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Simulation Of Positive Assortative Mating For Inbred Line ...

Simulation of Positive Assortative Mating for Inbred Line Development Using QU-GENE

Guoyou Ye, Mark Dieters, Alexander Pudmenzky, Kevin Micallef and Kaye Basford

School of Land and Food, The University of Queensland, Brisbane Qld 4072, Australia. Email g.ye@uq.edu.au

Abstract

Two positive assortative mating (PAM) schemes and the random single pair mating (RS) were compared by computer simulation for genetic gains over five breeding cycles and at each breeding cycle in the context of inbred line development. For the first scheme crosses were selected using the average genotypic value of the two parents (GV). For the second scheme, all parental lines were ranked in descending order based on their genotypic values, and then partial disconnected diallel mating was used to generate the required number of crosses (GP). Simulations carried out using 16 combinations of four inheritance modes (purely additive, dominant, and two-gene and three-gene epistasis), and four numbers of crosses (30, 60, 80, and 120) suggested that; 1) both GV and GP increased genetic gain substantially with GV being better than GP, 2) the benefit of PAM was greater under additive and dominant models, 3) the differences among the mating methods were largest in the first breeding cycle and decreased with subsequent breeding cycle, and 4) the resource allocation between making more crosses and testing more lines per cross under fixed testing capability (24,000 lines) was secondary to the mating method used. Though gain increased with the number of crosses for RS, 60-80 crosses were more appropriate for GV and GP. When number of crosses was fixed at 30, little extra gain could be achieved by testing more than 200 lines per cross. GV not only resulted in more gain but also reduced the number of lines per cross required to maximise gains.

Media summary

Computer simulation using QU-GENE indicated that the positive assortative mating substantially increases genetic gain over the random single pair mating in inbred line development.

Key Words

Positive assortative mating, random single-pair mating, computer simulation, QU-GENE

Introduction

Selection of good performing recombinant inbred lines from crosses among well tested potential parental lines is well established procedure for developing new inbred lines (Allard 1999). Typically, there is only one inter-mating step in a breeding cycle, though several steps of backcrossing are used when the objective is to transfer useful genes from unadapted materials to well-adapted lines (Allard 1999). Therefore, the best inbred lines achievable are determined once the crosses are made. Sufficiently large populations in the segregating generations are required to ensure a reasonable probability that the best genotypes will actually be available for selection. Making the right crosses and properly sampling the segregating generations are key steps to the success of inbred line development.

Using computer simulation Bernardo (2003) showed that selecting parents before crossing can substantially increase genetic gain. When the number of crosses is fewer than the number of possible cross combinations, which is true for most if not all breeding programs, random selection of parents is unlikely to be the best approach. Positive assortative mating (PAM) - the mating of individuals similar in genotype has been shown to increase genetic gain in the early selection cycles for mass selection (Smith and Hammond 1987).

As for sampling the segregating generations of the crosses, breeders seek to find the optimal balance between the number of crosses and the number of inbred lines per cross because resources are always restricted. Making more crosses will usually increase the total number of potential genotypes. This increases the opportunity for recombination to occur among all loci affecting the trait of interest. Increasing the number of lines per cross increases the probability of attaining the best possible recombinant from a cross. The optimum numbers of crosses is determined by testing capacity, number of selected crosses, number of selected lines from each selected cross, and trait heritability (Hühn 1996).

The objectives of this study were to, 1) compare three mating methods for producing the crosses for inbred line development under a range of inheritance models, and 2) investigate the balance between the number of crosses and the number of lines per cross.

Methods

The quantitative genetics computer simulation platform (QU-GENE) developed at the University of Queensland (Podlich and Cooper 1998, Ye 2003) was used to carry out the simulation.

GE systems

Only one environment was considered. The trait was assumed to be controlled by 72 independent biallelic loci with gene frequencies of 0.5. Four gene action modes (inheritance models) were assumed; (1) Additive model (A), all genes are purely additive, (2) Dominant model (D), all genes are completely dominant, (3) two-gene epistasis (E1), the 72 genes were assumed to be in 36 two-gene epistasis networks, and (4) three-gene epistasis (E2), the 72 genes were assumed to be 24 three-gene epistasis networks. The effects of the genes for A and D models were randomly sampled from a uniform [0, 1] distribution. The genotypic values of all possible genotypes for each epistasis network were randomly sampled from a uniform [0, 2] and [0, 3] distribution for the E1 and E2 models, respectively. The experimental error (V_E) (both among- and within-plot) was generated by setting the individual-based broad-sense heritability at 0.05. To reduce the influence of the randomness of gene effects for A and D models and of genotype values of the epistasis models, twenty random models were used. For each random model simulations were repeated ten times.

Mating methods

Three mating methods were considered. In the random single-pair method (RS), pairs of inbreds were selected at random from the 60 parental inbreds. In the second method, crosses were selected from all unique crosses excluding selfs using average genotypic value of the two parents (GV). In the third method (GP), all parental lines were ranked in descending order based on their genotypic values, and five-parent partial disconnected diallel mating staring with the top ranked parent was then used to generate the required number of crosses. The last two methods were positive assortative mating in the sense that similar genotypes were mated. The third method uses partial disconnected diallels (without selfs) mating to control the number of crosses involving each parental inbred.

