Re: Hardy-weinberg Equilibrium


John Harshman wrote:
rev.goetz wrote:

John Harshman wrote:

rev.goetz wrote:


John Harshman wrote:


rev.goetz wrote:



John Wilkins wrote:



John Harshman wrote:



John Wilkins wrote:




rev.goetz wrote:




John Wilkins wrote:




R Brown wrote:




"Dhananjay" <mani.dhananjay@xxxxxxxxx> wrote in message
news:1140053878.611011.133970@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx




Why is it difficult to have a population in Hardy-weinberg Equilibrium?


For a population to be in Hardy-Weinberg equilibrium, it must satisfy five
main conditions:
1. The population is very large.
2. The population is isolated; this is, there is no migration of
individuals or gametes into or out of the population.
3. Mutations (changes in genes) do not alter the gene pool.
4. Mating is random.
5. All individuals are equal in reproductive success; that is, natural
selection does not occur.
Pretty tough to pull off.


Don't you also need to have mating being equiprobable between any two
organisms in the population?

--
John S. Wilkins, Postdoctoral Research Fellow, Biohumanities Project
University of Queensland - Blog: evolvethought.blogspot.com
Servum tui ero, ipse vespera

Did you miss "4. Mating is random."?


Random <> equiprobable


That's what it was clearly intended to mean. Best just to use the
technical term: panmictic.


Well I don't think that panmixis and random mating are quite the same thing
(yes, that may be what R Brown intended it to mean), because strictly, a
random mating = nonassortative, while panmixis means equal probability of any
two organisms mating.

Think of it this way - non-assortative mating means you'll mate with equal
likelihood any nearby organism. Panmixic mating means you'll likely mate with
any organism in the deme, nearby or not. I might not have any qualms about
mating with the local gals based on their phenotypic variants such as skin
colour, but that doesn't mean I'm equally likely to mate with gals who are
more distant but still in the same gene pool.

--
John S. Wilkins, Postdoctoral Research Fellow, Biohumanities Project
University of Queensland - Blog: evolvethought.blogspot.com
Servum tui ero, ipse vespera


"Statistical randomness" means that everything has an equal
probability. Perhaps you read too much from Richard Dawkins.


Really? I wouldn't say so. I'd say you were right if we assumed a
uniform distribution. But suppose we assumed a normal distribution?
Results near the mean would be much more probable than results in either
tail. Are you claiming that statistical randomness requires a uniform
distribution?

I assume that statistical randomness requires a uniform distribution
because statistical randomness means that everything has the same
probability. And a normal distribution is probabalistic and nonrandom.
On the other hand, we can randomly pick any given value in a normal
distribution.

Could you explain the difference between "probabilistic" and "random"?
You can throw in "stochastic" if you like. When I took statistics,
nobody mentioned the term "statistical randomness", so perhaps you are
right. But a random variable can be associated with any distribution,
and I had always supposed that random variables displayed randomness. Is
statistical randomness different from randomness?


We will refer to dictionary definitions. "Random" has several
dictionary meanings, but the mathematical or statistical meaning always
implies that "everything has an equal probability." This was
hammered into me when I took some entry level graduate courses in
genetics and molecular evolution. And the term "random" in academic
genetics literature typical implies the mathematical meaning. And I use
the adjective "statistical" or "mathematical" before the term
"random" to clarify that I am using the mathematical definition of
"random." And in a genetics class, we should never need to clarify
that the term "random" and all of its cognates has any other
meaning but the statistical meaning. And it would surprise me if it
were any different in a statistics class. However, some professors
admitted to me that many people botch the technical meaning of
"random."

Likewise, the mathematical meaning of "nonrandom" implies that
everything does not have an equal probability. For example, mutation
rates are typically nonrandom because a mutation from a locus with A
typically does not have an equal probability of mutating to T or G or
C. Additionally, if mutations were statistically random, then all
potential indels would have the same probability.

"Probabilistic" may imply "randomness" or "nonrandomness."
And "stochastic" specifically implies random variables. And the
general meaning of stochastic implies probabilistic variables.

Wikipedia has a good article on "random variables"
(http://en.wikipedia.org/wiki/Random_variable). And here is a quote:

"For example, a random variable can be used to describe the process
of rolling a fair die and the possible outcomes { 1, 2, 3, 4, 5, 6 }.
Another random variable might describe the possible outcomes of picking
a random person and measuring his or her height."

I have been mostly referring to the first sentence above. But note that
the second sentence describes the possible outcomes of picking a random
person and measuring his or her height. In the latter case, the picking
of people is random, but picking a person of a specific height would
typically be nonrandom. The most common height for men may be 5' 10"
while picking any given man who is 5' 10" is just as probable as
picking anybody else. So picking a 5' 10" man would be nonrandom while
picking any particular man who is 5' 10" would be random.

I generalized my statement about normal distributions. I guess that it
is best to say that some aspects of a normal distribution are random
while specific results are nonrandom. So apart from uniform
distributions, I find it best to refer to distributions as
probabalistic. And I suppose that if we press it hard enough, there are
some exceptions to this.

Isn't "random variable" a misnomer in your world? Shouldn't it be called
"probabilistic variable"?

Yes, I made some mistakes here. "Random" in "random variable" means
unbiased. And, yes, I was wrong to say that a normal distribution is
not a random distribution, but I should have said that a normal
distribution indicates nonrandom probabilities in the particular
population. So yes, "random" in statistics sometimes means that
everything has an equal probability and other times it means unbiased.
And I suppose that in genetics literature, the former defintion is more
common than the latter defintion.

.

Relevant Pages

  • Re: Hardy-weinberg Equilibrium
    ... Mutations do not alter the gene pool. ... while panmixis means equal probability of any ... But suppose we assumed a normal distribution? ... Are you claiming that statistical randomness requires a uniform ...
    (talk.origins)
  • Re: Hardy-weinberg Equilibrium
    ... Mating is random. ... while panmixis means equal probability of any ... But suppose we assumed a normal distribution? ... Are you claiming that statistical randomness requires a uniform ...
    (talk.origins)
  • Re: Hardy-weinberg Equilibrium
    ... Mating is random. ... while panmixis means equal probability of any ... But suppose we assumed a normal distribution? ... Are you claiming that statistical randomness requires a uniform ...
    (talk.origins)
  • Re: Hardy-weinberg Equilibrium
    ... Mating is random. ... while panmixis means equal probability of any ... But suppose we assumed a normal distribution? ... Are you claiming that statistical randomness requires a uniform ...
    (talk.origins)
  • Re: Hardy-weinberg Equilibrium
    ... Mating is random. ... while panmixis means equal probability of any ... But suppose we assumed a normal distribution? ... Are you claiming that statistical randomness requires a uniform ...
    (talk.origins)