The Genetics of Backcrossing

"Tatume" squash.

"Lemon" squash.

A user over at the Tomatoville forums recently asked for thoughts on a squash breeding project they're thinking of starting. Tomatoville is generally focussed on all-things-tomato, but it has a large range of people interested in breeding of other garden vegetables (including squash).

The goal of the proposed project is to combine the color, flavor, and production of "Lemon" with the vining habit, vigor, and insect resistance of "Tatume". They were seeking input on what strategy to pursue with the F1 plants; backcrossing to "Tatume" or selfing.

Backcrossing is generally used to transfer a limited number of traits from one genetic background to another, without dragging along unrelated genetic baggage. This technique was used to transfer anthocyanin pigment production from wild tomato relatives (Solanum cheesmanii & S. chilense) into the garden tomato (S. lysopersicum var. "Indigo Rose") [1]. It was also used to transfer the red factor from the Pine Siskin (Carduellis cucullata) into Canary birds (Serinus canaria domestica) [2]. In both cases, there were many other traits of the donor species which were not desired in the final product and that were successfully filtered out via backcrossing.

     1. http://frogsleapfarm.blogspot.com/2011/03/anthocyanin-fruit-in-tomatoes.html
     2. http://www.avianweb.com/redfactorcanaries.html

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The genetics of squash color is relatively well worked out: two loci interact to produce green (wwgg), yellow (wwG_), or white (W_G_) immature fruit [3]. The genetics of vining habit is also known: one locus produces bush (Bu_) or trailing (bubu) vine habit [4]. The genetics of flavor, yield, and many other traits are less well understood.

If you don't know the genetics of the traits you're interested in, you should first grow out a reasonable number of F2 progeny in order to characterize the inheritance patterns. Growing 20 or so F2s from a selfed-F1 might not give you every expected combination of traits, but it will allow you to examine the ratios of each of the traits you're interested in. The recessive version of each trait will be in the minority.

     3. http://www.ndsu.edu/pubweb/~mcclean/plsc431/mendel/mendel6.htm
     4. http://hortsci.ashspublications.org/content/40/6/1620.full.pdf

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Backcrossing has specific consequences to a breeding program depending on the genetics of the trait(s) you're looking to transfer.

Dominant : color genetics. "Tatume" x "Lemon" P1 : (wwgg) green x (wwGG) yellow F1 : (wwGg) yellow "Tatume" x F1 P2 :  (wwgg) green x (wwGg) yellow BC1 : (wwGg) yellow + (wwgg) green

Recessive : hypothetical flavor genetics. "Tatume" x "Lemon" P1 : (BiBi) bitter x (aa) sweet F1 : (Bibi) bitter F2 : 3 (1 BiBi; 2 Bibi) bitter + 1 (bibi) sweet "Tatume" x F1 P2 : (BiBi) bitter x (Bibi) bitter BC1F1 : (1 BiBi; 1 Bibi) bitter "Tatume" x F2 P2 : (BiBi) bitter x (bibi) bitter BC1F1 : (Bibi) bitter

In the dominant case, it is apparent which of the progeny carry the trait of interest. You can immediately choose which plants to use in the next stage.

In the recessive case, it is not apparent which of the backcross progeny carry the trait of interest.  You will have a 50% chance of losing the recessive allele you're interested in during every backcross generation. The solution to this is to screen a set of F2s in every cycle to find progeny carrying two copies of the recessive allele.

Dominant : color genetics. "Tatume" x BC1 P3 :  (wwgg) green x (wwGg) yellow BC2 : (wwGg) yellow + (wwgg) green

Recessive : hypothetical flavor genetics. "Tatume" x BC1F2 P3 : (BiBi) bitter x (bibi) sweet BC2F1 : (Bibi) bitter BC2F2 : 3 (1 BiBi; 2 Bibi) bitter + 1 (bibi) sweet

After several cycles of recurrent backcrossing with a dominant trait, the final progeny will be very much like the backcross parent ("Tatume"), but with the exception that they will have both dominant and recessive alleles for the selected locus. A round of selfing to produce F2s, then another round of selfing to produce F2 families, then selecting those F2 families which did not produce any green squash will get rid of the undesired recessive allele from the "Tatume" parent line.

