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Old 05-27-2019, 06:51 AM   #1
business_kid
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Probabilities Question


I've been resurrecting what little knowledge of probability I had.

Gregor Mendel noted that dominant traits were three times as likely to be passed on as recessive ones, so for 1 trait & one generation, [P = 0.75] or [P = 1 in 1.33]. For several generations, this would become

[P = 1 in (1.33)^n]. Now for several traits, say 7, would it be
  1. [P = 1 in (7x1.33)^n]?
  2. [P = 1 in 7*(1.33)^n]
  3. [P = (1.33)^7n
  4. Something Else?
 
Old 05-27-2019, 07:53 AM   #2
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Depends on whether you're talking about an entire theoretical population that's sufficiently large that the frequencies of the genes in question are constant or a small subset of a population, such as a family group.

You'll make life easier for yourself if you just use P=0.75 instead of P=(1 in 1.33).

If you're talking about the large population then every dominant trait will will be three times as common as the corresponding recessive trait. That is, if you pick a random individual within the population and you have no knowledge about their parents then all you can predict is that they are three times as likely to have the dominant trait as the corresponding recessive one. If you're interested in (say) seven traits then the probability that a randomly chosen individual will have all seven dominant traits is 0.75^7=0.1335.

Edit: this assumes that half of the genes in the population are recessive and the other half are dominant (that is, neither trait has any advantage or disadvantage to the probability of the individual reproducing).

If you're talking about a small group and you have information about the individual's parents' traits you can make predictions about all of the traits you're interested in (too late at night for me to be sure of giving accurate examples right now).

Edit - probably should be in General (please excuse the pun)?

Last edited by fido_dogstoyevsky; 05-27-2019 at 08:06 AM.
 
Old 05-27-2019, 03:07 PM   #3
business_kid
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Quote:
Originally Posted by fido_dogstoyevsky
Edit - probably should be in General (please excuse the pun)?
Rats, I thought it was. Moderator, pls move this into General.

Quote:
You'll make life easier for yourself if you just use P=0.75 instead of P=(1 in 1.33).
You won't think that when you see the size of n!

Thank you for the genetics points, which I have no doubt are true. I was however looking for a dissertation on probabilities. Mendel put up his figures for pea plants. My present efforts deal with evolution. Accepting that P=0.75 holds for some unspecified human, bug or animal, and that the specific trait contains a mutation, I am trying to calculate the odds of it being retained over many generations, and calculating for general populations and localised (as on an island where inbreeding could occur, where the probabilities are capped at a lower figure). Hence the question for several traits.
 
Old 05-27-2019, 06:41 PM   #4
fido_dogstoyevsky
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Quote:
Originally Posted by business_kid View Post
...You won't think that when you see the size of n!...
Retired scientist and teacher, used to living with really big and really small numbers

Quote:
Originally Posted by business_kid View Post
...I was however looking for a dissertation on probabilities. Mendel put up his figures for pea plants. My present efforts deal with evolution. Accepting that P=0.75 holds for some unspecified human, bug or animal, and that the specific trait contains a mutation...
Whether a trait is more or less likely to be retained depends on whether that trait makes it more or less likely that an individual with the trait succesfully reproduces. If there's no reproductive advantage or disavantage to a mutation then the gene frequencies won't change, except in populations small enough to be troubled by inbreeding.

Quote:
Originally Posted by business_kid View Post
...I am trying to calculate the odds of it being retained over many generations, and calculating for general populations and localised (as on an island where inbreeding could occur, where the probabilities are capped at a lower figure). Hence the question for several traits.
Have a look at http://evolution.gs.washington.edu/popgen/popg.html for a simulator (an earlier version of which which I used in high school classes on genetics). You can change population size, initial gene frequencies etc and run through different numbers of generations. A quick read of the wikipedia pages on genetics and evolutionshould give you enough to get started with the software.
 
Old 05-28-2019, 04:02 AM   #5
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Thanks for your reply. Retired Electronics Engineer here. I'm not really a believer in Evolution, hence the probabilistic analysis :-/. I know scientists all swallow it. I'm not going to pursue this here as it's way off topic for a linux forum. I'm still hoping for a mathematician to pass by.

