Genetics Math

[Boutique Tomatoes]

I am struggling to force my brain to accept some new programming and be able to re-learn a bit about genetics. It's been a lot of years, so unlike the dozens of dead progamming languages that rattle around in my head it's not coming back quickly.

I'm trying to work out the odds of finding the desired tomato from a given cross. I know there are variables that I cannot reliably account for, especially with some of the unstable lines but I want to discount that for the time being.

To make it easy (I hope) I wanted to figure out the odds of finding an elongated striped antho GWR cherry tomato from my proposed cross of Blue Green Zebra and Fred Hemple's Green Tiger Cherry.

Both are GWR, so I believe they have to be homogeneous for gf so the results should also be gf.

Both are striped, so presumably both are homogeneous for gs and the results should be gs.

Blue Green Zebra has some combination of Abg, Aft and atv. Two of those are dominant, 1 recessive as far as my reading tells me. So my undestanding is that half of the F2's should have some degree of anthocyanin expression, but without knowing which of these are actually present in BGZ I don't know. My feeling is that 1 of 4 will be strongly antho, but I can't say for certain.

Where I really start losing my grasp on the math is in fruit shape. My assumption is that the elongated cherry type comes from some interplay that includes the sun gene, but shape seems to be complex and I haven't found it explained anywhere.

So my assumption is that this cross will produce a F1 with a globe shape, green flesh, stripes and some of the antho speckles or shadow that seems to be indicative of the associated genes in a heterogeneous state.

I believe that the F2's would be an assortment of shapes with green flesh and stripes with 25% being strongly antho. I wish I could figure the odds on the fruit shape, but I don't have enough information as to the different genes in play to work out the math for that.

Please point out the flaws in my understanding, and if you know of something that will help me understand how fruit shape is determined I would be happy to read some more... It's much more interesting than the latest greatest new software development environment I should be learning at the moment.

[doublehelix]

For every recessive trait that you are looking for you have to multiply x 4.

So if you have two traits it is 4 x 4 or 1 in 16 chance of finding both traits in a single plant. If you have 3 recessive traits then you have 4 x 4 x 4 or 1 in 32. Four traits would be 4 x 4 x 4 x 4 or 1 in 256 chances of finding a plant with all 4 traits.

None of this will apply in the first generaton. In the first generation ALL dominate traits will "dominate" all the recessive traits. If your cross is a good one then you should not see any recessive traits in the F1.

[Darren Abbey]

TGRC is a good source for information on the various known genes:
http://tgrc.ucdavis.edu/Genes.html
Another page with some overlap to above:
http://kdcomm.net/~tomato/Tomato/mutant.html
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The green fleshed trait is probably caused by the recessive 'gf'... so both are 'gf/gf'. The green striped trait is caused by the recessive 'gs'... so both are 'gs/gs'. All their offspring should be green fleshed, with green stripes.

'Abg' produces dark antho fruit shoulder in one copy, but lethal in two copies. 'Aft' produces dark antho coloring in two copies and a lighter color in one copy. 'atv' produces antho coloring in stems/leaves when in two copies. BGZ is a stable for the fruit color, so it is 'Aft/Aft'. FHGTC doesn't have the antho coloring, so it is 'Aft-/Aft-' 25% of your F2s should have the dark antho color, while another 50% should have some antho color.

This paper has some good discussion about tomato fruit shape genetics: http://www.plantphysiol.org/content/156/1/275.full.pdf. There are a number of genes involved in shape, but I suspect the 'sun' gene is responsible for the elongation and pointed shape in BGZ. FHGTC will have the dominant wild type allele only ('Sun/Sun'). 25% of your F2s should have the elongated trait.
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To get all three traits, multiple the probability of each separately: (gf/gf)(gs/gs)(Aft/Aft)(sun/sun) = (1.00)(1.00)(0.25)(0.25) = 0.0625

To calculate the number of plants you would expect to have to grow before you found one like you were looking for, invert the probability: 1/0.0625 = 16

[Boutique Tomatoes]

Originally Posted by Darren Abbey

This paper has some good discussion about tomato fruit shape genetics: http://www.plantphysiol.org/content/156/1/275.full.pdf. There are a number of genes involved in shape, but I suspect the 'sun' gene is responsible for the elongation and pointed shape in BGZ. FHGTC will have the dominant wild type allele only ('Sun/Sun'). 25% of your F2s should have the elongated trait.
----

To get all three traits, multiple the probability of each separately: (gf/gf)(gs/gs)(Aft/Aft)(sun/sun) = (1.00)(1.00)(0.25)(0.25) = 0.0625

To calculate the number of plants you would expect to have to grow before you found one like you were looking for, invert the probability: 1/0.0625 = 16

Thank you for the link to that paper. Now I've got something to read tonight.

Your calculation agrees with what my admittedly basic understanding was telling me, and if I include a 12.5% factor for BGZ not being stable at F4 yet I can figure out the approximate size of an F2 grow out needed to find the desired results.

Now to go figure out my odds on the currant project!

[Darren Abbey]

So long as the specific BGZ plant you start with has the traits you want... you won't need that 12.5% fudge factor.

if it has green flesh, it has 'gf/gf'
if it has green stripes, it has 'gs/gs'
if it has dark antho fruit, it has 'Aft/Aft'
if it has elongated fruit, it has 'sun/sun'

At F4, it won't be stable enough in lots of other traits to make it a a finished variety... but for these traits, you can be pretty confident in the genetics.

[now for the less confident version...] That said, there are other genes which produce green fleshed and elongated fruit traits... if you grow out a few dozen and don't find the plant you're looking for, the range of traits you do see will clarify if there are alternate genetics at work and then you will be able to improve the calculation of probabilities.

