1. Selective mapping and simulation study

2. high-density genome maps Are used for: Comparative mapping Map-based cloning Genome sequencing But genotyping costs time and money And density can surpass resolution because of cosegregation (i.e. bins)

3. bins and map resolution random selected

4. high-density mapping strategies Selective mapping Optimizes map resolution Requires less genotyping Bin mapping Provides “honest” marker placement Aids map integration

5. selective mapping Genotype a base population (many individuals, few markers) Construct a precise framework map Select a subsample with high resolution Genotype subsequent markers on subsample Vision et al. (2000) Genetics 155:407-420.

6. summarizing bin length distribution Average (ABL) Most breakpoints Maximum (MBL) Minimize areas of low resolution Sum of Squares (SSBL) or Expected (EBL) = SSBL/G

7. discrete optimization strategies Mathematical programming Integer program for exact breakpoints Linear program To derive lower bound Randomized rounding to obtain candidate samples Semi-greedy algorithm Avoids local optima Uses mixed objective function

8. comparing results Performance Ratio (PR) = L sample /L population Optimum is 1 Higher values are inferior Also useful: L sample /L random

9. simulation 100 doubled haploids 1000 cM genome performance ratio (MBL)

10. simulation: cumulative bin length distribution - whole pop. ▼expected × maximum ◊ average Δ non-optimized sample size=30

11. performance ratio (MBL) barley IGRI x Franka cross 150 doubled haploids 1100 cM genome data from http://wheat.pw.usda.gov/ggpages/maps.html

12. Simulation study

13. Number of breakpoint in different simulation

14. Additive effect: gamma(1,2)

15. Epistasis effect: beta(1,1), only two level interaction

16. Total: Sample: Analysis: Simulation procedure 500 10050100 10 LR IM MapPop Random

17. Simulation: Random: 1. 2QTL, h2:0.3,0.7,total size:500,marker:101;epi:0.5; 2. 10QTL, h2:0.3,0.7,total size:500, marker:101; epi:0.2; 3. Using QTL Cartographer to do 1,2. Fixed QTL position: 1. 5QTL,h2:0.7,total size:500, marker:101; no epi 2. 5QTL,h2:0.7, total size:1000, marker:101; no epi 3. 10 QTL h2:0.7, total size:500, marker:101; no epi Set QTL far apart (100cM away form each other): 1. random 5 QTL position, h2:0.5,total size 500; marker:101;epi:0.3 2. Samiliar to 1, only difference is marker:201 3. Maker: 101 to 201. 4. Uning mean traits for each line (2,5,10,100); Fixed population and samples to mapping different set of QTLs. *each has 100 replicate; threhold values are gotten from 300 rounds under corresponding H0

18. How about the power *2QTL, random position h2:0.3,0.7,total size:500,marker:101;epi:0.5; Average number of QTL detected

19. *10QTL, random position,h2:0.3,0.7,total size:500,marker:101;epi:0.5; Average number of QTL detected

20. How about the power with increased population size *F5500: 5QTL,h2:0.7,total size:500, marker:101; no epi *F51000: 5QTL,h2:0.7, total size:1000, marker:101; no epi Average number of QTL detected

21. How about the breakpoint number *F500: total size is 500 *F1000: total size is 1000

22. How about the detected QTLposition *5QTL far apart (100 cM away)

23. How about the QTL effects *5QTL far apart (100 cM away)

24. Fixed population and sample,mapping different trait genes *5QTL;far apart(100cM away);h2:0.5;epi:0.3

27. Future work: 1. Power v.s. resolution. 2. Sample size needed to achieve same power in random. 3. Analyzing the breakpoint number v.s. resolution theoretically. 4. Simulating to see how MapPop works in fine mapping.