Breeding strategies to eliminate an undesired trait

[bower]

Disclosure: this is not a tomato breeding issue... yet! Consider it hypothetical.

1) In many crops, cytoplasmic male sterility (CMS) is a trait used in the production of F1 seeds. This trait is passed only from mother to offspring. Since the mother is pollen sterile, it's easy to produce F1 seeds by surrounding those plants with the fertile male parent. So this strategy is used to the extent possible in commercial seed production.

2) There are "restorer of fertility" or "maintainer of fertility" genes in the nuclear DNA, which segregate normally, and which would come from the male parent in the cross, if they are present at all. When the gene is present in the male parent, the offspring of the male sterile mother plant are Rof/-, that is heterozygous for the restorer of fertility gene.

Let us assume that your mother plant is an F1 with CMS and Rof/-, and that you 'dehybridize' or grow F2 seeds.
All progeny will have CMS sterility. 3/4 will be fertile due to Rof and 1/4 sterile thus eliminated from future seed.

How will you eliminate male sterility from the population.
Can you devise a plan to produce and identify your Rof/Rof lines as they are segregating?

I know @Doffer and @Frosti and @KaguyaCloud are really good at genetics math, so I wanted to post this hypothetical problem to your attention, and any others who like a good problem. How would you design your plan if breeding with a CMS F1, to eliminate that trait from the population. And what would you do (without marker assist) to select Rof/Rof plants, and how long/how many would it take to establish an Rof/Rof population instead of 1/4 seedless.

[Doffer]

You want to outcross a recessive gene. I test this with a backcross.
Pollinate the rof/rof with your F2 plants and if 0 of the 5 plants are not rof/rof plants then you have found a +/+ F2 plant with >95% certainty.

[KaguyaCloud]

So for clarification, are you asking how to maintain the dominant Rof gene within the population? Based on your description, Rof is dominant gene that essentially masks CMS(reminds me of the human Bombay blood phenotype).

If so, Doffer's idea of crossing back to the F1 parent is pretty good at maintaining genetic stability:

If you cross a homo. fertile F2(Rof/Rof) with the F1(Rof/-), then 100% of the seeds should be dominant for Rof because the only combination of phenotypes are homozygous fertile and heterozygous fertile, meaning you have a pure line.

If you cross a het. fertile F2(Rof/-) with the F1(Rof/-), then 75% of the seeds are dominant(Rof/Rof and Rof/-) for Rof and 25% have CMS(-/-), meaning you have a heterozygous F2 parent.

However, if you're asking how to eliminate the cytoplasmic male sterility gene itself(and not mask it with the Rof), that might not be possible if you continue selfing the F1 progeny. The only way to get rid of that one would be to have the F1 be the pollen donor for another variety that does not have CMS. After that, you have an F2 cross. Then after planting the F2, you can use the same F1 as the pollen donor for the F3 generation. You could repeat the process for several generations until the cross is nearly genetically similar to the male F1 plant without cytoplasmic male sterility. This method would take a magnitude longer in terms of time to do compared to the first option, but it would eliminate CMS in one generation.

[bower]

Yes @KaguyaCloud - suppose there are two goals: or multiple goals and possibilities as to how to manage CMS input to your breeding situation. Where starting with a CMS Rof/- parent you end up with some sterile offspring, it's desirable to have lines that are homozygous Rof to ensure their crosses are fertile. Another goal would be to eliminate CMS from the population after making your cross with the CMS parent to begin with. So crossing to a non CMS plant is the one step required for that, as long as there is Rof to activate the pollen of the CMS parent it could be the one step to avoid all the issues with that.
OTOH for the purpose of future breeding work involving CMS parents, it would be valuable to isolate some Rof/Rof lines. The CMS plant is then necessary to identify the homozygous lines.

[KaguyaCloud]

@bower
Curious question, what is the reason of having an Rof/Rof line with the potential to develop CMS when the recessive -/- trait is what is required for CMS to be expressed? Is it not more beneficial to maintain a heterozygous Rof/- phenotype in this case? Although I suppose that the F1 is essentially that exact genotype.

To answer the rest of your question, you would need approximately 57-81 plants and just 3 generations. I am assuming that you do not have a Rof/Rof to begin with. However, you can likely get away with considerably less on your F3 generation since you only need one Rof/Rof(if you have average luck, you'll only need to grow 24-30 F3 plants total if you don't intend to grow out all your F3 generation).

First generation: 1 F1 plant to produce the F2 seeds.

Second generation: At least 8-10 F2 plants to isolate Rof/Rof. Here's a reason why:

This follows the equation y = (3/4)^x
y is the chance every plant will be either heterozygous(Rof/-) or sterile(-/-) and x is the number of plants.

Grow 1 F2 plants: (3/4)^1 = 75% chance you won't get a Rof/Rof genotype.
Grow 2 F2 plants: (3/4)^2 = 56% chance you won't get a Rof/Rof genotype.
Grow 4 F2 plants: (3/4)^4 = 32% chance you won't get a Rof/Rof genotype.
Grow 8 F2 plants: (3/4)^8 = 10% chance you won't get a Rof/Rof genotype.
Grow 10 F2 plants: (3/4)^10 = 5.6% chance you won't get a Rof/Rof genotype.

