>> if I grow a tomato that looks exactly like an Arkansas traveler picture, and I really love the taste, would it be safe to assume the seeds will grow an Arkansas traveler?
Does the packet print a short list of what varieties are in it? If the one you like does not look like any of the others, that would identify it. Or you could ask customer service what-all were in that packet, that year.
But if the packet only says "assorted mixed heirloom tomatoes", I don't think you can confidently identify the parent. There are thousands of heirloom varieties.
It would be safe to assume that around 80% of the seeds you save would look, grow and taste like the parent plant (if the weather and soil are similar next year) , but you might not be sure of the identification.
P.S. I have often wondered: one bloom produces one fruit. Does that mean that "one bloom uses one pollen grain to produce one fruit"? So that all the seeds in any one tomato are either all self-pollinated or all cross-pollinated by the same pollen donor?
or does each bloom use MANY pollen grains to produce its many seeds, and each seed MIGHT be cross-pollinated by a different pollen donor?
And is it the same for every species, that all the seeds in one pod came from one pollen donor? or do different plant species work different ways?