# Presentation: 709608

## Effects of Allele Frequency Estimation on Genomic Predictions and Inbreeding Coefficients 

## Experimental Design

**Predict April 2008 PTA from August 2003 PTA**
**3,576**** older Holstein bulls**
**1,759**** younger bulls  (total = ****5,335****)**
**Using 38,416 SNP from Illumina Bovine SNP50****TM**** Chip  **

**Notes:**
To quickly review the experimental design:   3576 Holstein Bulls were used to predict 1759 younger bulls.
Genotypes were obtained using the Bovine SNP50tm Beadchip.  From the original 51,000 SNP, minor allele frequencies < 0.05 were excluded;  SNP that were redundant or the same for all bulls were eliminated, bringing the total down to ~38,000 SNP.

## Goals

**Compare genomic to traditional relationships and inbreeding**
**Formulas to compute ****G**** and ****A**
**G – A**** differences for 5,335 bulls**
**Compare genomic predictions using different estimates of frequency **
**Estimate 38,416 allele frequencies**
**Simple estimates vs. base population**
**Or ignore frequency, use 0.5 instead**

## Differences in G and A 

**Detected clones, identical twins, and duplicate samples**
**Detected incorrect DNA samples**
**Detected incorrect pedigrees **
**Identified correct source of DNA by genomic relationships with other animals**

**Notes:**
One of the first things I noticed, by using an incorrect proc corr model, was finding bulls that had a corr of 1.  These 3 bulls were ET clones, also found a set of twins.
When samples are loaded on to the BEAD chip, sometimes things get reversed, or transposed, and we can readily pick this up.  (George)
The wide-spread use of marker research recently led to a pedigree correction: the maternal grandsire of the new and popular Delta bull Dudam Surprise is not Eastland Festival,
but the well-known longevity specialist Delta Luxemburg. Luxemburg is especially known as the sire of the Danish top bull Exces.
 Luxemburg being the real maternal grandsire of Surprise explains with greater clarity the good fitness qualities of the Dustin son Surprise (186 NVI). 
Bulls ... have been selected using markers and their parent-average index has a higher reliability than that of “normal” young sires.      HI Online Newsletter 2008-06-04
Mis-identification of samples, saying a sample is one bull, or a full sib to a bull, when in fact it is actually a son of another bull, can be detected.

## Genotype Data for Elevation             Chromosome 1

- 1000111220020012111011112111101111001121100020122002220111
- 1202101200211122110021112001111001011011010220011002201101
- 1200201101020222121122102010011100011220221222112021120120
- 2010020220200002110001120201122111211102201111000021220200
- 0221012020002211220111012100111211102112110020102100022000
- 2201000201100002202211022112101121110122220012112122200200
- 0200202020122211002222222002212111121002111120011011101120
- 0202220001112011010211121211102022100211201211001111102111
- 2110211122000101101110202200221110102011121111011202102102
- 1211011022122001211011211012022011002220021002110001110021
- 1021101110002220020221212110002220102002222121221121112002
- 0110202001222222112212021211210110012110110200220002001002
- 0001111011001211021212111201010121202210101011111021102112
- 2111111212111210110120011111021111011111220121012121101022
- 202021211222120222002121210121210201100111222121101

**Notes:**
0 = homozygous for first allele ; 1 = heterozygous ; 2 = homozygous for second allele 
This shows 864 alleles. (out of over 2000)  If we were to show all of the base pairs for the first chromosome, I would have to show you 1 slide, per second for over 3 days.
Vast portions of the chromosome are homozygous, and not interesting,,  ie all animals have the same DNA sequence.  Looking at a foundation bull such as elevation shows many alleles are heterozygous.
Pedigree analysis by Holstein Association 956 bulls in the April 2008 sire guide red book had 15.2% genes in common with Elevation.  Seven generations back, showed on average Elevation appearing 3.5 times in these bulls pedigrees.  8 generations 2 times.  Nine generations showed Elevation an average of once per bull.   
So what does this really mean?

## Genotype Data from Inbred BullChromosome 24 of Megastar

- 1021222101021021011102110112112211211002202000222020002020220
- 0000220020222202202000020020222222000020222200000220200002002
- 2002000000222200022220000000000020222022002000222020222220002
- 2022222222200002002202022202000200022000000002202220000002200
- 2020002222002020020020202220222222220222020002022022022220202
- 2202020202200022002220220022200000220200002002002000200222220
- 0022220202002220022202000020200000022222020200002002002222000
- 2022022220022000222202200222202020002202202222002220022000200
- 2202000002200220222000022000022000222202002222000220020020202
- 2020002220002220022202202200000220220020020020220002000222202
- 2002220020220200222202220000020220002020020202000220022000002
- 2022200202220200022002000200022002002000200220222220022022000
- 2000020002000020220020220200200002220000222002000200222000022
- 0220020022002202202020202020200022202000220200202202220220000
- 2020200002020200022222200222200020022022220000020220020200202
- 022022020200002000200220220002200

**Notes:**
Look at the genotype of an Inbred Bull.  This is chromosome 24 from Megastar, a double grandson of Aerostar, who has Elevation as a paternal grandsire, and is also on his maternal side.   Vast portions are homozygous;  due to Elevation.