EDIT: I've sent you a pm.

Last edited by business_kid; 05-28-2019 at 04:19 AM.
 
Old 05-28-2019, 07:25 AM   #6
onebuck
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Moderator Response

Moved: This thread is more suitable in <General> and has been moved accordingly to help your thread/question get the exposure it deserves.
 
Old 05-28-2019, 05:09 PM   #7
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Quote:
Originally Posted by business_kid View Post
Gregor Mendel noted that dominant traits were three times as likely to be passed on as recessive ones,
Both kinds of traits are passed on equally, domninant traits are expressed three times as often as recessive ones.

Quote:
for several generations, this would become

[P = 1 in (1.33)^n].
So in fact it would remain P = 1 in 1.33, regardless of n. If it was P = 1 in (1.33)^n, P would go to 0 as n goes to infinity (i.e., dominant traits would disappear over time).
 
Old 05-29-2019, 07:50 AM   #8
business_kid
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I'm being corrected on my use of '1 in <blah>' format

Yes, for P=0.75^n, P-->0 as n --> infinity. That's fine for 1 trait. The impossibility barrier (P= 1e-50) is passed at n=401.

I'm interested in the equation for x non conditional traits, where trait 2 is not conditional on trait 1, but all traits must remain. In Post 1 I used x=7, and every post in between has been interesting but hasn't answered that. In particular, I don't know whether to add or multiply exponents: If I simplify
  1. P = (0.75^n)*(0.75^n)*(0.75^n)… = 0.75^7n
  2. P = (0.75^n)+(0.75^n)+(0.75^n)… = 7*(0.75^n)

Which is the correct equation? Or are they both wrong?
 
Old 05-29-2019, 05:18 PM   #9
ntubski
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Quote:
Originally Posted by business_kid View Post
I'm being corrected on my use of '1 in <blah>' format
No, I wasn't correcting you on formatting.

Quote:
Yes, for P=0.75^n, P-->0 as n --> infinity. That's fine for 1 trait.
No, it's incorrect.

Quote:
Which is the correct equation? Or are they both wrong?
They're both wrong.
 
Old 05-30-2019, 05:13 AM   #10
business_kid
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>No, I wasn't correcting you on formatting.

Yes, for P=0.75^n, P-->0 as n --> infinity. That's fine for 1 trait.
>No, it's incorrect.

Which is the correct equation? Or are they both wrong?
>They're both wrong.

Do you know what the correct one is? Why are they both wrong?
 
Old 05-30-2019, 07:12 AM   #11
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Quote:
Originally Posted by business_kid View Post
Do you know what the correct one is? Why are they both wrong?
The probability of one dominant trait being expressed in a particular individual after n generations is 0.75. The probability of seven dominant traits being expressed in a particular individual after n generations is 0.75^7. It's independent of n, as long as we're using the simple dominant/recessive model with no accounting for probability of failure/success to reproduce as in Gregor Mendel's pea plant experiments.
 
Old 05-30-2019, 10:54 AM   #12
business_kid
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Great. Thanks. That's for one generation, right?

So the probability for carrying them on for n generations:P = (0.75^7)^n ??
 
Old 05-30-2019, 12:59 PM   #13
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Erm, I flunked a Biology degree but I take it you are referring to well-known single-gene phenotype to genotype relationships here? I thought "a ytrait" was, usually, due to a cpomplex link of genes and, depending upon the organism, growth circumstances?
 
Old 05-30-2019, 04:56 PM   #14
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Quote:
Originally Posted by business_kid View Post
Great. Thanks. That's for one generation, right?
No, for any number of generations.

Quote:
So the probability for carrying them on for n generations:P = (0.75^7)^n ??
No.
 
Old 05-31-2019, 03:35 AM   #15
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So the probability for carrying them on for n generations:P = (0.75^7)^n ??
No.

I don't know if you got the point of this thread. We have worked back to the question I asked in post #1, which nobody has answered

If the probability for carrying them on for n generations is not P = (0.75^7)^n, what exactly is it?
What's the correct equation pls so I can mark this solved and close this thread?
 
  


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