A kinship based method of measuring genetic diversity Herwin Eding ID-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) V Gw = V G [1 – f w ] –(Falconer and MacKay, 1996) Diversity proportional to (1- f W ) Max(diversity) => min(f W )

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, Correction for alleles Alike In State 1.not IBD

Marker Estimated Kinships (2) Similarity Index If Prob(AIS) = 0, E(S xy ) = f xy Genotype xyS xy AAAA1 AAAB½ ABAB½ ABBC¼ ABCD0

Marker Estimated Kinships (3) Correction for alleles Alike In State (AIS) When Prob(AIS) > 0 –S ij,l = f ij + (1 –f ij )s l = s l + (1 –s l )f ij s l = Prob(AIS) for locus l Estimate: –f ij = (S ij,l – s l )/ (1 –s l )

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)f P = s s l = sum(q il 2 ), where q il allele frequency in P –If (A,B) oldest fission: s = mean(A n, B m ) 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-S ijl ) = ln(1- f ij ) + ln(1-s 0,l ) – Y ij,l = (  Z + X ij a ) + X l b

Marker Estimated Kinships (6) Mixed Model: –  = between and within population mean kinship – W = var[ln(1-S ijl )], gives priority to more informative loci – I = to regress f ij 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 - f cs Describes fraction of diversity of founder population left. –f P = 0 -> Div(P) = 1

Application 10 Dutch cattle populations 11 Microsatellite markers Breeds Abrev.Marker loci# alleles Belgian BlueBBLBM18247 Dutch Red PiedDRPBM Dutch Black BeltedDBBETH0109 LimousineLIMETH2258 Holstein FriesianHFETH00311 GallowayGALINRA2311 Dutch FriesianDFSPS1157 Improved Red PiedIRPTGLA12223 Blonde d'AquitaineBATGLA1268 HeckHCKTGLA22714

Application (2) Kinship tree

Application (3)

Application (4)

Conclusions (1) Genetic diversity and kinships Defined: Gen Div  V G,W V G,W = (1 - f W )V G Gen Div proportional to (1 - f W ) 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 N breeds –Extend to individuals Results are promising