I intended to write about backcrossing a year ago, back when I was into this stuff. Here's that post.
So let's say you have a plant whose traits you want to keep. Let's say that it's bright red or something and you want to continue producing plants that are bright red. (For this example, let's assume our red plant is homozygous, RR) You have this female plant that is bright red but you don't have any males that are particularly special. You need to breed. What's the solution?
Backcrossing, and it works like this:
You mate your bright red plant RR with your random-ass male plant whose genotype we have no idea about, but we'll call it xx since it's not red.
You will get a bunch of heterozygous plants if the xx is also homozygous, and let's assume that it is for now. And let's say they're all red. Awesome. This tells us that red is a dominant trait. Our children must be:
Rx Rx Rx Rx (0% are RR, all hybrids)
But we also have our parent RR. That's our advantage. We already have one plant that we know is true breeding with regard to the characteristics that we want. So breed the RR parent with all the children and what happens?
We'll get 50% RR and 50% Rx
What happens if we mate these children with the RR parent AGAIN?
We get 75% RR and 25% Rx
See what's happening? The proportion of plants with the desired trait is increasing. We continue this and we get:
And this is what is known as backcrossing.
When I say you're mating the parent plant with the children, you will most likely be mating a CLONE of the parent plant with the children. The parent is unlikely to survive for this much time. So you clone the parent plant before each crossing and use that.
Notes: when you first mate the parent with the child, this is known as squaring. When you mate the grandchild with the grandparent, this is known as cubing. Stupid terms you will find elsewhere online.
I even figured an equation which predicts the proportions as seen above: if n is the number of crosses, the proportion will be