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Genetic similarity can be defined in several ways using:
A= pedigree data.  Wright, who was a USDA employee btw, used only pedigree data to calculate probabilities that gene pairs are identical by descent. G = Genomic relationships use genotype data to estimate the fraction of total DNA that individuals actually share. T = Fractions of alleles that two individuals share for loci that affect a certain trait will be termed QTL or T relationships.  The term QTL often refers only to loci with large effects, but here includes all loci that affect a trait.
Inheritance of DNA can be traced within and across families for hundreds of genes influencing quantitative traits by genotyping many markers across the genome.  Markers may or may not contain loci that affect a trait. Relationship matrix of markers….
Vq is the co-variance matrix of QTL’s
U =  breeding value or sum of genetic effects.
T = QTL relationship matrix.   
Use marker, as not many QTL have been indentified.
Unlikely, unless one gene controls the trait. 
Full sibs, genes in common at one loci.   I have named alleles from grandparents, w x y z. If wy, and w,y  have 2 alleles in common.   If wz, and w,y    have 1, xy, and w,y also 1.  x,z and w,y  0 in common.
Overall 25% have two, 50% have one, 25% have none,
Simple Mendelian genetics.    This is for one locus,  what about  multiple loci?????
Through simulations, Paul , and more recently  Mel, has shown that as the number of independent loci increase, SD decreases. From 35% for one locus,  16% for 2 loci, 11% for 10  up until we get to 100.    100 is about the maximum independent loci our simulations allow, because after that, loci are NOT independent. Hypothetically, if we know everything about Sibs,   SD is zero.    But, never get there…..  So how related are individuals?
IF pedigrees, stop at 1960,  ancestors are assumed to be unrelated.  But, actually, before the known pedigree,  somewhere they are related……
A better term may be gametic disequilibrium.
Look at these relationships…….  Hopefully, the previous slides will become clear.
We are all familiar with a traditional pedigree chart.   Animal is expected to be an average of his parents.
Here is a simple Genomic pedigree chart.  2 separate chromosome segments are shown for each ancestor.  (During meiosis , they divide-recombination). The earliest generation, are all one color for illustrative purposes.  Dairy cattle have 30 chromosomes, including the   X and Y.   On average each chromosome carries millions of base pairs, and thousands of genes.
1)For the first segment, the sire has inherited ½ from each piece.  In the second segment, the majority was inherited from one piece (both of these are an example of a crossover).   The individual has received portions of the first segment that are traced back to the grandparent generation.
2) The dam has inherited most of one segment from one portion of her sire’s piece, and a mixture (double crossover) from her dam’s piece.  The individual has segments that can be traced to all grandparents.
In this example….    Say the light green segment from the paternal grand dam was one that was high milk production;  the offspring, inheriting a large segment from her, could mean that through this recombination, this animal would have a higher PTA for milk that a full sib.   
SNP is a DNA sequence variation that occurs when a single nucleotide differs between members of a species…
SNP  2 alleles, 2 variants….
Haplotype definition derived from http://en.wikipedia.org/wiki/Haplotype
Very complex, as 100’s of genes, and 1000’s of base pairs….  How to trace these…..
A little better…..  Can trace, but still have difficulties……   so move from a haplotye to a genomic pedigree…..
One way to do this is to translate haplotype to genotype.  Ongoing discussions on how to best to accomplish this.    In this example aa is always zero, TT would be 2…..
0 = homozygous for first allele 1 = heterozygous 2 = homozygous for second allele    Many ways to count, this is counting alphabetically…. These numbers could be fed directly into a relationship matrix,  just 0,1,and 2’s. Major alleles, minor alleles… frequency, what is major in one breed, possibly not in another…  
In simulations, and Paul will go over the math in the next presentation. Lots of markers, 1000 QTL’s, not of major effect, and high rel sibs. As the number of full sibs increases,  in the A matrix, never rise above 50% reliability.  But with a genomic matix,  with 10 full sibs, already above 50%, with 100 77%.... More reliability for a genomic model than a traditional additive relationship matrix.
Paul follows this talk, and his presentation will hopefully answer any mathematics questions you may have…