Is a three-way cross the same thing as...
 

a double-cross? How exactly would you do something like that?

I have a vague understanding of crossing 2 varieties, but can't make sense of how you'd do that w/ 3 varieties.

Any help?

[A] x [B] => [F1]
[F1] x [C] => [F2']

We can examine one locus to get a more specific idea of what will happen.
[A] = AA
[B] = aa
[F1] = Aa

if ([C] = AA), [F2'] = 50% AA, 50% Aa.
if ([C] = Aa), [F2'] = 25% AA, 50% Aa, 25% aa.
if ([C] = aa), [F2'] = 50% Aa, 50% aa.

You can use this sort of cross to bias the final ([F2']) population towards specific allelic combinations. Perhaps a double recessive ('aa') results in a negative phenotype, while 'Aa' and 'AA' are positive phenotypes that you want in the final population. Using this type of cross, you can intentionally avoid any specific homozygous trait while still maintaining the heterozygous trait.

[QUOTE] Using this type of cross, you can intentionally avoid any specific homozygous trait while still maintaining the heterozygous trait. [/QUOTE]

This requires carefully selecting the parents. Using the above example,

((A X B) X C) would not necessarily give the same results as (A X (B X C)) In other words, you have to know which homozygous combination you want to avoid.

DarJones

Precisely. I can most readily imagine this being done by commercial growers who already have a set of inbred strains and a solid understanding of what alleles are found in each.

Another scenario where it might be useful is if your strain [C] is homozygous for an alternate allele (A') at the gene not found in either strains [A] or [B], then the final progeny would be a mix of AA' and aA'. These would be combinations you could not get if you had simply grown out a F2 population from the original cross.

Good posts Darren and Darrel.
For a list of genes go to TGRC.