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Lecture 1 Introduction I: Pedigrees, genetics and probabilities Magnus Dehli Vigeland Statistical methods in genetic relatedness and pedigree analysis NORBIS course, 6 th – 10 th of January 2020, Oslo

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Page 1: Lecture 1 Introduction I: Pedigrees, genetics and ... · Lecture 1 Introduction I: Pedigrees, genetics and probabilities Magnus Dehli Vigeland Statistical methods in genetic relatedness

Lecture 1

Introduction I: Pedigrees, genetics and probabilities

Magnus Dehli Vigeland

Statistical methods in genetic relatedness and pedigree analysis

NORBIS course, 6th – 10th of January 2020, Oslo

Page 2: Lecture 1 Introduction I: Pedigrees, genetics and ... · Lecture 1 Introduction I: Pedigrees, genetics and probabilities Magnus Dehli Vigeland Statistical methods in genetic relatedness

Outline

• Part I: Pedigrees

– Pedigree symbols and terminology

– Some common relationships

• Part II: Genetics

– Terminology

Locus, allele, genotype, marker

– Mendelian inheritance

Autosomal, X, Y

• Part III: Pedigree likelihoods

– Motivation: Real-life problems

– Ingredients:

Hardy-Weinberg equilibrium

Mendelian transition probabilities

– Likelihoods by hand

– Computer algorithms

Statistical methods in genetic relatedness and pedigree analysis

Page 3: Lecture 1 Introduction I: Pedigrees, genetics and ... · Lecture 1 Introduction I: Pedigrees, genetics and probabilities Magnus Dehli Vigeland Statistical methods in genetic relatedness

Outline

• Part I: Pedigrees

– Pedigree symbols and terminology

– Some common relationships

• Part II: Genetics

– Terminology

Locus, allele, genotype, marker

– Mendelian inheritance

Autosomal, X, Y

• Part III: Pedigree likelihoods

– Motivation: Real-life problems

– Ingredients:

Hardy-Weinberg equilibrium

Mendelian transition probabilities

– Likelihoods by hand

– Computer algorithms

Statistical methods in genetic relatedness and pedigree analysis

Page 4: Lecture 1 Introduction I: Pedigrees, genetics and ... · Lecture 1 Introduction I: Pedigrees, genetics and probabilities Magnus Dehli Vigeland Statistical methods in genetic relatedness

Pedigrees: Symbols and terminology

Statistical methods in genetic relatedness and pedigree analysis

= male

= female

Founders: No parents included

in the pedigree

Nonfounders

Page 5: Lecture 1 Introduction I: Pedigrees, genetics and ... · Lecture 1 Introduction I: Pedigrees, genetics and probabilities Magnus Dehli Vigeland Statistical methods in genetic relatedness

Pedigrees: Symbols and terminology

Statistical methods in genetic relatedness and pedigree analysis

= male

= female

Consanguineous marriage

Page 6: Lecture 1 Introduction I: Pedigrees, genetics and ... · Lecture 1 Introduction I: Pedigrees, genetics and probabilities Magnus Dehli Vigeland Statistical methods in genetic relatedness

Pedigrees: Symbols and terminology

Statistical methods in genetic relatedness and pedigree analysis

● ●

= affected

= unaffected

= carrier of disease allele●

Medical pedigrees:

Page 7: Lecture 1 Introduction I: Pedigrees, genetics and ... · Lecture 1 Introduction I: Pedigrees, genetics and probabilities Magnus Dehli Vigeland Statistical methods in genetic relatedness

Alternative ways of drawing pedigrees

Statistical methods in genetic relatedness and pedigree analysis

Standard

1

3

5

Simplified Directed acyclic graph

Page 8: Lecture 1 Introduction I: Pedigrees, genetics and ... · Lecture 1 Introduction I: Pedigrees, genetics and probabilities Magnus Dehli Vigeland Statistical methods in genetic relatedness

Statistical methods in genetic relatedness and pedigree analysis

Some common relationships

(and some less common...)

