- In self – pollinated species, it is th e easier self –pollination in F1is easier to produce, F2 generation. Segregation and recombination of genes would produce several new genotypes, in addition to the two parental types, in F2.
- The number of genotypes produced in F2 increases rapidly with the number of segregating gene.
- The number of phenotypes with and without dominance also increases rapidly with an increase in F2 and increases rapidly with the number increase in the number of segregating genes.
- If, for example 10 genes are segregating, the F1 would produce 1,024 types of gametes, 59,049 different genotypes in F2,1,024 different phenotypes with full dominance, and 59,049 different phenotypes without full dominance and epistasis.
- The smallest size of a perfect F2 population (a population that includes at least one plant of every genotype) would be 1,084,576.
- Most of the intervaietal crosses would differ for many more genes.
- It is, therefore, impractical to raise a perfect F2 population for any cross. Thus the difficulty in recovery of rare recombinants from segregating generation can be easily appreciated.
- This difficulty would be great enough even if the phenotypic effects of the genes were easily recognizable.
- However, in the case of quantitative characters the effects of genes are masked by those of the environment as well as by gene interactions making the identification of rare recombination even more difficult.
- In F2, vast majority of plants would be heterozygous for one or more genes.
- Hetrozygosity reduce the effectiveness of selection because such plants segregate to produce variable progeny,
- i.e., the genetic value of progeny is not the same as that of the parent plants.
- The genetic composition i.e., the frequency of plants heterozygous for different numbers of genes, in a segregating generation is obtained by expanding and solving the terms of the following binomial.
[1 + (2m – 1)]
- Where, m is the number generation of selfing and n is the number of genes that are segregating (independently). If we assume the values of m and n to be 3 and 4, respectively, the appropriate binomial and its expansion will be as follows.
[1 + (23 – 1)] 4 = (1+ (8-1)] 4
= (1+ 7)] 4
= 14+4 (1)3 (7) + 4(1) (7) 3(7) +3
- In the expanded binominal, each term has a coefficient, e.g., 1,4,6,4 and 1 in the above binominal, the factor (1) having indices from 4to0 and the factor (7) (=2m-1) having indices from 0 to 4. In each term, the index of (1) denotes the number of heterozygous genes, while that of (7) i.e., (2m - 1) signifies the number of homozygous genes.
- Further, the solution of a term gives the frequency of plants having the genetic constitution described by the term.
- In the above binominal, solution of the first term will give frequency of plants having 4 heterozygous and zero homozygous genes, that of second term will give the frequency of those having 3 heterozygous and one homozygous genes, of third term will be for plants having 3 heterozygous 2 homozygous genes, of fourth term will be for planting while that of fifth term will be for plants having all the four genes in homozygous state. The solution of the terms of the above binomial gives the following values.
= 1 + 28+ 294+1,372+2,401
- These value are interpreted as follows to give the frequencies of plants having different genetic constitutions.
- Four heterozygous and zero homozygous = 1 plant.
- Three heterozygous and one homozygous = 28 plants
- Two heterozygous and Two homozygous = 294 plants
|Frequency (in per cent) of completely homozygous plants
|Number of genes segregating
heterozygous and three homozygous = 1,372 plants
Zero heterozygous and four homozygous = 2,401 plants.
- Thus in f4 generation of a cross segregating for 4 genes, the frequencies of plants segregating for different numbers of genes will be as given above.
- Frequency of completely homozygous plants in F2 and the subsequent generations of crosses segregating for different number of genes.
- * The number of generations of self –pollination will be 1 in F2, 2 in F4 and n – 1 in Fn generation since F1 is the result of hybridization and only F2 and the subsequent generations are due to selfing.
- The frequency of completely homozygous plants = [(2m – 1) /2m)]n where, m is the number of generations of self- pollination increases, the frequency of completely homozygous plants increases sharply.
- Consequently, the confusing effects of heterozygote are reduced and selection becomes more effective in the advanced selfed generations.
- Therefore, many breeders feel that selection on individual plant basis should be delayed till F5 or even F6 generation.
- These considerations have assumed equal survival of all the genotypes, and no linkage.
- There is some evidence that heterozygotes may be favoured in nature,
- The increase in homozygosity, therefore, could be less than theoretically expected, Linkage would decrease the frequency of recombinant types and increase the frequency of completely homozygous plants.
- The latter effect is produced because linkage reduces the number of genes segregating independently.
- Linkage between favourable genes makes selection easier because the two desirable characters tend to be inherited together populations would be required to break this linkage.
- In case of quantitative characters, recombinations may produce genotypes superior to the two parents.
- For example, if a variety with the genotype AA bb cc dd is crossed with another variety with the genotype AA BB CC DD and aa bb cc dd would be produced.
- These plants would be superior and inferior, respectively to both the parents; such recombinants are known as transgressive segregants. Breeding for yield generally aims at the recovery of transgressive segregants.
- Frequency of such segregants in F2, which 2 out of 4n plants (where n is the number of genes segregating), it would be apparent that the chances of recovery of such genes from each parent, but rarely a plant in a small F2 population would have all the genes from both the parents.