## Close Inbreeding (F=14.7%): Double Grandson of Aerostar

**Aerostar**

**Aerostar**

**Megastar**

**Chromosome 24**

**Notes:**
More conventional way of looking at this.  So now, moving on to the actual experiment:

## 3 Formulas to Compute G

**Sum products of genotypes (g) adjusted for allele frequency (p)**
**G1****jk**** = ****∑ ****(g****ij****-p****i****) (g****ik****-p****i****) ****/**** [2 ****∑ ****p****i****(1-p****i****)]**
**Or individually weighted by p**
**G2****jk**** = ****∑ ****(g****ij****-p****i****) (g****ik****-p****i****) / 2p****i****(1-p****i****)**
**Or scaled by intercept (b****0****) and regression (b****1****) on A, using p = 0.5**
**G3****jk**** = ****[****∑ (****g****ij**** - 0.5) (g****ik**** - 0.5) – b****0****] / b****1**

**Notes:**
We have 3 formulas to compute the genomic matrix.
G1, developed by Paul VanRaden, Sums of the products of the genotypes,  and divides by sum of allele frequency.   (Markers give more information if they are at .5, rather than the 81% that at 0)
G2, by Leutenegger, the method used by Human genomics, uses an individual frequency for each allele. 
G3, sets the freq to .5, and when that is used, the scale is not the same as 1 and 2, so we need to make it similar to the A matrix by using regression.

## Compare A with 3 formulas for G Simulated Data

|  | Diagonals1 of G |  |  |
| --- | --- | --- | --- |
| Formula | Mean | SD | Corr. with A |
| A | 1.05 | .023 | 1.00 |
| G1 | 0.95 | .031 | 0.60 |
| G2 | 0.88 | .028 | 0.54 |
| G3 | 1.10 | .036 | 0.66 |

**1****Diagonal = 1 + Inbreeding**

**Notes:**
Before there was real data, we had simulated data.   Diagonals measure inbreeding, and the 3rd method had the best correlation with A, but also overestimated inbreeding.

## Compare A with 3 formulas for G  Actual Data

|  | Diagonals1 of G |  |  |
| --- | --- | --- | --- |
| Formula | Mean | SD | Corr. with A |
| A | 1.05 | .023 | 1.00 |
| G1 | 1.00 | .031 | 0.68 |
| G2 | 0.98 | .031 | 0.69 |
| G3 | 1.13 | .035 | 0.63 |

**1****Diagonal = 1 + Inbreeding**

**Notes:**
Real data!  G2 has the best correlation with A, inbreeding was underestimated.

## Summary of G Formulasfor Genomic Inbreeding

**Correlations ranked ****G3**** > ****G1**** > ****G2**** in simulation vs. ****G2**** > ****G1**** > ****G3 ****with real data (opposite)**
**G2**** and ****G1**** biased down, ****G3**** up**
**G1**** and ****G2**** can be adjusted toward ****A**** using b****0**** and b****1****, similar to ****G3**** formula**
**After adjusting, mean ****G1**** = 1.08 and ****G2**** = 1.09 compared to ****G3**** = 1.13 and ****A**** = 1.05 **
**G1**** was unbiased in simulation using true rather than estimated frequencies**

**Notes:**
Correlations ranked one way for simulated, and another for real data. Welcome to genomics 101.  To correct biases, Paul adjusted G1 and G2 using a similar formula to G3, and means looked better.  When know the true frequency, G1 was unbiased.    Until something better comes along, we will be using G1.

## Allele Frequency Estimation

**Base population frequencies**
**Combine genotypes and pedigrees**
**Efficient algorithm (Gengler, 2007)**
**Simple frequency estimates**
**p****i**** = ****∑**** g****ij**** / 2n**
**Extra simple estimates (****p = 0.5****)**
**Z = 0.5, 0, -0.5**** in mixed model**

**Notes:**
My coauthor, Nicolas, has an efficient algorithm to combine genotypes and pedigrees to obtain base population frequencies.  Another method is to use a simple frequency.  Or set the frequency to .5, and use 0.5, 0 or .5 in a mixed model,   Legarra and Mistal, 2008.

## Effects of Frequency on G1

| Frequency
Estimate | Mean of
Diagonal | Corr (G1, A) |  |
| --- | --- | --- | --- |
|  |  | Diagonal | Off-diag |
| Base | 1.00 | .68 | .86 |
| Simple | 1.00 | .32 | .75 |
| .5 | 1.26 | .63 | .83 |

**Notes:**
Looking at the effects of these 3 methods on inbreeding estimates, diagonal, or the proportion of genes they have in common, on average the off-diagonal.   Using the Base population was better method.

## R2 of Genomic Predictions

|  | Frequency estimates |  |  |
| --- | --- | --- | --- |
| Trait | .5 | Simple | Base |
| Net Merit | .276 | .278 | .284 |
| Milk | .467 | .480 | .485 |
| Protein yield | .468 | .469 | .470 |
| Fat % | .586 | .632 | .633 |
| Productive life | .248 | .263 | .274 |
| Somatic cell score | .369 | .375 | .383 |
| Dtr pregnancy rate | .283 | .284 | .290 |

**Notes:**
I needed to add another column here for PA.   R2 for traditional PA:  Net Merit  11; Milk 28; Protein Yld 27; Fat% 25; PL 17; SCS 23; DPR 20

## Conclusions

**Genomic relationships and inbreeding are more useful than Wright’s 1922 pedigree formulas**
**Formulas to compute ****G**** have**
**Large effects on inbreeding coefficients**
**Small effects on reliability of predictions**
**Estimates of allele frequencies **
**For base population better than simple**
**Not needed using regression of ****G**** on ****A**

## Acknowledgments

**Funding:**** **
**National Research Initiative grants**
**CDDR Contributors (NAAB, Semex)**
**Genotyping and DNA extraction:**
**BFGL, U. Missouri, U. Alberta, GeneSeek, GIFV, and Illumina**
**Computing**** from AIPL staff**
**George Wiggans, Leigh Walton**