A kinship based method of measuring genetic diversity

Herwin EdingID-Lelystad

Lelystad, The Netherlands

Short outline of presentation

• Definition of genetic diversity• Why kinships?• Marker Estimated Kinships

– Similarity index– Accounting for probability AIS

• Core set diversity• Application

Definition Genetic Diversity

• Maximum genetic variation of a

population in HW-equilibrium derived

from a set of conserved breeds

Kinships and genetic diversity (1)

•VGw = VG[1 – fw]

– (Falconer and MacKay, 1996)

• Diversity proportional to (1- fW)

• Max(diversity) => min(fW)

Kinships and genetic diversity (2)

• Kinship coefficients from pedigrees

• Between breed diversity– Within breed diversity relative to others

• No/insufficient administration• => Use marker information

Marker Estimated Kinships

1. Similarity score• Based on definition Malecot, 1948

2. Correction for alleles Alike In State1. not IBD

Marker Estimated Kinships (2)Similarity Index

• If Prob(AIS) = 0, E(Sxy) = fxy

Genotypex y Sxy

AA AA 1AA AB ½ AB AB ½ AB BC ¼ AB CD 0

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

(AIS)• When Prob(AIS) > 0

– Sij,l = fij + (1 –fij)sl

= sl + (1 –sl)fij

• sl = Prob(AIS) for locus l

• Estimate:– fij = (Sij,l – sl)/ (1 –sl)

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

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

Marker Estimated Kinships (6)

• Mixed Model:

= between and within population mean kinship

– W = var[ln(1-Sijl)], gives priority to more informative loci

I = to regress fij back to mean

Core set diversity (1)

• c’Mc = mean(Kinship)– if c’Mc is small, genetic diversity is large

• Adjust c so that average kinship is minimal

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 -> Div(P) = 1

Application

• 10 Dutch cattle populations• 11 Microsatellite markersBreeds Abrev. Marker loci # allelesBelgian Blue BBL BM1824 7Dutch Red Pied DRP BM2113 12Dutch Black Belted DBB ETH010 9Limousine LIM ETH225 8Holstein Friesian HF ETH003 11Galloway GAL INRA23 11Dutch Friesian DF SPS115 7Improved Red Pied IRP TGLA122 23Blonde d'Aquitaine BA TGLA126 8Heck HCK TGLA227 14

Application (2)• Kinship tree

Application (3)Unweighted Weighted

Breed =0 =0 (ci 0)Limousine 0.402 0.295 0.219Holstein Friesian 0.304 0.268 0.215Dutch Red Pied 0.215 0.194 0.152Dutch Friesian 0 0.130 0.123Blonde d'Aquitaine 0 0.035 0.099Heck 0.066 0.080 0.097Belgian Blue 0 0 0.047Improved Red Pied 0 0 0.027Dutch Black Belted0 0 0.022Galloway 0.013 0 0

Application (4)Loss in genetic diversity

Safe set Set % Lost Belgian Blue Safe only 0.68 Blonde d’Aquitaine Galloway +Dutch Red Pied 0.37 Holstein Friesian +Heck aurochs 0.43 Limousin +Dutch Friesian 0.45 +Improved Red Pied 0.59 +Dutch Black Belted 0.61

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

Conclusions (2)MEK and genetic diversity

• Kinship matrix from MEK:– AIS– Definition of founder population

• Measure between and within population diversity

Conclusions (3)General

• Not computer intensive– In theory no limits to Nbreeds

– Extend to individuals

• Results are promising