A kinship based method of measuring genetic diversity

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A kinship based method of measuring genetic
diversity

• Herwin Eding
• ID-Lelystad
• Lelystad, The Netherlands

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Short outline of presentation

• Definition of genetic diversity
• Why kinships?
• Marker Estimated Kinships
• Similarity index
• Accounting for probability AIS
• Core set diversity
• Application

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Definition Genetic Diversity

• Maximum genetic variation of a population in
  HW-equilibrium derived from a set of conserved
  breeds

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Kinships and genetic diversity (1)

• VGw VG1 fw
• (Falconer and MacKay, 1996)
• Diversity proportional to (1- fW)
• Max(diversity) gt min(fW)

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Kinships and genetic diversity (2)

• Kinship coefficients from pedigrees
• Between breed diversity
• Within breed diversity relative to others
• No/insufficient administration
• gt Use marker information

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Marker Estimated Kinships

• Similarity score
• Based on definition Malecot, 1948
• Correction for alleles Alike In State
• not IBD

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Marker Estimated Kinships (2)Similarity Index
Genotype x y Sxy AA AA 1 AA AB ½ AB AB ½
AB BC ¼ AB CD 0

• If Prob(AIS) 0, E(Sxy) fxy

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Marker Estimated Kinships (3) Correction for
alleles Alike In State (AIS)

• When Prob(AIS) gt 0
• Sij,l fij (1 fij)sl
• sl (1 sl)fij
• sl Prob(AIS) for locus l
• Estimate
• fij (Sij,l sl)/ (1 sl)

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Marker Estimated Kinships (4)Definition of value
of s

• Assume a founder population P, in which all
  relations are zero
• S(P) s (1 s)fP s
• sl sum(qil2), where qil allele frequency in P
• If (A,B) oldest fission s mean(An, Bm)
• Where n populations in cluster A and m
  populations in cluster B

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Marker Estimated Kinships (5)Linear estimation
of s and f

• ln(1 - S) ln(1-f)(1-s)
• ln(1-f ) ln(1-s )
• BLUP-like model
• ln(1-Sijl) ln(1- fij) ln(1-s0,l)
• Yij,l (?Z Xija) Xlb

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Marker Estimated Kinships (6)

• Mixed Model
• ? between and within population mean kinship
• W varln(1-Sijl), gives priority to more
  informative loci
• ?I to regress fij back to mean

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Core set diversity (1)

• cMc mean(Kinship)
• if cMc is small, genetic diversity is large
• Adjust c so that average kinship is minimal

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Core set diversity (2)Definition of genetic
diversity

• The genetic diversity in a set of populations
• Div(M) Div(cs) 1 - fcs
• Describes fraction of diversity of founder
  population left.
• fP 0 -gt Div(P) 1

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Application

• 10 Dutch cattle populations
• 11 Microsatellite markers

Breeds
Abrev.
Marker loci
alleles
Belgian Blue
BBL
BM1824
7
Dutch Red Pied
DRP
BM2113
12
Dutch Black Belted
DBB
ETH010
9
Limousine
LIM
ETH225
8
Holstein Friesian
HF
ETH003
11
Galloway
GAL
INRA23
11
Dutch Friesian
DF
SPS115
7
Improved Red Pied
IRP
TGLA122
23
Blonde d'Aquitaine
BA
TGLA126
8
Heck
HCK
TGLA227
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Application (2)

• Kinship tree

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Application (3)
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Application (4)
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Conclusions (1)Genetic diversity and kinships

• Defined Gen Div ? VG,W
• VG,W (1 - fW)VG
• Gen Div proportional to (1 - fW)
• Core set Set with minimum mean kinship

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Conclusions (2)MEK and genetic diversity

• Kinship matrix from MEK
• AIS
• Definition of founder population
• Measure between and within population diversity

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Conclusions (3)General

• Not computer intensive
• In theory no limits to Nbreeds
• Extend to individuals
• Results are promising

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