1. PLANT BREEDING TERMINOLOGY AND SYMBOLS
Plant breeders are a group of professional separated by a common language
It needs to be recognized that few plant breeding programs share the same terminology in describing generations, families, lines, plots and other trappings.
Desperation !
Dislocation !
Separation !
Condemnation !
Isolation !
Desolation !
‘Bad’-- U2

2. Ambiguity--The Example of the F1 Generation
All communications will be through the two-tiered system outlined by Fehr (1987). It is the most commonly understood system, theoretically correct, and makes ambiguity almost impossible.
Ambiguity--The Example of the F1 Generation
Cross between
Homozygous parents (A1A1 x A2A2) Heterozygous parents (A1A2 x A3A4)
Homogeneous F1 progeny Heterogeneous F1 progeny
A1A A1A3
A1A A1A4
A1A A2A3
A1A A2A4

3. Ambiguity: The Example of the F2 and S0 Generations
The symbol F refers to the word ‘filial’, and the subscript to the generation in the sequence of generations following a cross (F1, the first generation after the cross; F2, the second generation after the cross, etc.). The F symbol is usually, but certainly not always, used with reference to self-pollinated generations of a self-pollinated species.

4. Ambiguity: The Example of the F2 and S0 Generations
The symbol F refers to the word ‘filial’, and the subscript to the generation in the sequence of generations following a cross (F1, the first generation after the cross; F2, the second generation after the cross, etc.). The F symbol is usually, but certainly not always, used with reference to self-pollinated generations of a self-pollinated species.

5. Ambiguity: The Example of the F2 and S0 Generations
The F2 generation is the first segregating generation after the cross between two inbred lines. Because the parents were homozygous inbreds, a generation of selfing (F1 F2) was necessary to produce this 1:2:1 ratio.

6. The familiar 1:2:1 phenotypic ratio is observed at loci in the S0 generation if two contrasting alleles at a locus are each present at a frequency of The S0 generation, like the F2 generation, is the first segregating generation after the cross. (It is also the first generation after the cross in this case.) But in contrast to the F2, a generation of selfing is not necessary in order to produce the 1:2:1 phenotypic ratio. This is due to the fact that the parents making the cross are not only homozygotes.

7. Parents
Thus the S0 generation is equivalent in terms of genotypic frequencies to the F2 generation resulting from the cross between homozygous inbred parents. Seed obtained through random mating could technically be called F1 seed, but, because the genotypic frequencies in the population of hybrids obtained by random mating resembles an F2 generation, we will refer to it as S0 seed.

8. Many theoretical studies begin with a reference or base population which is heterozygous and heterogeneous and contain two alleles per locus at frequencies of This base population is referred to as the S0 or F2. With systematic schemes of inbreeding, it follows that: 
F3  S1
F4  S2
F5  S3
F6  S4
Other side of argument, S0 = F1, because neither has undergone
systematic self-pollination

9. Symbolism for Describing the Inbreeding of Lines from an F2 or S0 Population
The two-tiered system we utilize is applicable for both F and S inbreeding situations. The generalized formula is written as: 
Fx:y or Sx:y 
where x was the generation of the single plant that was harvested, separately, giving rise to the derived line, and y is the current generation of inbreeding of the plants within this derived line.

10. We are concerned about both values, x and y, because together they permit us to estimate the expected genotypic composition of the derived line at loci for which the parents had contrasting alleles.

13. Note that ‘F2:3 line’ is an abbreviation for ‘an F2-derived line in the F3 generation’.
Note that ‘S0:1 line’ is an abbreviation for ‘an S0-derived line in the S1 generation’.

14. The key to learning this system is to always identify the most recent generation in which a single plant was harvested to give rise to the current line of descent.
For example, for the F2:3 line, its single plant origin was in the F2 generation. For the F2:4 line, its single plant origin was the same F2 plant, because a bulk of several plants was harvested in the F3 generation.
However, the situation is different for the F4:5 line. The most recent generation in which a single plant was harvested to give rise to this line was the F4 generation.

15. . Similarly, for the S1:2 line, the most recent generation in which a single plant was harvested to give rise to this line was the S1 generation.
For the S1:3 line, the same plant is the single plant origin because a bulk of several plants was harvested in the S2 generation.
If a single plant within this S1:3 line is selected, selfed, and the seed from the selfed ear is kept separate, then you would have S3:4 seed in the envelope.