Page 9: Lecture 1 Introduction I: Pedigrees, genetics and ... · Lecture 1 Introduction I: Pedigrees, genetics and probabilities Magnus Dehli Vigeland Statistical methods in genetic relatedness

Cousin relationships

Statistical methods in genetic relatedness and pedigree analysis

Full siblings

First cousins

Second cousins

Page 10: Lecture 1 Introduction I: Pedigrees, genetics and ... · Lecture 1 Introduction I: Pedigrees, genetics and probabilities Magnus Dehli Vigeland Statistical methods in genetic relatedness

Cousin relationships

Statistical methods in genetic relatedness and pedigree analysis

First cousins once removed

Page 11: Lecture 1 Introduction I: Pedigrees, genetics and ... · Lecture 1 Introduction I: Pedigrees, genetics and probabilities Magnus Dehli Vigeland Statistical methods in genetic relatedness

Cousin relationships

Statistical methods in genetic relatedness and pedigree analysis

Aunt - nephew

Page 12: Lecture 1 Introduction I: Pedigrees, genetics and ... · Lecture 1 Introduction I: Pedigrees, genetics and probabilities Magnus Dehli Vigeland Statistical methods in genetic relatedness

Cousin relationships

Statistical methods in genetic relatedness and pedigree analysis

Grandaunt

Page 13: Lecture 1 Introduction I: Pedigrees, genetics and ... · Lecture 1 Introduction I: Pedigrees, genetics and probabilities Magnus Dehli Vigeland Statistical methods in genetic relatedness

Half cousin relationships

Statistical methods in genetic relatedness and pedigree analysis

Half siblings (paternal)

Half first cousins

Half second cousins

Page 14: Lecture 1 Introduction I: Pedigrees, genetics and ... · Lecture 1 Introduction I: Pedigrees, genetics and probabilities Magnus Dehli Vigeland Statistical methods in genetic relatedness

Half cousin relationships

Statistical methods in genetic relatedness and pedigree analysis

Half aunt /half nephew

Page 15: Lecture 1 Introduction I: Pedigrees, genetics and ... · Lecture 1 Introduction I: Pedigrees, genetics and probabilities Magnus Dehli Vigeland Statistical methods in genetic relatedness

Half cousin relationships

Statistical methods in genetic relatedness and pedigree analysis

Page 16: Lecture 1 Introduction I: Pedigrees, genetics and ... · Lecture 1 Introduction I: Pedigrees, genetics and probabilities Magnus Dehli Vigeland Statistical methods in genetic relatedness

More complicated relationships

Statistical methods in genetic relatedness and pedigree analysis

3/4 siblings

Page 17: Lecture 1 Introduction I: Pedigrees, genetics and ... · Lecture 1 Introduction I: Pedigrees, genetics and probabilities Magnus Dehli Vigeland Statistical methods in genetic relatedness

What about this?

Double first cousins

Page 18: Lecture 1 Introduction I: Pedigrees, genetics and ... · Lecture 1 Introduction I: Pedigrees, genetics and probabilities Magnus Dehli Vigeland Statistical methods in genetic relatedness

Quadruple half first cousins!

The connoisseur's favourite!

Page 19: Lecture 1 Introduction I: Pedigrees, genetics and ... · Lecture 1 Introduction I: Pedigrees, genetics and probabilities Magnus Dehli Vigeland Statistical methods in genetic relatedness

Outline

• Part I: Pedigrees

– Pedigree symbols and terminology

– Some common relationships

• Part II: Genetics

– Terminology

Locus, allele, genotype, marker

– Mendelian inheritance

Autosomal, X, Y

• Part III: Pedigree likelihoods

– Motivation: Real-life problems

– Ingredients:

Hardy-Weinberg equilibrium

Mendelian transition probabilities

– Likelihoods by hand

– Computer algorithms

Statistical methods in genetic relatedness and pedigree analysis

Page 20: Lecture 1 Introduction I: Pedigrees, genetics and ... · Lecture 1 Introduction I: Pedigrees, genetics and probabilities Magnus Dehli Vigeland Statistical methods in genetic relatedness

Genetics

• Human genome:

– Diploid

– 22 pairs of autosomes

– Sex chroms: X and Y

• Some important terms

– Locus

– Allele

– Genotype

– Genetic markers

SNPs

microsatellites

Statistical methods in genetic relatedness and pedigree analysis

Page 21: Lecture 1 Introduction I: Pedigrees, genetics and ... · Lecture 1 Introduction I: Pedigrees, genetics and probabilities Magnus Dehli Vigeland Statistical methods in genetic relatedness