Basic breeding strategy

A simple single seed descent method was used as the basic breeding strategy. Different numbers of crosses (30, 60, 80 or 120) were generated using the three mating methods. Individual F₂ plants were advanced by four generations using the single seed descent procedure to form inbred lines. In each case the F₂ population size was determined by assuming the total number of inbred lines was 24,000. Multilocational tests were used in F₇, F₈ and F₉ to select the best 60 inbred lines. The original 60 parental lines were replaced by the selected 60 lines before the next breeding cycle started. Five breeding cycles were simulated. In subsequent simulation to investigate the effect of number of lines per cross 50, 100, 200, 400 or 800 lines per cross were used from 30 crosses selected by both GV and RS methods.

Analysis

The incremental genetic gains were computed by taking the differences between population mean genotypic values of two consecutive cycles. The accumulative gain was computed as the difference between the genotypic mean at end of a breeding cycle and that of the initial population divided by that of the initial population. However, different scales in different genetic-environment systems make it inappropriate to compare gain on the basis of the original scales. Therefore, the gains computed using the genotypic values adjusted for extreme genotypes were used in all the analysis. The adjusted genotype value was computed as

where is the adjusted genotype value, g is the unadjusted genotype value, is the genotype value of the worst genotype, and is the genotype value of the best genotype.

Results

From the analysis of variance of the incremental gains at each cycle and total gain over five cycles (Table 1), it can be seen that mating method (MM) was the main contributor to the overall variation followed by inheritance model in the first three cycles. For cycle 4 and 5 the inheritance model (IM) was more important than the mating method. The number of crosses (NC), and all the two-way and three-way interactions were far less important for all cycles, though they were statistically significant in some cycles. For total gain, again mating method and inheritance model were more important than other sources of variation.

Table 1. Sum of square from analysis of variance of incremental genetic gains at each breeding cycle and total gain over five breeding cycles.


Source	DF	Breeding Cycle					Total gain
Source	DF	1	2	3	4	5	Total gain
IM	3	5800.62^***	2499.75^***	1378.66^***	682.76^***	295.22^***	90459.88^***
MM	2	24060.32^***	3167.95^***	305.09^***	18.28^***	266.92^***	80703.51^***
IM*MM	6	896.25^***	83.52^***	7.22	13.20^***	17.00^***	2073.84^***
NC	3	178.91^***	12.33^***	28.14	33.57^***	42.45^***	307.19^***
IM*NC	9	9.05^**	17.29^***	2.71^**	3.56^***	1.86	117.66^***
MM*NC	6	430.56^***	33.52^***	4.39^**	11.41^***	18.49^***	529.25^***
IMMM	18	25.01^***	15.52^***	8.21^**	3.54^***	2.56^**	68.93^***
Error	912	518.40	519.50	350.44	205.58	142.37	1162.90

NC= number of crosses; MM= mating method; IM= inheritance model.^***= p< 0.001;^**= P < 0.01; ns= p > 0.05

The differences among mating methods were highly significant in all cycles for all inheritance models. Compared to RS, both GV and GP increased gain substantially in the first three breeding cycles with GV being better than GP. In cycle 5 RS was better than GV and GP. The differences among mating methods decreased with each breeding cycle. However, the highest total percent gain after five breeding cycles was achieved by GV followed by GP and RS. The differences among mating methods were larger for additive and dominant models than for the two epistasis models.

Table 2. Mean and standard error (SE) of incremental gain at five breeding cycles.


Breeding Cycle	Mating Method	Inheritance Model
		A		D		E1		E2
		Mean	SE	Mean	SE	Mean	SE	Mean	SE
	GV	32.8	1.61	33.0	1.58	27.5	1.57	24.9	1.06
1	GP	26.2	0.80	26.4	0.87	21.5	0.59	20.5	0.55
	RS	18.1	1.15	18.8	1.36	17.1	0.64	15.4	0.65
	GV	16.9	0.81	16.6	0.95	13.8	0.55	13.8	0.47
2	GP	17.1	1.04	16.9	0.97	12.9	0.72	13.0	0.58
	RS	12.7	1.05	12.6	0.98	9.9	0.50	10.0	0.53
	GV	10.8	0.72	10.8	0.72	8.0	0.44	8.6	0.38
3	GP	10.6	0.85	10.5	0.81	8.2	0.56	8.5	0.59
	RS	9.6	0.82	9.4	0.66	7.0	0.47	7.3	0.48
	GV	6.8	0.58	6.8	0.61	5.1	0.48	5.4	0.42
4	GP	7.0	0.58	7.0	0.59	5.5	0.48	5.6	0.41
	RS	7.4	0.66	7.3	0.61	5.2	0.39	5.5	0.35
	GV	4.1	0.52	4.0	0.60	3.1	0.51	3.2	0.39
5	GP	4.6	0.46	4.6	0.40	3.7	0.39	3.7	0.34
	RS	5.7	0.59	5.6	0.61	4.1	0.36	4.2	0.34

GV= crosses are selected using average genotypic value of the two parents; GP= all parental lines are ranked in descending order, and five-parent partial disconnected diallel mating is then used to generate the required number of crosses; RS: the crosses are generated by randomly selecting a pair of parents (without selfing). A: all genes are additive; D: all genes are dominant; E1: two-gene epistasis; E2: three-gene epistasis.

