Genetic Basis for the Backcross Method
In the F1, many loci will be heterozygous (those loci which had different gene alleles coming from the two parents). These loci will include the gene of interest as well as many other loci containing genes for other traits. With backcrossing, homozygosity for the alleles from the recurrent parent will increase at the same rate as is seen with the approach to homozygosity with selfing (one form of inbreeding). The formula for calculating this rate is given below:
Figure 4. A comparison of alleles on a homozygous chromosome pair (parental lines) and a heterozygous chromosome pair (in the F1 generation). A chromosome pair homozygous for a gene (left) will have the same allele for that gene on each chromosome. A chromosome pair heterozygous for a gene (right) will have different alleles on each chromosome due to making a cross. Recreated by M. Sutter, 2023 with permission.
where n = number of bc generations and m = number of loci
Example of homozygosity from selfing:
Rr x Rr
F2 : 1/4RR : 1/2Rr : 1/4rr
Example of homozygosity from backcrossing:
Rr x rr (21 - 1)1 or ((2 x 1)-1) / 21 = 1/2 homozygosity
BC1: 1/2Rr : 1/2rr
In the BC1 generation, half the plants homozygous for the recurrent parent allele and half the plants are heterozygous for the recurrent and donor parent allele. Similarly, in the F2 generation, 1/2 the plants are also homozygous (RR or rr, note they are not homozygous for only one of the two alleles).
Let’s think back to our original example of leaf rust resistance (RR, Rr). One of the goals of backcrossing is to remove the donor parent’s genes (except the one of interest, RR; the others are nontarget genes) and increase the recurrent parent’s genes except for the gene of disinterest (rr). The amount of remaining genetic information (the nontarget genes), on the average, from the nonrecurrent parent (donor parent) is reduced by 50% with each backcross (Fig. 5).
The calculation for this data is:
(RR, Rr) Percentage of nontarget genes from donor parent = (1/2)n+1
where n = number of backcrosses.
Figure 5. The percentage of recurrent parent genes increases with every generation of crossing. In this instance, 4 backcrosses results in 93.75% Pawnee genes when a rust resistant variety is backcrossed to the Pawnee line. Note these values are averages without selection. In practice the values will be close with some variation due to random segregation of alleles. If the background phenotype or genotype (using molecular markers) is selected for, the number of backcrosses may be reduced to achieve the same level of recurrent parent genetics compared to the traditional backcross. Recreated by M. Sutter, 2023 with permission.
However, the rate at which genes entering a cross from the donor parent (R = rust resistant) are eliminated during backcrossing will be influenced by linkage. Linkage is a term used to describe genes that do not independently assort (one of the requirements for Mendelian inheritance). Linked genes tend to segregate (stay) together and unlinked genes independently assort. The physical basis for linkage is how close the genes are to each other on a chromosome and how frequently crossovers occur between the genes. If genes are far apart or on different chromosomes, they are unlinked and independently assort. If they are near to each other on the chromosome they are more frequently passed on together than separately (Fig. 6).
Linkage is measured by the recombination frequencies/map distance. Factors such as centromere location and chromosome structural abnormalities can reduce crossover events during meiosis. For example, if an undesirable allele d, for dwarfing is linked to R (rust resistant), and selection is only for R, d tends to be brought along in the F1. However, when reintroducing R each backcross, the number of opportunities for crossing over between the R and d loci increases. Therefore, the probability of eliminating d is:
1 - (1-p)n
where, n = number of backcrosses.
p = recombination frequency between loci.
It should be noted that if d and R are close together (small map distance), it will be very hard to select R and eliminate d. In this case linkage reduces breeding progress and increases the number of backcrosses needed to eliminate d. However, it should be remembered that linked molecular markers to the gene of interest are needed for marker assisted backcrossing. In this case linkage between the marker and the gene is very beneficial. In practice, rarely do breeders know all the traits which are linked to the gene of interest in the donor parent selected for a backcrossing program.
Figure 6. Genes less than 50 map units apart are considered linked. The closer genes are located on a chromosome, the more likely they are to be passed on to offspring together. Recreated by M. Sutter, 2023 with permission.