After several cycles of recurrent backcrossing with a recessive trait, the final progeny will be very much like the backcross parent ("Tatume"), with the exception that they will have two recessive alleles at the selected locus. No further selection will be required to stabilize the line, but it will have taken twice as many years to get here compared to the case of transferring a dominant trait.

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If you instead screen large numbers of F2s from the original "Tatume" x "Lemon" cross, you might find the combination of dominant and recessive traits you're looking for in the second year. The recessive traits will already be stabilized, while the dominant traits will require more work. Self each F2 plant and save the seeds separately to make F2 families. Growing out the F2 families will let you see which F2 plants had a recessive allele hiding under the desired dominant trait. In addition, this method will let you examine a large number of combinations of genes you weren't expecting in advance.

If one parent was poisonous or had many other negative traits, you would get very few edible progeny and your time would probably be better spent using a backcrossing strategy to filter out everything except the few traits you're interested in transferring.

Both parents in the proposed project are highly edible and only differ in a few charismatic traits, so the vast majority of F2 progeny will be highly edible and have some combination of those traits. In this case, the potential to uncover interesting combinations of hidden alleles out-ranks the limited potential to produce inedible progeny.

Genetics of Squash Shape (2/2)

In my first blog post, I examined a small biology puzzle: the classical model of squash shape genetics (at left) didn't seem to match what I was seeing in my own garden.

The classical model involves two genes ('A' and 'B', respectively).   The dominant allele of both genes must be present (A_B_) to produce a disk-shaped squash.   If one gene is present in the dominant form and the other is in the recessive form (A_bb or aaB_), spherical-shaped squash will result.   If only the recessive alleles of both genes are present (aabb), then elongated squash will result.   After some digging, I found this model comes from a 1927 paper by Edmund W. Sinnott in the research journal, The American Naturalist.

This model predicts that crossing a (AABB) PattyPan to a (aabb) Zucchini should result in (AaBb) progeny plants with disc-shaped squash.   The progeny plants I grew, instead each produced intermediate/elongated-fat squash.   I assumed this meant my original PattyPan squash was a hybrid that contained both recessive alleles (AaBb) and so I then calculated the probabilities of producing (aabb) progeny from crossing the potential male parents (PattyPan and Zucchini) to the female parent (PattyPan).   The best probability I calculated was \( p = \frac{1}{16} \).   I wasn't pleased with this result and decided I needed further data.

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The magic of the internet then made its presence known: Ottawa Gardener was forwarded to my original post in a discussion of their recent post.   They had grown Zucchini, PattyPan, and some Pumpkins, then tossed some of the PattyPan squash to their chickens.   The next year when they moved the chicken run, up came a batch of hybrid squash.   Most appeared to be intermediate between the Zucchini and the PattyPan, with a few looking intermediate between the PattyPan and the Pumpkin.   (I've rearranged their photo to make the diagram at left.)

Because there are three potential male parents (and two offspring types), the calculations of probability get somewhat more intricate and I won't go into them here.   The detail I found most interesting was the recreation of the intermediate/elongated-fat shaped squash at the bottom-left.

Upon digging into the research literature further, I found a 1910 paper by R.A. Emerson, again in The American Naturalist.   In this paper, the author describes the result of crossing "White Scallop" (disc) and "Yellow Crookneck" (elongated) squash as being intermediate in shape.   This is contrary to the Sinnott model of shape genetics and is the result that both I and Ottawa Gardener observed in our gardens.

It seems like the Emerson result was never followed up on and the Sinnott result erroneously became the standard model of squash shape genetics that has been used in textbooks ever since.

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I'm really happy to know that my garden results are consistent with results from others, but I still need more data.

The simplest model I've come up with requires there to be a third gene (C) that allows the first two genes (A & B) to produce disc-shaped squash.   Sorting out the genetics of a cross involving three genes is much harder than a cross involving one or two genes.   Fortunately, I've got several hundred F2 seeds from the F1 plants I grew.

