## Determining marker-QTL phase of active sires, with respect to mapped QTL

We deal with identifying marker-QTL phase in young elite sires on the basis of their initial progeny test, generally consisting of a small group of 100-200 daughters. Since elite young sires produce the next generation of candidate bulls, the gains from early information on marker-QTL phase in a young sire are two-fold:

- Shortening the generation interval between information and its use; and

- Increasing the proportion of progeny for which information is available.

In the direct progeny of a young sire, all QTL that are phased in the sire are informative, since the progeny must receive one or other of the sire haplotypes.

But only half of the grandprogeny receive one or other of the sire haplotypes. Hence, half of the QTL information in the grandsire is lost in transmission. Feasibility of identifying marker-QTL phase in young elite sires was investigated using a deterministic analysis and also by simulation based on daughter data from RP1 and RP4.

Deterministic analysis, Methods: We consider a situation where a QTL has been mapped to a known chromosomal region (QTLR) and a marker haplotype in close association with the QTL is known. A deterministic Bayesian analysis of power and proportion of false positives as a function of Type I error (a = 0.05, 0.10, 0.15 and 0.20), allele substitution effect in units of phenotypic standard deviation (d=0.2 and 0.3 ), and number of daughters in the progeny test (N=100,200,300,500,1000) was implemented.

The analysis assumed that the proportion of heterozygosity at the QTL was 0.40, and provided power, and proportion of false positives (PFP) among declaration of heterozygosity. Accepting a proportion of false positive is equivalent to diluting the anticipated effects of MAS by this proportion. Results: With N=100, and a=0.20, d=0.2, power was 0.57 with PFP = 0.34; with d=0.3, power was 0.75 with PFP = 0.29. With N=200, a=0.20, d=0.2, power was 0.72 with PFP = 0.29; with d=0.3, power was 0.90 with PFP= 0.25. For 300 or more daughters, power at a=0.20 was very high (0.82 or more), even for d=0.2, and PFP approaches its limit value of 0.23. Roughly similar results, showing power of about 0.40 for N= 150 and d= 0.3. were obtained by P3 by simulation based on a different set of assumptions. Simulation:

Simulations of ability of small samples to determine phase in young sires were carried out using data from two sires from RP1, 1392 daughters of S1, known heterozygous for a QTL affecting EBVPY on BTA4; 303 daughters of S2, known homozygous for the same QTL; 240 daughters of S3 from RP4, known heterozygous for a QTL affecting EBVPP on BTA13; and 368 daughters of sire S4 (RP4) , known heterozygous for a QTL affecting EBVPP on BTA14. The daughters were those in the high and low 10% of the total daughter population for the analyzed trait. Haplotypes spanning the QTLR were used to assign sire haplotypes to the daughters. Informativity of the haplotypes was 0.725, 0.751, 0.900, 0.690 for S1, S2, S3, and S4, respectively. To implement the simulations, the desired number of daughters were chosen at random from each of the two tails.

A t-test for significance (non-Bayesian) was then carried out. Power of the test was calculated as the proportion of tests reaching the given significance level. The simulation variables were (1) The number of daughters in each tail (N=40, 80, 160), and (2) the P value required for significance (a = 0.05, 0.10, 0.15 and 0.20). Each Nxa combination was run 100 times for each sire. With 20 daughters in each tail (equivalent to progeny test of 100 daughters), and a = 0.20, the proportion of significant results was 0.34 and 0.28 for S1 and S3, but only 0.16 (about equal to a) for S2. With 40 daughters in each tail, power was 0.29, 0.34 for S1 and S3, and again, 0.16, for S2. With 160 daughters in each tail (equivalent to progeny test of 400 daughters), power was 0.42, 0.47 and 0.23, respectively. These values are less than those obtained in the deterministic analysis.

However, application of the Bayesian approach used in the deterministic analysis to the young sire analysis, should bring the deterministic and simulated results closer. Increase in d, simulated by cross transfer of specific genotypes from high to low tails of the population distribution, strongly increased power and decreased PFP. This might be achieved in practice by multi-trait analysis.

