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My mathematical approach to punnet square calculations for multiple morph pairings.

We all know that figuring out the odds for any specific outcome in a multi-morph project can be difficult at best. I've devised the following method to calculate the odds:

First off, look at each morph separately. It's much easier to run a punnet square on one morph at a time then combine back later.

Only concern yourself with phenotypic outcomes,

For example, the following, semi complicated, cross:

Sunglow het anery (one hypo gene, two albino genes and one anery gene) mated to:
TH moonglow (one each hypo, albino and anery genes)

Would be divided into three morph calculations:

Hypo = het x het (dominant)
¾ hypo (possible super)
¼ normal

Albino = Homozygous x het (recessive)
½ albino
½ het albino

Anery = het x het (recessive)
¼ anery
¾ pos het anery

For any multi-morph pairing the total number of possible phenotypes is determined by multiplying the individual morph phenotypes. In the example 2x2x2=8

List out the various possible phenotypes:

Hypo(pos super), albino, anery
Hypo(pos super), albino, pos het anery
Hypo(pos super), het albino, anery
Hypo(pos super), het albino, pos het anery
Normal, albino, anery (note: I listed the "normal outcome for the hypo pairing)
Normal, albino, pos het anery
Normal, het albino, anery
Normal, het albino, pos het anery

Then multiply together the individual phenotype fractions:

Hypo(pos super)(¾), albino(½), anery(¼) = ¾ x ½ x ¼ = 3/32
Hypo(pos super), albino, pos het anery = ¾ x ½ x ¾ = 9/32
Hypo(pos super), het albino, anery = ¾ x ½ x ¼ = 3/32
Hypo(pos super), het albino, pos het anery = ¾ x ½ x ¾ = 9/32
Normal, albino, = ¼ x ½ x ¼ = 1/32
Normal, albino, pos het anery = ¼ x ½ x ¾ = 3/32
Normal, het albino, anery = ¼ x ½ x ¼ = 1/32
Normal, het albino, pos het anery = ¼ x ½ x ¾ = 3/32

Clear as mud?
-----
Thanks,

Dave Colling

www.rainbows-r-us-reptiles.com

0.1 Wife (WC and still very fiesty)
0.2 kids (CBB, a big part of our selective breeding program)

LOL, to many snakes to list, last count:
21.29 BRB
19.19 BCI
And those are only the breeders

lots.lots.lots feeder mice and rats

as clear as mud could be ill tell you what tho if i want to know what what equalls ill shoot you a e-mail and you can figure it out lol

Very good, Dave. This is the technique called forkline, the arithmetic method, branching system, and I don't know how many other names. An automobile odometer uses it on rotors to produce 100,000 unique number combinations for mileage. My genetics prof taught it to all his students. I can do a two-locus forkline in half the time and with greater accuracy than a two-locus Punnett square. Three and four locus forklines are not particularly difficult. I've done a three-locus Punnett square once. Never again! That is why I have written more than once that only a masochist uses a Punnett square for more than 1 locus.

The forkline technique can substitute even for a one-locus Punnett square. And it is not limited to two choices. The technique can do straight genotype problems, straight phenotype problems and problems that are a mix of genotype and phenotype.

A forkline is much easier to turn into a computerized genetics program than a Punnett square is. As far as I know, this is the basis for the Genetics Wizard.

Paul Hollander

Thanks Paul, I figured I had not invented the wheel, just reinvented it. I was hoping you'd chime in.

