A common question asked by breeders is "How can breeders utilize more
than a few markers in a real breeding program?" Since few workable
answers have been provided, a computer program
(http://www.ndsu.nodak.edu/instruct/hammond/GeneAssistedSelection.zip)
was coded to generate actual alleles that can be genotyped and displayed
for selection.
Initially the idea was a classroom tool for breeding students. However,
a breeding plan that was workable was identified. The idea was to
generate an F2 population segregating at a given number of loci. The
objective was to develop a breeding plan to select an individual that was
homozygous for all loci. The basic plan that seemed to work involved
generating a population of F2 individuals (the number of individuals
equal to twice the number of loci was a good starting point). From this
population and each cycle of selection, we
1) selected individuals for crossing that collectively had at least one
favorable allele at each locus and
2) from this subset, we selected the cross that had the highest average
frequency of favorable alleles over all loci.
As an example, let us assume that 10 F2 individuals from a cross of 2
homozygotes segregating at 5 independent loci were generated (Table 1).
The question that a breeder must answer is which individual(s) could be
utilized to develop a homozygous individual at all five loci.
Table 1. A simulation of 10 individuals from an F2 population of five
independently segregating loci produced individuals with values from 4 to
7.
Gamete from
Individual p1
p2
sum of alleles
1
11110 11101
8
2
00000 01111
4
3
00111 01100
5
4
11011 01110
7
5
01000 10111
5
6
01100 11110
6
7
01011 01000
4
8
10001 10001
4
9
01100 10010
4
10
00110 11111
7
Our plan would be to select 2 individuals (selfing is acceptable) such
that
1) no locus would be lost and
2) the highest average frequency of favorable alleles would be chosen.
In this example we would select individual 1 and self to generate a new
group of individuals (Table 2).
Table 2. A simulation of 10 individuals from self mating of 11110/11101
produced individuals with genotypic values from 7 to 10.
Gamete from
Individual p1
p2
sum of alleles
1
11110 11100
7
2
11110 11100
7
3
11111 11111
10
4
11110 11100
7
5
11110 11110
8
6
11100 11101
7
7
11101 11100
7
8
11110 11111
9
9
11101 11110
8
10
11110 11101
8
Individual 3 represented the best possible genotype. In total, 20
individuals were evaluated. Ten individuals in each of the cycles (C0C1) were simulated. In contrast, with 5 independently segregating loci
one would expect 1 in 1024 F2 individuals to have all five loci in a
homozygous state. This would seem feasible. However, with 10 on 15 loci
the probability of observing the best possible individual in the F2 is
rather low (Table 3).
Table 3. The probability of observing the best homozygous individual
among F2 individuals based on the number of independently segregating
loci.
Loci
2
3
4
5
10
15
20
25
30
Probability = 1/4loci
1/16
1/64
1/256
1/1024
1/1,048,576
1/1,073,741,824
1/1,099,511,627,776
1/1,125,899,906,842,624
1/1,152,921,504,606,846,976
Based on the simulation program it should be possible to fix all loci in
a reasonable amount of time and with limited resources (Table 5). For
example with 10 loci, we would evaluate 20 F2 individuals plus 20
individual would be evaluated each addition cycle. A total of (20 +
2.981 *20) individuals would be evaluated on the average.
Table 4. Given the following individuals representing a population with
10 loci segregating, how would you proceed?
Individual
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Gametes from P1 Gametes from P2 Sum of alleles
0100111001
1011011010
11
0000001001
0000001100
4
1110010000
0110010110
9
1011001111
1001001100
11
0110000000
1101001111
9
1010101111
0000010001
9
0000010010
0101111101
9
1000000110
0000011001
6
0100011100
1110100011
10
1110101111
1100110011
14
1111000010
1101011101
12
0011000000
1001010110
7
0010111011
0011110011
12
0000101011
1101111100
11
1101101111
0110001010
12
1111001111
0110100110
13
1000011000
1010010100
7
1111010101
1011010110
13
1101001001
0010110101
10
0000101000
1001011110
8
Table 5. Simulation results from 1000 runs for varying number of loci
and individuals per cycle.
Loci
5
10
15
20
25
30
Individuals per
cycle
10
20
30
40
50
60
Cycles required
Evaluations
2.082
2.981
3.696
4.324
4.961
5.453
30.82
79.62
140.88
212.96
298.05
387.18