New ball pythons morphs/mutations

Originally Posted by evansnakes

BUT, with genetics you are actually just as likely to get 1 albino as you are to get 9 and if you absorb and sorty a huge amount of data you would realize that.

Call Ralph Davis, Brian Barcyzk, Mark Bell, Tracy Barker or any other breeder who has been doing this for a very long time and they will tell you about the many many times that the outcome defied the odds both good and bad in extreme ways. This is because the odds are per each egg individually and not based on clutch size. They go hand in hand but are two different factors. Argue all you want, I have watched it in my incubators for years and years now.

You only have equal probabilities of hatching out 1 and 9 if the odds of hatching out an albino in the first place, so this would be true in an albino to het albino breeding. However, this would not be true in a het x het pairing.

It doesn't matter who those breeders or how much experience they have, unless their sample size is approaching infinity which is quite obviously not the case. A sample size of 100 wouldn't be enough. 1000 and you might get something close to the EV's (expected values), but there is no guarantee. By the time you hit a million, it'd be unlikely for you not to have numbers close to the EV's, but it's still possible. In order to guarantee that the actual results will match up with the EV's, you need to be approaching infinity, which obviously can only be proven by logic and not by data.

Perhaps I should use an example to illustrate my point. Consider that you have two die (dice). The combined number of dots can range anywhere between 2 and 12. Now, as any craps player could tell you, some numbers are more likely to come up than others. The reason being, as I've explained before, is because of the number of combinations.

Now, take 2 for example. The only way you'll get 2 is if you roll 1 on the first dice, and 1 on the second dice.

For 3, you have 2 combinations. You can roll a 1 on the first dice and roll a 2 on the second dice, or roll a 2 on the first dice and roll a 1 on the second dice.

The most combinations are for the middle numbers, 6 and 7.

Now, just because it's unlikely to roll a 2 doesn't mean it doesn't happen. However, in the long run, 6 and 7 are going to come up more often.

The same thing applies to breeding morphs. The only difference is, instead of die, you have a pair of alleles, instead of 1 to 6 it is either the mutation or not, and instead of two of them, you have whatever your clutch size or sample size is. The exact same rules apply.

Originally Posted by The BoidSmith

Evan and Han,

You both bring up excellent points. When crossing two heterozygous for albino ball pythons each egg has ¼ (25%) chance of being albino, ¼ (25%) chance of being normal, and ½ (50%) chance of being heterozygous for albino. My genetics and probability are probably a little rusty but I agree with Evan, each egg is an independent event. What I think is different is that in a series of “independent events” (eggs) the probability of an albino to show up every time in a clutch is the product of the probabilities of each individual event (egg). This means that the odds of 9 albinos showing in the same clutch is 0.25 x 0.25 x 0.25 x 0.25 x 0.25 x 0.25 x 0.25 x 0.25 x 0.25 = 0.06 or 6% (compared to 25% for each individual egg). Although it might seem small it’s huge when compared to winning the lottery Statisticians and mathematicians please correct me if I’m wrong!

Regards.

With what clutch size? Your calculation would be correct if the clutch size was 9, but for any other clutch size (greater than 9 obviously), that would not be the case.

However, if we stick to example where there are 10 eggs, that calculation would be inaccurate. Now, since there's only one other egg to account for it's pretty easy to count all the combinations where you hatch out 9 albinos and 1 normal in a clutch of 10. The case where the normal is the first egg, the case where the normal is the second egg, .... etc. The probability of each one of those cases will thus be 0.75 * (0.25)^9 = approximately 0.000003 , where 0.75 is the odds of hatching out a normal and 0.25 is the odds of hatching out the morph. Since all 9 combinations would have the same probability, you would simply multiply 0.000003 x 9, and the result of 0.000027 would be the odds of hatching out 9 albinos.

What Evan is arguing is that because each egg is an independent event, each of the possible outcomes (as in the number of eggs that are the desired mutation and the number of eggs that are not) has an equal probability, and that is untrue. There is a direct relationship between the probability of each trial, the number of trials, and the desired number of successful trials, and the number of combinations for that desired number of successful trials, as is how the formula for a binomial distribution works.

I think I found the source of some of the confusion in this thread:

This statement was supposed to be followed by:

here is only one possible combination each for the outcomes you've described while there are 252 ways to hatch out 5 of each. Hence, that would be a much more likely outcome, and would happen

the most often.

[quote=evansnakes]As to your comments, you aggree with me but don't aggree with me. [quote]
In the midst of your argument, you made a very general statement about statistics that I disagreed with. What I agreed with is that there shouldn't be anything different with an albino x pied than any other albino x. What I didn't agree with is your statement that the odds applied only per egg, and that the clutch size doesn't matter.

I really am impressed with your credentials as a math major in college but your comments suggest that because of that you know more than everyone else. I am educated both formally and practically in working with reptiles and would be willing to wager that I have worked with, produced more animals, species and mutations than you and have more practical hands on experience in the area than you do and I am telling you that it is not simple probability and statistics and that the odds of Medel's genetics are based on each individual egg and not on the number of eggs produced.