The other thing I really like about this method is it ALSO works on codominant morphs. For example:

Albino Motley x het albino Motley

albino x het albino
1/2 albino
1/2 het albino

Motley x Motley
1/4 homozygous motley (aka super motley)
1/2 motley
1/4 normal

Total phenotypes = 2 x 3 = 6

Albino super motley = 1/2 x 1/4 = 1/8
Albino Motley = 1/2 x 1/2 = 1/4
Albino = 1/2 x 1/4 = 1/8
Het Albino super motley = 1/2 x 1/4 = 1/8
Het Albino Motley = 1/2 x 1/2 = 1/4
Het Albino = 1/2 x 1/4 = 1/8
-----
Thanks,

Dave Colling

www.rainbows-r-us-reptiles.com

0.1 Wife (WC and still very fiesty)
0.2 kids (CBB, a big part of our selective breeding program)

LOL, to many snakes to list, last count:
21.29 BRB
19.19 BCI
And those are only the breeders

lots.lots.lots feeder mice and rats

The approach also works with multiple alleles:

Paradigm x arabesque het Sharp albino -->

is broken down into

normal x arabesque -->
1/2 arabesque
1/2 normal

and

paradigm x het Sharp albino -->
1/2 normal (50% probability het Sharp albino, 50% probability het boawoman caramel)
1/4 paradigm
1/4 Sharp albino

Result:
1/2 arabesque - 1/2 normal = 1/4 arabesque
1/2 arabesque - 1/4 paradigm = 1/8 arabesque paradigm
1/2 arabesque - 1/4 Sharp albino = 1/8 arabesque Sharp albino
1/2 normal - 1/2 normal = 1/4 normal
1/2 normal - 1/4 paradigm = 1/8 paradigm
1/2 normal - 1/4 Sharp albino = 1/8 Sharp albino

I wish this forum would do real forklines. Then I'd only have to write "1/2 arabesque" and "1/2 normal" once instead of three times.

Paul Hollander

Forkline can do anything a Punnett square can do only faster. And if you only want the probability of one particular outcome and don't particularly care about the rest, forkline can give it to you without making you figure out all the possible results of a mating. The Punnett square cannot do this.

Example: What is the expected fraction of moonglow babies from a salmon het Kahl albino het anerythristic x Kahl albino het anerythristic mating?

Salmon x normal -->
1/2 salmon
1/2 normal

het Kahl albino x Kahl albino -->
1/2 Kahl albino
1/2 het Kahl albino

het anerythristic x het anerythristic -->
3/4 normal looking (66% probability het anerythristic)
1/4 anerythristic

Moonglow is salmon, Kahl albino, anerythristic.
1/2 - 1/2 - 1/4 = 1/16 moonglow.

Paul Hollander

LOL, I do that all the time, just figuring out the probabilitiy of the one(s) I want.
-----
Thanks,

Dave Colling

www.rainbows-r-us-reptiles.com

0.1 Wife (WC and still very fiesty)
0.2 kids (CBB, a big part of our selective breeding program)

LOL, to many snakes to list, last count:
21.29 BRB
19.19 BCI
And those are only the breeders

lots.lots.lots feeder mice and rats

Paul,
I'm not quite sure I undestand what you are getting with the Paradigm X Het Sharp Albino pairing. This is mostly because I'm new to actually figuring out the genetics of the whole thing. It appears that the Paradigm and Albino genes are not completely compatible in the same way that two normal albino gene are compatible. In your pairing I see that there are 1/4 Normal het Paradigm, 1/4 normal het sharp albino, 1/4 albino and 1/4 paradigm. What I fail to get is how you get the 1/4 albino and 1/4 paradigm. Is there some type of masking going on where the paradigm can appear as an albino gene depending on where it resides in the chain and as a Hypo if it resides in another locus? I guess I just don't understand how this gene works yet.

Thanks
Chris

Paradigm is believed to be three possible genes within one gene pair, Normal, Boawoman Caramel, and sharp albino.

2x boawoman caramel genes = visual boawoman caramel
2x Sharp albino genes = visual Sharp albino
1x boawoman plus 1x sharp albino = paradigm
1x normal plus 1x Sharp albino = het sharp albino
1x normal plus 1x boawoman caramel = het boawoman caramel

so, to break down Pauls example:

paradigm x het Sharp albino -->
1/2 normal (50% probability het Sharp albino, 50% probability het boawoman caramel)
1/4 paradigm
1/4 Sharp albino

The paradigm would have one boawoman caramel paired with a sharp albino gene.