Locus, allele, genotype

Statistical methods in genetic relatedness and pedigree analysis

M F

BA locus

alleles

Homologous chromosomes

• LOCUS = a specific place in the genome, e.g. a base pair, a gene or a region

• ALLELE = any of the alternative forms of a locus

• GENOTYPE = the set of alleles carried by an individual at a given locus

genotype: A/B

Page 22: Lecture 1 Introduction I: Pedigrees, genetics and ... · Lecture 1 Introduction I: Pedigrees, genetics and probabilities Magnus Dehli Vigeland Statistical methods in genetic relatedness

Genetic markers

• Small parts of the genome which ...– have known position

– vary in the population

– are easy to genotype

• SNPs (single nucleotide polymorphisms)– two alleles

– usual requirement: MAF > 1%

– very common in the genome (millions!)

– used in medical genetics +++

• STRs (short tandem repeats) = microsatellites

– consecutive repeats of 2-5 bases

– multiallelic: 5 - 50 alleles

– allele names: # repeats

– used in forensics

Statistical methods in genetic relatedness and pedigree analysis

...CCGTTATATGGGC...

...CCGTTAGATGGGC...

...CCGTTATATGGGC...

...CCGTTATATGGGC...

...CCGTTAGATGGGC...

= minor allele frequency

...ACG TTAG TTAG TTAG TTAG AAC..

...ACG TTAG TTAG AAC..

...ACG TTAG TTAG TTAG TTAG TTAG AAC..

Page 23: Lecture 1 Introduction I: Pedigrees, genetics and ... · Lecture 1 Introduction I: Pedigrees, genetics and probabilities Magnus Dehli Vigeland Statistical methods in genetic relatedness

Outline

• Part I: Brief introductions

– Pedigrees symbols and terminology

– Some common relationships

– Genetics

Locus, allele, genotype, marker

– Mendelian inheritance

Autosomal

X, Y

• Part II: Pedigree likelihoods

– Motivation: Real-life problems

– Ingredients:

Hardy-Weinberg equilibrium

Mendelian transition probabilities

– Likelihoods by hand

– Computer algorithms

Statistical methods in genetic relatedness and pedigree analysis

Page 24: Lecture 1 Introduction I: Pedigrees, genetics and ... · Lecture 1 Introduction I: Pedigrees, genetics and probabilities Magnus Dehli Vigeland Statistical methods in genetic relatedness

Mendelian inheritance: Autosomal (chromosomes 1-22)

Statistical methods in genetic relatedness and pedigree analysis

A/A B/C

A/B A/B

B/C

A/C

Example: autosomal marker with 3 alleles: A, B, C

homozygous heterozygous

Probability of transmitting either allele: always 50%

Page 25: Lecture 1 Introduction I: Pedigrees, genetics and ... · Lecture 1 Introduction I: Pedigrees, genetics and probabilities Magnus Dehli Vigeland Statistical methods in genetic relatedness

Mendelian inheritance: X-linked

Statistical methods in genetic relatedness and pedigree analysis

A B/C

A/C C

A

A/B

Example: X-linked marker with 3 alleles: A, B, C

no transmisison from father to son

males are hemizygous

forced transmission from father to daughter

Page 26: Lecture 1 Introduction I: Pedigrees, genetics and ... · Lecture 1 Introduction I: Pedigrees, genetics and probabilities Magnus Dehli Vigeland Statistical methods in genetic relatedness

Mendelian inheritance: Y-linked

Statistical methods in genetic relatedness and pedigree analysis

A

B

B

Example: Y-linked marker with 2 alleles: A, B

• no transmission involving females

• father-son forced

Page 27: Lecture 1 Introduction I: Pedigrees, genetics and ... · Lecture 1 Introduction I: Pedigrees, genetics and probabilities Magnus Dehli Vigeland Statistical methods in genetic relatedness

Assumptions throughout (most of) this course

• Diploid species

• No cytogenetic abnormalitites

• No de novo mutations

Statistical methods in genetic relatedness and pedigree analysis

COFFEE BREAK!

