EM Algorithm for Mapping Quantitative Trait Loci in Multivalent Tetraploids

Table 1

Maximum likelihood estimates of the double reduction, recombination fraction, overall mean, additive effects, and dominant effects under different simulation scenarios in a mapping population of size 100. Numbers in parentheses are the standard errors of the estimates.

True value					μ	𝑎1	𝑎2	𝑎3	𝑑12	𝑑13	𝑑14	𝑑23	𝑑24	𝑑34
𝛼	𝑟	𝐻^2	𝛼	𝑟̂	1	0.6	0.6	0.6	0.5	0.5	0.5	0.5	0.5	0.5
0.3	0.25	0.1	0.295	0.314	1.153	0.047	0.116	0.037	2.228	3.007	−1.953	2.375	−2.661	−2.107
			(0.047)	(0.120)	(1.139)	(2.339)	(2.651)	(2.496)	(4.013)	(4.237)	(4.499)	(4.349)	(4.453)	(4.407)
0.3	0.25	0.4	0.301	0.251	1.095	0.556	0.496	0.546	0.677	0.625	0.313	0.482	0.181	0.138
			(0.048)	(0.098)	(0.540)	(0.986)	(1.003)	(1.133)	(1.744)	(1.861)	(2.143)	(1.947)	(2.103)	(1.931)
0.3	0.05	0.1	0.297	0.142	0.961	0.659	0.580	0.512	1.216	1.130	−0.036	1.286	0.119	−0.084
			(0.041)	(0.114)	(0.767)	(1.330)	(1.293)	(1.303)	(1.967)	(2.208)	(2.301)	(2.129)	(2.193)	(2.102)
0.3	0.05	0.4	0.296	0.057	0.998	0.642	0.643	0.533	0.445	0.562	0.428	0.601	0.488	0.594
			(0.045)	(0.051)	(0.296)	(0.461)	(0.581)	(0.497)	(0.868)	(0.787)	(0.851)	(0.973)	(0.762)	(0.687)
0.15	0.25	0.1	0.150	0.305	1.058	0.244	0.821	0.945	1.232	1.334	0.167	0.660	−0.150	−0.373
			(0.034)	(0.155)	(1.067)	(1.800)	(1.794)	(1.965)	(2.707)	(2.645)	(2.819)	(2.820)	(2.658)	(2.614)
0.15	0.25	0.4	0.152	0.239	1.061	0.522	0.548	0.598	0.645	0.484	0.449	0.492	0.382	0.230
			(0.031)	(0.097)	(0.369)	(0.777)	(0.812)	(0.794)	(1.082)	(1.166)	(1.100)	(1.203)	(1.227)	(1.238)
0.15	0.05	0.1	0.144	0.168	0.837	0.411	0.540	0.930	1.616	1.242	0.271	1.033	−0.037	−0.313
			(0.035)	(0.127)	(1.108)	(2.103)	(1.962)	(1.635)	(2.854)	(2.698)	(2.488)	(2.452)	(3.147)	(2.700)
0.15	0.05	0.4	0.143	0.057	0.921	0.372	0.736	0.545	0.685	0.965	0.621	0.677	0.282	0.453
			(0.035)	(0.058)	(0.488)	(0.877)	(0.759)	(0.775)	(1.192)	(1.148)	(1.085)	(1.085)	(1.167)	(1.147)
0.05	0.25	0.1	0.052	0.371	0.769	0.356	0.300	0.455	2.239	2.178	−0.691	2.031	−0.426	−0.588
			(0.022)	(0.180)	(1.293)	(2.122)	(2.576)	(2.392)	(3.425)	(3.478)	(3.104)	(2.787)	(2.998)	(3.563)
0.05	0.25	0.4	0.051	0.253	0.643	0.440	0.406	0.458	1.243	1.202	0.500	1.224	0.553	0.362
			(0.022)	(0.111)	(0.699)	(1.067)	(1.003)	(1.105)	(1.522)	(1.605)	(1.341)	(1.541)	(1.483)	(1.482)
0.05	0.05	0.1	0.052	0.193	1.008	0.056	1.012	0.362	1.552	1.977	−0.065	1.068	−1.077	−0.438
			(0.025)	(0.136)	(1.346)	(2.119)	(2.537)	(2.121)	(3.110)	(2.718)	(3.191)	(3.427)	(3.354)	(3.391)
0.05	0.05	0.4	0.052	0.064	0.762	0.525	0.361	0.337	1.119	1.175	0.193	1.255	0.303	0.351
			(0.024)	(0.059)	(0.736)	(1.005)	(0.959)	(1.076)	(1.480)	(1.482)	(1.542)	(1.636)	(1.473)	(1.285)