The het sharp albino would have a sharp albino paired with a normal.

Using the het sharp as a starting point, 1/2 of the babies would get a normal gene, the other gene supplied by the paradigm would be 50/50 boawoman caramel / sharp albino or
1/2 normal (50% het Sharp albino, 50% het boawoman caramel)

the other half of the babies would get the sharp albino gene and again would get 50/50 caramel/albino from the other parent or:
1/4 paradigm (sharp albino paired with boawoman caramel)
1/4 Sharp albino (sharp albino paired with sharp albino)
-----
Thanks,

Dave Colling

www.rainbows-r-us-reptiles.com

0.1 Wife (WC and still very fiesty)
0.2 kids (CBB, a big part of our selective breeding program)

LOL, to many snakes to list, last count:
21.29 BRB
19.19 BCI
And those are only the breeders

lots.lots.lots feeder mice and rats

From the breeding information that I have seen on a couple of web pages, it looks like paradigm is not a mutant gene. Instead, it is the appearance of a boa that got a Sharp albino mutant gene from one parent and a boawoman hypo (AKA caramel hypo) mutant gene from the other parent.

I have written a piece about the paradigm boa (see the link). I hope it will be helpful. Please let me know what part or parts of it do not make sense so I can make improvements.

Paul Hollander
The Paradigm Boa and Multiple Alleles

>>Thanks Paul, I figured I had not invented the wheel, just reinvented it. I was hoping you'd chime in.
>>
>>The other thing I really like about this method is it ALSO works on codominant morphs. For example:
>>
>>Albino Motley x het albino Motley
>>
>>albino x het albino
>>1/2 albino
>>1/2 het albino
>>
>>Motley x Motley
>>1/4 homozygous motley (aka super motley)
>>1/2 motley
>>1/4 normal
>>
>>Total phenotypes = 2 x 3 = 6
>>
>>Albino super motley = 1/2 x 1/4 = 1/8
>>Albino Motley = 1/2 x 1/2 = 1/4
>>Albino = 1/2 x 1/4 = 1/8
>>Het Albino super motley = 1/2 x 1/4 = 1/8
>>Het Albino Motley = 1/2 x 1/2 = 1/4
>>Het Albino = 1/2 x 1/4 = 1/8
>>-----
>>Thanks,
>>
>>
>>Dave Colling
>>
>>www.rainbows-r-us-reptiles.com
>>
>>
>>
>>0.1 Wife (WC and still very fiesty)
>>0.2 kids (CBB, a big part of our selective breeding program)
>>
>>LOL, to many snakes to list, last count:
>>21.29 BRB
>>19.19 BCI
>>And those are only the breeders
>>
>>lots.lots.lots feeder mice and rats

>>>>Thanks Paul, I figured I had not invented the wheel, just reinvented it. I was hoping you'd chime in.
>>>>
>>>>The other thing I really like about this method is it ALSO works on codominant morphs. For example:
>>>>
>>>>Albino Motley x het albino Motley
>>>>
>>>>albino x het albino
>>>>1/2 albino
>>>>1/2 het albino
>>>>
>>>>Motley x Motley
>>>>1/4 homozygous motley (aka super motley)
>>>>1/2 motley
>>>>1/4 normal
>>>>
>>>>Total phenotypes = 2 x 3 = 6
>>>>
>>>>Albino super motley = 1/2 x 1/4 = 1/8
>>>>Albino Motley = 1/2 x 1/2 = 1/4
>>>>Albino = 1/2 x 1/4 = 1/8
>>>>Het Albino super motley = 1/2 x 1/4 = 1/8
>>>>Het Albino Motley = 1/2 x 1/2 = 1/4
>>>>Het Albino = 1/2 x 1/4 = 1/8
>>>>-----
>>>>Thanks,
>>>>
>>>>
>>>>Dave Colling
>>>>
>>>>www.rainbows-r-us-reptiles.com
>>>>
>>>>
>>>>
>>>>0.1 Wife (WC and still very fiesty)
>>>>0.2 kids (CBB, a big part of our selective breeding program)
>>>>
>>>>LOL, to many snakes to list, last count:
>>>>21.29 BRB
>>>>19.19 BCI
>>>>And those are only the breeders
>>>>
>>>>lots.lots.lots feeder mice and rats
-----
Thanks,