Page 28: Lecture 1 Introduction I: Pedigrees, genetics and ... · Lecture 1 Introduction I: Pedigrees, genetics and probabilities Magnus Dehli Vigeland Statistical methods in genetic relatedness

Outline

• Part I: Pedigrees

– Pedigree symbols and terminology

– Some common relationships

• Part II: Genetics

– Terminology

Locus, allele, genotype, marker

– Mendelian inheritance

Autosomal, X, Y

• Part III: Pedigree likelihoods

– Motivation: Real-life problems

– Ingredients:

Hardy-Weinberg equilibrium

Mendelian transition probabilities

– Likelihoods by hand

– Computer algorithms

Statistical methods in genetic relatedness and pedigree analysis

Page 29: Lecture 1 Introduction I: Pedigrees, genetics and ... · Lecture 1 Introduction I: Pedigrees, genetics and probabilities Magnus Dehli Vigeland Statistical methods in genetic relatedness

Questions related to pedigrees with genotypes

• Will my child have the disease?

• Is NN the true father?

• Brothers or half brothers?

• Is NN related to this family? How?

• Predict the missing genotype?

Statistical methods in genetic relatedness and pedigree analysis

Page 30: Lecture 1 Introduction I: Pedigrees, genetics and ... · Lecture 1 Introduction I: Pedigrees, genetics and probabilities Magnus Dehli Vigeland Statistical methods in genetic relatedness

Questions related to pedigrees with genotypes

Statistical methods in genetic relatedness and pedigree analysis

? D

Disease locus:alleles D and N

Will my child have the disease?

D/N

Page 31: Lecture 1 Introduction I: Pedigrees, genetics and ... · Lecture 1 Introduction I: Pedigrees, genetics and probabilities Magnus Dehli Vigeland Statistical methods in genetic relatedness

Questions related to pedigrees with genotypes

Statistical methods in genetic relatedness and pedigree analysis

Who is the true father?

13/18

1 2

11/18

11/13 -/-

Suppose:• 11 is common• 18 is rare

Page 32: Lecture 1 Introduction I: Pedigrees, genetics and ... · Lecture 1 Introduction I: Pedigrees, genetics and probabilities Magnus Dehli Vigeland Statistical methods in genetic relatedness

Questions related to pedigrees with genotypes

Statistical methods in genetic relatedness and pedigree analysis

Brothers or half brothers?

Page 33: Lecture 1 Introduction I: Pedigrees, genetics and ... · Lecture 1 Introduction I: Pedigrees, genetics and probabilities Magnus Dehli Vigeland Statistical methods in genetic relatedness

Questions related to pedigrees with genotypes

Statistical methods in genetic relatedness and pedigree analysis

Is this woman related to the family?

12/1432/407/116/21

12/1634/40

7/712/21 11/16

32/417/136/25

11/1432/4013/136/25

Page 34: Lecture 1 Introduction I: Pedigrees, genetics and ... · Lecture 1 Introduction I: Pedigrees, genetics and probabilities Magnus Dehli Vigeland Statistical methods in genetic relatedness

Questions related to pedigrees with genotypes

Statistical methods in genetic relatedness and pedigree analysis

Can we predict the missing genotype?

A/B A/A

A/A A/B

A/B

?/?

Page 35: Lecture 1 Introduction I: Pedigrees, genetics and ... · Lecture 1 Introduction I: Pedigrees, genetics and probabilities Magnus Dehli Vigeland Statistical methods in genetic relatedness

• Common to all of these: The need to calculate probabilities

• Called the likelihood of the pedigree.

Statistical methods in genetic relatedness and pedigree analysis

P( genotypes | pedigree, marker info, allele freqs, .. )

Page 36: Lecture 1 Introduction I: Pedigrees, genetics and ... · Lecture 1 Introduction I: Pedigrees, genetics and probabilities Magnus Dehli Vigeland Statistical methods in genetic relatedness

Ingredients for likelihood computations

Statistical methods in genetic relatedness and pedigree analysis

A/B A/A

A/A A/A

A/B

-/-

founder probabilities

untypedindividuals

transition probabilities

Page 37: Lecture 1 Introduction I: Pedigrees, genetics and ... · Lecture 1 Introduction I: Pedigrees, genetics and probabilities Magnus Dehli Vigeland Statistical methods in genetic relatedness

Ingredient 1: Founder probabilities

• Suppose the allele frequencies are:

𝑃 𝐴 = 𝑝𝑃 𝐵 = 𝑞

• What are the frequencies of the genotypes AA, AB, BB?