[Fusion_power]

I think you have an error in your description of the genes involved, but will let you work out some of the details. Here would be some thoughts to look at.

gs - causes green stripes. You state both varieties are homozygous therefore can ignore this gene.
gs--green stripe Irregular longitudinal green stripes in epidermis of unripe fruit; retaininng chlorophyll for longer period during ripening, and eventually assuming paler color in fully ripe fruit; changes limited to epidermis. Striping may be observed on stem under conditions of high humidity and low light; heterozygotes exhibit some faint striping on fruit, but scored as a recessive.

el - causes elongated fruit, could be a different gene, there are 7 genes that cause various flavors of elongated fruit, same math so which one you are using does not matter. Please note that TGRC does not describe all of the variants.
el--elongated eElongated fruits as in Oxheart.

Aft - causes petunidin to accumulate in the fruit where exposed to light.
Aft--Anthocyanin fruit Anthocyanin in green and ripe fruit; environmentally sensitive, absent when shaded

atv - atroviolaceum
atv--atroviolacium Excess anthocyanin on leaves, stems, and fruits.

gwr - this is an interplay between the r gene (yellow fruit) and gf gene which is a phytochrome regulator that disables production of carotenoids. Since these genes are presumably already homozygous, you can ignore them.
gf--green flesh Persistent chlorophyll giving ripe fruit purplish-brown color.

gs - causes green stripes. You state both varieties are homozygous but you can't ignore this gene, it tends to do an unusual on/off dance. Most of the time, it will be on since you are using two varieties that are homozygous for the trait. It is a visual trait so easy to select for.

Since you are combining 4 genes, and 3 are from 1 parent and 1 is from the other parent, you should see the desired segregant in a growout of 256 plants. If you choose to grow in 3 seasons instead of 2, then you could do the job by growing a total of 16 plants but with a caveat that it would take an extra generation or two and one extra cross to fully stabilize the variety. Please note that the above ignores linkage. I did not check to see if any of the genes are on the same chromosome. You could take advantage of the fact that all of the above genes are somewhat penetrant meaning they can be visially selected for even when they are heterozygous.

DarJones

[Boutique Tomatoes]

Completely possible that I have erred in my analysis of the genes involved, very much a beginner at this.

But I'm having challenges. With the two parents presumably sharing the same recessive genes for GWR and stripes, doesn't that really mean that those really aren't a variable in the equation?

[Darren Abbey]

this is the case if the trait in both parents is caused by the same genes.

The paper I linked suggests the 'el' gene is the same as the 'sun' gene... but they're both recessive and have the same genetics pattern.

The green when ripe trait is caused by both the 'gf' and the 'y' traits... however, since both parents have both traits, the math doesn't change.

[Worth1]

I'm going to chime in here and say something that has been bothering me.
It is more of a question.

How can I be so adept at electronics, how to build things. hydraulics and so forth.
Many of these things I mentioned baffle most people but it has always came to me naturally.

I can see everything in my mind before it is complete and have all of the problems worked out.

But the above conversion has me totally lost the more I read the more it hurts.
Just wondering.

Worth

[Redbaron]

Originally Posted by Worth1

I'm going to chime in here and say something that has been bothering me.
It is more of a question.

How can I be so adept at electronics, how to build things. hydraulics and so forth.
Many of these things I mentioned baffle most people but it has always came to me naturally.

I can see everything in my mind before it is complete and have all of the problems worked out.

But the above conversion has me totally lost the more I read the more it hurts.
Just wondering.

Worth

Try drawing a Punnett square on a piece of paper and then read the text again. It should become clear.

[Boutique Tomatoes]

Worth, I design computer software for a living. You can find systems I've designed pretty much everwhere. I can visualize complex solutions to unusual business problems in my head immediately, in a way that I really cannot explain to anyone else. Like your gifts with electronics or mechanics for me it's as natural as breathing. I can also remember computer code pretty much forever, but I cannot remember peoples names at a party to save my life. The mind is weird.

Trying to learn and understand this genetics stuff is not coming naturally for me. I'm telling myself I just have to go back to school and learn something new. Exercise some new muscles.

[Boutique Tomatoes]

Originally Posted by Darren Abbey

this is the case if the trait in both parents is caused by the same genes.

The paper I linked suggests the 'el' gene is the same as the 'sun' gene... but they're both recessive and have the same genetics pattern.

The green when ripe trait is caused by both the 'gf' and the 'y' traits... however, since both parents have both traits, the math doesn't change.

One other paper I read that led me to the sun conclusion found that the sausage types that have a nipple share the sun gene so I assumed it was different than el which appears to be related to hearts as Darrel mentioned. I suspect that there are a couple in play and it's not as simple as we'd hope.

Genetics is a lot different than comp sci, and nature is a lot more complex than any computer system I've ever worked on. ;-)

[Fred Hempel]

Hi Mark,

I think if you are crossing an elongated cherry (specifically Green Tiger) you should expect semi-dominance in the F1 and roughly 1:2:1 (round:somewhat elongated:elongated) segregation in the F2. Even if it isn't that simple, if you pick a few long F2 cherries you will likely get what you want in another generation or to (I think the semi-dominance is key).

That's all I know about what to expect, and it is based solely on my qualitative memory of rough field ratios in F2 populations.

Can't help you more because I passed my lifetime limit for reading genetics papers in grad school. Now it's all phenotype all the time (for me)! And there are so many...

[Boutique Tomatoes]

Thanks Fred, I was hoping you'd pop in and offer some insight. The F1's should be interesting then and the F2's should be easy to segregate. I think I can manage this one along with my currant/small tomato project.

[Fred Hempel]

How many plants are you going to have in that F2 population?