With 8 plants, the chances getting a Rof/Rof genotype is 90%. It is up to you on how much you're willing to gamble on this stage. The more plants the better.

Theoretically, at 8 F2 plants, you'll have 2 that are Rof/Rof, 4 that are Rof/-, and 2 that are sterile(-/-).
Now you have several options, you can self the 6 fertile plants or backcross the 6 fertile plants with a known sterile plant.
For simplicity sake let's say you self the 6 fertile plants and make the F3 generation.

Third Generation:

So let's assume you were to test one single F2 line at a time. And also let's assume that it is heterozygous(Rof/-) to show why we need to grow X amount for this generation. We need to guarantee that you will get a sterile plant in order to determine if a line is not pure(Rof/-).

This equation calculates the probability of seeing a sterile plant at least once in a heterozygous F3:

y = 1 - (3/4)^x
y is the percent chance you will see a sterile plant appear and x is the number of plants. It is subtracting from 1 because the formula originally intended to calculate the probability of never seeing a sterile genotype in a cross.

Grow 1 F3 plants: 25% chance you will see a -/- genotype appear.
Grow 2 F3 plants: 44% chance you will see a -/- genotype.
Grow 4 F3 plants: 68% chance you will see a -/- genotype.
Grow 8 F3 plants: 90% chance you will see a -/- genotype.
Grow 10 F3 plants: 94% chance you will see a -/- genotype.

So again, growing out 8-10 plants per F3 line would statistically guarantee that you will know if your F3 is heterozygous or homozygous for Rof. So this equates to 48-60 plants total(6 fertile F2 multiplied by 8-10).

Conservatively, if you were to gamble at 90% certainty and grow 8 plants for every step of this method, you would need:
1 F1 plant
8 F2 plants(which you select 6 fertile plants from)
48 F3 plants(6 F2 plants multiplied by 8).
Total: 57 plants.

Playing it safe, if you were to have a 94% certainty, you would need:
1 F1 plant
10 F2 plants(which you select 7 fertile plants from)
70 F3 plants(7 F2 plants multiplied by 10).
Total: 81 plants.

[Tormato]

When you get around to the strategy of eliminating the undesirable trait of green gel, let me know.

[KaguyaCloud]

When you get around to the strategy of eliminating the undesirable trait of green gel, let me know.

What exactly is wrong with the green gel trait and do we know anything about the genetics? My Rosella Cherry tomatoes have green gel and taste completely fine, if not better than the other varieties I grew with clear ones.

[Tormato]

When you get around to the strategy of eliminating the undesirable trait of green gel, let me know.

What exactly is wrong with the green gel trait and do we know anything about the genetics? My Rosella Cherry tomatoes have green gel and taste completely fine, if not better than the other varieties I grew with clear ones.

Inside joke, literally and figuratively.

[bower]

@KaguyaCloud Rof genes are in the nuclear DNA and are not linked to the CMS, which is in mitochondrial DNA and therefore only passed on by maternal descent.
The problem of CMS has turned up in some cases where pollen from F1s was introduced to a population without addressing the CMS issue.
The majority of F1s are (still at present) legally available to breed with, since the breeders' right to be paid for their work is accomplished by keeping the parents secret and not released - they are private breeding lines. There are reasons why you might want or need certain traits that are present in an F1, disease resistance for example, to breed with.
The only reason the Rof/Rof plants would be useful is if you needed to introduce some other genetics from F1's into your breeding project.

I don't know all the ins and outs, but from what little I have read, I understand there are a couple of reasons for the breeder to use Rof when creating F1 seed using a CMS parent. One reason is that CMS can cause defects to the crop plant, which are remediated by the presence of Rof. Another reason is that it makes it possible to use the F1 for further breeding, to create a new non CMS line. Otherwise, if you have no Rof, then the seeds from the CMS line will only produce more CMS plants, and can never be used as pollen donor.

There may be crops where Rof genes are not necessary to the production of F1 seed. (as I understand?)
If other genetic strategies for example are developed to overcome any defects caused by the CMS.
So there may exist (or could in future be) CMS F1's that can accept pollen from an OP (non CMS, non Rof) and produce seeds. However those seeds will always produce CMS pollen sterile plants. And you cannot eliminate the CMS from the population because maternal is the only possible descent.
Therefore it is useful to develop Rof/Rof breeding lines, where that is possible, in order to use F1's of that crop for breeding OP's that are free of CMS.

Suppose I have a turnip F1 that is CMS and -/-. (Rof genes for B. rapa are not in general use, although they may have been discovered and are not yet genetically characterized.) I can only get seeds with this turnip genetics if I cross it with pollen from another turnip line. However all my plants will be CMS. I can't escape that unless I have a line with Rof genes present.

Suppose that other means of overcoming crop defects associated with CMS become available, and no longer a strong reason to use Rof genes in F1s. We could end up with a seed industry mostly CMS plants. Just saying, it's a worthy project to collect Rof genetics and preserve those genes in OP lines.