With all three mating methods, more gains were achieved when epistasis was absent (Table 2). The more complex the gene-interaction (epistasis) the less gain was achieved. There were only slight differences between additive and dominant models. Larger differences among inheritance models were found when GV or GP was used (Table 2). The differences among inheritance models were similar at different breeding cycles.

The differences among different numbers of crosses were only marginal (Table 3). Increasing the number of crosses resulted in higher gain when RS was used. However the difference between 80 and 120 crosses was not significant. When either GV or GP were used the differences among the number of crosses were even smaller. Making 60 crosses seemed to be best for GV, while 80 was best for GP.

Gain increased with the number of lines per cross for both GV and RS. However, the increase of gain was not proportional to the number of lines per cross. More gain was achieved by increasing population size from 50 to 100. More than 150 and 200 lines per cross were not necessary for GV and RS, respectively (Table 4).

Table 3. Mean and standard error (SE) of genetic gain (%) after five breeding cycles.


Inheritance Model	Cross Number	Mating Method
		GV		GP		RS
		Mean	SE	Mean	SE	Mean	SE
A	30	91.0	1.44	81.8	1.32	61.8	2.26
A	60	92.0	1.46	82.4	1.24	65.0	1.33
A	80	91.0	0.94	83.9	1.27	67.2	1.88
A	120	90.0	0.98	83.4	1.40	67.2	1.43
D	30	90.4	0.86	81.6	1.23	62.8	2.40
D	60	91.3	0.81	82.3	1.40	65.6	1.78
D	80	91.3	1.08	83.3	1.25	66.4	1.14
D	120	90.1	0.95	83.1	1.03	67.7	1.54
E1	30	70.1	0.78	62.3	1.04	49.5	1.04
E1	60	70.2	0.76	62.1	0.79	50.6	0.87
E1	80	69.7	0.83	62.6	0.65	51.1	0.65
E1	120	68.8	0.68	61.6	0.93	51.4	0.91
E2	30	68.6	0.67	61.2	0.74	47.6	0.89
E2	60	68.1	0.57	62.0	0.68	49.9	0.69
E2	80	68.1	0.46	62.2	0.60	50.2	0.67
E2	120	67.2	0.55	61.2	0.70	50.8	0.59

Table 4. The effect of number of lines per cross on accumulative gains at each breeding cycles.


Mating method	Line/ cross	Breeding Cycle
		1		2		3		4		5
		Mean	SE	Mean	SE	Mean	SE	Mean	SE	Mean	SE
GV	50	27.8	4.59	45.5	7.15	57.6	7.33	65.8	7.05	72.0	6.87
GV	100	30.5	4.34	49.8	6.53	63.1	7.22	71.5	7.36	76.6	7.56
GV	200	31.4	4.21	50.1	5.77	63.1	6.85	71.6	7.28	76.7	7.57
GV	400	32.6	4.41	50.9	5.83	63.9	6.72	72.8	7.79	77.4	8.56
GV	800	33.0	4.21	52.1	5.38	65.0	6.28	72.6	6.50	76.2	6.42
RS	50	10.4	2.95	18.5	4.12	26.6	5.20	33.9	6.21	40.1	6.54
RS	100	13.0	3.25	23.6	4.39	32.6	5.67	40.3	6.67	46.4	6.71
RS	200	15.0	4.02	27.1	6.08	37.0	6.20	45.7	7.02	52.5	7.83
RS	400	15.3	2.85	28.0	4.38	38.4	5.16	47.0	5.73	54.0	6.89
RS	800	16.3	2.80	29.3	4.11	40.4	5.12	49.4	6.12	57.1	7.41

Conclusion

Mating method is much more important than the allocation of resources between the number of crosses and the number of lines tested per cross. The two schemes of positive assortative mating tested resulted in much higher genetic gain than the random single pair mating. Even if the inheritance is more complex than a purely additive model, the two schemes based on genotypic value can bring more gain.

References

Allard RW (1999). Principle of Plant Breeding. 2^nd Edition. John Wiley and Sons, New York.

Bernardo, R. 2003 Parental selection, number of breeding populations, and size of each population in inbred development. Theoretical and Applied Genetics 107: 1252-1256.

Hühn, M., 1996, Optimum number of crosses and progeny per cross in breeding self-fertilizing crops. I. General approach and first numerical results. Euphytica 91:365–374.

Simth, S.P., and K. Hammond 1987. Assortative mating and artificial selection: a second appraisal. Genetics, Selection Evolution 19: 181-196.

Podlich DW and Cooper M (1998). QU-GENE: a platform for quantitative analysis of genetic models. Bioinformatics 14: 632-653.

Ye, G. (2003) QuLine user’s manual. The University of Queensland.

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