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:

Fig. 4. A chromosome pair homozygous for a gene will have the same allele for that gene on each chromosome. A chromosome pair heterozygous for a gene will have different alleles on each chromosome.

where n = number of bc generations and m = number of loci.

Rr x Rr

Rr x rr (21 - 1)1 or ((2 x 1)-1) / 21 = 1/2 homozygosity

F2 : 1/4RR : 1/2Rr : 1/4rr

BC1: 1/2Rr : 1/2rr

Similarly in the F2 generation, 1/2 the plants are also homozygous (RR or rr).

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.

The calculation for this data is:

(RR, Rr) Percentage of nontarget genes from donor parent = (1/2)n+1

where n = number of backcross.

Fig. 5. The percentage of recurrent parent genes increases with every generation of crossing.

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 stay together and unlinked genes independently assort. The physical basis for linkage is how close the genes are to each other on a chromosome. 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.

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 occur. 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 is eliminated. Rarely do breeders know all the traits which are linked to the gene of interest in a backcrossing program.

Fig. 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.