1. But what if we test more than one locus? The future of genetic studies of complex human diseases. RefRef (Note above graphs are active spreadsheets -- just click) GRR = Genotypic relative risk

2. Why multiple genes? alleles? covariance cis & trans Haplotyping Multiple loci models (additive, multiplicative, mean…)

3. SNPs & Covariance in proteins ApoE e4 RRR e3 RCR e2 RCC Ancestral = Thr 61 Arg 112 Genotype frequencies Allelee2e3e4 10.0%e21.7%15.0%1.7%18.3% 75.0%e315.0%55.0%25.0%95.0% 15.0%e41.6%25.0%1.7%28.3% 100.0% 18.3%95.0%28.4%100.0% (61 112 158) Risk ratio: e2/3=0.5 ; e3/3=1; e3/4=2.5 ; e4/4=15

4. Covariance in RNA ref " 1 72

5. Covariance M ij =  fx i x j log 2 [fx i x j /(fx i fx j )] M=0 to 2 bits; x=base type x i x j see Durbin et al p. 266-8. D-stem anticodon TCTC 3’acc

6. Mutual Information ACUUAU M 1,6 =  = fAU log 2 [fAU/(fA*fU)]... CCUUAG x 1 x 6 GCUUGC =4*.25log 2 [.25/(.25*.25)]=2 UCUUGA i =1 j =6 M 1,2 = 4*.25log 2 [.25/(.25*1)]=0 M ij =  fx i x j log 2 [fx i x j /(fx i fx j )] M=0 to 2 bits; x=base type x i x j see Durbin et al p. 266-8. See Shannon entropy, multinomial GrendarGrendar

7. .