Multigenerational probability?

[Gomojoe]

Does anyone calculate out a few generations? I'm pretty sure the percentages multiply. So an example would be getting to a firefly axanthic from a firefly and axanthic. I've calculated that its a 25% chance of getting a firefly het. axanthic. Then assuming I had a clutch of 8 that would mean two of them. Out of those 2 I would then have a 75% chance of having a male. Then the chance of getting a firefly axanthic by breeding that male back to momma is 12.5%. So 0.25 x 0.75 x 0.125= .0234 x 100= 2.34% chance that I get a firefly axanthic in 2 generations.

At least I think that is right!


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[loonunit]

I'm going to tackle the 8 egg clutch first, because that's a hard calculation that comes up a lot.

So, the first pairing, a firefly to an axanthic, all of the babies are *guaranteed* het axanthic. Firefly is two traits on two separate genes (non-allelic). Each baby has a 50% chance of having either. 0.5 * 0.5 = 0.25. So 25 % chance of having a firefly in a particular egg.

25% chance per egg, and each egg has a presumed 50/50 shot at either gender. So if you really want a male to breed back to momma axanthic, okay, that's .25 * .5 = .125. So a 12.5 % chance of getting the firefly het axanthic MALE you really want. Good.

The first weirdness happens at the 8 egg clutch. This is a tricky calculation. The formula for just the firefly, either sex, is: one minus (0.75 to the eighth power), or

p = 1 - (.75^8).

For a MALE specifically, it becomes:

p = 1 - (.875&^8).

0.75 is the probability that a particular egg is NOT a firely, 75%. For specifically a male it's 87.5%, 0.875. You multiple that times it's self as many times as there are eggs. For 8 eggs, that's:

0.875*0.875*0.875*0.875*0.875*0.875*0.875*0.875 = 0.875^8 = 0.3436

That's the chance there will be NO male fireflies AT ALL in the clutch. There's a 34.36% chance of NO male fireflies AT ALL.... Therefore chance of having AT LEAST one male firefly in clutch of 8 eggs is 75.64%

[Gomojoe]

So your treating each egg as its own event?


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[Gomojoe]

I get everything else you did but how'd you get the percentage it wouldn't be a male firefly het?


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[loonunit]

SORRY BIG TYPO at the end of last post. That's 65.6% for 8 eggs, not 75.6%.

Calculating that out, the chances of having a firefly, or specifically a male firefly, in a particular clutch of eggs look like this:


at least 1 ff || at least 1 MALE ff

1 egg : 25% || 12.5%
2 eggs: 43.8% || 23.4%
3 eggs: 57.8% || 33.0%
4 eggs: 68.4% || 41.4%
5 eggs: 76.3% || 48.7%
6 eggs: 82.2% || 55.1%
7 eggs: 86.7% || 60.7%
8 eggs: 90.0% || 65.6%


Now... the multi-generational thing is also weird. Because the instant you get that male firefly het axanthic that you want, the probability jumps from whatever it was to 100%, and you're back to the single generational calculation for that breeding. So 12.5% per egg for a firefly axanthic (either sex).

And you're not going to proceed with the 2nd breeding until you get the boy firefly, right?

But okay, let's just assume we have a momma snake who we magically know always lays exactly 8 eggs. The chance of getting the male firefly het axanthic in the first generation followed by the firefly axanthic in the second for two 8-egg clutches is 0.656 * 0.656 = 0.5679, or 43.00%

Which, hey, is almost 50/50. I say go for it.

[Gomojoe]

Lol! I appreciate your explanation! I'm not really trying to figure out if it's worth it, more about understanding the math so thank you!


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[loonunit]

The percent chance that it wouldn't be a male firefly het is just 1 - 0.125 = 0.875. So if every egg has a one in 8 shot at being a firefly male, then every egg has a 7 in 8 chance of NOT being that firefly male.

[Gomojoe]

Got ya! Thanks!


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[Gomojoe]

So why are you dealing with the probability it won't happen vs the probability it will?


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[OmNomNom]

Hmm, curiosity question! I love snooping in other people's genetics. Why do you prefer probability or % over regular ol' Mendelian ratios? You know in a het x het cross 25% should be homozygotes, so in a clutch of 8 eggs 2 of them should be FF from a Ff x Ff cross.

Course, anyone who's done genetics long enough knows that you only get Mendelian ratios when you don't want them... But why the long, horrid calculations? Let me see if I can get to the same result doing it differently.....hrrm, so you have a Firefly and a Axanthic, and I'm assuming the Firefly is a dominant allele? (I know nothing about snake genetics, wheeee!) But if it is, and you have say a het male Firefly, Ff (F being the "firefly" gene, and f "wild-type") and a het female Axanthic Aa (A being the Axanthic gene). Then from that cross 25% will be Ff/Aa or het Firefly, het Axanthic. In an 8 egg clutch, two of them will be Ff/Aa (why the 75% chance of male anyway?). Say you take that Ff/Aa boy and mate him back to his ff/Aa momma then you.....hang on (draws little punnet's square) have a 37.5% chance of getting a snake with both F and A in 'em, and a 12.5% chance of getting Ff/AA. Still a 25% chance of getting Ff/Aa. Assuming I did all that right.....it's late and me brain be tired, hah!