Genetics Math
 

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.;)

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.

TGRC is a good source for information on the various known genes:
[URL="http://tgrc.ucdavis.edu/Genes.html"]http://tgrc.ucdavis.edu/Genes.html[/URL]
Another page with some overlap to above:
[URL="http://kdcomm.net/~tomato/Tomato/mutant.html"]http://kdcomm.net/~tomato/Tomato/mutant.html[/URL]
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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: [URL="http://www.plantphysiol.org/content/156/1/275.full.pdf"]http://www.plantphysiol.org/content/156/1/275.full.pdf[/URL]. 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

[QUOTE=Darren Abbey;322726]This paper has some good discussion about tomato fruit shape genetics: [URL]http://www.plantphysiol.org/content/156/1/275.full.pdf[/URL]. 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[/QUOTE]

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

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!

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.

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

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?

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.

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.:lol:
Just wondering.

Worth

[QUOTE=Worth1;322748]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.:lol:
Just wondering.

Worth[/QUOTE]

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

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.

[QUOTE=Darren Abbey;322743]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.[/QUOTE]

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. ;-)

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...

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.

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

That's what I'm trying to work out. Unfortunately I believe experience is probably a better teacher than statistics at some of this process, so I'm hoping to learn from those breeders who've been doing this on a larger scale.

If I do a pre-screen well before transplant for antho in the leaves and stem I presume that will let me select for atv/atv at that point. The connection with Aft isn't completely clear to me yet, but my current understanding is that this is a useful early screen that can reduce the sheer number of plants required when selecting for anthocyanin accumulation.

So, if I started 160 seeds and selected the expected 25% showing strong antho at the seeding stage that would have me planting out 40 plants looking for the Aft + elongated cherry combination and I would presumably find 2-3 of them in that population. I'm not sure if in practice that is too few or if that's overkill, but that's where my current thoughts are given where the math is leading me.

For the currant/small tomato types it would appear to require much smaller grow outs if I start with a dark antho cherry and cross to the various currant/small cherry types I can apply the antho foilage screen early and have a good chance of finding strongly antho types in the remaining population. Then the subsequent generations require larger numbers looking for the less easily quantified factors like fruit size, set, plant vigor, etc.

I'm intriqued by reports that the Sungold taste and foilage smell seem to be linked, which would be another useful early screen for crosses with parents descending from a Sungold cross.

[QUOTE=marktutt;322851]
So, if I started 160 seeds and selected the expected 25% showing strong antho at the seeding stage that would have me planting out 40 plants looking for the Aft + elongated cherry combination and I would presumably find 2-3 of them in that population. I'm not sure if in practice that is too few or if that's overkill, but that's where my current thoughts are given where the math is leading me.
[/QUOTE]

This is exactly how I would do it.

With the two genes you are looking for you would be able to easily find the 2 or 3 segregates that are homozygous for both target traits, but do not neglect the heterozygous expressions either. With the two traits mentioned the heterozygous expressions for both should be easy to spot, and should be screened for taste just in case one of them contains an invisible combination of superior tasting genetics. I find many so-called recessive traits very easy to spot in a heterozygous expression, and these two you are looking for are only partially recessive so will be very easy to spot.

So, after you have selected for atv at seedling stage your 40 plants would include 5 that are homo for Aft and hetero for sun (or el or whatever), 5 that are hetero for Aft and homo for sun and 10 that are hetero for both, in addition to the already mentioned 2.5 (2 or 3) that are homozygous for both traits. That leaves 17.5 plants that either inherit one or the other or none of your desired traits and can safely be culled when they are old enough to phenotype, which would be well before the ripe fruit stage. If this was me doing the growout I would plant out twice as densely as normal and cull almost half the plants before first ripe fruit.

Out of the 22.5 remaining plants I would select first for flavour rather than preferring the homozygous expressions of the two genes, because those will be easy to segregate out in the subsequent generations.

Ahh, that sounds like experience kicking in. What was puzzling me was just having the 2-3 plants that were homozygous at F2 didn't seem like that would give me great odds of finding the combination of the right look along with flavor,vigor, etc.

With 22.5 (the half plant I guess I can top ;)) to select from the odds of finding a winner look much better.

Yep, you don't have to immediately select for black or white, you can choose gray if you like and do the fine tuning later. As long as you can spot the desired phenotype you know you have something to work with.

[QUOTE=Worth1;322748]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.:lol:
Just wondering.

Worth[/QUOTE]

I'm on the opposite end. Genetics is second nature to me... but I keep getting confused in electronics because the convention for electric flow is opposite of what the physics says is actually happening. And though I've studied hydraulics from a physics standpoint, I have no intuition whatsoever when it comes to application.

[QUOTE=Darren Abbey;322946]I'm on the opposite end. Genetics is second nature to me... but I keep getting confused in electronics because the convention for electric flow is opposite of what the physics says is actually happening. And though I've studied hydraulics from a physics standpoint, I have no intuition whatsoever when it comes to application.[/QUOTE]

Very good point. Try reading a schematic that includes both electrical and electronic conventions in the same diagram!!!!!!

How to keep a nerd occupied for hours. Ask this question.

Does electricity flow from negative to positive? or from positive to negative?

DarJones

[QUOTE=Fusion_power;323114]How to keep a nerd occupied for hours. Ask this question.

Does electricity flow from negative to positive? or from positive to negative?

DarJones[/QUOTE]

If he ever does come back with an answer, really confuse him by asking him, "What about hole theory?":))

Then ask about an ionized gas where there really are both positive and negative charge carriers.

[COLOR=black][FONT=Verdana]These[/FONT][/COLOR][FONT=Verdana] questions get easier to figure out once you understand that lightning travels from the ground to the sky.[/FONT]
[FONT=Verdana]Dutch[/FONT]