I plan to grow several F2s this coming year and I've managed to find homes for a few more in others' gardens.   It may take several years of this to collect sufficient data to get an idea of what is going on.

Would you be willing to grow some of my experimental squash seeds, then send me photos/measurements of the fruit that grow?   Get a message to me and we'll work out how to get seeds to you.

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Citations and notes :

1. Emerson RA.   The Inheritance of Sizes and Shapes in Plants.   1910, The American Naturalist 44: 739-746.   (https://archive.org/details/jstor-2455667)
• "Yellow Crookneck" x "White Scallop" -> F1 "intermediate".
• This matches the results I found in my garden


2. Sinnott EW.   Inheritance of Fruit Shape in Curcurbita pepo.   1922, Botanical Gazette 74: 95-103.   (https://archive.org/details/jstor-2470204)
• Sphere x Scallop -> F1 disc -> F2 (3 disc):(1 sphere).


3. Sinnott EW.   A Factorial Analysis of Certain Shape Characters in Squash Fruits.   1927, The American Naturalist 61: 333-344. (http://www.jstor.org/discover/10.2307/2456386)
• Sphere(#103) x disc -> F1 disc -> F2 (3 disc):(1 sphere).
• Sphere(#22) x disc -> F1 disc -> F2 (3 disc):(1 spheroid).
• Sphere(#103) x sphere(#22) -> F1 disc -> F2 (9 disc):(6 sphere):(1 elongate).

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Part 1

Genetics of Squash Shape (1/2)

In 2012, I saved some seeds from a "Patty Pan" squash I grew in the garden.   This spring, I grew three of the saved seeds and had two survive to maturity.   I was expecting the plants to produce the flying-saucer shaped fruit that the "Patty Pan" squash is known for, so I was surprised to see what developed.   The fruit from both plants was elongated and grew in yellow (later maturing to orange).

I decided it was time to investigate the genetics of squash fruit shape.   I recalled seeing this figure in some ancient genetics text book explaining the common shapes of squash as being due to two interacting genes and eventually I found a version of it.   The "Patty Pan" squash shape is caused by having a dominant allele for each of the two genes, while the elongated "Zucchini" shape is caused by being homozygous recessive for each of the two genes.   A squash with a spherical/pumpkin shape has a dominant allele for only one of the two genes.

Since my "Patty Pan" squash produced elongated children, it had to carry a recessive allele for each gene, thus it had the genetic composition of (AaBb).   I didn't control the pollination which led two the seeds I grew, so the father is unknown.

The first model for this cross is that the pollen came from a male flower on the same plant.

(AaBb) x (AaBb) -> (aabb)

Both pollen and egg had to carry recessive versions of each gene.   A quarter of the egg and pollen cells would be double-recessive (or double-dominant), so the probability of this cross resulting in the observed progeny would be 1/16.   The probability that two progeny would have the double-recessive trait is (1/16)^2 = 1/256.   This is not exactly a likely probability.
The second model for this cross is that the pollen came from a male flower on a nearby "Zucchini" squash I was also growing.

(AaBb) x (aabb) -> (aabb)

A quarter of the egg cells and every pollen cell would be double-recessive, so the probability of this cross resulting in the observed progeny would be 1/4.   The probability that two progeny would have the double-recessive trait is (1/4)^2 = 1/16.   This is also not exactly a likely probability.

A third model is that the classical story of squash shape is wrong for the genetics I am playing with.   Generally, I would consider this also to not exactly be a likely probability.

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To discriminate between the three models, I need more data.   Right now there are too few data points to be certain and unlikely events happen all the time.

I still have six viable-looking seeds from the parental "Patty Pan" squash and this season I saved almost every seed from a fruit each of the two progeny plants.

Next year, I plan to grow out the six remaining first generation seeds and as many of the second generation seeds as I can find homes for.   I expect I will be sharing lots of squash with everyone I know.

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Part 2