Amphibian, I bow to your superior knowledge re F1's, however, your answer is too "text book" like for me to comprehend, so is there any chance of explaining what you mean in easy english?
I'll try, but I find it hard to explain complex subjects without it sounding complicated.
Okay.
Tomatoes are inbreeding, the flower contains both male and female parts and hangs downward. When the pollen is shed by the male parts it pollinates the female parts on the same flower. The plant breeds with itself. Tomatoes are happy to do this, as are French beans, lettuce and many other crops.
Now humans are outbreeders, we all know what happens if we inbreed, i.e. breed with people too closely related to us genetically, yes?
Some plants similarly have to breed with other plants, plants that are genetically sufficiently dissimilar enough as to not cause issues, sweet corn is one of the prime examples of this along with most brassicas. In outbreeding crops, teh variety is genetically similar in the characteristics which matter, say form, colour, taste but vary in lots of unseen and unimportant characteristics.
Plants can breed sexually, like we do, or they can reproduce vegetatively, by a part of the plant establishing a new plant, this is seen naturally with potatoes, strawberries, bindweed, raspberries, blackberries. This state also occurs unnaturally in fruit trees and bushes, where instead of growing the plant by seed we take a cutting. Where vegetative reproduction occurs the offspring is identical to its parent.
This has a profound effect on the gentic nature of the plants.
Imagine some tomatoes (a natural inbreeder) we have a indeterminate red tomato and an determinate yellow tomato, these traits are controlled by two genes, the growth habit we will call A and the colour B. Each plant has one of two possible versions of each gene, A or a; A is dominant to a and causes indeterminate growth, B is dominant to b and causes a red tomato. Most living creatures inherit two copies of each gene, one from each parent, our red indeterminate is AABB or yellow determinate is aabb.
What happens if we cross them? The F1 will inherit one of the pair from each parent, and will be AaBb, because A and B are dominant our F1 will look just like the AABB plant, it will be a red indeterminate, every single F1 would be exactly teh same to this, though the F2 (their children) would be different to one another.
Now let's us imagine a potato, many years ago a breeder crossed two potato plants, let's assume that each of the potato plants were genetically stable plant 1 being AABBCC and plant 2 being aabbcc, the F1 would be AaBbCc, they would all be identical. The F1 wasn't what the breeder wanted, he wanted some of teh traits from the paprent with the recessive (non-dominant) genes. So the breeder sows some seed from his F1 plants (by seed here I mean from the potato fruit, not tubers) the genes wil all resegregate, one of the children is AaBbcc and has all the traits the breeder wants, if you were to grow its children from seed again, they would be different to one another, the breder doesn't want this, he wants the traits he's got now. But it doesn't matter because he can take tubers and grow from these, all the children will be exactly the same, clones of the AaBbcc parent. This is how all potatoes have been bred, as a result potatoes are not stable, if you grow them from the fruit seed rather than the tubers you'd get offspring that vary from one another. Because of this if you cross two potatoes the F1s from ths cross will be different to one another too. This is true for all the crops we grow from cuttings, tubers, rhizomes, from suckers, bulbs or by layering.
A strawberry plant is identical to its parent, because it is a clone of its parent, but the parent contains differnt versions of the genes, these different versions would appear if we grew it from its seed instead. Just as an identical human twin is a clone of its sibling, but their children differ from one another.
As allaboutliverpool has mentioned above, because of the insatbility contained in cloned plants seed, you can just sow some seed, the children will all be different, if you find a winner, take cuttings and you have a new variety of your own.
I hope this makes sense.