Well, I am really impressed with your breeding credentials, but the point I originally addressed and have been responding to ever since, as well as the issues we disagree has all been about mathematics, and not about who has more experience or is better at producing animals.

If you say, as I have stated twice previously, that from 10 eggs you would be more likely to produce albinos from a het x het breeding than if you had 5 eggs, that is just common sense and basic logic.

Well, you previously stated otherwise, which I will again quote for emphasis.

I'm sorry but you are wrong. You are applying your form of logic to a scientific formula that works on it's own logic. Yes, technically by the odds of just pure chance your odds are better with the more eggs that you get but that is only perception.

Call Ralph Davis, Brian Barcyzk, Mark Bell, Tracy Barker or any other breeder who has been doing this for a very long time and they will tell you about the many many times that the outcome defied the odds both good and bad in extreme ways. This is because the odds are per each egg individually and not based on clutch size. They go hand in hand but are two different factors.

Just because the odds can be "defied" in extremely small sample sizes does not mean the odds do not apply. And the odds of producing at least one of the desired mutation is certainly directly affected by the clutch size.

What I think is different is that in a series of “independent events” (eggs) the probability of an albino to show up every time in a clutch is the product of the probabilities of each individual event (egg). This means that the odds of 9 albinos showing in the same clutch is 0.25 x 0.25 x 0.25 x 0.25 x 0.25 x 0.25 x 0.25 x 0.25 x 0.25 = 0.06 or 6% (compared to 25% for each individual egg).

Han,

In the statement in the quote I was referring to 9 eggs. That’s why I bolded and underlined “every time” and “in the same clutch”. What I still think is wrong as was pointed out already was my calculation. Initially I came out with a 6% figure which is huge, whereas now if I multiply 9 times 0.25 my result is 0.000000954, which are the odds of hatching 9 albinos out of 9 eggs. Which one is the right number?

This reminds me of the farmers saying they have a bull that throws mostly female offspring. We know that the odds of either sex are 50% but they still insist as a bull shows 90% female offspring in his records. If one looks at the current records of the millions of calvings for the U.S. the odds are 51:49, close to what it can be predicted mathematically, but still not exact. As Han said “exactness” will only be achieved when you approach infinity. This is far the case of any ball python breeder on its own, not even if we combined all their years of experience together.

Thanks.

Originally Posted by The BoidSmith

Initially I came out with a 6% figure which is huge, whereas now if I multiply 9 times 0.25 my result is 0.000000954, which are the odds of hatching 9 albinos out of 9 eggs. Which one is the right number?

They are both wrong. 0.000000954 is 0.25 to the tenth power, not to the nineth power.

They are both wrong. 0.000000954 is 0.25 to the tenth power, not to
the nineth power.

You and your scientific calculator! Well...that’s it for my mathematic endeavors. Breeding ball pythons is more of an art than a science anyways!

On a side note on the comment of probabilities, we have all heard of families
that have five or more boys and no girls. When we say those have defied the
odds is because we tend to think about that individual family and not that
family as being a part of a population. In reality they are helping confirm the
odds because somewhere there’s another family that has 5 girls and no boys. We
have one example of such an “odd”¨ outcome in this very same site. If I’m not mistaken Al Guetzkow hatched all albinos in one clutch when
breeding two heterozygous together. How many other similar cases have we heard
of? The interesting thing is that the smaller the clutch the greater the
probability of hatching all albinos.

Regards.

We
have one example of such an “odd”¨ outcome in this very same site. If I’m not mistaken Al Guetzkow hatched all albinos in one clutch when
breeding two heterozygous together.

Close, I got 5 eggs from an albino to possible het breeding and all 5 were albinos, still against the odds.

Han, I understand where you are coming from but as I am not a big math enthusiast, but do watch eggs hatch quite often I still say that your assumption that in the end, ifyou have enough data you will balance out the equation of production of morph and non morph through volume there by eliminating the "odd" outcomes like 10 albinos from 10 eggs or no albinos from 10 eggs. What I would respond to you with is that there have been thousands and thousands of clutches produced each year for the past several years by those people I noted previously and I will tell you that I beleive there are enough clutches hatched to gather good data. If you take the outcome of 5,000 or 10,000 clutches, while it is far from infinity, it is more than enough for a scientific study to have valid data. Most drug trials, voter data and so many other important statistics are based on just hundreds to maybe a couple thousand people sampled. Why would this be impossible to develope a strong hypothosis when you have thousands of clutches to survey as data? Ball pythons almost never produce 16 eggs and yet so many animals have been produced in multiples out of 5 or 6 egg clutches that are 1 in 16 odds. Also, after looking at many many outcomes there are far more non conforming outcomes (i.e., far more or far less morphs from a breeding than there should be) than the ones you should see through statistics and probability.

As many of you know, I am NOT a ball python enthusiast (but I did recently admit to an interest in a few of the morphs). getting back to the albino pied discussion - I read the explanation of what happens and why pieds are pied. It made me think of the partial albinos (I don't know if there is another name for them - the albinos with the dark patches). could that be the manifestation of the "blocking" in an already amelanistic animal??