• Under certain assumptions, the alleles can be treated as independent:

Statistical methods in genetic relatedness and pedigree analysis

𝑃(𝐴𝐴) = 𝑃 𝐴 ∗ 𝑃 𝐴 = 𝑝2

𝑃 𝐵𝐵 = 𝑃 𝐵 ∗ 𝑃 𝐵 = 𝑞2

𝑃 𝐴𝐵 = 𝑃 𝐴𝐵 𝑜𝑟 𝐵𝐴 = 𝑝𝑞 + 𝑞𝑝 = 2𝑝𝑞

two possible orderings!

Page 38: Lecture 1 Introduction I: Pedigrees, genetics and ... · Lecture 1 Introduction I: Pedigrees, genetics and probabilities Magnus Dehli Vigeland Statistical methods in genetic relatedness

The Hardy-Weinberg principle

Assumptions:

• infinite population

• random mating

• no selection

• no mutations

• no migration

Hardy (1908): Shows

«... using a little mathemathics of the multiplication table kind»:

• allele freqs are unchanged from generation to generation

• after 1 generation the genotype freqs stay unchanged

Statistical methods in genetic relatedness and pedigree analysis

𝑝2

AA

2𝑝𝑞

AB

𝑞2

BB

𝑝A 𝑞B

𝑝2

AA

2𝑝𝑞

AB

𝑞2

BB

𝑝A 𝑞B

AA

AB

BB

𝑝A 𝑞B

HW equilibrium𝑃 𝐴𝐴 = 𝑝2

𝑃 𝐴𝐵 = 2𝑝𝑞𝑃(𝐵𝐵) = 𝑞2

Page 39: Lecture 1 Introduction I: Pedigrees, genetics and ... · Lecture 1 Introduction I: Pedigrees, genetics and probabilities Magnus Dehli Vigeland Statistical methods in genetic relatedness

Statistical methods in genetic relatedness and pedigree analysis

Allele frequencies

Genotype frequencies

assuming HWE

𝑝 = 𝑝𝐴𝐴 + 0.5 𝑝𝐴𝐵𝑞 = 𝑝𝐵𝐵 + 0.5 𝑝𝐴𝐵

𝑝𝐴𝐴 = 𝑝2

𝑝𝐴𝐵 = 2𝑝𝑞𝑝𝐵𝐵 = 𝑞2

always

Page 40: Lecture 1 Introduction I: Pedigrees, genetics and ... · Lecture 1 Introduction I: Pedigrees, genetics and probabilities Magnus Dehli Vigeland Statistical methods in genetic relatedness

Ingredient 2: Transition probabilities

• Easy - follows directly from Mendel's laws!

Statistical methods in genetic relatedness and pedigree analysis

childparents

A/A AB BB

AA×AA 1 0 0

AA×AB 0.5 0.5 0

AA×BB 0 1 0

AB×AA 0.5 0.5 0

AB×AB 0.25 0.5 0.25

AB×BB 0 0.5 0.5

BB×AA 0 1 0

BB×AB 0 0.5 0.5

BB×BB 0 0 1

A/B

-/-

A/A

P(gchild | gparents)

Page 41: Lecture 1 Introduction I: Pedigrees, genetics and ... · Lecture 1 Introduction I: Pedigrees, genetics and probabilities Magnus Dehli Vigeland Statistical methods in genetic relatedness

Example

Statistical methods in genetic relatedness and pedigree analysis

1 2

3

A/B

A/B

A/A

L = 𝑃 𝑔1, 𝑔2, 𝑔3

= 𝑃 𝑔1) ∙ 𝑃(𝑔2) ∙ 𝑃(𝑔3 | 𝑔1, 𝑔2

= 𝑃 𝐴𝐴 ∙ 𝑃 𝐴𝐵 ∙ 𝑃 𝐴𝐵 parents = 𝐴𝐴 × 𝐴𝐵)

= 𝑝2 ∙ 2𝑝𝑞 ∙ 0.5

= 𝑝3𝑞

assuming HWE!

