    in two books
  • Handbook of Human Genetic Linkage by J.D.
    Terwilliger J. Ott (1994) Johns Hopkins
    University Press. Ordered, not available at the
  • Analysis of Human Genetic Linkage by J. Ott,
    3rd Edition (1999), Johns Hopkins
    University Press.

Problem with standard P-values
If a single test was to be employed to test a
null hypothesis, using 0.05 as the significance
level and if the null hypothesis was actually
true the probability of reaching the right
conclusion (i.e., not significant) is 0.95. If
two such hypotheses were tested, then the
probably of reaching the right conclusion (i.e.,
not significant) on both occasions would be
0.95X0.95 0.90. If more hypotheses (n) were
tested and if all of them were in fact true, the
probability of being right on all occasions would
decrease substantially (0.95n). In other words,
the probability of being wrong at least once (or
getting a significant result erroneously) would
increase drastically (1-0.95n). Put simply, by
running more tests on a given data set, there is
an increasing likelihood of getting a significant
result by chance alone
Source http//
The Bonferroni Correction for Non-statisticians
The Bonferroni correction for multiple
significance testing is simply to multiply the p
value by the number of tests k carried out. The
corrected value k?p is then compared against the
level of 0.05 to decide if it is significant. If
the corrected value is still less than 0.05, only
then is the null hypothesis rejected.
Source http//
Some Problems with the Bonferroni Correction 1
  • This test is for independent tests not for
    depended ones.
  • If one carries out multiple tests on a single set
    of data, the interpretation of a single
    relationship between two variables (or the p
    value) would actually depend on how many other
    tests were performed.
  • Perhaps too cautious. This means that significant
    results are lost and the power of the study is
  • If Bonferroni correction were to be made
    universal, to make results significant, authors
    would not include many other tests they would
    have done with non-significant results and thus
    would not apply Bonferroni to same extent they
  • Also for tests published in other papers
    on the same set of patients or tests done
    subsequently would need to be corrected taking
    into account the number of previous tests.

Source (modified from) http//
When to use Bonferroni Correction ?
  • Because of the above problems due to the
    disagreements among statisticians over its
    universal use, the use of the Bonferroni
    correction may best be limited to instances like
  • a group of cases and controls subjected to a
    number of independent tests of associations with
    different biological parameters
  • the same test being repeated in many subsamples,
    such as when stratified by age, sex, income
    status, etc.
  • Even in these instances, if there is a biological
    explanation for the null hypothesis to be
    rejected and only the non-corrected p value is
    significant, but k?p is not, one is allowed to
    conclude (with appropriate explanations, of
    course!), the significant nature of the findings.

Source http//
References to Bonferonni and other multiple test
  1. Perneger, T.V. Whats wrong with Bonferroni
    adjustments. BMJ, 1998. 316(7139)p. 1236-1238.
  2. Bender, R. and S. Lange, Multiple test procedures
    other than Bonferronis deserve wide use. BMJ,
    1999. 318(7138)p.600-601.
  3. Sankoh, A.J., M.F. Huque, and S.D. Dubey, Some
    comments on frequently used multiple endpoint
    adjustment methods in clinical trials. Stat Med,
    1997. 16(22)p.2529-2542.

Source http//
Replication of results
This has recently become a big issue with complex
diseases, especially in psychiatry. Nature
Genetics suggested in May 1998 that they will
require replication before publishing results
mapping complex traits. Simulations by Suarez et
al (1994) show that sample sizes necessary for
replication may be substantially greater than
that needed for first detection.
Chromosome Description Types
  • Our description of chromosomes has three distinct
  • the genetic description, derived from studies of
    the inheritance of traits
  • the morphological description, derived from
    microscopic examination of chromosomes and
  • the molecular description, derived from analysis
    of the DNA of chromosomes.
  • Each description can be related experimentally to
    the others.

Source (modified from) http//
The Genetic Chromosome
The genetic chromosome is represented by a
genetic map.
  • Genetic maps are unbranched lines or circles with
    marks indicating the relative positions of
    genetic markers.
  • Genetic markers are genetically determined traits
    or characters that are polymorphic in the
    population being studied. Polymorphic means that
    at least two forms of the trait occur in the
  • If two markers are genetically linked, they are
    on the same genetic map, also called a linkage
    map. The set of all markers on the same linkage
    map is called a linkage group.
  • If two markers are not genetically linked they
    are said to be unlinked markers and belong to
    different linkage groups.

Source (modified from) http//
A linkage map of tomatoes chromosomes from 1952
Picture from L.A. Butler.(Griffiths et al,
The Morphological Chromosome
  • Chromosome appearance varies with stage of the
    cell cycle and with cell type.
  • Interphase nuclei have distinct regions
    discernable by staining.
  • Metaphase chromosomes
  • exhibit a condensed structure and
  • can be distinguished by size and chromosome
  • Polytene chromosomes occur in insect salivary
    gland cells.
  • Lampbrush chromosomes are observed during
    amphibian development.

