Effects of QTL parameters and marker density on efficiency of Haley–Knott regression interval mapping of QTL with complex traits and use of artificial neural network for prediction of the efficiency of HK method in livestock

Figures & data

Table 1. The different combinations of simulated parameters which were analysed using optimal ANN model.

Population size	Marker space	SD of QTL	Ratio of additive to dominance SD	Relative position of QTL to bracket
300	5	0.2	0.25	0.0
350	6	0.3	0.35	0.05
400	7	0.4	0.45	0.1
450	8	0.5	0.55	0.15
500	9	0.6	0.65	0.2
550	10	0.7	0.75	0.25
600		0.8		0.3
650				0.35
700				0.4
750				0.45
800				0.5
850
900

Table 2. Powers of different combinations of parameters with SDQ of 0.2.

	PS = 300						PS = 600						PS = 900
	Rad = 0.25		Rad = 0.5		Rad = 0.75		Rad = 0.25		Rad = 0.5		Rad = 0.75		Rad = 0.25		Rad = 0.5		Rad = 0.75
	MS =		MS =		MS =		MS =		MS =		MS =		MS =		MS =		MS =
rpQ	5	10	5	10	5	10	5	10	5	10	5	10	5	10	5	10	5	10
0	49	49	51	34	60	45	85	88	81	65	83	86	98	96	96	94	98	98
0.25	54	46	51	34	53	40	86	73	76	65	88	78	97	95	92	87	98	95
0.5	51	44	38	40	55	45	90	72	80	63	90	81	97	91	92	89	94	95

Table 3. Average precision of QTL position (in CM) in combination of PS, SDQ and MS.

PS = 300						PS = 600						PS = 900
SDQ = 0.2		SDQ = 0.5		SDQ = 0.8		SDQ = 0.2		SDQ = 0.5		SDQ = 0.8		SDQ = 0.2		SDQ = 0.5		SDQ = 0.8
MS =		MS =		MS =		MS =		MS =		MS =		MS =		MS =		MS =
5	10	5	10	5	10	5	10	5	10	5	10	5	10	5	10	5	10
9.43	14.70	3.45	4.14	1.30	1.84	6.74	8.99	1.56	1.92	0.91	1.13	6.11	7.28	1.03	1.49	0.74	0.95

Table 4. Average precision of estimated QTL position (in CM) in the context of SDQ, Rad and rpQ.

	SDQ = 0.2			SDQ = 0.5			SDQ = 0.8
rpQ	Rad = 0.25	Rad = 0.5	Rad = 0.75	Rad = 0.25	Rad = 0.5	Rad = 0.75	Rad = 0.25	Rad = 0.5	Rad = 0.75
0	7.252	8.295	9.074	1.185	2.475	2.390	0.737	0.861	0.970
0.25	7.670	9.805	10.760	1.895	2.436	2.666	1.152	1.386	1.508
0.5	7.829	9.485	9.719	1.879	2.522	2.936	1.085	1.360	1.428

Table 5. Effects of PS, MS and SDQ on precision of estimated additive effect.

	PS = 300			PS = 600			PS = 900
MS	SDQ = 0.2	SDQ = 0.5	SDQ = 0.8	SDQ = 0.2	SDQ = 0.5	SDQ = 0.8	SDQ = 0.2	SDQ = 0.5	SDQ = 0.8
5	0.0834	0.0866	0.0828	0.0593	0.0577	0.0584	0.0479	0.0477	0.0480
10	0.0894	0.0890	0.0847	0.0580	0.0633	0.0593	0.0485	0.0490	0.0478

Table 6. Average precision of combined different levels of PS, SDQ and MS on estimated dominance effect.

	PS = 300			PS = 600			PS = 900
MS	SDQ = 0.2	SDQ = 0.5	SDQ = 0.8	SDQ = 0.2	SDQ = 0.5	SDQ = 0.8	SDQ = 0.2	SDQ = 0.5	SDQ = 0.8
5	0.1349	0.1248	0.1242	0.0912	0.0802	0.0872	0.0716	0.0689	0.0704
10	0.1566	0.1289	0.1227	0.0888	0.0853	0.0888	0.0726	0.0762	0.0708

Table 7. Average precision of estimated dominance effect of different SDQ, Rad and rpQ levels combination.

	SDQ = 0.2			SDQ = 0.5			SDQ = 0.8
rpQ	Rad = 0.25	Rad = 0.5	Rad = 0.75	Rad = 0.25	Rad = 0.5	Rad = 0.75	Rad = 0.25	Rad = 0.5	Rad = 0.75
0	0.0835	0.0993	0.1150	0.0901	0.0928	0.0917	0.0955	0.0884	0.0992
0.25	0.0757	0.1147	0.1270	0.0877	0.0962	0.0980	0.0970	0.0934	0.0989
0.5	0.0862	0.1014	0.1214	0.1013	0.0889	0.0995	0.0953	0.0922	0.1006

Table 8. Adequacy parameters of the best ANN model and their standard deviations for every HK efficiency parameters.

	R ^2	T	RMSE train	RMSE test
Power^a
Mean	0.96243	0.958991	0.04825	0.047323
SD	0.020912	0.019571	0.00224	0.014315
QPP^b
Mean	0.926694	0.916424	0.04825	0.058877
SD	0.019578	0.020838	0.00224	0.007371
QAP^c
Mean	0.830139	0.813477	0.04825	0.093546
SD	0.035477	0.038894	0.00224	0.010656
QDP^d
Mean	0.862731	0.844178	0.04825	0.072032
SD	0.045061	0.043949	0.00224	0.009603
^aPower of QTL detection.
^bPrecision of QTL position.
^cPrecision of QTL additive effect.
^dPrecision of QTL dominance effect.

Plot 1.  Effect of population size and marker space on mean of precision of QTL position (PQP).

Plot 2.  Effect of population size and marker space on power of QTL detection mean.

Plot 3.  Effect of population size and marker space on mean of precision of QTL additive effect (PQA).

Plot 4.  Effect of population size and marker space on mean of precision of QTL dominance effect (PQD).

Plot 5.  Effect of SDQ and Rad on mean of power of QTL detection given PS300 MS10.

Plot 6.  Effect of SDQ and Rad on mean of precision of dominance effect given PS300 MS10.

Table 9. Combinations of simulated parameters that obtained higher and lower precisions and power of detection at demanding level of PS (300) and MS (10 cm).

Efficiency parameter	PS	MS	SDQ	Rad	rpQ
Lower precise for qpp	300	10	0.2	0.65	0.4
Lower precise for qpa	300	10	0.3	0.25	0.5
Lower precise for qpd	300	10	0.2	0.75	0.5
Lowest qpower	300	10	0.2	0.55	0.3
Highest precise for qpp	300	10	0.8	0.25	0.3
Highest precise for qpa	300	10	0.2	0.75	0.5
Highest precise for qpd	300	10	0.4	0.25	0
Highest qpower	300	10	0.8	0.25	0
qpp: precision of QTL position.
qpa: precision of QTL additive effect.
qpd: precision of QTL dominance effect.
qpower: power of QTL detection.