Page 42: Lecture 1 Introduction I: Pedigrees, genetics and ... · Lecture 1 Introduction I: Pedigrees, genetics and probabilities Magnus Dehli Vigeland Statistical methods in genetic relatedness

Example on X

Statistical methods in genetic relatedness and pedigree analysis

𝐿 = 𝑃 𝑔𝑒𝑛𝑜𝑡𝑦𝑝𝑒𝑠 | 𝑝𝑒𝑑𝑖𝑔𝑟𝑒𝑒, 𝑝, 𝑞

= 𝑝 ∙ 2𝑝𝑞 ∙ 0.5 ∙ 0.5 ∙ 𝑞2 ∙ 1

= 0.5 𝑝2 𝑞3

21

4

A/B

A/B

A

3

6

5

B

B/B

B/B

1 2 3 4 5 6 contribution from each individual

Page 43: Lecture 1 Introduction I: Pedigrees, genetics and ... · Lecture 1 Introduction I: Pedigrees, genetics and probabilities Magnus Dehli Vigeland Statistical methods in genetic relatedness

Ingredient 3: How to deal with untyped individuals

Solution: Sum of all possible genotypes for the untyped

Statistical methods in genetic relatedness and pedigree analysis

1 2

3

-/-

A/B

A/A

𝑃 𝑔1, 𝑔3 =

𝑔2

𝑃(𝑔1, 𝑔2, 𝑔3) =

𝑔2

𝑃 𝑔1) ∙ 𝑃(𝑔2) ∙ 𝑃(𝑔3|𝑔1, 𝑔2

= 𝑃(𝐴𝐴) ∙ 𝑃(𝐴𝐴) ∙ 𝑃 𝐴𝐵 𝐴𝐴 × 𝐴𝐴) + 𝑃(𝐴𝐴) ∙ 𝑃(𝐴𝐵) ∙ 𝑃 𝐴𝐵 𝐴𝐴 × 𝐴𝐵) + 𝑃(𝐴𝐴) ∙ 𝑃(𝐵𝐵) ∙ 𝑃 𝐴𝐵 𝐴𝐴 × 𝐵𝐵)

= 𝑝2 ∙ 𝑝2 ∙ 0 + 𝑝2 ∙ 2𝑝𝑞 ∙ 0.5 + 𝑝2∙ 𝑞2 ∙ 1

= 𝑝3𝑞 + 𝑝2𝑞2 = 𝑝2𝑞 𝑝 + 𝑞 = 𝑝2𝑞

Page 44: Lecture 1 Introduction I: Pedigrees, genetics and ... · Lecture 1 Introduction I: Pedigrees, genetics and probabilities Magnus Dehli Vigeland Statistical methods in genetic relatedness

Pedigree likelihood: General formula

• Given:

– pedigree with n individuals

– k members are genotyped: g1, g2, …, gk

• Then:

𝑃 𝑔1, ..., 𝑔𝑘 =

𝐺1

𝐺2

𝐺𝑛

𝑃 𝑔1 ⋯𝑃 𝑔𝑗 ∙ 𝑃 𝑔𝑗+1 𝑝𝑎𝑟 ⋯𝑃 𝑔𝑛 𝑝𝑎𝑟

• If everyone is typed: Only one term → easy

• Number of terms grows exponentially in #(untyped)

– but clever algorithms exist!

Statistical methods in genetic relatedness and pedigree analysis

founders non-founders

Gi = set of possible genotypes for individual i

Page 45: Lecture 1 Introduction I: Pedigrees, genetics and ... · Lecture 1 Introduction I: Pedigrees, genetics and probabilities Magnus Dehli Vigeland Statistical methods in genetic relatedness

Computer algorithms for pedigree likelihoods

• Elston-Stewart algorithm

– a peeling algorithm

– linear in pedigree size!

• Lander-Green

– based on inheritance vectors

– hidden Markov model

– best choice with many linked markers

– small/medium pedigrees only

Statistical methods in genetic relatedness and pedigree analysis

A/B A/A

A/A A/A

A/B

-/-

Page 46: Lecture 1 Introduction I: Pedigrees, genetics and ... · Lecture 1 Introduction I: Pedigrees, genetics and probabilities Magnus Dehli Vigeland Statistical methods in genetic relatedness

Software

• R/pedprobr

– Part of the ped suite

– Elston-Stewart

– general likelihoods, inbreeding, genotype distributions ++

• Familias

– GUI for forensic applications

– Elston-Stewart

– handles mutations, HW deviations, ++

• MERLIN

– command line program

– Lander-Green

– medical applications: multipoint linkage

Statistical methods in genetic relatedness and pedigree analysis