Conclusion: It should be possible to determine marker-QTL phase in young progeny tested sires for known mapped QTL, with power of 0.50, and PFP of about 0.25. This information will be useful to organizations that are implementing MAS programs, encouraging them to implement marker-QTL phasing of their young elite sires.

- Shortening the generation interval between information and its use; and

- Increasing the proportion of progeny for which information is available.

In the direct progeny of a young sire, all QTL that are phased in the sire are informative, since the progeny must receive one or other of the sire haplotypes.

But only half of the grandprogeny receive one or other of the sire haplotypes. Hence, half of the QTL information in the grandsire is lost in transmission. Feasibility of identifying marker-QTL phase in young elite sires was investigated using a deterministic analysis and also by simulation based on daughter data from RP1 and RP4.

Deterministic analysis, Methods: We consider a situation where a QTL has been mapped to a known chromosomal region (QTLR) and a marker haplotype in close association with the QTL is known. A deterministic Bayesian analysis of power and proportion of false positives as a function of Type I error (a = 0.05, 0.10, 0.15 and 0.20), allele substitution effect in units of phenotypic standard deviation (d=0.2 and 0.3 ), and number of daughters in the progeny test (N=100,200,300,500,1000) was implemented.

The analysis assumed that the proportion of heterozygosity at the QTL was 0.40, and provided power, and proportion of false positives (PFP) among declaration of heterozygosity. Accepting a proportion of false positive is equivalent to diluting the anticipated effects of MAS by this proportion. Results: With N=100, and a=0.20, d=0.2, power was 0.57 with PFP = 0.34; with d=0.3, power was 0.75 with PFP = 0.29. With N=200, a=0.20, d=0.2, power was 0.72 with PFP = 0.29; with d=0.3, power was 0.90 with PFP= 0.25. For 300 or more daughters, power at a=0.20 was very high (0.82 or more), even for d=0.2, and PFP approaches its limit value of 0.23. Roughly similar results, showing power of about 0.40 for N= 150 and d= 0.3. were obtained by P3 by simulation based on a different set of assumptions. Simulation:

Simulations of ability of small samples to determine phase in young sires were carried out using data from two sires from RP1, 1392 daughters of S1, known heterozygous for a QTL affecting EBVPY on BTA4; 303 daughters of S2, known homozygous for the same QTL; 240 daughters of S3 from RP4, known heterozygous for a QTL affecting EBVPP on BTA13; and 368 daughters of sire S4 (RP4) , known heterozygous for a QTL affecting EBVPP on BTA14. The daughters were those in the high and low 10% of the total daughter population for the analyzed trait. Haplotypes spanning the QTLR were used to assign sire haplotypes to the daughters. Informativity of the haplotypes was 0.725, 0.751, 0.900, 0.690 for S1, S2, S3, and S4, respectively. To implement the simulations, the desired number of daughters were chosen at random from each of the two tails.

A t-test for significance (non-Bayesian) was then carried out. Power of the test was calculated as the proportion of tests reaching the given significance level. The simulation variables were (1) The number of daughters in each tail (N=40, 80, 160), and (2) the P value required for significance (a = 0.05, 0.10, 0.15 and 0.20). Each Nxa combination was run 100 times for each sire. With 20 daughters in each tail (equivalent to progeny test of 100 daughters), and a = 0.20, the proportion of significant results was 0.34 and 0.28 for S1 and S3, but only 0.16 (about equal to a) for S2. With 40 daughters in each tail, power was 0.29, 0.34 for S1 and S3, and again, 0.16, for S2. With 160 daughters in each tail (equivalent to progeny test of 400 daughters), power was 0.42, 0.47 and 0.23, respectively. These values are less than those obtained in the deterministic analysis.

However, application of the Bayesian approach used in the deterministic analysis to the young sire analysis, should bring the deterministic and simulated results closer. Increase in d, simulated by cross transfer of specific genotypes from high to low tails of the population distribution, strongly increased power and decreased PFP. This might be achieved in practice by multi-trait analysis.

Conclusion: It should be possible to determine marker-QTL phase in young progeny tested sires for known mapped QTL, with power of 0.50, and PFP of about 0.25. This information will be useful to organizations that are implementing MAS programs, encouraging them to implement marker-QTL phasing of their young elite sires.