Dave Colling

www.rainbows-r-us-reptiles.com

0.1 Wife (WC and still very fiesty)
0.2 kids (CBB, a big part of our selective breeding program)

LOL, to many snakes to list, last count:
21.29 BRB
19.19 BCI
And those are only the breeders

lots.lots.lots feeder mice and rats

about that..What I wanted to say is I like those odds! good job with the math.

I am fairly new to boa genetics, I never studied genetics until I got back into boa's in 05. I came up with the same results on my site (not published yet) and I cant even use a punnet square.
Does that make me talanted??
Or is that the norm?? LOL
Not trying to steal any thunder just curious
"SAME PAIRING"
12.5% ALBINO SUPER MOTLEY
12.5% SUPER MOTLEY HET
ALBINO
25% ALBINO MOTLEY
25% MOTLEY HET ALBINO
12.5% ALBINO
12.5% NORMAL HET ALBINO
-----
1.0 Poss super PC Salmon 05 (Rich Ihle)
0.1 Dubay Pastel 04 (Clay English)
1.0 Sharp Albino 05 (Mike Wilbanks)
0.1 Normal BCI 04 (????)

I did this one in my head too...
This one was a real killer I actually worked up a sweat from this one...
I'm not trying to show off, I'm just curious if this is normal to be able to figure it in your head..

Motley het albino X Motley het albino
20% SUPER MOTLEY 66%
POSS HET ALBINO
5% ALBINO SUPER MOTLEY
25% NORMAL 66% POSS
HET ALBINO
10% ALBINO
10% ALBINO MOTLEY
15% NORMAL 66% POSS
HET ALBINO
15% MOTLEY 66% POSS
HET ALBINO
-----
1.0 Poss super PC Salmon 05 (Rich Ihle)
0.1 Dubay Pastel 04 (Clay English)
1.0 Sharp Albino 05 (Mike Wilbanks)
0.1 Normal BCI 04 (????)

Yeah, I've played with so many combos I do it in my head as well. Your numbers are slightly off

Motley het albino X Motley het albino

(your list with my numbers)

SUPER MOTLEY 66% POSS HET ALBINO (3/16 = 18.75%)
ALBINO SUPER MOTLEY (1/16 = 6.25%)
NORMAL 66% POSS HET ALBINO (3/16 = 18.75%)
ALBINO (1/16 = 6.25%)
ALBINO MOTLEY (2/16 = 1/8 = 12.5%)
NORMAL 66% POSS HET ALBINO (ALREADY LISTED ABOVE)
MOTLEY 66% POSS HET ALBINO (6/16 = 3/8 = 37.5%)

Your original list:

>>Motley het albino X Motley het albino
>>20% SUPER MOTLEY 66%
>>POSS HET ALBINO
>>5% ALBINO SUPER MOTLEY
>>25% NORMAL 66% POSS
>>HET ALBINO
>>10% ALBINO
>>10% ALBINO MOTLEY
>>15% NORMAL 66% POSS
>>HET ALBINO
>>15% MOTLEY 66% POSS
>>HET ALBINO
-----
Thanks,

Dave Colling

www.rainbows-r-us-reptiles.com

0.1 Wife (WC and still very fiesty)
0.2 kids (CBB, a big part of our selective breeding program)

LOL, to many snakes to list, last count:
21.29 BRB
19.19 BCI
And those are only the breeders

lots.lots.lots feeder mice and rats

I can do two-locus and simple three-locus problems in my head as long as I use fractions. It took a fair amount of practice with pencil and paper first, though. Converting the fractions to percentages smaller than 25% always takes pencil and paper.