Source (modified from) http//
Fluorescent In Situ Hybridization (FISH)
????? ?????????? ?? ???? ??"? ???????? ?????? ???
????? ????? ???? ???. ??????????? ????? ????
???? ????? ???"?, ???? ??????. ????? 2-
????????? ????? ??? ????????.
????? ?????????? ?- FISH ?? ??? ???? ?? ??
The Molecular Chromosome
Several kinds of maps are useful in understanding
the molecular description of a chromosome
  1. Restriction maps locate the relative positions of
    specific sequences by selected restriction
    enzymes. Main examples for specific sequences
    are RFLP (restriction fragment length
    polymorphism), and VNTR (variable naumber tandem
  2. Conting maps locate the relative positions of
    cloned sequences from a library.
  3. Nucleotide sequences represent the ultimate
    molecular map, being the linear order of
    nucleotides in the nucleic acid.

Source (modified from) http//
Linkage map of human chromosome 1, correlated
with chromosome banding pattern. Distances are
given in centimorgans. Total length is 356 cM
the longest human chromosome.
Figure 5-16 in Griffiths et al, pp.155. Taken
from B.R. Jasney et al.,Science, September 30,
Restriction Fragment Length Polymorphism
Bacterial restriction enzymes cut DNA at specific
target sequences that exist by chance on other
organisms (e.g. human).
The probe (say AACCTT) cuts the second Homolog
(say the middle of TTGGAA) into two pieces. It
does not cut the first Homolog because the target
sequence AACCTT is absent. These represent two
alleles at that locus. There are thousands of
RFLP markers.
Measuring the alleles uses electric field to
separate the fragments according to their
molecular weights (Using Southern blotting).
RFLPs in mapping
If an individual is heterozygous for presence and
absence (/-) of that target sequence, then this
locus can be used for mapping, like any other
genetic marker. Consider the two individuals
Homolog 1
Homolog 2
Homolog 1
Homolog 2
Half the progeny would show three fragments when
probed and half only one fragment, following
Mendels first law of equal segregation.
Variable Number Tandem Repeats (VNTRs)
Some locations have different number of repeats
of the same basic unit. Say AAAAA versus AAA.
These can be regarded as two alleles. A probe
that cuts after the first three As can
distinguish long from short.
As before, if an individual is heterozygous for
Long and short (L/s) target sequences, then this
locus can be used for mapping.
Measuring genetic distanceHaldanes mapping
A natural measure of genetic distance is the
expected number of recombinants, denoted by m.
Let ? denote the expected number of
crossovers. We assume that m 0.5 ? because the
expected number of recombinants is believed to
equal half the expected number of crossovers ?.
Can we measure m ?
The observed Recombination Fraction RF (just r
for short) is thus given by r 0.5 Prob(no
crossover) 0.5(1 - e-2m )
Inverting the formula yields Haldanes mapping
m -(1/2) ln(1-2r).
Recall that ln(1-x)x for small x, hence m ? r
for small m. In practice 10 centi morgan (r
0.1) is considered small. So small ms are
The Poisson Distribution
  • Suppose a (rare) event of interest occurs with
    rate ? (per length or time units).
  • For example number of dead birds along a highway.
    Number of births in one hour. Or the number of
    crossovers along a chromosome.
  • If we assume that
  • For an arbitrarily small unit ? of distance
    (time) the probability of observing an event is
    approximately equal to ??, and equals virtually
    zero for more than one event.
  • The rate ? is constant over the entire region.
  • The number of events occurring in one interval is
    independent of the number of events occurring in
    a previous disjoint interval,
  • then, the probability for the number of events i
    occurring at an interval of length 1 is the
    Poisson distribution given by

In our case ? 2 m.
Additivity for small regions
Consider three closely linked loci
rdf rde ref 2 rde ref 0.06 0.08
2(0.0048) ? 0.14
So in practice, for short chromosome segments,
map distance observed recombination fraction,
i.e., 4 observed recombination 4cm 8
crossover events.
Non-Additivity for longer regions
Consider three loci each separated by more than
If there is no interference
rac does not equal rabrbc 40 but rather rac
rabrbc 2 rab rbc
Namely, rac 0.20.2-2(0.04) 0.32
Chaismata Interference
Morgans data. Breed Drosophila so as to obtain
female parental gametes v cv ct and v cv
ct and breed these females with triple
recessive males. The female gametic genotypes
are shown out of a sample of 1448 flies
v cv ct 580
v cv ct 592
v cv ct 45
v cv ct 40
v cv ct 89
v cv ct 94
v cv ct 3
v cv ct 5
rv,cv (45408994)/1448 18.5
rv,ct (899435)/1448 13.2
rct,cv (454035)/1448 6.4
Can we conclude the order just by inspecting the
table ?
rac does not equal rabrbc0.196 but maybe rac
rabrbc 2 rab rbc,
assuming no interference.
mac 0.1320.064 -2(0.132 0.064 ) 0.1943
(Haldanes mapping function)
However, we observed recombination fraction rac
between a and c is 0.185 , namely, less
recombinations then expected, even if we take
(independent) double crossovers into
account. Use Kosambis mapping function or other
that take interference into account.
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