Paul Hollander

Thanks Dave,
I knew I couldn't have been a genius....LOL
I'm glad I got close..
I cant even convert fractions to decimals...LOL
I'm a Carpenters school drop out..
-----
1.0 Poss super PC Salmon 05 (Rich Ihle)
0.1 Dubay Pastel 04 (Clay English)
1.0 Sharp Albino 05 (Mike Wilbanks)
0.1 Normal BCI 04 (????)

That's why I prefer to go with the fractional outcomes. To me it's way easier to think of the litter in terms of say 1/8 sunglows then 12.5% sunglows
-----
Thanks,

Dave Colling

www.rainbows-r-us-reptiles.com

0.1 Wife (WC and still very fiesty)
0.2 kids (CBB, a big part of our selective breeding program)

LOL, to many snakes to list, last count:
21.29 BRB
19.19 BCI
And those are only the breeders

lots.lots.lots feeder mice and rats

Thanks a lot guys. just when I was getting the hang of the punnet's square you go ahead and throw a wrench into it. No really, I understand the mechanics behind what you are doing, it's just the first time I've seen it since I just got the punnet thing figured out to a 6 by 6 matrix. Here's a curve ball for you to chew on for a while. Try Salmontine het Argentine T Pos X Super Salmontine Het Argintine T Pos. Let me know what you get....

Thanks,
Chris

Not much of a curve ball. Only difficulty is what to call the individual phenotypes so I'll just leave out the naming of the combo morphs.

Salmontine het Argentine T Pos X Super Salmontine Het Argintine T Pos.

broken down is:

Salmontine x super salmontine
all salmontine poss super (assuming you can't tell the difference between salmontine and super salmontine)

Het argentine t-pos x het argentine t-pos
1/4 argentine t-pos
3/4 pos het argentine t-pos

so combined is:
1/4 salmontine (pos super) argentine t-pos
3/4 salmontine (pos super) pos het argentine t-pos

I'm not familiar with the argentine morphs so may need to change if salmon is not dominant and/or t-pos is not recessive.
-----
Thanks,

Dave Colling

www.rainbows-r-us-reptiles.com

0.1 Wife (WC and still very fiesty)
0.2 kids (CBB, a big part of our selective breeding program)

LOL, to many snakes to list, last count:
21.29 BRB
19.19 BCI
And those are only the breeders

lots.lots.lots feeder mice and rats

Yeh, I was tired when I typed it in. I didn't mean to make the second animal a super, just a regular. With the two Samlontine het T Pos Argentine's I was expecting a little more variation.
This is what I actually was looking for:

18.75% (3) - 50% Columbian 50% Argentine 66% Pos Het T Pos (1 normal cross, 2 Het)
6.25% (1) - T Pos 50% Columbian 50% Argentine
37.5% (6) - Salmontine 66% Pos Het T Pos Argentine (2 regular, 4 het)
12.5% (2) - T Pos Salmontine
18.75% (3) - Super Salmontine 66% Pos Het T Pos Argentine (1 regular, 2 Het)
6.25% (1) - T Pos Super Salmontine

I thought I might be able to catch you off guard with the 50/50 crosses. I would expect these to have a pattern similar to that of the columbians with the colors of the Argentines like some of the crosses I have seen posted as Salmontines over the last few months. I actually had the regular and het animals seperated out at first because I am assuming that these will also carry identifiers (markers) like their columbian cousins. we just haven't worked with them long enough to know just what to look for yet. I've was told that the Argentine T Pos hets have a Yellow base color in the striping in the tail. Have not been able to proove this yet but I'm hoping that the adult pair of 100% Het T Pos Argintines I am getting will help me determine this for sure. As soon as I produce my first litter of T Pos animals I will be using my Salmon Male to start working on this to prove it out.

Thanks
Chris